Split (3)

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answer string	metadata dict	data_source string	prompt string	extra_info dict
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)), then if ('David prepared slides for his class talk' is true), then (('Clara celebrated a friend’s birthday in the dorm' is true) and ('Brian went to the professor’s office hours' is true)).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'Yara stayed awake through the night revising' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'David prepared slides for his class talk' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true. - If 'Umar missed the bus to campus' is true, then 'Quinn practiced for the theater play' is true. - If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true. - If 'Tina voted in the student council elections' is true, then if ('Samuel volunteered at a campus event' is true), then ('William participated in the sports tournament' is true). Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). - ('Paul forgot to bring his homework' is false) or ('Quinn practiced for the theater play' is true). - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). Can we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then ('Brian went to the professor’s office hours' is true) and ('Rachel joined a late evening tutorial' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 0, "question": "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 '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 'Xander had lunch at the cafeteria' is true.\n- If 'Quinn practiced for the theater play' 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 'David prepared slides for his class talk' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Clara celebrated a friend’s 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 'Brian went to the professor’s office hours' is true.\n- If 'Umar missed the bus to campus' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Tina voted in the student council elections' is true, then if ('Samuel volunteered at a campus event' 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 ('Clara celebrated a friend’s birthday in the dorm' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n- ('Paul forgot to bring his homework' is false) or ('Quinn practiced for the theater play' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n\nCan we draw a conclusion about the truth of If 'David prepared slides for his class talk' is true, then ('Brian went to the professor’s office hours' is true) and ('Rachel joined a late evening tutorial' is true).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' is true. - If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Brian went to the professor’s office hours' is true. - If 'David prepared slides for his class talk' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Quinn practiced for the theater play' is true. - If 'Paul forgot to bring his homework' is true, then 'Alice presented at the science symposium' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Umar missed the bus to campus' is true, then 'Yara stayed awake through the night revising' is true. - If 'Tina voted in the student council elections' is true, then 'Victoria attended the career fair' is true. - If 'Tina voted in the student council elections' is true, then 'Olivia submitted her essay before the deadline' is true. Now we know that: - ('Yara stayed awake through the night revising' is true) or ('Zach cheered at the football match' is true). - 'Quinn practiced for the theater play' is false. - ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true). - ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true). Can we draw a conclusion about the truth of 'Samuel volunteered at a campus event' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 1, "question": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' 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 'Brian went to the professor’s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Paul forgot to bring his homework' 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 'Xander had lunch at the cafeteria' is true.\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 'Victoria attended the career fair' is true.\n- If 'Tina voted in the student council elections' is true, then 'Olivia submitted her essay before the deadline' 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- 'Quinn practiced for the theater play' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of 'Samuel volunteered at a campus event' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true. - If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true. - If 'Mia printed notes at the computer lab' is true, then 'Quinn practiced for the theater play' is true. - If 'Noah gathered with his study group in the library' is true, then 'Yara stayed awake through the night revising' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Samuel volunteered at a campus event' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Umar missed the bus to campus' is true. - If 'Alice presented at the science symposium' is true, then 'Victoria attended the career fair' is true. Now we know that: - 'Olivia submitted her essay before the deadline' is false. - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). - ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true). Can we draw a conclusion about the truth of 'Mia printed notes at the computer lab' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 2, "question": "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 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Noah gathered with his study group in the library' 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’s 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’s birthday in the dorm' is true.\n- If 'Brian went to the professor’s 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 'Samuel volunteered at a campus event' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Umar missed the bus to campus' 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- 'Olivia submitted her essay before the deadline' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true).\n\nCan we draw a conclusion about the truth of 'Mia printed notes at the computer lab' is true.?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor’s office hours' is true) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is true) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (('David prepared slides for his class talk' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Paul forgot to bring his homework' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Yara stayed awake through the night revising' is true. - If 'Alice presented at the science symposium' is true, then 'David prepared slides for his class talk' is true. - If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true. - If 'Samuel volunteered at a campus event' is true, then 'Paul forgot to bring his homework' is true. - If 'Umar missed the bus to campus' is true, then 'Zach cheered at the football match' is true. - If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true. Now we know that: - ('Noah gathered with his study group in the library' is false) or ('Olivia submitted her essay before the deadline' is true). - ('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true). - 'David prepared slides for his class talk' is false. - ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true). Can we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 3, "question": "We know the following rules:\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s 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 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Olivia submitted her essay before the deadline' 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 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Umar missed the bus to campus' 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- ('Noah gathered with his study group in the library' is false) or ('Olivia submitted her essay before the deadline' is true).\n- ('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true).\n- 'David prepared slides for his class talk' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true).\n\nCan we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true. - If 'Quinn practiced for the theater play' is true, then 'Zach cheered at the football match' is true. - If 'Victoria attended the career fair' is true, then 'Alice presented at the science symposium' is true. - If 'Umar missed the bus to campus' is true, then if ('Tina voted in the student council elections' is true), then ('David prepared slides for his class talk' is true). - If 'Quinn practiced for the theater play' is true, then 'Samuel volunteered at a campus event' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Alice presented at the science symposium' is true. Now we know that: - 'Clara celebrated a friend’s birthday in the dorm' is false. - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). - ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true). - ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true). Can we draw a conclusion about the truth of 'Paul forgot to bring his homework' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 4, "question": "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 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Paul forgot to bring his homework' 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 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Zach cheered at the football match' is true.\n- If 'Victoria attended the career fair' is true, then 'Alice presented at the science symposium' is true.\n- If 'Umar missed the bus to campus' is true, then if ('Tina voted in the student council elections' is true), then ('David prepared slides for his class talk' is true).\n- If 'Quinn practiced for the theater play' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Alice presented at the science symposium' is true.\n\nNow we know that:\n- 'Clara celebrated a friend’s birthday in the dorm' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of 'Paul forgot to bring his homework' is true.?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true))), then ('Brian went to the professor’s office hours' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Paul forgot to bring his homework' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Zach cheered at the football match' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'David prepared slides for his class talk' is true, then 'Tina voted in the student council elections' is true. - If 'Umar missed the bus to campus' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Umar missed the bus to campus' is true, then 'Samuel volunteered at a campus event' is true. - If ('Xander had lunch at the cafeteria' is true) and ('Victoria attended the career fair' is true), then 'Rachel joined a late evening tutorial' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). - ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true). - ('Noah gathered with his study group in the library' is false) or ('Olivia submitted her essay before the deadline' is true). - ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true). Can we draw a conclusion about the truth of If 'Quinn practiced for the theater play' is true, then 'David prepared slides for his class talk' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 5, "question": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Brian went to the professor’s 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 'Yara stayed awake through the night revising' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' 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 'Tina voted in the student council elections' is true.\n- If 'Umar missed the bus to campus' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Umar missed the bus to campus' is true, then 'Samuel volunteered at a campus event' is true.\n- If ('Xander had lunch at the cafeteria' is true) and ('Victoria attended the career fair' is true), then 'Rachel joined a late evening tutorial' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true).\n- ('Noah gathered with his study group in the library' is false) or ('Olivia submitted her essay before the deadline' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true).\n\nCan we draw a conclusion about the truth of If 'Quinn practiced for the theater play' is true, then 'David prepared slides for his class talk' is true.?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and (('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>However, we don't have the following information provided: ('David prepared slides for his class talk' → 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Brian went to the professor’s office hours' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'Yara stayed awake through the night revising' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Tina voted in the student council elections' is true. - If 'Samuel volunteered at a campus event' is true, then 'Xander had lunch at the cafeteria' is true. Now we know that: - ('David prepared slides for his class talk' is true) or ('Rachel joined a late evening tutorial' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). - ('Paul forgot to bring his homework' is false) or ('Quinn practiced for the theater play' is true). - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). - ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true). Can we draw a conclusion about the truth of ('Clara celebrated a friend’s birthday in the dorm' is true) or ('Xander had lunch at the cafeteria' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 6, "question": "We know the following rules:\n- If 'Brian went to the professor’s 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 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Quinn practiced for the theater play' 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 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' 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’s birthday in the dorm' is true, then 'Tina voted in the student council elections' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Xander had lunch at the cafeteria' is true.\n\nNow we know that:\n- ('David prepared slides for his class talk' is true) or ('Rachel joined a late evening tutorial' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n- ('Paul forgot to bring his homework' is false) or ('Quinn practiced for the theater play' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n- ('Xander had lunch at the cafeteria' 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’s birthday in the dorm' is true) or ('Xander had lunch at the cafeteria' is true).?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Mia printed notes at the computer lab' is true. - If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true. - If 'William participated in the sports tournament' is true, then 'Alice presented at the science symposium' is true. - If 'Liam asked a question after the lecture' is true, then 'William participated in the sports tournament' is true. - If 'Kelly lost her internet connection during class' is true, then 'Liam asked a question after the lecture' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Brian went to the professor’s office hours' is true, then 'Yara stayed awake through the night revising' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Kelly lost her internet connection during class' is true. - If 'Quinn practiced for the theater play' is true, then 'Zach cheered at the football match' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true. - If 'Noah gathered with his study group in the library' is true, then 'David prepared slides for his class talk' is true. - If ('Noah gathered with his study group in the library' is true) and ('Umar missed the bus to campus' is true), then 'Victoria attended the career fair' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Tina voted in the student council elections' is true, then 'Xander had lunch at the cafeteria' is true. Now we know that: - ('Zach cheered at the football match' is false) or ('Xander had lunch at the cafeteria' is true). - ('Zach cheered at the football match' is false) or ('Paul forgot to bring his homework' is true). Can we draw a conclusion about the truth of ('Quinn practiced for the theater play' is false) or ('Olivia submitted her essay before the deadline' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 7, "question": "We know the following rules:\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' 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 'Alice presented at the science symposium' is true.\n- If 'Liam asked a question after the lecture' is true, then 'William participated in the sports tournament' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Brian went to the professor’s 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 'Kelly lost her internet connection during class' is true.\n- If 'Quinn practiced for the theater play' 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’s office hours' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'David prepared slides for his class talk' is true.\n- If ('Noah gathered with his study group in the library' is true) and ('Umar missed the bus to campus' is true), then 'Victoria attended the career fair' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Tina voted in the student council elections' 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 ('Xander had lunch at the cafeteria' is true).\n- ('Zach cheered at the football match' is false) or ('Paul forgot to bring his homework' is true).\n\nCan we draw a conclusion about the truth of ('Quinn practiced for the theater play' is false) or ('Olivia submitted her essay before the deadline' is true).?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>However, we don't have the following information provided: ('Clara celebrated a friend’s birthday in the dorm' ∨ 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true. - If 'Henry presented his project in class' is true, then 'Jack joined the debate club meeting' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Henry presented his project in class' is true. - If 'Kelly lost her internet connection during class' is true, then 'Mia printed notes at the computer lab' is true. - If 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true. - If 'David prepared slides for his class talk' is true, then 'Isabella met a friend at the campus café' is true. - If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true. - If 'Isabella met a friend at the campus café' is true, then 'Kelly lost her internet connection during class' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true. - If 'Grace’s lab session ran longer than planned' is true, then 'Yara stayed awake through the night revising' is true. - If 'Paul forgot to bring his homework' is true, then 'Samuel volunteered at a campus event' is true. - If ('William participated in the sports tournament' is true) and ('Tina voted in the student council elections' is true), then 'Zach cheered at the football match' is true. - If 'Jack joined the debate club meeting' is true, then if ('Victoria attended the career fair' is true), then ('Umar missed the bus to campus' is true). Now we know that: - ('Frank stayed in the dorm to study' is true) or ('Rachel joined a late evening tutorial' is true). - ('Frank stayed in the dorm to study' is false) or ('Grace’s lab session ran longer than planned' is true). Can we draw a conclusion about the truth of ('Paul forgot to bring his homework' is true) and ('Quinn practiced for the theater play' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 8, "question": "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 'Rachel joined a late evening tutorial' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Henry presented his project in class' is true, then 'Jack joined the debate club meeting' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Henry presented his project in class' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true.\n- If 'David prepared slides for his class talk' is true, then 'Isabella met a friend at the campus café' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true.\n- If 'Isabella met a friend at the campus café' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Grace’s lab session ran longer than planned' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Samuel volunteered at a campus event' is true.\n- If ('William participated in the sports tournament' is true) and ('Tina voted in the student council elections' is true), then 'Zach cheered at the football match' is true.\n- If 'Jack joined the debate club meeting' is true, then if ('Victoria attended the career fair' is true), then ('Umar missed the bus to campus' is true).\n\nNow we know that:\n- ('Frank stayed in the dorm to study' is true) or ('Rachel joined a late evening tutorial' is true).\n- ('Frank stayed in the dorm to study' is false) or ('Grace’s lab session ran longer than planned' is true).\n\nCan we draw a conclusion about the truth of ('Paul forgot to bring his homework' is true) and ('Quinn practiced for the theater play' is true).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and (('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s office hours' is true)) and (('David prepared slides for his class talk' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Alice presented at the science symposium' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>However, we don't have the following information provided: ('David prepared slides for his class talk' → 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Mia printed notes at the computer lab' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Noah gathered with his study group in the library' is true. - If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Kelly lost her internet connection during class' is true, then 'Liam asked a question after the lecture' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Liam asked a question after the lecture' is true, then 'Yara stayed awake through the night revising' is true. - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' is true. - If ('Umar missed the bus to campus' is true) and ('Victoria attended the career fair' is true), then 'Liam asked a question after the lecture' is true. - If 'Noah gathered with his study group in the library' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Tina voted in the student council elections' is true. Now we know that: - ('David prepared slides for his class talk' is true) or ('Mia printed notes at the computer lab' is true). - 'Noah gathered with his study group in the library' is false. - ('Xander had lunch at the cafeteria' is false) or ('Kelly lost her internet connection during class' is true). Can we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 9, "question": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s 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 'Mia printed notes at the computer lab' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Liam asked a question after the lecture' 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’s office hours' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' is true.\n- If ('Umar missed the bus to campus' is true) and ('Victoria attended the career fair' is true), then 'Liam asked a question after the lecture' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Tina voted in the student council elections' is true.\n\nNow we know that:\n- ('David prepared slides for his class talk' is true) or ('Mia printed notes at the computer lab' is true).\n- 'Noah gathered with his study group in the library' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('Kelly lost her internet connection during class' is true).\n\nCan we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>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.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Noah gathered with his study group in the library' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Yara stayed awake through the night revising' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'David prepared slides for his class talk' is true. - If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true. - If 'Brian went to the professor’s office hours' is true, then 'Paul forgot to bring his homework' is true. - If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true. - If 'Tina voted in the student council elections' is true, then 'Alice presented at the science symposium' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Samuel volunteered at a campus event' is true. - If 'Victoria attended the career fair' is true, then 'Rachel joined a late evening tutorial' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true). - ('Xander had lunch at the cafeteria' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). - 'Paul forgot to bring his homework' is true. Can we draw a conclusion about the truth of 'Quinn practiced for the theater play' is false.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 10, "question": "We know the following rules:\n- If 'Clara celebrated a friend’s 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 'Noah gathered with his study group in the library' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Olivia submitted her essay before the deadline' 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 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Quinn practiced for the theater play' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true.\n- If 'Tina voted in the student council elections' is true, then 'Alice presented at the science symposium' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Victoria attended the career fair' is true, then 'Rachel joined a late evening tutorial' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n- 'Paul forgot to bring his homework' is true.\n\nCan we draw a conclusion about the truth of 'Quinn practiced for the theater play' is false.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Mia printed notes at the computer lab' is true, then 'Paul forgot to bring his homework' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Noah gathered with his study group in the library' is true, then 'Yara stayed awake through the night revising' is true. - If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'Mia printed notes at the computer lab' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Quinn practiced for the theater play' is true. - If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Victoria attended the career fair' is true, then 'Samuel volunteered at a campus event' is true. - If 'Tina voted in the student council elections' is true, then 'Yara stayed awake through the night revising' is true. - If 'Quinn practiced for the theater play' is true, then 'Umar missed the bus to campus' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true). - 'Olivia submitted her essay before the deadline' is false. Can we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 11, "question": "We know the following rules:\n- If 'Mia printed notes at the computer lab' is true, then 'Paul forgot to bring his homework' 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 'Noah gathered with his study group in the library' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Paul forgot to bring his homework' 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 'Quinn practiced for the theater play' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Victoria attended the career fair' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Tina voted in the student council elections' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Umar missed the bus to campus' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true).\n- 'Olivia submitted her essay before the deadline' is false.\n\nCan we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor’s office hours' is true) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (('David prepared slides for his class talk' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>However, we don't have the following information provided: ('David prepared slides for his class talk' → 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true. - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Xander had lunch at the cafeteria' is true, then 'David prepared slides for his class talk' is true. - If 'Quinn practiced for the theater play' is true, then 'Zach cheered at the football match' is true. - If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Rachel joined a late evening tutorial' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Umar missed the bus to campus' is true. - If 'Victoria attended the career fair' is true, then 'Tina voted in the student council elections' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). - 'Brian went to the professor’s office hours' is false. - ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true). - ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true). Can we draw a conclusion about the truth of 'Samuel volunteered at a campus event' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 12, "question": "We know the following rules:\n- If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'David prepared slides for his class talk' is true.\n- If 'Quinn practiced for the theater play' 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 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Clara celebrated a friend’s 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 'Rachel joined a late evening tutorial' 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 'Umar missed the bus to campus' is true.\n- If 'Victoria attended the career fair' is true, then 'Tina voted in the student council elections' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n- 'Brian went to the professor’s office hours' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true).\n- ('Clara celebrated a friend’s 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 'Samuel volunteered at a campus event' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Zach cheered at the football match' is true. - If 'Brian went to the professor’s office hours' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' is true. - If 'Alice presented at the science symposium' is true, then 'Brian went to the professor’s office hours' is true. - If 'Zach cheered at the football match' is true, then 'Alice presented at the science symposium' is true. - If 'David prepared slides for his class talk' is true, then 'Quinn practiced for the theater play' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Umar missed the bus to campus' is true, then 'Alice presented at the science symposium' is true. - If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true. - If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Yara stayed awake through the night revising' is true. Now we know that: - ('William participated in the sports tournament' is true) or ('Yara stayed awake through the night revising' is true). - 'Paul forgot to bring his homework' is false. - ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true). Can we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 13, "question": "We know the following rules:\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' 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 'Brian went to the professor’s office hours' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor’s 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 'Quinn practiced for the theater play' 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 '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 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Rachel joined a late evening tutorial' 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 true) or ('Yara stayed awake through the night revising' is true).\n- 'Paul forgot to bring his homework' is false.\n- ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true).\n\nCan we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Brian went to the professor’s office hours' is false) or ('Clara celebrated a friend’s 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).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Brian went to the professor’s office hours' is false) or ('Clara celebrated a friend’s birthday in the dorm' is false))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is false).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is false))), then ('Brian went to the professor’s office hours' is false) or ('Clara celebrated a friend’s birthday in the dorm' is false).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend’s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'Mia printed notes at the computer lab' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true. - If 'Mia printed notes at the computer lab' is true, then 'Yara stayed awake through the night revising' is true. - If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true. - If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Zach cheered at the football match' is true. - If 'Zach cheered at the football match' is true, then 'Umar missed the bus to campus' is true. - If 'Victoria attended the career fair' is true, then 'Rachel joined a late evening tutorial' is true. Now we know that: - ('Noah gathered with his study group in the library' is false) or ('Xander had lunch at the cafeteria' is false). - ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true). - ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true). Can we draw a conclusion about the truth of ('Paul forgot to bring his homework' is true) and ('Quinn practiced for the theater play' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 14, "question": "We know the following rules:\n- If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Clara celebrated a friend’s 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 'Mia printed notes at the computer lab' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s 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 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Zach cheered at the football match' is true.\n- If 'Zach cheered at the football match' is true, then 'Umar missed the bus to campus' is true.\n- If 'Victoria attended the career fair' is true, then 'Rachel joined a late evening tutorial' is true.\n\nNow we know that:\n- ('Noah gathered with his study group in the library' is false) or ('Xander had lunch at the cafeteria' is false).\n- ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true).\n\nCan we draw a conclusion about the truth of ('Paul forgot to bring his homework' is true) and ('Quinn practiced for the theater play' is true).?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>However, we don't have the following information provided: (¬'David prepared slides for his class talk' ∨ 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Xander had lunch at the cafeteria' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Brian went to the professor’s office hours' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true. - If 'William participated in the sports tournament' is true, then 'Brian went to the professor’s office hours' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true. - If 'Samuel volunteered at a campus event' is true, then 'William participated in the sports tournament' is true. - If 'David prepared slides for his class talk' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Victoria attended the career fair' is true, then 'Umar missed the bus to campus' is true. - If 'Tina voted in the student council elections' is true, then 'Yara stayed awake through the night revising' is true. Now we know that: - 'Alice presented at the science symposium' is true. - ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true). - ('Rachel joined a late evening tutorial' is false) or ('Xander had lunch at the cafeteria' is true). Can we draw a conclusion about the truth of 'Clara celebrated a friend’s birthday in the dorm' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 15, "question": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Clara celebrated a friend’s 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 'William participated in the sports tournament' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'William participated in the sports tournament' is true.\n- If 'David prepared slides for his class talk' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Victoria attended the career fair' is true, then 'Umar missed the bus to campus' is true.\n- If 'Tina voted in the student council elections' 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 true.\n- ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true).\n- ('Rachel joined a late evening tutorial' 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’s birthday in the dorm' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>However, we don't have the following information provided: (¬'David prepared slides for his class talk' ∨ 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Zach cheered at the football match' is true, then 'Paul forgot to bring his homework' is true. - If 'Frank stayed in the dorm to study' is true, then 'Henry presented his project in class' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true. - If 'Emma borrowed books from the library' is true, then 'Yara stayed awake through the night revising' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Frank stayed in the dorm to study' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Grace’s lab session ran longer than planned' is true, then 'David prepared slides for his class talk' is true. - If 'David faced a surprise quiz from the professor' is true, then 'Emma borrowed books from the library' is true. - If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true. - If 'Henry presented his project in class' is true, then 'Jack joined the debate club meeting' is true. - If 'Noah gathered with his study group in the library' is true, then 'Quinn practiced for the theater play' is true. - If 'Kelly lost her internet connection during class' is true, then 'Isabella met a friend at the campus café' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true. - If 'Isabella met a friend at the campus café' is true, then 'Grace’s lab session ran longer than planned' is true. - If 'Paul forgot to bring his homework' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Umar missed the bus to campus' is true, then 'William participated in the sports tournament' is true. - If 'Victoria attended the career fair' is true, then 'Mia printed notes at the computer lab' is true. - If 'Jack joined the debate club meeting' is true, then 'Tina voted in the student council elections' is true. - If 'Zach cheered at the football match' is true, then 'Samuel volunteered at a campus event' is true. Now we know that: - ('Liam asked a question after the lecture' is false) or ('David faced a surprise quiz from the professor' is true). Can we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Quinn practiced for the theater play' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 16, "question": "We know the following rules:\n- If 'Zach cheered at the football match' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Frank stayed in the dorm to study' is true, then 'Henry presented his project in class' is true.\n- If 'Brian went to the professor’s 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 'Brian went to the professor’s office hours' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Emma borrowed books from the library' 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’s birthday in the dorm' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Frank stayed in the dorm to study' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Grace’s lab session ran longer than planned' is true, then 'David prepared slides for his class talk' is true.\n- If 'David faced a surprise quiz from the professor' is true, then 'Emma borrowed books from the library' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'Henry presented his project in class' is true, then 'Jack joined the debate club meeting' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Isabella met a friend at the campus café' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Isabella met a friend at the campus café' is true, then 'Grace’s lab session ran longer than planned' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Umar missed the bus to campus' is true, then 'William participated in the sports tournament' is true.\n- If 'Victoria attended the career fair' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Tina voted in the student council elections' is true.\n- If 'Zach cheered at the football match' is true, then 'Samuel volunteered at a campus event' is true.\n\nNow we know that:\n- ('Liam asked a question after the lecture' is false) or ('David faced a surprise quiz from the professor' is true).\n\nCan we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Quinn practiced for the theater play' is true).?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor’s office hours' is true) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (('David prepared slides for his class talk' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is false), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>However, we don't have the following information provided: ('Clara celebrated a friend’s birthday in the dorm' ∨ 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Quinn practiced for the theater play' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Paul forgot to bring his homework' is true, then 'Yara stayed awake through the night revising' is true. - If 'Umar missed the bus to campus' is true, then 'William participated in the sports tournament' is true. - If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true. - If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Brian went to the professor’s office hours' is true. Now we know that: - ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is false). - ('Olivia submitted her essay before the deadline' is false) or ('Paul forgot to bring his homework' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). - ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true). - 'Brian went to the professor’s office hours' is false. Can we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 17, "question": "We know the following rules:\n- If 'David prepared slides for his class talk' 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 '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 '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’s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Umar missed the bus to campus' 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 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Brian went to the professor’s office hours' is true.\n\nNow we know that:\n- ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is false).\n- ('Olivia submitted her essay before the deadline' is false) or ('Paul forgot to bring his homework' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true).\n- 'Brian went to the professor’s office hours' is false.\n\nCan we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>However, we don't have the following information provided: ('Clara celebrated a friend’s birthday in the dorm' ∨ 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Samuel volunteered at a campus event' is true, then 'William participated in the sports tournament' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true. - If 'Zach cheered at the football match' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true. - If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true. - If 'Victoria attended the career fair' is true, then 'Umar missed the bus to campus' is true. - If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true. - If 'David prepared slides for his class talk' is true, then 'Tina voted in the student council elections' is true. Now we know that: - ('Zach cheered at the football match' is false) or ('Xander had lunch at the cafeteria' is true). - ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true). - 'William participated in the sports tournament' is false. Can we draw a conclusion about the truth of 'Clara celebrated a friend’s birthday in the dorm' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 18, "question": "We know the following rules:\n- If 'Samuel volunteered at a campus event' is true, then 'William participated in the sports tournament' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Rachel joined a late evening tutorial' 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 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Brian went to the professor’s office hours' 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 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true.\n- If 'Victoria attended the career fair' is true, then 'Umar missed the bus to campus' is true.\n- If 'Victoria attended the career fair' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'David prepared slides for his class talk' is true, then 'Tina voted in the student council elections' is true.\n\nNow we know that:\n- ('Zach cheered at the football match' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true).\n- 'William participated in the sports tournament' is false.\n\nCan we draw a conclusion about the truth of 'Clara celebrated a friend’s birthday in the dorm' is true.?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and (('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s office hours' is true)) and (('David prepared slides for his class talk' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Alice presented at the science symposium' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true. - If 'Alice presented at the science symposium' is true, then 'Brian went to the professor’s office hours' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Mia printed notes at the computer lab' is true. - If 'William participated in the sports tournament' is true, then 'Yara stayed awake through the night revising' is true. - If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Brian went to the professor’s office hours' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Paul forgot to bring his homework' is true. - If 'Noah gathered with his study group in the library' is true, then 'William participated in the sports tournament' is true. - If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'David prepared slides for his class talk' is true, then 'Alice presented at the science symposium' is true. - If 'Brian went to the professor’s office hours' is true, then 'Quinn practiced for the theater play' is true. - If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Umar missed the bus to campus' is true. - If 'Victoria attended the career fair' is true, then 'David prepared slides for his class talk' is true. Now we know that: - ('David prepared slides for his class talk' is true) or ('Olivia submitted her essay before the deadline' is true). - ('Brian went to the professor’s office hours' is false) or ('Zach cheered at the football match' is true). - 'Paul forgot to bring his homework' is false. Can we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 19, "question": "We know the following rules:\n- If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'William participated in the sports tournament' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend’s 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 'Brian went to the professor’s office hours' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Rachel joined a late evening tutorial' 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- ('David prepared slides for his class talk' is true) or ('Olivia submitted her essay before the deadline' is true).\n- ('Brian went to the professor’s office hours' is false) or ('Zach cheered at the football match' is true).\n- 'Paul forgot to bring his homework' is false.\n\nCan we draw a conclusion about the truth of 'Quinn practiced for the theater play' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true))), then ('Brian went to the professor’s office hours' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true))), then ('Brian went to the professor’s office hours' is false) or ('David prepared slides for his class talk' is true).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true. - If 'Noah gathered with his study group in the library' is true, then 'Zach cheered at the football match' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Paul forgot to bring his homework' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Umar missed the bus to campus' is true. - If 'Victoria attended the career fair' is true, then 'Alice presented at the science symposium' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true). - ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true). - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). - ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true). Can we draw a conclusion about the truth of ('Quinn practiced for the theater play' is false) or ('David prepared slides for his class talk' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 20, "question": "We know the following rules:\n- If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Noah gathered with his study group in the library' 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 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s 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 'Xander had lunch at the cafeteria' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Umar missed the bus to campus' is true.\n- If 'Victoria attended the career fair' 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 ('William participated in the sports tournament' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Mia printed notes at the computer lab' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true).\n\nCan we draw a conclusion about the truth of ('Quinn practiced for the theater play' is false) or ('David prepared slides for his class talk' is true).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor’s office hours' is true) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s office hours' is true)) and (('David prepared slides for his class talk' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Alice presented at the science symposium' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Victoria attended the career fair' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true. - If 'Kelly lost her internet connection during class' is true, then 'Yara stayed awake through the night revising' is true. - If 'Jack joined the debate club meeting' is true, then 'Kelly lost her internet connection during class' is true. - If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true. - If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true. - If 'Brian went to the professor’s office hours' is true, then 'Liam asked a question after the lecture' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Mia printed notes at the computer lab' is true. - If 'William participated in the sports tournament' is true, then 'Tina voted in the student council elections' is true. - If 'Umar missed the bus to campus' is true, then 'Mia printed notes at the computer lab' is true. - If 'Brian went to the professor’s office hours' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Brian went to the professor’s office hours' is true, then 'Samuel volunteered at a campus event' is true. Now we know that: - ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true). - ('Xander had lunch at the cafeteria' is false) or ('Jack joined the debate club meeting' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). Can we draw a conclusion about the truth of ('Paul forgot to bring his homework' is true) or ('Quinn practiced for the theater play' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 21, "question": "We know the following rules:\n- If 'Victoria attended the career fair' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s 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 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Clara celebrated a friend’s 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 'Victoria attended the career fair' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'William participated in the sports tournament' is true, then 'Tina voted in the student council elections' is true.\n- If 'Umar missed the bus to campus' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Samuel volunteered at a campus event' is true.\n\nNow we know that:\n- ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Jack joined the debate club meeting' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of ('Paul forgot to bring his homework' is true) or ('Quinn practiced for the theater play' is true).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and (('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true))), then ('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'David prepared slides for his class talk' is true, then 'Kelly lost her internet connection during class' is true. - If 'Kelly lost her internet connection during class' is true, then 'Mia printed notes at the computer lab' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Tina voted in the student council elections' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Jack joined the debate club meeting' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true. - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true. - If 'Isabella met a friend at the campus café' is true, then 'Zach cheered at the football match' is true. - If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Henry presented his project in class' is true, then 'Isabella met a friend at the campus café' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true. - If 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true. - If 'Paul forgot to bring his homework' is true, then 'Rachel joined a late evening tutorial' is true. - If ('Umar missed the bus to campus' is true) and ('Zach cheered at the football match' is true), then 'Victoria attended the career fair' is true. - If 'Samuel volunteered at a campus event' is true, then 'Henry presented his project in class' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Henry presented his project in class' is true). - ('Tina voted in the student council elections' is true) or ('Yara stayed awake through the night revising' is true). Can we draw a conclusion about the truth of ('Quinn practiced for the theater play' is true) or ('Rachel joined a late evening tutorial' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 22, "question": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Tina voted in the student council elections' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Jack joined the debate club meeting' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Isabella met a friend at the campus café' is true, then 'Zach cheered at the football match' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Henry presented his project in class' is true, then 'Isabella met a friend at the campus café' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Alice presented at the science symposium' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Rachel joined a late evening tutorial' is true.\n- If ('Umar missed the bus to campus' is true) and ('Zach cheered at the football match' is true), then 'Victoria attended the career fair' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Henry presented his project in class' is true.\n- If 'Zach cheered at the football match' 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 ('Henry presented his project in class' is true).\n- ('Tina voted in the student council elections' is true) or ('Yara stayed awake through the night revising' is true).\n\nCan we draw a conclusion about the truth of ('Quinn practiced for the theater play' is true) or ('Rachel joined a late evening tutorial' is true).?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)), then if ('Brian went to the professor’s office hours' is true), then (('David prepared slides for his class talk' is true) and ('Clara celebrated a friend’s birthday in the dorm' is true)).</step> <step>However, we don't have the following information provided: ('Clara celebrated a friend’s birthday in the dorm' → 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Alice presented at the science symposium' is true, then 'Brian went to the professor’s office hours' is true. - If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' is true. - If 'Yara stayed awake through the night revising' is true, then 'David prepared slides for his class talk' is true. - If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Quinn practiced for the theater play' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'William participated in the sports tournament' is true, then 'Yara stayed awake through the night revising' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Brian went to the professor’s office hours' is true. - If 'William participated in the sports tournament' is true, then 'Tina voted in the student council elections' is true. - If 'Umar missed the bus to campus' is true, then 'Samuel volunteered at a campus event' is true. - If 'Paul forgot to bring his homework' is true, then 'Victoria attended the career fair' is true. Now we know that: - ('Brian went to the professor’s office hours' is false) or ('Zach cheered at the football match' is true). - ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true). Can we draw a conclusion about the truth of If 'Quinn practiced for the theater play' is true, then ('David prepared slides for his class talk' is true) and ('Rachel joined a late evening tutorial' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 23, "question": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Paul forgot to bring his homework' 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 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'William participated in the sports tournament' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'William participated in the sports tournament' is true, then 'Tina voted in the student council elections' is true.\n- If 'Umar missed the bus to campus' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Victoria attended the career fair' is true.\n\nNow we know that:\n- ('Brian went to the professor’s office hours' is false) or ('Zach cheered at the football match' is true).\n- ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).\n\nCan we draw a conclusion about the truth of If 'Quinn practiced for the theater play' is true, then ('David prepared slides for his class talk' is true) and ('Rachel joined a late evening tutorial' is true).?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>However, we don't have the following information provided: (¬'Clara celebrated a friend’s birthday in the dorm' ∨ 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Quinn practiced for the theater play' is true, then 'Yara stayed awake through the night revising' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'Xander had lunch at the cafeteria' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Alice presented at the science symposium' is true, then 'Victoria attended the career fair' is true. - If 'Umar missed the bus to campus' is true, then 'Tina voted in the student council elections' is true. - If 'Samuel volunteered at a campus event' is true, then 'Victoria attended the career fair' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true. Now we know that: - 'David prepared slides for his class talk' is true. - ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true). - ('Paul forgot to bring his homework' is false) or ('David prepared slides for his class talk' is true). - ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). Can we draw a conclusion about the truth of 'Clara celebrated a friend’s birthday in the dorm' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 24, "question": "We know the following rules:\n- If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s 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 'Quinn practiced for the theater play' 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 'Brian went to the professor’s office hours' is true, then 'Xander had lunch at the cafeteria' 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- If 'Umar missed the bus to campus' is true, then 'Tina voted in the student council elections' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Victoria attended the career fair' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true.\n\nNow we know that:\n- 'David prepared slides for his class talk' is true.\n- ('Xander had lunch at the cafeteria' is false) or ('Paul forgot to bring his homework' is true).\n- ('Paul forgot to bring his homework' is false) or ('David prepared slides for his class talk' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true).\n- ('Xander had lunch at the cafeteria' 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’s birthday in the dorm' is true.?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true))), then ('Brian went to the professor’s office hours' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>However, we don't have the following information provided: (¬'Clara celebrated a friend’s birthday in the dorm' ∨ 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Rachel joined a late evening tutorial' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true. - If 'Paul forgot to bring his homework' is true, then 'Yara stayed awake through the night revising' is true. - If 'Umar missed the bus to campus' is true, then 'Brian went to the professor’s office hours' is true. - If 'Tina voted in the student council elections' is true, then 'Victoria attended the career fair' is true. - If 'Samuel volunteered at a campus event' is true, then 'Brian went to the professor’s office hours' is true. Now we know that: - ('Olivia submitted her essay before the deadline' is false) or ('Xander had lunch at the cafeteria' is true). - ('Xander had lunch at the cafeteria' is false) or ('Quinn practiced for the theater play' is true). - ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). Can we draw a conclusion about the truth of If 'Rachel joined a late evening tutorial' is true, then 'David prepared slides for his class talk' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 25, "question": "We know the following rules:\n- If 'Rachel joined a late evening tutorial' 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 'Brian went to the professor’s 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 'Xander had lunch at the cafeteria' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Clara celebrated a friend’s 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 'Brian went to the professor’s office hours' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Umar missed the bus to campus' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Tina voted in the student council elections' is true, then 'Victoria attended the career fair' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Brian went to the professor’s office hours' is true.\n\nNow we know that:\n- ('Olivia submitted her essay before the deadline' is false) or ('Xander had lunch at the cafeteria' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Quinn practiced for the theater play' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Olivia submitted her essay before the deadline' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n\nCan we draw a conclusion about the truth of If 'Rachel joined a late evening tutorial' is true, then 'David prepared slides for his class talk' is true.?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s office hours' is false) or ('David prepared slides for his class talk' is true))), then ('Alice presented at the science symposium' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>However, we don't have the following information provided: (¬'David prepared slides for his class talk' ∨ 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Quinn practiced for the theater play' is true, then 'Yara stayed awake through the night revising' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Xander had lunch at the cafeteria' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Umar missed the bus to campus' is true, then 'Alice presented at the science symposium' is true. - If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true. - If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true). - ('Xander had lunch at the cafeteria' is false) or ('David prepared slides for his class talk' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). - ('Paul forgot to bring his homework' is false) or ('Quinn practiced for the theater play' is true). Can we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 26, "question": "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 'Brian went to the professor’s office hours' 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 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Quinn practiced for the theater play' 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 'Rachel joined a late evening tutorial' 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’s office hours' is true.\n- If 'Umar missed the bus to campus' 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 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('David prepared slides for his class talk' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n- ('Paul forgot to bring his homework' is false) or ('Quinn practiced for the theater play' is true).\n\nCan we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Brian went to the professor’s office hours' is false) or ('Clara celebrated a friend’s 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).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Brian went to the professor’s office hours' is false) or ('Clara celebrated a friend’s 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).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Zach cheered at the football match' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true. - If 'Samuel volunteered at a campus event' is true, then 'William participated in the sports tournament' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Alice presented at the science symposium' is true, then 'Zach cheered at the football match' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Rachel joined a late evening tutorial' is true. - If 'David prepared slides for his class talk' is true, then 'Victoria attended the career fair' is true. - If 'Alice presented at the science symposium' is true, then 'Umar missed the bus to campus' is true. - If 'David prepared slides for his class talk' is true, then 'Tina voted in the student council elections' is true. Now we know that: - ('Zach cheered at the football match' is false) or ('Alice presented at the science symposium' is true). - ('Zach cheered at the football match' is false) or ('Brian went to the professor’s office hours' is true). - ('Zach cheered at the football match' is false) or ('Xander had lunch at the cafeteria' is true). - ('Zach cheered at the football match' is false) or ('Yara stayed awake through the night revising' is true). Can we draw a conclusion about the truth of ('Clara celebrated a friend’s birthday in the dorm' is false) or ('William participated in the sports tournament' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 27, "question": "We know the following rules:\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Zach cheered at the football match' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Zach cheered at the football match' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'William participated in the sports tournament' is true.\n- If 'Brian went to the professor’s office hours' 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 'Xander had lunch at the cafeteria' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'David prepared slides for his class talk' is true, then 'Victoria attended the career fair' is true.\n- If 'Alice presented at the science symposium' is true, then 'Umar missed the bus to campus' is true.\n- If 'David prepared slides for his class talk' is true, then 'Tina voted in the student council elections' 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 false) or ('Brian went to the professor’s office hours' is true).\n- ('Zach cheered at the football match' is false) or ('Xander had lunch at the cafeteria' 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’s birthday in the dorm' is false) or ('William participated in the sports tournament' is true).?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is false.</step> <step>However, we don't have the following information provided: ('David prepared slides for his class talk' → 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Xander had lunch at the cafeteria' is true, then 'Quinn practiced for the theater play' is true. - If 'Rachel joined a late evening tutorial' is true, then 'William participated in the sports tournament' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Brian went to the professor’s office hours' is true, then 'Alice presented at the science symposium' is true. - If 'Zach cheered at the football match' is true, then 'Yara stayed awake through the night revising' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Brian went to the professor’s office hours' is true. - If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Victoria attended the career fair' is true, then 'Zach cheered at the football match' is true. - If 'Alice presented at the science symposium' is true, then 'Umar missed the bus to campus' is true. - If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true. Now we know that: - 'William participated in the sports tournament' is false. Can we draw a conclusion about the truth of 'David prepared slides for his class talk' is false.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 28, "question": "We know the following rules:\n- If 'Xander had lunch at the cafeteria' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'William participated in the sports tournament' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Alice presented at the science symposium' 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’s birthday in the dorm' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Victoria attended the career fair' is true, then 'Zach cheered at the football match' is true.\n- If 'Alice presented at the science symposium' is true, then 'Umar missed the bus to campus' is true.\n- If 'Tina voted in the student council elections' is true, then 'Samuel volunteered at a campus event' is true.\n\nNow we know that:\n- 'William participated in the sports tournament' is false.\n\nCan we draw a conclusion about the truth of 'David prepared slides for his class talk' is false.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s 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’s office hours' is false) or ('Clara celebrated a friend’s birthday in the dorm' is false).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend’s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.</step> <step>However, we don't have the following information provided: (¬'David prepared slides for his class talk' ∨ 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Noah gathered with his study group in the library' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true. - If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Mia printed notes at the computer lab' is true, then 'Zach cheered at the football match' is true. - If 'Liam asked a question after the lecture' is true, then 'Mia printed notes at the computer lab' is true. - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'David prepared slides for his class talk' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true. - If 'Liam asked a question after the lecture' is true, then 'Victoria attended the career fair' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true. - If 'Liam asked a question after the lecture' is true, then 'Tina voted in the student council elections' is true. - If 'Liam asked a question after the lecture' is true, then 'Umar missed the bus to campus' is true. Now we know that: - ('Olivia submitted her essay before the deadline' is false) or ('Xander had lunch at the cafeteria' is false). - ('Xander had lunch at the cafeteria' is true) or ('Liam asked a question after the lecture' is true). - ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true). Can we draw a conclusion about the truth of (('Paul forgot to bring his homework' is true) and ('Quinn practiced for the theater play' is true)) is false.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 29, "question": "We know the following rules:\n- If 'Brian went to the professor’s 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 'Noah gathered with his study group in the library' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Zach cheered at the football match' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'David prepared slides for his class talk' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s 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 'Liam asked a question after the lecture' is true, then 'Victoria attended the career fair' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Tina voted in the student council elections' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Umar missed the bus to campus' is true.\n\nNow we know that:\n- ('Olivia submitted her essay before the deadline' is false) or ('Xander had lunch at the cafeteria' is false).\n- ('Xander had lunch at the cafeteria' is true) or ('Liam asked a question after the lecture' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('William participated in the sports tournament' is true).\n\nCan we draw a conclusion about the truth of (('Paul forgot to bring his homework' is true) and ('Quinn practiced for the theater play' is true)) is false.?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Alice presented at the science symposium' is true) or ('David prepared slides for his class talk' is true).</step> <step>However, we don't have the following information provided: ('Clara celebrated a friend’s birthday in the dorm' ∨ 'David prepared slides for his class talk'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Umar missed the bus to campus' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Kelly lost her internet connection during class' is true, then 'Mia printed notes at the computer lab' is true. - If 'Jack joined the debate club meeting' is true, then 'Yara stayed awake through the night revising' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Kelly lost her internet connection during class' is true. - If 'Noah gathered with his study group in the library' is true, then 'Liam asked a question after the lecture' is true. - If 'Zach cheered at the football match' is true, then 'Umar missed the bus to campus' is true. - If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Liam asked a question after the lecture' is true, then 'David prepared slides for his class talk' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Paul forgot to bring his homework' is true, then 'Victoria attended the career fair' is true. - If 'Samuel volunteered at a campus event' is true, then if ('Brian went to the professor’s office hours' is true), then ('William participated in the sports tournament' is true). - If ('Tina voted in the student council elections' is true) and ('Olivia submitted her essay before the deadline' is true), then 'Rachel joined a late evening tutorial' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Isabella met a friend at the campus café' is true). - ('Isabella met a friend at the campus café' is false) or ('Jack joined the debate club meeting' is true). Can we draw a conclusion about the truth of ('Olivia submitted her essay before the deadline' is true) or ('Xander had lunch at the cafeteria' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 30, "question": "We know the following rules:\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Umar missed the bus to campus' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' 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’s birthday in the dorm' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Zach cheered at the football match' is true, then 'Umar missed the bus to campus' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Liam asked a question after the lecture' is true, then 'David prepared slides for his class talk' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Victoria attended the career fair' is true.\n- If 'Samuel volunteered at a campus event' is true, then if ('Brian went to the professor’s office hours' is true), then ('William participated in the sports tournament' is true).\n- If ('Tina voted in the student council elections' is true) and ('Olivia submitted her essay before the deadline' is true), then 'Rachel joined a late evening tutorial' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Isabella met a friend at the campus café' is true).\n- ('Isabella met a friend at the campus café' is false) or ('Jack joined the debate club meeting' is true).\n\nCan we draw a conclusion about the truth of ('Olivia submitted her essay before the deadline' is true) or ('Xander had lunch at the cafeteria' is true).?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false))), then ('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Tina voted in the student council elections' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Jack joined the debate club meeting' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true. - If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Samuel volunteered at a campus event' is true, then 'Quinn practiced for the theater play' is true. - If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true. - If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true. - If 'Noah gathered with his study group in the library' is true, then 'Liam asked a question after the lecture' is true. - If 'Yara stayed awake through the night revising' is true, then 'Henry presented his project in class' is true. - If 'Liam asked a question after the lecture' is true, then 'Jack joined the debate club meeting' is true. - If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true. - If 'Kelly lost her internet connection during class' is true, then 'David prepared slides for his class talk' is true. - If 'Zach cheered at the football match' is true, then 'Tina voted in the student council elections' is true. - If 'William participated in the sports tournament' is true, then 'Kelly lost her internet connection during class' is true. - If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true. Now we know that: - ('Isabella met a friend at the campus café' is false) or ('Xander had lunch at the cafeteria' is false). - ('Henry presented his project in class' is false) or ('Isabella met a friend at the campus café' is true). Can we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Samuel volunteered at a campus event' is false).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 31, "question": "We know the following rules:\n- If 'Tina voted in the student council elections' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Henry presented his project in class' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Jack joined the debate club meeting' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'Clara celebrated a friend’s 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’s office hours' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Tina voted in the student council elections' is true.\n- If 'William participated in the sports tournament' is true, then 'Kelly lost her internet connection during class' 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- ('Isabella met a friend at the campus café' is false) or ('Xander had lunch at the cafeteria' is false).\n- ('Henry presented his project in class' is false) or ('Isabella met a friend at the campus café' is true).\n\nCan we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Samuel volunteered at a campus event' is false).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>However, we don't have the following information provided: (¬'David prepared slides for his class talk' ∨ 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Brian went to the professor’s office hours' is true, then 'Mia printed notes at the computer lab' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true. - If 'Victoria attended the career fair' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Kelly lost her internet connection during class' is true, then 'Liam asked a question after the lecture' is true. - If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true. - If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true. - If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Noah gathered with his study group in the library' is true, then 'David prepared slides for his class talk' is true. - If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true. - If 'Liam asked a question after the lecture' is true, then 'Yara stayed awake through the night revising' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true. - If 'William participated in the sports tournament' is true, then 'Zach cheered at the football match' is true. - If 'Tina voted in the student council elections' is true, then 'Umar missed the bus to campus' is true. - If 'Kelly lost her internet connection during class' is true, then 'Samuel volunteered at a campus event' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). - ('Xander had lunch at the cafeteria' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true). - ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true). Can we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Quinn practiced for the theater play' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 32, "question": "We know the following rules:\n- If 'Mia printed notes at the computer lab' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Victoria attended the career fair' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Zach cheered at the football match' is true, then 'Victoria attended the career fair' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'David prepared slides for his class talk' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'David prepared slides for his class talk' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Liam asked a question after the lecture' 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 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true.\n- If 'William participated in the sports tournament' 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 'Kelly lost her internet connection during class' is true, then 'Samuel volunteered at a campus event' 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- ('Xander had lunch at the cafeteria' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true).\n\nCan we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Quinn practiced for the theater play' is true).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s birthday in the dorm' is true))), then ('David prepared slides for his class talk' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>However, we don't have the following information provided: (¬'David prepared slides for his class talk' ∨ 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true. - If 'Brian went to the professor’s office hours' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Yara stayed awake through the night revising' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true. - If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Noah gathered with his study group in the library' is true, then 'Yara stayed awake through the night revising' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'David prepared slides for his class talk' is true, then 'Victoria attended the career fair' is true. - If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true. - If 'Samuel volunteered at a campus event' is true, then 'Victoria attended the career fair' is true. - If 'Alice presented at the science symposium' is true, then 'Umar missed the bus to campus' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true). - ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true). - ('Xander had lunch at the cafeteria' is true) or ('Mia printed notes at the computer lab' is true). Can we draw a conclusion about the truth of If 'Rachel joined a late evening tutorial' is true, then 'Quinn practiced for the theater play' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 33, "question": "We know the following rules:\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Paul forgot to bring his homework' is true, then 'David prepared slides for his class talk' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Brian went to the professor’s 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 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Alice presented at the science symposium' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Noah gathered with his study group in the library' 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 'Mia printed notes at the computer lab' is true, then 'Noah gathered with his study group in the library' 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 'Victoria attended the career fair' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Victoria attended the career fair' is true.\n- If 'Alice presented at the science symposium' is true, then 'Umar missed the bus to campus' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Alice presented at the science symposium' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Zach cheered at the football match' is true).\n- ('Xander had lunch at the cafeteria' is true) or ('Mia printed notes at the computer lab' is true).\n\nCan we draw a conclusion about the truth of If 'Rachel joined a late evening tutorial' is true, then 'Quinn practiced for the theater play' is true.?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s 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’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true))), then ('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and (('Alice presented at the science symposium' is false) or ('David prepared slides for his class talk' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>However, we don't have the following information provided: (¬'David prepared slides for his class talk' ∨ 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Alice presented at the science symposium' is true. - If 'Victoria attended the career fair' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Liam asked a question after the lecture' is true, then 'Zach cheered at the football match' is true. - If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true. - If 'Mia printed notes at the computer lab' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true. - If 'Paul forgot to bring his homework' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true. - If 'Samuel volunteered at a campus event' is true, then 'Quinn practiced for the theater play' is true. - If 'David prepared slides for his class talk' is true, then 'Noah gathered with his study group in the library' is true. - If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true. - If ('Umar missed the bus to campus' is true) and ('William participated in the sports tournament' is true), then 'Noah gathered with his study group in the library' is true. - If 'Zach cheered at the football match' is true, then 'Tina voted in the student council elections' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Victoria attended the career fair' is true). - ('Kelly lost her internet connection during class' is false) or ('Liam asked a question after the lecture' is true). - ('Xander had lunch at the cafeteria' is false) or ('Quinn practiced for the theater play' is true). Can we draw a conclusion about the truth of ('Samuel volunteered at a campus event' is false) or ('Rachel joined a late evening tutorial' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 34, "question": "We know the following rules:\n- If 'Clara celebrated a friend’s 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 'Xander had lunch at the cafeteria' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Zach cheered at the football match' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Zach cheered at the football match' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Quinn practiced for the theater play' is true.\n- If 'David prepared slides for his class talk' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Alice presented at the science symposium' is true, then 'Yara stayed awake through the night revising' is true.\n- If ('Umar missed the bus to campus' is true) and ('William participated in the sports tournament' is true), then 'Noah gathered with his study group in the library' is true.\n- If 'Zach cheered at the football match' is true, then 'Tina voted in the student council elections' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Victoria attended the career fair' is true).\n- ('Kelly lost her internet connection during class' is false) or ('Liam asked a question after the lecture' is true).\n- ('Xander had lunch at the cafeteria' is false) or ('Quinn practiced for the theater play' is true).\n\nCan we draw a conclusion about the truth of ('Samuel volunteered at a campus event' is false) or ('Rachel joined a late evening tutorial' is true).?", "split": "train" }
<think> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true), then if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Brian went to the professor’s 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’s office hours' is false) or ('Alice presented at the science symposium' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Brian went to the professor’s office hours' is false) or ('Clara celebrated a friend’s birthday in the dorm' is false))), then ('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is false).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and (('David prepared slides for his class talk' is false) or ('Alice presented at the science symposium' is false))), then ('Brian went to the professor’s office hours' is false) or ('Clara celebrated a friend’s birthday in the dorm' is false).</step> <step>We know that If (if ('Clara celebrated a friend’s 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’s office hours' is true)) and (('Alice presented at the science symposium' is false) or ('Brian went to the professor’s office hours' is false))), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false).</step> <step>We know that If ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is false), then (('Clara celebrated a friend’s birthday in the dorm' is true) and ('David prepared slides for his class talk' is true)) is false.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Noah gathered with his study group in the library' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Mia printed notes at the computer lab' is true, then 'Yara stayed awake through the night revising' is true. - If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true. - If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'David prepared slides for his class talk' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Xander had lunch at the cafeteria' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Brian went to the professor’s office hours' is true, then 'Victoria attended the career fair' is true. - If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true. - If 'Victoria attended the career fair' is true, then 'Umar missed the bus to campus' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Liam asked a question after the lecture' is true). - ('Liam asked a question after the lecture' is false) or ('Mia printed notes at the computer lab' is true). - ('Alice presented at the science symposium' is false) or ('Xander had lunch at the cafeteria' is false). Can we draw a conclusion about the truth of ('Quinn practiced for the theater play' is true) and ('Rachel joined a late evening tutorial' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 35, "question": "We know the following rules:\n- If 'Noah gathered with his study group in the library' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'David prepared slides for his class talk' is true.\n- If 'Clara celebrated a friend’s 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’s 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 'Rachel joined a late evening tutorial' is true, then 'Paul forgot to bring his homework' 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 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Victoria attended the career fair' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Tina voted in the student council elections' is true.\n- If 'Victoria attended the career fair' is true, then 'Umar missed the bus to campus' is true.\n\nNow we know that:\n- ('Xander had lunch at the cafeteria' is false) or ('Liam asked a question after the lecture' is true).\n- ('Liam asked a question after the lecture' is false) or ('Mia printed notes at the computer lab' is true).\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 ('Quinn practiced for the theater play' is true) and ('Rachel joined a late evening tutorial' is true).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and (('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Alice presented at the science symposium' is true) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('Alice presented at the science symposium' is true) or ('David prepared slides for his class talk' is true))), then ('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Brian went to the professor’s 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’s office hours' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Paul forgot to bring his homework' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Jack joined the debate club meeting' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Kelly lost her internet connection during class' is true, then 'David prepared slides for his class talk' is true. - If 'Zach cheered at the football match' is true, then 'Tina voted in the student council elections' is true. - If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Liam asked a question after the lecture' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Henry presented his project in class' is true, then 'Isabella met a friend at the campus café' is true. - If 'Tina voted in the student council elections' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Paul forgot to bring his homework' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true. - If 'Noah gathered with his study group in the library' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Isabella met a friend at the campus café' is true, then 'Yara stayed awake through the night revising' is true. - If 'Umar missed the bus to campus' is true, then 'Alice presented at the science symposium' is true. - If 'Victoria attended the career fair' is true, then 'Samuel volunteered at a campus event' is true. - If 'William participated in the sports tournament' is true, then 'Alice presented at the science symposium' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('Henry presented his project in class' is true). - ('Mia printed notes at the computer lab' is true) or ('Noah gathered with his study group in the library' is true). Can we draw a conclusion about the truth of ('Quinn practiced for the theater play' is true) or ('Rachel joined a late evening tutorial' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 36, "question": "We know the following rules:\n- If 'Paul forgot to bring his homework' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Jack joined the debate club meeting' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'David prepared slides for his class talk' is true.\n- If 'Zach cheered at the football match' is true, then 'Tina voted in the student council elections' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Henry presented his project in class' is true, then 'Isabella met a friend at the campus café' is true.\n- If 'Tina voted in the student council elections' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Isabella met a friend at the campus café' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Umar missed the bus to campus' is true, then 'Alice presented at the science symposium' is true.\n- If 'Victoria attended the career fair' is true, then 'Samuel volunteered at a campus event' is true.\n- If 'William participated in the sports tournament' 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 ('Henry presented his project in class' is true).\n- ('Mia printed notes at the computer lab' is true) or ('Noah gathered with his study group in the library' is true).\n\nCan we draw a conclusion about the truth of ('Quinn practiced for the theater play' is true) or ('Rachel joined a late evening tutorial' is true).?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ('David prepared slides for his class talk' is true), then 'Clara celebrated a friend’s birthday in the dorm' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Noah gathered with his study group in the library' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Yara stayed awake through the night revising' is true. - If 'Zach cheered at the football match' is true, then 'William participated in the sports tournament' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true. - If 'William participated in the sports tournament' is true, then 'Xander had lunch at the cafeteria' is true. - If 'David prepared slides for his class talk' is true, then 'Paul forgot to bring his homework' is true. - If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true. - If 'Tina voted in the student council elections' is true, then 'Noah gathered with his study group in the library' is true. - If 'Samuel volunteered at a campus event' is true, then 'Umar missed the bus to campus' is true. - If 'Victoria attended the career fair' is true, then 'William participated in the sports tournament' is true. Now we know that: - 'Brian went to the professor’s office hours' is true. - ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true). Can we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 37, "question": "We know the following rules:\n- If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Olivia submitted her essay before the deadline' 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 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' 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 'Paul forgot to bring his homework' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'David prepared slides for his class talk' is true.\n- If 'Tina voted in the student council elections' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Umar missed the bus to campus' 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- 'Brian went to the professor’s office hours' is true.\n- ('Xander had lunch at the cafeteria' is false) or ('Noah gathered with his study group in the library' is true).\n\nCan we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.?", "split": "train" }
<think> <step>We know that If if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is false) or ('David prepared slides for his class talk' is true).</step> <step>We know that If (if ('Brian went to the professor’s office hours' is true), then ('Clara celebrated a friend’s 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’s office hours' is true))), then ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If ('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true), then if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and (('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true))), then ('Clara celebrated a friend’s birthday in the dorm' is true) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and (('David prepared slides for his class talk' is true) or ('Alice presented at the science symposium' is true))), then ('Brian went to the professor’s office hours' is true) or ('Clara celebrated a friend’s birthday in the dorm' is true).</step> <step>We know that If (('Clara celebrated a friend’s birthday in the dorm' is true) or ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is false), then 'David prepared slides for his class talk' is true.</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('David prepared slides for his class talk' is true)) and ('Clara celebrated a friend’s birthday in the dorm' is true), then 'David prepared slides for his class talk' is true.</step> <step>However, we don't have the following information provided: ('David prepared slides for his class talk' → 'Clara celebrated a friend’s birthday in the dorm'). Therefore, we cannot draw a conclusion about the truth of conclusion.</step> </think> <answer>no</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Paul forgot to bring his homework' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true. - If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true. - If 'Xander had lunch at the cafeteria' is true, then 'Liam asked a question after the lecture' is true. - If 'Liam asked a question after the lecture' is true, then 'Mia printed notes at the computer lab' is true. - If 'Mia printed notes at the computer lab' is true, then 'William participated in the sports tournament' is true. - If 'Noah gathered with his study group in the library' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Zach cheered at the football match' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Brian went to the professor’s office hours' is true, then 'David prepared slides for his class talk' is true. - If 'William participated in the sports tournament' is true, then 'Yara stayed awake through the night revising' is true. - If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true. - If 'Samuel volunteered at a campus event' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'William participated in the sports tournament' is true, then 'Tina voted in the student council elections' is true. Now we know that: - ('David prepared slides for his class talk' is true) or ('Noah gathered with his study group in the library' is true). - 'Paul forgot to bring his homework' is false. Can we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "no", "index": 38, "question": "We know the following rules:\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Quinn practiced for the theater play' is true, then 'Rachel joined a late evening tutorial' is true.\n- If 'Xander had lunch at the cafeteria' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'William participated in the sports tournament' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Brian went to the professor’s office hours' 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’s birthday in the dorm' 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 'Xander had lunch at the cafeteria' is true.\n- If 'Brian went to the professor’s 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 'Yara stayed awake through the night revising' is true.\n- If 'Umar missed the bus to campus' is true, then 'Victoria attended the career fair' is true.\n- If 'Samuel volunteered at a campus event' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'William participated in the sports tournament' is true, then 'Tina voted in the student council elections' is true.\n\nNow we know that:\n- ('David prepared slides for his class talk' is true) or ('Noah gathered with his study group in the library' is true).\n- 'Paul forgot to bring his homework' is false.\n\nCan we draw a conclusion about the truth of 'Rachel joined a late evening tutorial' is true.?", "split": "train" }
<think> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Brian went to the professor’s office hours' is true)) and ((if ('Clara celebrated a friend’s 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’s birthday in the dorm' is false) or ('Brian went to the professor’s office hours' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Clara celebrated a friend’s birthday in the dorm' is true), then ('Alice presented at the science symposium' is true)) and ((if ('Brian went to the professor’s office hours' is true), then ('David prepared slides for his class talk' is true)) and (('David prepared slides for his class talk' is false) or ('Clara celebrated a friend’s birthday in the dorm' is true))), then ('Brian went to the professor’s office hours' is false) or ('Alice presented at the science symposium' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>We know that If (if ('Alice presented at the science symposium' is true), then ('Clara celebrated a friend’s birthday in the dorm' is true)) and ((if ('David prepared slides for his class talk' is true), then ('Brian went to the professor’s office hours' is true)) and (('Brian went to the professor’s 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’s birthday in the dorm' is true).</step> <step>Therefore, since we know all the rules and premises, we can draw a conclusion about the truth of the conclusion.</step> </think> <answer>yes</answer>	{ "theme": "university" }	logic-implication	We know the following rules: - If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true. - If 'Rachel joined a late evening tutorial' is true, then 'Olivia submitted her essay before the deadline' is true. - If 'Henry presented his project in class' is true, then 'Jack joined the debate club meeting' is true. - If 'Isabella met a friend at the campus café' is true, then 'Grace’s lab session ran longer than planned' is true. - If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true. - If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true. - If 'Noah gathered with his study group in the library' is true, then 'Quinn practiced for the theater play' is true. - If 'Emma borrowed books from the library' is true, then 'Yara stayed awake through the night revising' is true. - If 'Zach cheered at the football match' is true, then 'Paul forgot to bring his homework' is true. - If 'Kelly lost her internet connection during class' is true, then 'Isabella met a friend at the campus café' is true. - If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true. - If 'David faced a surprise quiz from the professor' is true, then 'Emma borrowed books from the library' is true. - If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true. - If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true. - If 'Frank stayed in the dorm to study' is true, then 'Henry presented his project in class' is true. - If 'Paul forgot to bring his homework' is true, then 'Xander had lunch at the cafeteria' is true. - If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Frank stayed in the dorm to study' is true. - If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true. - If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true. - If 'Grace’s lab session ran longer than planned' is true, then 'David prepared slides for his class talk' is true. - If 'Umar missed the bus to campus' is true, then 'William participated in the sports tournament' is true. - If 'Umar missed the bus to campus' is true, then 'Zach cheered at the football match' is true. - If 'Victoria attended the career fair' is true, then 'Tina voted in the student council elections' is true. - If 'Samuel volunteered at a campus event' is true, then 'Zach cheered at the football match' is true. Now we know that: - ('Xander had lunch at the cafeteria' is false) or ('David faced a surprise quiz from the professor' is true). Can we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Quinn practiced for the theater play' is true).? Start your response with a <think> tag. Within this tag, reason step by step by placing each atomic reasoning step inside <step> </step> tags. All reasoning steps must be enclosed within a single <think> block. After the reasoning block, provide the final answer separately, enclosed within <answer> </answer> tags. The final answer must be either "Yes" or "No" only. Expected output format: ``` <think> <step>First atomic step of reasoning.</step> <step>Second atomic step of reasoning.</step> ... </think> <answer>Final answer</answer> ``` Now, please present your reasoning process and final answer using the format above.	{ "answer": "yes", "index": 39, "question": "We know the following rules:\n- If 'Brian went to the professor’s office hours' is true, then 'Zach cheered at the football match' is true.\n- If 'Rachel joined a late evening tutorial' is true, then 'Olivia submitted her essay before the deadline' is true.\n- If 'Henry presented his project in class' is true, then 'Jack joined the debate club meeting' is true.\n- If 'Isabella met a friend at the campus café' is true, then 'Grace’s lab session ran longer than planned' is true.\n- If 'Mia printed notes at the computer lab' is true, then 'Kelly lost her internet connection during class' is true.\n- If 'Jack joined the debate club meeting' is true, then 'Liam asked a question after the lecture' is true.\n- If 'Noah gathered with his study group in the library' is true, then 'Quinn practiced for the theater play' is true.\n- If 'Emma borrowed books from the library' is true, then 'Yara stayed awake through the night revising' is true.\n- If 'Zach cheered at the football match' is true, then 'Paul forgot to bring his homework' is true.\n- If 'Kelly lost her internet connection during class' is true, then 'Isabella met a friend at the campus café' is true.\n- If 'Olivia submitted her essay before the deadline' is true, then 'Mia printed notes at the computer lab' is true.\n- If 'David faced a surprise quiz from the professor' is true, then 'Emma borrowed books from the library' is true.\n- If 'Alice presented at the science symposium' is true, then 'Clara celebrated a friend’s birthday in the dorm' is true.\n- If 'Yara stayed awake through the night revising' is true, then 'Alice presented at the science symposium' is true.\n- If 'Frank stayed in the dorm to study' is true, then 'Henry presented his project in class' is true.\n- If 'Paul forgot to bring his homework' is true, then 'Xander had lunch at the cafeteria' is true.\n- If 'Clara celebrated a friend’s birthday in the dorm' is true, then 'Frank stayed in the dorm to study' is true.\n- If 'Liam asked a question after the lecture' is true, then 'Noah gathered with his study group in the library' is true.\n- If 'David prepared slides for his class talk' is true, then 'Brian went to the professor’s office hours' is true.\n- If 'Grace’s lab session ran longer than planned' is true, then 'David prepared slides for his class talk' is true.\n- If 'Umar missed the bus to campus' is true, then 'William participated in the sports tournament' is true.\n- If 'Umar missed the bus to campus' is true, then 'Zach cheered at the football match' is true.\n- If 'Victoria attended the career fair' is true, then 'Tina voted in the student council elections' is true.\n- If 'Samuel volunteered at a campus event' 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 ('David faced a surprise quiz from the professor' is true).\n\nCan we draw a conclusion about the truth of ('Rachel joined a late evening tutorial' is false) or ('Quinn practiced for the theater play' is true).?", "split": "train" }