{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Yara stayed awake through the night revising' is true, then ('Zach cheered at the football match' is true) and ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)), then if ('Brian went to the professor\u2019s office hours' is true), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is false.\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).\n- 'Alice presented at the science symposium' is false.\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is false)) is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'William participated in the sports tournament' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Victoria attended the career fair' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- (('Victoria attended the career fair' is true) and ('William participated in the sports tournament' is true)) is false.\n\nCan we draw a conclusion about the truth of ('William participated in the sports tournament' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- 'Alice presented at the science symposium' is false.\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Yara stayed awake through the night revising' is false).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is false) and ('Alice presented at the science symposium' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Victoria attended the career fair' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'William participated in the sports tournament' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- (('Victoria attended the career fair' is true) and ('William participated in the sports tournament' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Yara stayed awake through the night revising' is false).\n- ('Victoria attended the career fair' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Victoria attended the career fair' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Umar missed the bus to campus' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) and ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is false.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of (('Alice presented at the science symposium' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Yara stayed awake through the night revising' is false).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is false).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is false).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If ('David prepared slides for his class talk' is true) and ('Alice presented at the science symposium' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is false).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If ('David prepared slides for his class talk' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- (('Yara stayed awake through the night revising' is true) and ('Zach cheered at the football match' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then ('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).\n- ('Alice presented at the science symposium' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true)) is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is false.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Umar missed the bus to campus' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'David prepared slides for his class talk' is true, then 'Umar missed the bus to campus' is true.\n\nNow we know that:\n- ('Victoria attended the career fair' is false) or ('Xander had lunch at the cafeteria' is false).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Victoria attended the career fair' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Victoria attended the career fair' is true).\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If ('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true), then 'Alice presented at the science symposium' is true.\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is false).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- (('Yara stayed awake through the night revising' is true) and ('Zach cheered at the football match' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Victoria attended the career fair' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true).\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is false).\n\nCan we draw a conclusion about the truth of If 'Zach cheered at the football match' is true, then 'Yara stayed awake through the night revising' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is false.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) and ('Zach cheered at the football match' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Yara stayed awake through the night revising' is false).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If ('David prepared slides for his class talk' is true) and ('Zach cheered at the football match' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is false.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Victoria attended the career fair' is false).\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of If 'Zach cheered at the football match' is true, then 'Yara stayed awake through the night revising' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'William participated in the sports tournament' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is false.\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If ('Alice presented at the science symposium' is true) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Victoria attended the career fair' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)) is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is false.?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is false.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Victoria attended the career fair' is false) or ('William participated in the sports tournament' is true).\n- ('William participated in the sports tournament' is false) or ('Yara stayed awake through the night revising' is false).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is true.\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'William participated in the sports tournament' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'William participated in the sports tournament' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Umar missed the bus to campus' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Tina voted in the student council elections' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is false.\n- ('Umar missed the bus to campus' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Umar missed the bus to campus' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true.\n- If 'Victoria attended the career fair' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Tina voted in the student council elections' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If ('Zach cheered at the football match' is true) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).\n\nCan we draw a conclusion about the truth of (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'Zach cheered at the football match' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).\n\nCan we draw a conclusion about the truth of (('Yara stayed awake through the night revising' is false) and ('Alice presented at the science symposium' is true)) is false.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nCan we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n- ('Zach cheered at the football match' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nCan we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- (('Yara stayed awake through the night revising' is true) and ('Zach cheered at the football match' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is false).\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'William participated in the sports tournament' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Victoria attended the career fair' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- (('Victoria attended the career fair' is true) and ('William participated in the sports tournament' is false)) is false.\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Umar missed the bus to campus' is true.\n\nNow we know that:\n- ('Umar missed the bus to campus' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is true) or ('Zach cheered at the football match' is true).\n- 'Yara stayed awake through the night revising' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Victoria attended the career fair' is true) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is true) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).\n- 'Brian went to the professor\u2019s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is true.\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- 'Yara stayed awake through the night revising' is false.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is false.\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Yara stayed awake through the night revising' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'William participated in the sports tournament' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- (('William participated in the sports tournament' is false) and ('Xander had lunch at the cafeteria' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is true.\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is false.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is false.\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Victoria attended the career fair' is true).\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then ('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is false).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Umar missed the bus to campus' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('Victoria attended the career fair' is true), then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Victoria attended the career fair' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- 'Xander had lunch at the cafeteria' is false.\n- ('Victoria attended the career fair' is true) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is false.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).\n\nCan we draw a conclusion about the truth of (('Yara stayed awake through the night revising' is true) and ('Alice presented at the science symposium' is false)) is false.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If ('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true), then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If ('Brian went to the professor\u2019s office hours' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is false).\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('Brian went to the professor\u2019s office hours' is true), then 'Xander had lunch at the cafeteria' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Umar missed the bus to campus' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Tina voted in the student council elections' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then if ('David prepared slides for his class talk' is true), then ('Zach cheered at the football match' is true).\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of If 'Zach cheered at the football match' is true, then ('Alice presented at the science symposium' is true) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)), then if ('Brian went to the professor\u2019s office hours' is true), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Xander had lunch at the cafeteria' is true).\n\nNow we know that:\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n- ('Zach cheered at the football match' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If ('David prepared slides for his class talk' is true) and ('Zach cheered at the football match' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Zach cheered at the football match' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'William participated in the sports tournament' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Yara stayed awake through the night revising' is false).\n- ('Victoria attended the career fair' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If ('Xander had lunch at the cafeteria' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n\nCan we draw a conclusion about the truth of ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is true) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'Alice presented at the science symposium' is true, then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) and ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Umar missed the bus to campus' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Tina voted in the student council elections' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- 'Yara stayed awake through the night revising' is false.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is true) and ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is true) and ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n- ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then if ('Yara stayed awake through the night revising' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n- ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'Zach cheered at the football match' is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Umar missed the bus to campus' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is true.\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is false.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n- ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Victoria attended the career fair' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Umar missed the bus to campus' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "Now we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Umar missed the bus to campus' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of If 'Zach cheered at the football match' is true, then ('Yara stayed awake through the night revising' is true) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nCan we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n- ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Umar missed the bus to campus' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Victoria attended the career fair' is false) or ('Xander had lunch at the cafeteria' is false).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is false).\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'William participated in the sports tournament' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Umar missed the bus to campus' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- (('Umar missed the bus to campus' is false) and ('Victoria attended the career fair' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then if ('Victoria attended the career fair' is true), then ('David prepared slides for his class talk' is true).\n\nNow we know that:\n- ('Victoria attended the career fair' is false) or ('Xander had lunch at the cafeteria' is false).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n- ('Zach cheered at the football match' is true) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Umar missed the bus to campus' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Tina voted in the student council elections' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Alice presented at the science symposium' is true).\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true), then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('Brian went to the professor\u2019s office hours' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)), then if ('Brian went to the professor\u2019s office hours' is true), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)).", "However, we don't have the following information provided: 'Brian went to the professor\u2019s office hours' \u2192 ('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Victoria attended the career fair' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Victoria attended the career fair' is true) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is true) and ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If ('Brian went to the professor\u2019s office hours' is true) and ('Yara stayed awake through the night revising' is true), then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then if ('Zach cheered at the football match' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is false.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then ('Zach cheered at the football match' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) and ('Zach cheered at the football match' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then ('Zach cheered at the football match' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is false).\n- 'Brian went to the professor\u2019s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then if ('William participated in the sports tournament' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "Now we know that:\n- ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) and ('David prepared slides for his class talk' is false).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Alice presented at the science symposium' is true).\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'Zach cheered at the football match' is false.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is false.\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true.\n- If 'Umar missed the bus to campus' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Tina voted in the student council elections' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true), then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Umar missed the bus to campus' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- 'Clara celebrated a friend\u2019s birthday in the dorm' is false.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is false.?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'William participated in the sports tournament' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Victoria attended the career fair' is true) or ('Xander had lunch at the cafeteria' is true).\n- 'Brian went to the professor\u2019s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Zach cheered at the football match' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Zach cheered at the football match' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Umar missed the bus to campus' is true) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Yara stayed awake through the night revising' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Brian went to the professor\u2019s office hours' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then ('Zach cheered at the football match' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Alice presented at the science symposium' is true, then 'William participated in the sports tournament' is true.\n- If 'David prepared slides for his class talk' is true, then if ('Zach cheered at the football match' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is false).\n\nCan we draw a conclusion about the truth of (('Alice presented at the science symposium' is false) and ('Brian went to the professor\u2019s office hours' is true)) is false.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If ('Alice presented at the science symposium' is true) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Zach cheered at the football match' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 \u00ac'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is false.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- (('Zach cheered at the football match' is true) and ('Alice presented at the science symposium' is false)) is false.\n\nCan we draw a conclusion about the truth of (('Brian went to the professor\u2019s office hours' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) is false.?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Brian went to the professor\u2019s office hours' is false).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is false) or ('David prepared slides for his class talk' is false).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) and ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'David prepared slides for his class talk' \u2228 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Yara stayed awake through the night revising' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Victoria attended the career fair' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then if ('Victoria attended the career fair' is true), then ('David prepared slides for his class talk' is true).\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Umar missed the bus to campus' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('Yara stayed awake through the night revising' is true), then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is false).\n\nCan we draw a conclusion about the truth of ('Yara stayed awake through the night revising' is true) or ('Alice presented at the science symposium' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Zach cheered at the football match' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Zach cheered at the football match' is true.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: \u00ac'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- (('Yara stayed awake through the night revising' is true) and ('Zach cheered at the football match' is true)) is false.\n\nCan we draw a conclusion about the truth of (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) is false.?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "However, we don't have the following information provided: \u00ac('Clara celebrated a friend\u2019s birthday in the dorm' \u2227 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- (('Xander had lunch at the cafeteria' is true) and ('Yara stayed awake through the night revising' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is false).?", "answer": "no", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Umar missed the bus to campus' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is true).\n\nCan we draw a conclusion about the truth of If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Alice presented at the science symposium' is false).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Alice presented at the science symposium' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Zach cheered at the football match' is false.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: (\u00ac'Clara celebrated a friend\u2019s birthday in the dorm' \u2228 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Umar missed the bus to campus' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true.\n- If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Yara stayed awake through the night revising' is false) or ('Victoria attended the career fair' is true).\n- ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Alice presented at the science symposium' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor\u2019s office hours' is true) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true.\n- If ('Brian went to the professor\u2019s office hours' is true) and ('Zach cheered at the football match' is true), then 'David prepared slides for his class talk' is true.\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is false) or ('Zach cheered at the football match' is true).?", "answer": "no", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- (('Alice presented at the science symposium' is true) and ('Brian went to the professor\u2019s office hours' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true).?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of ('Brian went to the professor\u2019s office hours' is false) or ('Zach cheered at the football match' is true).?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is true.\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "yes", "proof": ["We know that If if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is true) or ('Alice presented at the science symposium' is true).\n- 'Zach cheered at the football match' is false.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is true.\n- ('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n- 'Yara stayed awake through the night revising' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend\u2019s birthday in the dorm' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Zach cheered at the football match' is true.\n\nNow we know that:\n- (('Yara stayed awake through the night revising' is true) and ('Zach cheered at the football match' is true)) is false.\n\nCan we draw a conclusion about the truth of ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).?", "answer": "yes", "proof": ["We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false, then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor\u2019s office hours' is false))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Yara stayed awake through the night revising' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Xander had lunch at the cafeteria' is true) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: ('Clara celebrated a friend\u2019s birthday in the dorm' \u2192 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n- ('Zach cheered at the football match' is true) or ('Brian went to the professor\u2019s office hours' is true).\n- ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Clara celebrated a friend\u2019s birthday in the dorm' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).\n\nCan we draw a conclusion about the truth of ('David prepared slides for his class talk' is false) or ('Zach cheered at the football match' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Brian went to the professor\u2019s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and (('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).\n\nNow we know that:\n- 'Alice presented at the science symposium' is false.\n\nCan we draw a conclusion about the truth of 'Brian went to the professor\u2019s office hours' is false.?", "answer": "no", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend\u2019s birthday in the dorm' is false.", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.", "However, we don't have the following information provided: ('David prepared slides for his class talk' \u2192 'Clara celebrated a friend\u2019s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true.\n\nNow we know that:\n- 'Brian went to the professor\u2019s office hours' is false.\n- ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is true.?", "answer": "no", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "However, we don't have the following information provided: 'David prepared slides for his class talk'. Therefore, we cannot draw a conclusion about the truth of conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor\u2019s office hours' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of If 'Brian went to the professor\u2019s office hours' is true, then ('Alice presented at the science symposium' is true) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true).?", "answer": "yes", "proof": ["We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('Brian went to the professor\u2019s office hours' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (('Brian went to the professor\u2019s office hours' is false) or ('Alice presented at the science symposium' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true).", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('Brian went to the professor\u2019s office hours' is true)) and (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then (('Brian went to the professor\u2019s office hours' is true) and ('David prepared slides for his class talk' is true)).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor\u2019s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If ('Yara stayed awake through the night revising' is true) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- ('William participated in the sports tournament' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true).?", "answer": "yes", "proof": ["We know that If ('Clara celebrated a friend\u2019s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor\u2019s office hours' is true)) and ((if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Clara celebrated a friend\u2019s birthday in the dorm' is true))), then ('Brian went to the professor\u2019s office hours' is true) or ('David prepared slides for his class talk' is true).", "We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true)) and ((if ('Brian went to the professor\u2019s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Alice presented at the science symposium' is true) or ('Brian went to the professor\u2019s office hours' is true))), then ('Clara celebrated a friend\u2019s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}
{"problem": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor\u2019s office hours' is true, then 'Alice presented at the science symposium' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend\u2019s birthday in the dorm' is true.\n\nNow we know that:\n- 'Yara stayed awake through the night revising' is true.\n\nCan we draw a conclusion about the truth of 'Alice presented at the science symposium' is true.?", "answer": "yes", "proof": ["We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "We know that If (if ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend\u2019s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.", "Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion."], "metadata": {"theme": "university"}}