env stringclasses 1
value | prompt stringlengths 85 3.69k | extra dict |
|---|---|---|
logic-v2 | 检验这些表达式：
A. not not (((氮的化学符号是P。) and (法国位于欧洲。)) or (墨西哥的货币是谢克尔。))
B. (四月有29天。) or (not not (英国位于欧洲。))
C. not not (not not (((-16 * -16) >= (4 * 4 - 9 * 7)) and ((12 + -5) != (17 % 10))))
D. not (中国位于北美洲。)
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 54517964,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. not not (((氮的化学符号是P。) and (法国位于欧洲。)) or (墨西哥的货币是谢克尔。))\nB. (四月有29天。) or (not not (英国位于欧洲。))\nC. not not (not not (((-16 * -16) >= (4 * 4 - 9 * 7)) and ((12 + -5) != (17 % 10))))\nD. not (中国位于北美洲。)\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 54517964,
"true_count": 2
},
"seed": 54517964,
"task_id": 654517964,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. ((5 % 7) <= (1 - -19)) or (The capital of Italy is Rome.)
B. (not (not (Humans have three lungs.))) or (not not (Silver is a gas at room temperature.))
C. not (((Diamonds are made of carbon.) or (Chile is in Antarctica.)) and (((-8 * -3 - -10 * 8) <= (16 + -10)) or (There are 30 days in September.)))
D. (((3 ** 1) == (1 ** 3)) or (((-16 - -20) == (-15 - -1)) or ((-15 * -17) != (12 + -18)))) or (149 is an even number.)
E. (((38 % 1) == (-3 * 3)) and (((19 - -1) <= (-10 * -10 + -2 * 8) <= (-11 - 7)) or ((7 * -2 * 8 * -8) <= (3 * -12)))) or ((not not (Uranus is the 1st planet from the Sun.)) or (The Great Fire of London occurred in 1666.))
F. not (not ((-20 - -8) != (30 % 4)))
G. not not ((not not ((6 + 9) >= (-17 - -14))) and (A ant has 10 legs.))
H. (((3 ** 2) != (14 + 6)) or (not ((-3 - -7) >= (15 % 7)))) or (not not (not ((1 * 2 + 3 * 6) > (4 ** 2))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,D,E,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 52031338,
"true_count": 5
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. ((5 % 7) <= (1 - -19)) or (The capital of Italy is Rome.)\nB. (not (not (Humans have three lungs.))) or (not not (Silver is a gas at room temperature.))\nC. not (((Diamonds are made of carbon.) or (Chile is in Antarctica.)) and (((-8 * -3 - -10 * 8) <= (16 + -10)) or (There are 30 days in September.)))\nD. (((3 ** 1) == (1 ** 3)) or (((-16 - -20) == (-15 - -1)) or ((-15 * -17) != (12 + -18)))) or (149 is an even number.)\nE. (((38 % 1) == (-3 * 3)) and (((19 - -1) <= (-10 * -10 + -2 * 8) <= (-11 - 7)) or ((7 * -2 * 8 * -8) <= (3 * -12)))) or ((not not (Uranus is the 1st planet from the Sun.)) or (The Great Fire of London occurred in 1666.))\nF. not (not ((-20 - -8) != (30 % 4)))\nG. not not ((not not ((6 + 9) >= (-17 - -14))) and (A ant has 10 legs.))\nH. (((3 ** 2) != (14 + 6)) or (not ((-3 - -7) >= (15 % 7)))) or (not not (not ((1 * 2 + 3 * 6) > (4 ** 2))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 52031338,
"true_count": 5
},
"seed": 52031338,
"task_id": 652031338,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not ((not not (not (Oxygen is necessary for human survival.))) and ((-14 * -18) <= (5 - 3) <= (2 + 7)))
B. ((((61 is a prime number.) and ((13 * 2) >= (8 * -11))) or (The currency of India is the Peso.)) or ((10 * 15) <= (-16 + -18)) or (A beetle is a reptile.)) and ((The 2004 Olympics were held in Tokyo.) or (not (The 2004 Olympics were held in Atlanta.)))
C. (((5 ** 3) < (20 * 9)) or ((((-5 + -19) >= (-2 * -6 - -1 * 3)) and ((6 + 20) != (15 - 5))) and (not (748 is a Fibonacci number.)))) or (((not ((1 + 0) > (2 * 4 - 10 * -6))) and ((Iron is a liquid at room temperature.) or (There are 28 days in November.))) and ((The Earth revolves around the Sun.) or ((6 * 18) <= (-3 - 7))) and ((4 ** 1) <= (-1 * -12) <= (-5 - 10)))
D. not not ((((The chemical symbol for Mercury is Hg.) and (122 is an even number.)) and ((3 * 5 + 5 * -5) == (-1 + -19))) or ((A dog has 4 legs.) and ((9 - 17) > (13 + -18))) or ((not (The 2024 Olympics were held in Paris.)) and (Italy is in Africa.)))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 18147299,
"true_count": 3
},
"question": "Consider the following logical expressions:\n\nA. not ((not not (not (Oxygen is necessary for human survival.))) and ((-14 * -18) <= (5 - 3) <= (2 + 7)))\nB. ((((61 is a prime number.) and ((13 * 2) >= (8 * -11))) or (The currency of India is the Peso.)) or ((10 * 15) <= (-16 + -18)) or (A beetle is a reptile.)) and ((The 2004 Olympics were held in Tokyo.) or (not (The 2004 Olympics were held in Atlanta.)))\nC. (((5 ** 3) < (20 * 9)) or ((((-5 + -19) >= (-2 * -6 - -1 * 3)) and ((6 + 20) != (15 - 5))) and (not (748 is a Fibonacci number.)))) or (((not ((1 + 0) > (2 * 4 - 10 * -6))) and ((Iron is a liquid at room temperature.) or (There are 28 days in November.))) and ((The Earth revolves around the Sun.) or ((6 * 18) <= (-3 - 7))) and ((4 ** 1) <= (-1 * -12) <= (-5 - 10)))\nD. not not ((((The chemical symbol for Mercury is Hg.) and (122 is an even number.)) and ((3 * 5 + 5 * -5) == (-1 + -19))) or ((A dog has 4 legs.) and ((9 - 17) > (13 + -18))) or ((not (The 2024 Olympics were held in Paris.)) and (Italy is in Africa.)))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 18147299,
"true_count": 3
},
"seed": 18147299,
"task_id": 618147299,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not (((not (企鹅是爬行动物。)) and (not (((1 * -2 - -10 * 1) == (3 ** 2)) and (not not (太平洋是最大的海洋。))))) or (not (not (罗马尼亚的首都是伯尔尼。))))
B. not (not ((((((4 * 10 + -1 * 9) == (-16 * 10)) and ((5 % 6) >= (3 ** 1))) and (not ((2 + 1) < (0 * -5) < (16 - -9)))) or (土耳其的首都是安卡拉。)) or ((((地球是距离太阳第8近的行星。) and ((18 - -6) >= (7 * 1 + 3 * 0))) and (not ((2 ** 2) >= (-10 - 1)))) or (((12 - -12) >= (-18 + -15)) or (肯尼亚位于北美洲。)) or (not not ((3 - -5) >= (-3 * -4 - -3 * -10))))))
C. ((not (not not ((not not (钻石由碳元素组成。)) and (((3 + 5) != (-2 * -20)) or ((14 - -6) < (0 * 0) < (2 - -19)))))) or (not ((((-5 * -8 - -5 * 8) > (-3 + 15)) or (木星是距离太阳第5近的行星。)) and ((1918年是闰年。) and (埃及位于非洲。)) and (2050年是闰年。)))) or (not (((海王星是距离太阳第8近的行星。) and (人类首次登月发生在1969年。)) or ((1948年奥运会在巴黎举办。) or (火星是距离太阳第6近的行星。))))
D. not (((not (not not (not not (第一部iPhone发布发生在2009年。)))) or ((not not (not (2000年奥运会在悉尼举办。))) and (人体有150块骨头。))) and ((((not not (尼日利亚的首都是阿布贾。)) and ((-4 - -13) < (16 - 18))) and (not (not not (以色列的货币是克朗。)))) and (((2 ** 3) <= (16 + 20)) and (酒精在常温下是气体。))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 2018264,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. not not (((not (企鹅是爬行动物。)) and (not (((1 * -2 - -10 * 1) == (3 ** 2)) and (not not (太平洋是最大的海洋。))))) or (not (not (罗马尼亚的首都是伯尔尼。))))\nB. not (not ((((((4 * 10 + -1 * 9) == (-16 * 10)) and ((5 % 6) >= (3 ** 1))) and (not ((2 + 1) < (0 * -5) < (16 - -9)))) or (土耳其的首都是安卡拉。)) or ((((地球是距离太阳第8近的行星。) and ((18 - -6) >= (7 * 1 + 3 * 0))) and (not ((2 ** 2) >= (-10 - 1)))) or (((12 - -12) >= (-18 + -15)) or (肯尼亚位于北美洲。)) or (not not ((3 - -5) >= (-3 * -4 - -3 * -10))))))\nC. ((not (not not ((not not (钻石由碳元素组成。)) and (((3 + 5) != (-2 * -20)) or ((14 - -6) < (0 * 0) < (2 - -19)))))) or (not ((((-5 * -8 - -5 * 8) > (-3 + 15)) or (木星是距离太阳第5近的行星。)) and ((1918年是闰年。) and (埃及位于非洲。)) and (2050年是闰年。)))) or (not (((海王星是距离太阳第8近的行星。) and (人类首次登月发生在1969年。)) or ((1948年奥运会在巴黎举办。) or (火星是距离太阳第6近的行星。))))\nD. not (((not (not not (not not (第一部iPhone发布发生在2009年。)))) or ((not not (not (2000年奥运会在悉尼举办。))) and (人体有150块骨头。))) and ((((not not (尼日利亚的首都是阿布贾。)) and ((-4 - -13) < (16 - 18))) and (not (not not (以色列的货币是克朗。)))) and (((2 ** 3) <= (16 + 20)) and (酒精在常温下是气体。))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 2018264,
"true_count": 4
},
"seed": 2018264,
"task_id": 602018264,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not (((not ((((8 * 6) <= (5 ** 1) <= (12 * 16)) and ((3 - -6) <= (4 * -19) <= (-2 + 11))) and (not (183是奇数。)))) and (((((-9 * 10 + -1 * 6) < (2 * 4 - -5 * 7) < (-10 * 10 * -10 * 4)) and (苍蝇是昆虫。)) and (not ((31 % 2) != (-17 - -6)))) and (人类有2条腿。))) and ((not not ((7 - -9) < (-15 * 9) < (-3 - 1))) and (人类只使用了大脑的10%。) and (not not (意大利位于亚洲。))) and (not not (not (not not (((38 % 1) < (3 % 2) < (-17 + 17)) and (178是奇数。))))))
B. not not (not (((not not (水星是距离太阳第1近的行星。)) and ((苏联解体发生在1981年。) or (哥伦比亚的首都是波哥大。))) and (not not (((菲律宾的货币是比索。) or (1980年奥运会在莫斯科举办。)) or ((罗马尼亚的首都是布宜诺斯艾利斯。) or (1896年奥运会在北京举办。))))))
C. not not ((((((韩国的货币是韩元。) and (1920年是闰年。)) and (not (木头在常温下是固体。))) or ((-5 * -8) == (2 ** 3))) and (not ((芬兰的首都是赫尔辛基。) and ((-13 * 16) < (-5 * -3 - -6 * 7))))) or (((2046年是闰年。) and (not ((蚂蚁是鱼类。) or (印度尼西亚的首都是雅加达。)))) and ((88能被8整除。) and (((1 ** 1) < (6 * 0 + 10 * -4) < (21 % 1)) and ((8 - -19) < (10 - -5) < (-19 * -18))) and (((-3 - 2) >= (7 * 10 * -8 * 3)) and (not (秘鲁的首都是利马。))))))
D. not not ((((not not (澳大利亚位于大洋洲。)) or ((1 * -8 * -6 * -9) > (6 + -18)) or ((((29 % 1) <= (7 * 16)) and (海王星是距离太阳第5近的行星。)) and (((46 % 10) > (-17 - 15)) and (火星是距离太阳最近的行星。)))) and ((((钴的化学符号是Zn。) and (金的化学符号是Pb。)) or (天王星是距离太阳第3近的行星。)) or (越南的首都是河内。))) and (not not (not not ((-8 + 18) < (0 + 8) < (-15 - 3)))))
E. not (not not ((((not not ((6 * 7 * -3 * -2) >= (2 * 3 - 9 * -1))) or (((3 ** 1) <= (4 - -14) <= (2 + 4)) or (水蒸气在常温下是气体。))) and (莱特兄弟首次飞行发生在1903年。)) or (not not (((氯的化学符号是Au。) or (俄罗斯的首都是阿姆斯特丹。)) or (not ((12 - -1) != (25 % 4)))))))
F. (not not (((not not (((18 + 18) >= (5 ** 2)) and (猪有4条腿。))) or (((蚂蚁是哺乳动物。) or (1944年是闰年。)) or (芬兰的首都是东京。))) and (not (((捷克的货币是里亚尔。) or ((14 * 0) <= (6 * 9 - 5 * -4) <= (4 - 6))) or ((土星是距离太阳第6近的行星。) or (碳的化学符号是C。)))))) or (not not ((((-10 - 20) == (-2 * 4)) and ((8 * 11) < (-7 * 4 + 4 * 0))) and ((not ((锌的化学符号是Co。) or (七月有30天。))) or ((1953年是闰年。) or ((18 * -13) < (-18 * 5) < (36 % 3))) or (not (空气在常温下是气体。)))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 48923796,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. not (((not ((((8 * 6) <= (5 ** 1) <= (12 * 16)) and ((3 - -6) <= (4 * -19) <= (-2 + 11))) and (not (183是奇数。)))) and (((((-9 * 10 + -1 * 6) < (2 * 4 - -5 * 7) < (-10 * 10 * -10 * 4)) and (苍蝇是昆虫。)) and (not ((31 % 2) != (-17 - -6)))) and (人类有2条腿。))) and ((not not ((7 - -9) < (-15 * 9) < (-3 - 1))) and (人类只使用了大脑的10%。) and (not not (意大利位于亚洲。))) and (not not (not (not not (((38 % 1) < (3 % 2) < (-17 + 17)) and (178是奇数。))))))\nB. not not (not (((not not (水星是距离太阳第1近的行星。)) and ((苏联解体发生在1981年。) or (哥伦比亚的首都是波哥大。))) and (not not (((菲律宾的货币是比索。) or (1980年奥运会在莫斯科举办。)) or ((罗马尼亚的首都是布宜诺斯艾利斯。) or (1896年奥运会在北京举办。))))))\nC. not not ((((((韩国的货币是韩元。) and (1920年是闰年。)) and (not (木头在常温下是固体。))) or ((-5 * -8) == (2 ** 3))) and (not ((芬兰的首都是赫尔辛基。) and ((-13 * 16) < (-5 * -3 - -6 * 7))))) or (((2046年是闰年。) and (not ((蚂蚁是鱼类。) or (印度尼西亚的首都是雅加达。)))) and ((88能被8整除。) and (((1 ** 1) < (6 * 0 + 10 * -4) < (21 % 1)) and ((8 - -19) < (10 - -5) < (-19 * -18))) and (((-3 - 2) >= (7 * 10 * -8 * 3)) and (not (秘鲁的首都是利马。))))))\nD. not not ((((not not (澳大利亚位于大洋洲。)) or ((1 * -8 * -6 * -9) > (6 + -18)) or ((((29 % 1) <= (7 * 16)) and (海王星是距离太阳第5近的行星。)) and (((46 % 10) > (-17 - 15)) and (火星是距离太阳最近的行星。)))) and ((((钴的化学符号是Zn。) and (金的化学符号是Pb。)) or (天王星是距离太阳第3近的行星。)) or (越南的首都是河内。))) and (not not (not not ((-8 + 18) < (0 + 8) < (-15 - 3)))))\nE. not (not not ((((not not ((6 * 7 * -3 * -2) >= (2 * 3 - 9 * -1))) or (((3 ** 1) <= (4 - -14) <= (2 + 4)) or (水蒸气在常温下是气体。))) and (莱特兄弟首次飞行发生在1903年。)) or (not not (((氯的化学符号是Au。) or (俄罗斯的首都是阿姆斯特丹。)) or (not ((12 - -1) != (25 % 4)))))))\nF. (not not (((not not (((18 + 18) >= (5 ** 2)) and (猪有4条腿。))) or (((蚂蚁是哺乳动物。) or (1944年是闰年。)) or (芬兰的首都是东京。))) and (not (((捷克的货币是里亚尔。) or ((14 * 0) <= (6 * 9 - 5 * -4) <= (4 - 6))) or ((土星是距离太阳第6近的行星。) or (碳的化学符号是C。)))))) or (not not ((((-10 - 20) == (-2 * 4)) and ((8 * 11) < (-7 * 4 + 4 * 0))) and ((not ((锌的化学符号是Co。) or (七月有30天。))) or ((1953年是闰年。) or ((18 * -13) < (-18 * 5) < (36 % 3))) or (not (空气在常温下是气体。)))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 48923796,
"true_count": 1
},
"seed": 48923796,
"task_id": 648923796,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not (not (not ((((9 * 4 * 8 * -3) != (3 * 10 - 4 * -10)) and (not (印度位于亚洲。))) and (not (2016年奥运会在里约热内卢举办。)) and ((((-11 + 3) == (3 ** 3)) or ((15 + 6) <= (5 ** 3))) or (not not ((0 * -9 * -6 * -10) >= (11 - -11)))))))
B. (not (not (not not ((not (2025年是闰年。)) or (not not ((10 * 3 + -1 * 7) <= (4 * 8) <= (-4 * 7))))))) and (not not (((not (1912年奥运会在斯德哥尔摩举办。)) and (考拉是爬行动物。)) and ((-16 - 0) >= (-9 - 9)) and (not not (声音在真空中传播更快。))))
C. not (((not not ((19 + -9) <= (-7 - 19))) and (((not not ((1 ** 1) < (39 % 2) < (4 ** 2))) and (荷兰的首都是阿姆斯特丹。)) or ((-19 - 3) == (42 % 1)))) or ((((not (中国长城是在一年内建成的。)) or ((空气在常温下是气体。) or ((1 * -15) <= (-17 * -15) <= (18 - 19)))) and (((伦敦大火发生在1664年。) or ((-20 * 12) >= (48 % 9))) and (not ((-8 * -5 * 1 * -8) != (13 * 14))))) or ((not (39小于等于14。)) or (电流比光速更快。)) or ((((1 ** 1) <= (29 % 7)) or (木星是距离太阳第1近的行星。)) and (not (木头在常温下是固体。)))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 849053,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. not (not (not ((((9 * 4 * 8 * -3) != (3 * 10 - 4 * -10)) and (not (印度位于亚洲。))) and (not (2016年奥运会在里约热内卢举办。)) and ((((-11 + 3) == (3 ** 3)) or ((15 + 6) <= (5 ** 3))) or (not not ((0 * -9 * -6 * -10) >= (11 - -11)))))))\nB. (not (not (not not ((not (2025年是闰年。)) or (not not ((10 * 3 + -1 * 7) <= (4 * 8) <= (-4 * 7))))))) and (not not (((not (1912年奥运会在斯德哥尔摩举办。)) and (考拉是爬行动物。)) and ((-16 - 0) >= (-9 - 9)) and (not not (声音在真空中传播更快。))))\nC. not (((not not ((19 + -9) <= (-7 - 19))) and (((not not ((1 ** 1) < (39 % 2) < (4 ** 2))) and (荷兰的首都是阿姆斯特丹。)) or ((-19 - 3) == (42 % 1)))) or ((((not (中国长城是在一年内建成的。)) or ((空气在常温下是气体。) or ((1 * -15) <= (-17 * -15) <= (18 - 19)))) and (((伦敦大火发生在1664年。) or ((-20 * 12) >= (48 % 9))) and (not ((-8 * -5 * 1 * -8) != (13 * 14))))) or ((not (39小于等于14。)) or (电流比光速更快。)) or ((((1 ** 1) <= (29 % 7)) or (木星是距离太阳第1近的行星。)) and (not (木头在常温下是固体。)))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 849053,
"true_count": 1
},
"seed": 849053,
"task_id": 600849053,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. The currency of Hungary is the Forint.
B. not not (((15 * 5) == (-5 - 14)) and ((8 + 20) <= (2 * 1) <= (1 * -3 + 9 * 4)))
C. (The capital of Turkey is Santiago.) and ((-17 * -11) <= (-7 * 14) <= (-1 * 3))
D. ((Venus is the 2nd planet from the Sun.) or (Russia is in Oceania.)) or ((20 + -15) != (-9 + 4))
E. (-10 * 8) != (-2 * -1 + 3 * -2)
F. ((Oxygen is a solid at room temperature.) or (World War I began occurred in 1914.)) or (Plants produce oxygen through photosynthesis.)
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 60579944,
"true_count": 4
},
"question": "Given the following boolean expressions:\n\nA. The currency of Hungary is the Forint.\nB. not not (((15 * 5) == (-5 - 14)) and ((8 + 20) <= (2 * 1) <= (1 * -3 + 9 * 4)))\nC. (The capital of Turkey is Santiago.) and ((-17 * -11) <= (-7 * 14) <= (-1 * 3))\nD. ((Venus is the 2nd planet from the Sun.) or (Russia is in Oceania.)) or ((20 + -15) != (-9 + 4))\nE. (-10 * 8) != (-2 * -1 + 3 * -2)\nF. ((Oxygen is a solid at room temperature.) or (World War I began occurred in 1914.)) or (Plants produce oxygen through photosynthesis.)\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 60579944,
"true_count": 4
},
"seed": 60579944,
"task_id": 660579944,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (-16 + 19) >= (-8 * 8 - 0 * 7)
B. (((12 + -16) == (-6 + -1)) and ((3 ** 1) == (2 ** 2))) or ((The Moon orbits the Earth.) and ((6 * -2 - 1 * 4) != (-3 - -19)))
C. ((The 1952 Olympics were held in Rio de Janeiro.) and (The chemical symbol for Neon is Ne.)) and (The Pacific Ocean is the largest ocean.)
D. (((-3 + 4) != (-12 * -1)) and ((7 * 8 - 0 * 3) > (0 - 3))) or ((The currency of South Korea is the Won.) and (The 1904 Olympics were held in Montreal.))
E. (not not (World War I began occurred in 1914.)) and ((Jupiter is the 5th planet from the Sun.) or ((8 - 15) > (-8 + -10)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 12055855,
"true_count": 4
},
"question": "Below are several boolean expressions:\n\nA. (-16 + 19) >= (-8 * 8 - 0 * 7)\nB. (((12 + -16) == (-6 + -1)) and ((3 ** 1) == (2 ** 2))) or ((The Moon orbits the Earth.) and ((6 * -2 - 1 * 4) != (-3 - -19)))\nC. ((The 1952 Olympics were held in Rio de Janeiro.) and (The chemical symbol for Neon is Ne.)) and (The Pacific Ocean is the largest ocean.)\nD. (((-3 + 4) != (-12 * -1)) and ((7 * 8 - 0 * 3) > (0 - 3))) or ((The currency of South Korea is the Won.) and (The 1904 Olympics were held in Montreal.))\nE. (not not (World War I began occurred in 1914.)) and ((Jupiter is the 5th planet from the Sun.) or ((8 - 15) > (-8 + -10)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 12055855,
"true_count": 4
},
"seed": 12055855,
"task_id": 612055855,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not (Water boils at 100 degrees Celsius at sea level.)
B. The Moon orbits the Earth.
C. (((Neptune is the 8th planet from the Sun.) or (There are 29 days in October.)) or (((-2 * 10 + 5 * 4) > (7 + 19)) or ((14 * -17) > (8 * 2 + -10 * 7)))) and ((The capital of Peru is Buenos Aires.) and ((50 % 4) <= (-5 + 20))) and (Steam is a liquid at room temperature.)
D. ((((4 * 3 * 8 * -9) >= (13 * 17)) or ((12 - 7) < (5 * -3 + -9 * 8))) or (Mars is the 8th planet from the Sun.)) and ((The chemical symbol for Mercury is Hg.) or ((15 - -17) == (13 * 5))) and ((A kangaroo has 2 legs.) or (not ((-14 - -7) < (-6 * 2 * 2 * 1))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 66387080,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. not (Water boils at 100 degrees Celsius at sea level.)\nB. The Moon orbits the Earth.\nC. (((Neptune is the 8th planet from the Sun.) or (There are 29 days in October.)) or (((-2 * 10 + 5 * 4) > (7 + 19)) or ((14 * -17) > (8 * 2 + -10 * 7)))) and ((The capital of Peru is Buenos Aires.) and ((50 % 4) <= (-5 + 20))) and (Steam is a liquid at room temperature.)\nD. ((((4 * 3 * 8 * -9) >= (13 * 17)) or ((12 - 7) < (5 * -3 + -9 * 8))) or (Mars is the 8th planet from the Sun.)) and ((The chemical symbol for Mercury is Hg.) or ((15 - -17) == (13 * 5))) and ((A kangaroo has 2 legs.) or (not ((-14 - -7) < (-6 * 2 * 2 * 1))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 66387080,
"true_count": 1
},
"seed": 66387080,
"task_id": 666387080,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (-6 - 16) < (1 * 3 + -5 * 6)
B. not not ((委内瑞拉的首都是加拉加斯。) and ((-16 * -11) <= (4 * -10 * -6 * -3) <= (36 % 4)))
C. (袋鼠有2条腿。) and (美国的货币是里拉。)
D. 地球绕太阳运转。
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 90641364,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. (-6 - 16) < (1 * 3 + -5 * 6)\nB. not not ((委内瑞拉的首都是加拉加斯。) and ((-16 * -11) <= (4 * -10 * -6 * -3) <= (36 % 4)))\nC. (袋鼠有2条腿。) and (美国的货币是里拉。)\nD. 地球绕太阳运转。\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 90641364,
"true_count": 1
},
"seed": 90641364,
"task_id": 690641364,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not ((Copper is a gas at room temperature.) or (not not ((-8 - -8) != (3 - 11))))
B. (not (not (The currency of Switzerland is the Franc.))) or (not ((6 - 12) == (3 ** 3))) or (not not (((-4 * -7 + 6 * -10) <= (48 % 7)) and (Nitrogen is a solid at room temperature.)))
C. (not not (not not (Mercury is the 7th planet from the Sun.))) or ((The currency of Egypt is the Pound.) or (The 1988 Olympics were held in Seoul.)) or ((not ((7 + 7) < (-9 * -1))) or (not (The capital of Finland is Buenos Aires.)))
D. (92 is divisible by 5.) or (((427 is a Fibonacci number.) and (Mars is the 4th planet from the Sun.)) or ((A cow has 4 legs.) and (The French Revolution began occurred in 1789.)))
E. ((((15 * -4) != (3 ** 3)) or (The currency of Japan is the Yen.)) or (2088 is a leap year.)) or ((not ((18 + 16) == (30 % 5))) or (Mercury is the 8th planet from the Sun.))
F. (((The capital of Spain is Stockholm.) and ((17 - 20) <= (3 + -6))) and (((2 ** 3) < (-3 * -6 - 10 * -1) < (1 * -1)) and ((6 % 7) > (19 - -5)))) or ((((-1 * 10 + 6 * 2) != (-10 * 1 * -3 * 8)) or (Diamond is a gas at room temperature.)) or ((88 is divisible by 10.) and ((-3 - -5) < (-10 + -17) < (6 - 15))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 19406762,
"true_count": 6
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not ((Copper is a gas at room temperature.) or (not not ((-8 - -8) != (3 - 11))))\nB. (not (not (The currency of Switzerland is the Franc.))) or (not ((6 - 12) == (3 ** 3))) or (not not (((-4 * -7 + 6 * -10) <= (48 % 7)) and (Nitrogen is a solid at room temperature.)))\nC. (not not (not not (Mercury is the 7th planet from the Sun.))) or ((The currency of Egypt is the Pound.) or (The 1988 Olympics were held in Seoul.)) or ((not ((7 + 7) < (-9 * -1))) or (not (The capital of Finland is Buenos Aires.)))\nD. (92 is divisible by 5.) or (((427 is a Fibonacci number.) and (Mars is the 4th planet from the Sun.)) or ((A cow has 4 legs.) and (The French Revolution began occurred in 1789.)))\nE. ((((15 * -4) != (3 ** 3)) or (The currency of Japan is the Yen.)) or (2088 is a leap year.)) or ((not ((18 + 16) == (30 % 5))) or (Mercury is the 8th planet from the Sun.))\nF. (((The capital of Spain is Stockholm.) and ((17 - 20) <= (3 + -6))) and (((2 ** 3) < (-3 * -6 - 10 * -1) < (1 * -1)) and ((6 % 7) > (19 - -5)))) or ((((-1 * 10 + 6 * 2) != (-10 * 1 * -3 * 8)) or (Diamond is a gas at room temperature.)) or ((88 is divisible by 10.) and ((-3 - -5) < (-10 + -17) < (6 - 15))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 19406762,
"true_count": 6
},
"seed": 19406762,
"task_id": 619406762,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (((((32 % 6) < (-3 * -3 - 7 * -8)) and ((There are 31 days in October.) and (Diamond is a gas at room temperature.))) and (Uranus is the 1st planet from the Sun.)) or ((Helium is a gas at room temperature.) or ((-14 - -16) > (-2 - -4)))) and (not (not not (((India is in Asia.) or (The chemical symbol for Copper is Si.)) or (((-9 + 16) >= (-4 + 17)) and (The 1996 Olympics were held in Rio de Janeiro.)))))
B. not not (not not ((((The currency of Australia is the Dollar.) or ((-11 * 0) <= (20 % 5) <= (-9 * -2 * 3 * 3))) or ((-3 - 0) > (10 * -1 - 4 * -2))) and (not not (Carbon dioxide is a gas at room temperature.)) and ((((-16 - 14) < (2 * 3 - 10 * 9) < (17 + 3)) or (There are 31 days in March.)) or (not (The currency of Mexico is the Real.)))))
C. not ((((not not (Wood is a solid at room temperature.)) and (not ((3 ** 1) > (8 * 9 + 7 * 7)))) or (Wood is a gas at room temperature.)) and (not not ((Carbon dioxide is a liquid at room temperature.) and (not (Neptune is the 8th planet from the Sun.)))))
D. (not not (((((-13 + 14) != (8 + 19)) or (Light travels faster than sound.)) and (((13 * 1) == (50 % 10)) and (A lobster has 10 legs.))) or (((4 * -7 + 5 * -1) < (19 + -14)) and ((8 + -6) == (7 - -15))) or (((Wood is a solid at room temperature.) and (Germany is in Africa.)) and (not not ((33 % 5) > (-4 - -19)))))) and (not not (not not ((not (Mexico is in North America.)) or (((-1 * -13) < (0 * -14)) and (Canada is in Africa.)))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 53437293,
"true_count": 2
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (((((32 % 6) < (-3 * -3 - 7 * -8)) and ((There are 31 days in October.) and (Diamond is a gas at room temperature.))) and (Uranus is the 1st planet from the Sun.)) or ((Helium is a gas at room temperature.) or ((-14 - -16) > (-2 - -4)))) and (not (not not (((India is in Asia.) or (The chemical symbol for Copper is Si.)) or (((-9 + 16) >= (-4 + 17)) and (The 1996 Olympics were held in Rio de Janeiro.)))))\nB. not not (not not ((((The currency of Australia is the Dollar.) or ((-11 * 0) <= (20 % 5) <= (-9 * -2 * 3 * 3))) or ((-3 - 0) > (10 * -1 - 4 * -2))) and (not not (Carbon dioxide is a gas at room temperature.)) and ((((-16 - 14) < (2 * 3 - 10 * 9) < (17 + 3)) or (There are 31 days in March.)) or (not (The currency of Mexico is the Real.)))))\nC. not ((((not not (Wood is a solid at room temperature.)) and (not ((3 ** 1) > (8 * 9 + 7 * 7)))) or (Wood is a gas at room temperature.)) and (not not ((Carbon dioxide is a liquid at room temperature.) and (not (Neptune is the 8th planet from the Sun.)))))\nD. (not not (((((-13 + 14) != (8 + 19)) or (Light travels faster than sound.)) and (((13 * 1) == (50 % 10)) and (A lobster has 10 legs.))) or (((4 * -7 + 5 * -1) < (19 + -14)) and ((8 + -6) == (7 - -15))) or (((Wood is a solid at room temperature.) and (Germany is in Africa.)) and (not not ((33 % 5) > (-4 - -19)))))) and (not not (not not ((not (Mexico is in North America.)) or (((-1 * -13) < (0 * -14)) and (Canada is in Africa.)))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 53437293,
"true_count": 2
},
"seed": 53437293,
"task_id": 653437293,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (not not (((not ((7 * 2 * 1 * 6) >= (-1 * -12))) or (not (法国大革命开始发生在1789年。))) or (((捷克的货币是克朗。) or (1924年奥运会在巴黎举办。)) and ((8 * -1 - 5 * 7) > (-2 - 16))))) or (((水星是距离太阳第1近的行星。) and (not (汞在常温下是液体。))) and (((((-5 * 19) != (-2 * -7 + -9 * 10)) and (人类有100条腿。)) and ((鸡有8条腿。) or ((1 * -14) > (40 % 3)))) and (not (1964年奥运会在罗马举办。))))
B. not (not (not not ((not not ((22 % 10) > (4 * -6 * 10 * -10))) or (地球是距离太阳第2近的行星。))))
C. ((not not ((-16 + -3) <= (-11 + 6) <= (5 - 17))) or (not ((not ((-5 * 4 - 0 * -6) < (-3 * 20) < (8 * -9 + -4 * 1))) or (莱特兄弟首次飞行发生在1901年。)))) or (((空气在常温下是气体。) or (2020年奥运会在东京举办。)) and ((-20 + 8) < (7 * 5 + -1 * 7)) and (((6 * 3) < (6 * -4 + 7 * -8)) and ((古巴的首都是利雅得。) and (尼日利亚位于非洲。)) and ((not not (新加坡的货币是索尔。)) and (((-12 + -15) < (42 % 1) < (-11 - -14)) or ((16 * -2) >= (6 - -18))))))
D. ((((巴西的首都是马尼拉。) or ((36 % 10) >= (20 + 9))) and (木星是距离太阳第7近的行星。) and (not not (not ((-14 - -19) == (21 % 9))))) and ((1962年是闰年。) or (246是完全平方数。) or ((氮的化学符号是O。) and (十一月有30天。)))) or ((not not (not not ((-11 * 9) <= (-10 * 3 + -6 * -4)))) or (not (not ((7 - -3) == (-11 - 7))))) or (not not (not ((((3 * -10 + -2 * -2) <= (1 ** 1)) or ((25 % 4) == (-2 * -1 + 9 * -7))) or ((-15 - -19) != (-8 * -6 + 5 * 0)))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 32185074,
"true_count": 1
},
"question": "给定以下布尔表达式：\n\nA. (not not (((not ((7 * 2 * 1 * 6) >= (-1 * -12))) or (not (法国大革命开始发生在1789年。))) or (((捷克的货币是克朗。) or (1924年奥运会在巴黎举办。)) and ((8 * -1 - 5 * 7) > (-2 - 16))))) or (((水星是距离太阳第1近的行星。) and (not (汞在常温下是液体。))) and (((((-5 * 19) != (-2 * -7 + -9 * 10)) and (人类有100条腿。)) and ((鸡有8条腿。) or ((1 * -14) > (40 % 3)))) and (not (1964年奥运会在罗马举办。))))\nB. not (not (not not ((not not ((22 % 10) > (4 * -6 * 10 * -10))) or (地球是距离太阳第2近的行星。))))\nC. ((not not ((-16 + -3) <= (-11 + 6) <= (5 - 17))) or (not ((not ((-5 * 4 - 0 * -6) < (-3 * 20) < (8 * -9 + -4 * 1))) or (莱特兄弟首次飞行发生在1901年。)))) or (((空气在常温下是气体。) or (2020年奥运会在东京举办。)) and ((-20 + 8) < (7 * 5 + -1 * 7)) and (((6 * 3) < (6 * -4 + 7 * -8)) and ((古巴的首都是利雅得。) and (尼日利亚位于非洲。)) and ((not not (新加坡的货币是索尔。)) and (((-12 + -15) < (42 % 1) < (-11 - -14)) or ((16 * -2) >= (6 - -18))))))\nD. ((((巴西的首都是马尼拉。) or ((36 % 10) >= (20 + 9))) and (木星是距离太阳第7近的行星。) and (not not (not ((-14 - -19) == (21 % 9))))) and ((1962年是闰年。) or (246是完全平方数。) or ((氮的化学符号是O。) and (十一月有30天。)))) or ((not not (not not ((-11 * 9) <= (-10 * 3 + -6 * -4)))) or (not (not ((7 - -3) == (-11 - 7))))) or (not not (not ((((3 * -10 + -2 * -2) <= (1 ** 1)) or ((25 % 4) == (-2 * -1 + 9 * -7))) or ((-15 - -19) != (-8 * -6 + 5 * 0)))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 32185074,
"true_count": 1
},
"seed": 32185074,
"task_id": 632185074,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. (((The chemical symbol for Platinum is Pt.) and ((not ((-13 - -13) > (15 - -10))) and ((-2 - 20) < (11 - 9)))) or (((not ((19 - 1) >= (-4 - 15))) and (2057 is a leap year.)) and ((2022 is a leap year.) or (The currency of Argentina is the Forint.)) and ((-7 * -10) == (-15 * -4)))) or (not not (((4 + 18) >= (2 * 9 - -5 * 10)) and (not not ((9 + -2) >= (-10 + 16))) and (not ((-9 - -3) >= (9 + -1)))))
B. not not (((not (The currency of Egypt is the Pound.)) or (((-12 - 10) <= (-11 - -17) <= (-13 * -1)) and (not (291 is a perfect square.)))) and (((Russia is in Europe.) or (Earth is the 3rd planet from the Sun.)) or ((Humans only use 10% of their brain.) or ((-7 * -1 - 5 * -4) >= (30 % 2)))) and (((((9 * -6 * -2 * 10) < (-14 + 3)) and (There are 30 days in September.)) or ((A swan is a bird.) and (The chemical symbol for Oxygen is O.))) and ((-18 * -17) >= (-15 - 9))))
C. not not (not (not (((Water is a gas at room temperature.) or ((3 ** 2) >= (20 + 3))) or (not not ((13 + 16) == (3 + -19))))))
D. ((((16 * -4) <= (17 * 0)) and (Gold is a solid at room temperature.)) or ((((-7 - 12) != (-9 * 7)) and (Thailand is in Antarctica.)) and (Mercury is the 7th planet from the Sun.)) or (not ((((7 % 9) > (-5 + 8)) and ((-2 + 15) != (3 ** 3))) or (Nitrogen is a gas at room temperature.)))) or ((not not ((Earth is the 3rd planet from the Sun.) and ((12 - 15) < (-14 * -3)))) and (not (not (((36 % 8) <= (-4 * -3)) or (Steam is a gas at room temperature.)))))
E. not (not not ((Saturn is the 6th planet from the Sun.) or (((9 + 15) != (6 * -6 - 10 * 3)) or (((-14 + -7) <= (-3 * 2 * -1 * 6) <= (4 * -8)) and ((-15 * -3) > (14 + 6))))))
F. not (not not (((-9 * 1 - -7 * 2) == (5 ** 1)) and ((-3 * -10 - -2 * -4) >= (-2 - -2))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 54419339,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. (((The chemical symbol for Platinum is Pt.) and ((not ((-13 - -13) > (15 - -10))) and ((-2 - 20) < (11 - 9)))) or (((not ((19 - 1) >= (-4 - 15))) and (2057 is a leap year.)) and ((2022 is a leap year.) or (The currency of Argentina is the Forint.)) and ((-7 * -10) == (-15 * -4)))) or (not not (((4 + 18) >= (2 * 9 - -5 * 10)) and (not not ((9 + -2) >= (-10 + 16))) and (not ((-9 - -3) >= (9 + -1)))))\nB. not not (((not (The currency of Egypt is the Pound.)) or (((-12 - 10) <= (-11 - -17) <= (-13 * -1)) and (not (291 is a perfect square.)))) and (((Russia is in Europe.) or (Earth is the 3rd planet from the Sun.)) or ((Humans only use 10% of their brain.) or ((-7 * -1 - 5 * -4) >= (30 % 2)))) and (((((9 * -6 * -2 * 10) < (-14 + 3)) and (There are 30 days in September.)) or ((A swan is a bird.) and (The chemical symbol for Oxygen is O.))) and ((-18 * -17) >= (-15 - 9))))\nC. not not (not (not (((Water is a gas at room temperature.) or ((3 ** 2) >= (20 + 3))) or (not not ((13 + 16) == (3 + -19))))))\nD. ((((16 * -4) <= (17 * 0)) and (Gold is a solid at room temperature.)) or ((((-7 - 12) != (-9 * 7)) and (Thailand is in Antarctica.)) and (Mercury is the 7th planet from the Sun.)) or (not ((((7 % 9) > (-5 + 8)) and ((-2 + 15) != (3 ** 3))) or (Nitrogen is a gas at room temperature.)))) or ((not not ((Earth is the 3rd planet from the Sun.) and ((12 - 15) < (-14 * -3)))) and (not (not (((36 % 8) <= (-4 * -3)) or (Steam is a gas at room temperature.)))))\nE. not (not not ((Saturn is the 6th planet from the Sun.) or (((9 + 15) != (6 * -6 - 10 * 3)) or (((-14 + -7) <= (-3 * 2 * -1 * 6) <= (4 * -8)) and ((-15 * -3) > (14 + 6))))))\nF. not (not not (((-9 * 1 - -7 * 2) == (5 ** 1)) and ((-3 * -10 - -2 * -4) >= (-2 - -2))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 54419339,
"true_count": 3
},
"seed": 54419339,
"task_id": 654419339,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not ((not (not ((3 ** 2) >= (-12 + -17)))) or ((Oil is a solid at room temperature.) and (not ((The chemical symbol for Phosphorus is P.) and ((21 % 9) < (11 + 11))))) or (not (not not ((((8 + -5) >= (12 * 19)) and ((-5 + 6) > (-13 + 2))) and (((7 * 0 - 10 * 6) != (-4 * 2 - -7 * -10)) or (A day on Earth is 24 hours.))))))
B. not not (not not ((not ((((2 * -9 * -3 * 5) < (-16 * -14) < (20 % 7)) and ((3 + -17) < (4 - -13))) and (((-7 * 9 * -4 * 2) <= (18 - -4)) and ((10 * 4 * 1 * -2) == (6 - 15))))) or (not (((2 ** 1) > (4 ** 3)) and ((The currency of Vietnam is the Koruna.) or (The currency of United Kingdom is the Pound.))))))
C. not not (not not ((((not ((-12 + -9) >= (-7 - -13))) or ((The chemical symbol for Calcium is Ca.) and (The chemical symbol for Sodium is Na.))) and ((((-6 * -4 + 6 * -1) <= (11 % 5) <= (8 * -2 - -9 * 8)) and (The currency of South Africa is the Krona.)) or (Electricity flows faster than light.))) or (not not (((-3 * -19) < (7 - -15)) or ((Vietnam is in Oceania.) and (A bee is an insect.))))))
D. not not (not not (not (((((9 * -9 * 5 * 5) <= (-10 - 7)) and (The square root of 49 is 7.)) and (((22 % 1) != (4 * -3)) and (Carbon dioxide is a gas at room temperature.))) or (((-3 + 6) < (-1 - -7)) or ((3 * 1 * -2 * 7) > (-3 * 4 + -4 * -10))) or ((2 * 18) >= (-9 * -3 + -1 * 4)))))
E. not not (not not ((not ((-17 * -15) >= (48 % 9))) or (not ((((2 * -9) == (11 * 20)) or ((6 + 2) <= (-16 + -10))) or ((19 + -18) > (-4 - -4))))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 34316504,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not ((not (not ((3 ** 2) >= (-12 + -17)))) or ((Oil is a solid at room temperature.) and (not ((The chemical symbol for Phosphorus is P.) and ((21 % 9) < (11 + 11))))) or (not (not not ((((8 + -5) >= (12 * 19)) and ((-5 + 6) > (-13 + 2))) and (((7 * 0 - 10 * 6) != (-4 * 2 - -7 * -10)) or (A day on Earth is 24 hours.))))))\nB. not not (not not ((not ((((2 * -9 * -3 * 5) < (-16 * -14) < (20 % 7)) and ((3 + -17) < (4 - -13))) and (((-7 * 9 * -4 * 2) <= (18 - -4)) and ((10 * 4 * 1 * -2) == (6 - 15))))) or (not (((2 ** 1) > (4 ** 3)) and ((The currency of Vietnam is the Koruna.) or (The currency of United Kingdom is the Pound.))))))\nC. not not (not not ((((not ((-12 + -9) >= (-7 - -13))) or ((The chemical symbol for Calcium is Ca.) and (The chemical symbol for Sodium is Na.))) and ((((-6 * -4 + 6 * -1) <= (11 % 5) <= (8 * -2 - -9 * 8)) and (The currency of South Africa is the Krona.)) or (Electricity flows faster than light.))) or (not not (((-3 * -19) < (7 - -15)) or ((Vietnam is in Oceania.) and (A bee is an insect.))))))\nD. not not (not not (not (((((9 * -9 * 5 * 5) <= (-10 - 7)) and (The square root of 49 is 7.)) and (((22 % 1) != (4 * -3)) and (Carbon dioxide is a gas at room temperature.))) or (((-3 + 6) < (-1 - -7)) or ((3 * 1 * -2 * 7) > (-3 * 4 + -4 * -10))) or ((2 * 18) >= (-9 * -3 + -1 * 4)))))\nE. not not (not not ((not ((-17 * -15) >= (48 % 9))) or (not ((((2 * -9) == (11 * 20)) or ((6 + 2) <= (-16 + -10))) or ((19 + -18) > (-4 - -4))))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 34316504,
"true_count": 2
},
"seed": 34316504,
"task_id": 634316504,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not ((not not ((16 + -6) > (-5 - -7))) or ((-6 - -12) <= (2 ** 1)))
B. ((not not (153是完全平方数。)) and ((第一次世界大战结束发生在1918年。) or (十二月有31天。))) and ((((2 ** 3) > (2 * 3)) or (莱特兄弟首次飞行发生在1903年。)) and ((58是质数。) and (沙特阿拉伯的首都是利雅得。)))
C. ((not (龙虾有10条腿。)) and (not (螃蟹有100条腿。))) and (not (((0 + -1) >= (3 ** 2)) and ((4 ** 3) > (5 * -2 + -7 * -2))))
D. ((铬的化学符号是Cr。) and (((-18 - 0) <= (49 % 6)) and (水星是距离太阳第1近的行星。))) and (not not (((-1 * 2 * 9 * -6) != (-6 + -17)) or ((-7 - -6) >= (14 % 5))))
E. (((电流比光速更快。) or ((15 * 6) < (2 ** 3))) or (新西兰位于大洋洲。)) or (((韩国的货币是韩元。) or (六月有30天。)) and ((-19 * -11) <= (47 % 1)))
F. (not ((冰在常温下是固体。) and (老虎是哺乳动物。))) and (not ((11 - -6) <= (-20 + -6))) and (not not (1908年奥运会在伦敦举办。))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 66328665,
"true_count": 2
},
"question": "评估以下每个表达式：\n\nA. not ((not not ((16 + -6) > (-5 - -7))) or ((-6 - -12) <= (2 ** 1)))\nB. ((not not (153是完全平方数。)) and ((第一次世界大战结束发生在1918年。) or (十二月有31天。))) and ((((2 ** 3) > (2 * 3)) or (莱特兄弟首次飞行发生在1903年。)) and ((58是质数。) and (沙特阿拉伯的首都是利雅得。)))\nC. ((not (龙虾有10条腿。)) and (not (螃蟹有100条腿。))) and (not (((0 + -1) >= (3 ** 2)) and ((4 ** 3) > (5 * -2 + -7 * -2))))\nD. ((铬的化学符号是Cr。) and (((-18 - 0) <= (49 % 6)) and (水星是距离太阳第1近的行星。))) and (not not (((-1 * 2 * 9 * -6) != (-6 + -17)) or ((-7 - -6) >= (14 % 5))))\nE. (((电流比光速更快。) or ((15 * 6) < (2 ** 3))) or (新西兰位于大洋洲。)) or (((韩国的货币是韩元。) or (六月有30天。)) and ((-19 * -11) <= (47 % 1)))\nF. (not ((冰在常温下是固体。) and (老虎是哺乳动物。))) and (not ((11 - -6) <= (-20 + -6))) and (not not (1908年奥运会在伦敦举办。))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 66328665,
"true_count": 2
},
"seed": 66328665,
"task_id": 666328665,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (not (((((15 - -10) > (-1 * 9 * 7 * 9)) and (鲤鱼是哺乳动物。)) or (((大象有6条腿。) and ((2 * -4 + -6 * 6) >= (20 + -1))) and ((-1 * -7 * 4 * 6) == (7 * 1)))) or (not ((-5 * -18) <= (11 + 8) <= (9 * -9 + 8 * -10))))) or (not ((not not (not (not not (第一次世界大战结束发生在1918年。)))) or ((not (((9 - 9) != (3 ** 3)) and ((-18 * 12) > (-11 - -14)))) and ((-8 * -15) >= (-7 * 0 + -1 * 1)))))
B. ((not not (not not ((鸡有10条腿。) or (光速比声速快。)))) or (((龙虾有10条腿。) and (钴的化学符号是Ag。)) or ((not not ((木星是距离太阳第5近的行星。) or (加拿大的首都是渥太华。))) or ((-1 + 5) >= (-6 * 9 + -10 * -9))))) and (not ((not (not not (not (土星是距离太阳第6近的行星。)))) or (not (((8 + -7) == (7 + -11)) and (金在常温下是固体。)))))
C. ((not not (((木星是距离太阳第5近的行星。) and ((9 - 7) <= (6 * 9 - 5 * -9))) and ((not (挪威的货币是克朗。)) and (not ((3 ** 1) < (5 ** 2)))))) or (not (not not (not not ((锡的化学符号是He。) and ((-7 * 4 - -2 * 2) != (5 * -8 + 10 * -9))))))) or ((not (((((2 ** 2) <= (5 - 15) <= (11 + 20)) and ((5 ** 2) <= (-20 - -15))) and (not not (哥伦布到达美洲发生在1482年。))) and ((not ((2 ** 1) == (-10 * -15))) and ((0 + -3) <= (5 ** 1) <= (-12 - -5))))) or (not not (((-5 + -16) >= (-15 * -4)) or ((-8 + 14) != (-14 * 20)))))
D. not (((((19 - -7) <= (14 % 8) <= (4 + -14)) or ((5 ** 3) == (-11 - 12))) and (not not (not (莱特兄弟首次飞行发生在1913年。))) and (((((23 % 5) <= (7 * -10)) or ((-7 - -18) >= (2 ** 2))) and ((3 * 10 * 3 * 7) == (10 - -4))) or ((((5 ** 1) < (3 + -8)) and ((-15 - -14) != (1 ** 2))) or (not not (第二次世界大战开始发生在1939年。))))) and (not not ((埃及位于北美洲。) and (1952年奥运会在墨尔本举办。) and ((((-9 * -7) < (42 % 8) < (17 % 3)) or (氧气在常温下是液体。)) or (not not (1980年奥运会在莫斯科举办。))))))
E. not (not (((not (((9 * 18) == (1 ** 1)) and ((18 * -16) == (8 - -11)))) or ((4 ** 3) < (5 ** 3))) or (((5 * 5) > (5 + -4)) and ((366是完全平方数。) or ((26 % 2) < (5 * 8))) and ((-7 + 17) < (-5 * 4 * 10 * 3) < (5 * -1 - -8 * -3)))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 5,
"seed": 52542217,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. (not (((((15 - -10) > (-1 * 9 * 7 * 9)) and (鲤鱼是哺乳动物。)) or (((大象有6条腿。) and ((2 * -4 + -6 * 6) >= (20 + -1))) and ((-1 * -7 * 4 * 6) == (7 * 1)))) or (not ((-5 * -18) <= (11 + 8) <= (9 * -9 + 8 * -10))))) or (not ((not not (not (not not (第一次世界大战结束发生在1918年。)))) or ((not (((9 - 9) != (3 ** 3)) and ((-18 * 12) > (-11 - -14)))) and ((-8 * -15) >= (-7 * 0 + -1 * 1)))))\nB. ((not not (not not ((鸡有10条腿。) or (光速比声速快。)))) or (((龙虾有10条腿。) and (钴的化学符号是Ag。)) or ((not not ((木星是距离太阳第5近的行星。) or (加拿大的首都是渥太华。))) or ((-1 + 5) >= (-6 * 9 + -10 * -9))))) and (not ((not (not not (not (土星是距离太阳第6近的行星。)))) or (not (((8 + -7) == (7 + -11)) and (金在常温下是固体。)))))\nC. ((not not (((木星是距离太阳第5近的行星。) and ((9 - 7) <= (6 * 9 - 5 * -9))) and ((not (挪威的货币是克朗。)) and (not ((3 ** 1) < (5 ** 2)))))) or (not (not not (not not ((锡的化学符号是He。) and ((-7 * 4 - -2 * 2) != (5 * -8 + 10 * -9))))))) or ((not (((((2 ** 2) <= (5 - 15) <= (11 + 20)) and ((5 ** 2) <= (-20 - -15))) and (not not (哥伦布到达美洲发生在1482年。))) and ((not ((2 ** 1) == (-10 * -15))) and ((0 + -3) <= (5 ** 1) <= (-12 - -5))))) or (not not (((-5 + -16) >= (-15 * -4)) or ((-8 + 14) != (-14 * 20)))))\nD. not (((((19 - -7) <= (14 % 8) <= (4 + -14)) or ((5 ** 3) == (-11 - 12))) and (not not (not (莱特兄弟首次飞行发生在1913年。))) and (((((23 % 5) <= (7 * -10)) or ((-7 - -18) >= (2 ** 2))) and ((3 * 10 * 3 * 7) == (10 - -4))) or ((((5 ** 1) < (3 + -8)) and ((-15 - -14) != (1 ** 2))) or (not not (第二次世界大战开始发生在1939年。))))) and (not not ((埃及位于北美洲。) and (1952年奥运会在墨尔本举办。) and ((((-9 * -7) < (42 % 8) < (17 % 3)) or (氧气在常温下是液体。)) or (not not (1980年奥运会在莫斯科举办。))))))\nE. not (not (((not (((9 * 18) == (1 ** 1)) and ((18 * -16) == (8 - -11)))) or ((4 ** 3) < (5 ** 3))) or (((5 * 5) > (5 + -4)) and ((366是完全平方数。) or ((26 % 2) < (5 * 8))) and ((-7 + 17) < (-5 * 4 * 10 * 3) < (5 * -1 - -8 * -3)))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 5,
"seed": 52542217,
"true_count": 3
},
"seed": 52542217,
"task_id": 652542217,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not ((There are 30 days in April.) and (The chemical symbol for Hydrogen is H.))
B. (((Copper is a solid at room temperature.) and (There are 29 days in July.)) or ((Mars is the 5th planet from the Sun.) and (A butterfly has 8 legs.))) and (((The capital of Cuba is Havana.) and (The capital of Singapore is Havana.)) or ((4 * 16) <= (9 * 0 + -1 * 8) <= (-7 * -10 - -2 * 9)))
C. (Ice is a solid at room temperature.) or ((((7 - -18) == (12 - 2)) and ((7 * -8 - 7 * 2) == (-11 - -20))) or (((1 * -1) < (-14 - 17)) or (Diamonds are made of carbon.)))
D. not not (((8 * -8) < (8 * -8 * 7 * -1)) and (Penguins can fly.))
E. ((((0 * 6 - 3 * 8) > (5 * 5 * -1 * -9)) and ((-5 * -12) > (-6 * -4))) and ((The chemical symbol for Carbon is Na.) or (Mars is the 2nd planet from the Sun.))) or ((3 - -1) > (5 ** 3))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 34635352,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. not ((There are 30 days in April.) and (The chemical symbol for Hydrogen is H.))\nB. (((Copper is a solid at room temperature.) and (There are 29 days in July.)) or ((Mars is the 5th planet from the Sun.) and (A butterfly has 8 legs.))) and (((The capital of Cuba is Havana.) and (The capital of Singapore is Havana.)) or ((4 * 16) <= (9 * 0 + -1 * 8) <= (-7 * -10 - -2 * 9)))\nC. (Ice is a solid at room temperature.) or ((((7 - -18) == (12 - 2)) and ((7 * -8 - 7 * 2) == (-11 - -20))) or (((1 * -1) < (-14 - 17)) or (Diamonds are made of carbon.)))\nD. not not (((8 * -8) < (8 * -8 * 7 * -1)) and (Penguins can fly.))\nE. ((((0 * 6 - 3 * 8) > (5 * 5 * -1 * -9)) and ((-5 * -12) > (-6 * -4))) and ((The chemical symbol for Carbon is Na.) or (Mars is the 2nd planet from the Sun.))) or ((3 - -1) > (5 ** 3))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 34635352,
"true_count": 1
},
"seed": 34635352,
"task_id": 634635352,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (((((水蒸气在常温下是固体。) and (柏林墙倒塌发生在1984年。)) and (not ((3 * 4 - -7 * -3) < (1 * -9 + 2 * 8)))) and ((天王星是距离太阳第7近的行星。) and (((-10 - -1) != (7 * 14)) and ((-12 + -9) == (2 * 7 + -6 * 0))))) and (((1 - -4) != (-3 * 2)) and ((-7 * 14) > (-8 * -14)))) or ((南非的货币是人民币。) or (((10 * 4) <= (2 ** 3)) or (美国宣布独立发生在1776年。))) or (((not (泰国的首都是曼谷。)) and (水星是距离太阳第1近的行星。)) or (not ((17 * -17) <= (-3 * 9 + 1 * 8))))
B. (((德国位于欧洲。) and ((-12 * -13) > (-16 - 18))) or ((金在常温下是固体。) or (not (not (青蛙有10条腿。))))) or (not not (冰在常温下是固体。)) or (not not (not (not (太阳绕地球运转。))))
C. ((((((45 % 1) <= (-7 * 16) <= (10 * 5 * 9 * -7)) and (金鱼是鱼类。)) and (((4 * 1 - -2 * 2) == (-6 + 7)) or ((-14 - 13) < (11 * -16) < (-20 + 9)))) or (螃蟹有6条腿。)) or ((((-1 - 18) <= (3 + -8)) or ((-1 * -10 * -2 * 8) <= (-6 - 16) <= (-3 * 2 - -10 * -9))) or (not not (墨西哥位于北美洲。))) or ((((新加坡的首都是新加坡。) or ((17 - -18) >= (-4 * 2))) or (1980年奥运会在东京举办。)) or ((139是偶数。) and (((3 - 3) <= (-8 + 3)) or ((0 * -11) > (6 * 0)))))) or ((not ((15 % 9) <= (15 + 12))) or (((2 - 7) <= (34 % 7)) or (not not (巴西的首都是柏林。))))
D. not not (((not not ((95是质数。) or ((-10 - -14) < (2 ** 3)))) or ((2 ** 3) > (3 ** 3))) or (not ((14 * -20) > (9 * -9 + -1 * -5))))
E. ((((新西兰的货币是新西兰元。) or (not not ((15 + 3) < (1 ** 2) < (8 * -2 + 1 * -3)))) and (十二月有29天。)) and ((not ((8 * -13) < (-20 + 17) < (-3 - 10))) or (((38 % 2) < (10 * 4 * 6 * -6) < (3 ** 1)) and (1954年是闰年。)) or (蝴蝶是哺乳动物。))) or (((not not (汞在常温下是液体。)) or (not not (not (龙虾有10条腿。)))) or (not ((1924年奥运会在雅典举办。) and (南非位于非洲。))) or (not not ((-10 * 10) > (7 - 6))))
F. not ((((-14 + 5) <= (-7 - 8) <= (5 ** 1)) or (((金的化学符号是Au。) and (1996年奥运会在罗马举办。)) or ((5 ** 2) >= (18 * 4)))) and (((((5 * 8 + 3 * 0) < (12 - 3) < (-3 * 10 + 10 * -4)) or (锡的化学符号是Al。)) or (not (中国长城是在一年内建成的。))) or (not not ((51是质数。) or (新西兰的首都是内罗毕。)))))
G. (((泰国的货币是泰铢。) or (not not (二月有28天。)) or (not not (孔雀是鱼类。))) and (月球绕地球运转。) and (not not (not not (not not ((-9 * 8 + 9 * 9) <= (-12 - -18)))))) or ((((not (俄罗斯的货币是卢布。)) or (匈牙利的首都是布达佩斯。)) or (((-14 - 13) == (20 + 8)) or (古巴的首都是布鲁塞尔。)) or (not not ((美国位于亚洲。) and (第二次世界大战结束发生在1955年。)))) or (not not (not (十月有31天。))) or ((1900年奥运会在巴黎举办。) or ((not not ((-19 * -14) <= (-16 - 20))) and ((-12 * 19) == (2 - -16)))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B,C,D,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 67713408,
"true_count": 7
},
"question": "研究以下逻辑语句：\n\nA. (((((水蒸气在常温下是固体。) and (柏林墙倒塌发生在1984年。)) and (not ((3 * 4 - -7 * -3) < (1 * -9 + 2 * 8)))) and ((天王星是距离太阳第7近的行星。) and (((-10 - -1) != (7 * 14)) and ((-12 + -9) == (2 * 7 + -6 * 0))))) and (((1 - -4) != (-3 * 2)) and ((-7 * 14) > (-8 * -14)))) or ((南非的货币是人民币。) or (((10 * 4) <= (2 ** 3)) or (美国宣布独立发生在1776年。))) or (((not (泰国的首都是曼谷。)) and (水星是距离太阳第1近的行星。)) or (not ((17 * -17) <= (-3 * 9 + 1 * 8))))\nB. (((德国位于欧洲。) and ((-12 * -13) > (-16 - 18))) or ((金在常温下是固体。) or (not (not (青蛙有10条腿。))))) or (not not (冰在常温下是固体。)) or (not not (not (not (太阳绕地球运转。))))\nC. ((((((45 % 1) <= (-7 * 16) <= (10 * 5 * 9 * -7)) and (金鱼是鱼类。)) and (((4 * 1 - -2 * 2) == (-6 + 7)) or ((-14 - 13) < (11 * -16) < (-20 + 9)))) or (螃蟹有6条腿。)) or ((((-1 - 18) <= (3 + -8)) or ((-1 * -10 * -2 * 8) <= (-6 - 16) <= (-3 * 2 - -10 * -9))) or (not not (墨西哥位于北美洲。))) or ((((新加坡的首都是新加坡。) or ((17 - -18) >= (-4 * 2))) or (1980年奥运会在东京举办。)) or ((139是偶数。) and (((3 - 3) <= (-8 + 3)) or ((0 * -11) > (6 * 0)))))) or ((not ((15 % 9) <= (15 + 12))) or (((2 - 7) <= (34 % 7)) or (not not (巴西的首都是柏林。))))\nD. not not (((not not ((95是质数。) or ((-10 - -14) < (2 ** 3)))) or ((2 ** 3) > (3 ** 3))) or (not ((14 * -20) > (9 * -9 + -1 * -5))))\nE. ((((新西兰的货币是新西兰元。) or (not not ((15 + 3) < (1 ** 2) < (8 * -2 + 1 * -3)))) and (十二月有29天。)) and ((not ((8 * -13) < (-20 + 17) < (-3 - 10))) or (((38 % 2) < (10 * 4 * 6 * -6) < (3 ** 1)) and (1954年是闰年。)) or (蝴蝶是哺乳动物。))) or (((not not (汞在常温下是液体。)) or (not not (not (龙虾有10条腿。)))) or (not ((1924年奥运会在雅典举办。) and (南非位于非洲。))) or (not not ((-10 * 10) > (7 - 6))))\nF. not ((((-14 + 5) <= (-7 - 8) <= (5 ** 1)) or (((金的化学符号是Au。) and (1996年奥运会在罗马举办。)) or ((5 ** 2) >= (18 * 4)))) and (((((5 * 8 + 3 * 0) < (12 - 3) < (-3 * 10 + 10 * -4)) or (锡的化学符号是Al。)) or (not (中国长城是在一年内建成的。))) or (not not ((51是质数。) or (新西兰的首都是内罗毕。)))))\nG. (((泰国的货币是泰铢。) or (not not (二月有28天。)) or (not not (孔雀是鱼类。))) and (月球绕地球运转。) and (not not (not not (not not ((-9 * 8 + 9 * 9) <= (-12 - -18)))))) or ((((not (俄罗斯的货币是卢布。)) or (匈牙利的首都是布达佩斯。)) or (((-14 - 13) == (20 + 8)) or (古巴的首都是布鲁塞尔。)) or (not not ((美国位于亚洲。) and (第二次世界大战结束发生在1955年。)))) or (not not (not (十月有31天。))) or ((1900年奥运会在巴黎举办。) or ((not not ((-19 * -14) <= (-16 - 20))) and ((-12 * 19) == (2 - -16)))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 67713408,
"true_count": 7
},
"seed": 67713408,
"task_id": 667713408,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. not ((not ((((19 + 10) <= (5 - 16)) or (not not (丹麦的货币是克朗。))) and ((2067年是闰年。) or ((8 - 18) >= (32 % 2))) and ((not (26是斐波那契数。)) or (十二月有30天。)))) and (not not ((瑞典的货币是克朗。) and (not (not not (2072年是闰年。))))))
B. not (not ((not not ((((-1 - -2) == (3 ** 3)) and (秘鲁的货币是索尔。)) or ((1912年奥运会在斯德哥尔摩举办。) and (2085年是闰年。)))) or (((-14 * -8) < (-12 * -4) < (1 * -19)) or ((4 % 5) != (-7 * -16)))))
C. (not (not not ((not not (((4 * -2 * -1 * -3) == (10 + -10)) and ((0 * 20) < (8 % 10)))) or ((((-1 * -4 * -2 * 0) == (-5 + 8)) or ((1 ** 3) < (-10 * 9 + 2 * -4) < (-10 - -19))) or (秘鲁的货币是索尔。))))) and (((not ((铀的化学符号是He。) or ((美国的货币是美元。) and (氧气在常温下是液体。)))) and (not not (not not ((4 ** 2) > (2 ** 3))))) and (((美国位于北美洲。) or (not not (金在常温下是液体。)) or (柏林墙倒塌发生在1988年。)) or ((1921年是闰年。) or (水蒸气在常温下是气体。) or ((((6 * -17) <= (1 + -17)) or (第一部iPhone发布发生在2007年。)) and (月球自己发光。)))))
D. not not (not (not not (not ((太阳绕地球运转。) or ((德国位于欧洲。) and (秘鲁的首都是加拉加斯。))))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 34496763,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. not ((not ((((19 + 10) <= (5 - 16)) or (not not (丹麦的货币是克朗。))) and ((2067年是闰年。) or ((8 - 18) >= (32 % 2))) and ((not (26是斐波那契数。)) or (十二月有30天。)))) and (not not ((瑞典的货币是克朗。) and (not (not not (2072年是闰年。))))))\nB. not (not ((not not ((((-1 - -2) == (3 ** 3)) and (秘鲁的货币是索尔。)) or ((1912年奥运会在斯德哥尔摩举办。) and (2085年是闰年。)))) or (((-14 * -8) < (-12 * -4) < (1 * -19)) or ((4 % 5) != (-7 * -16)))))\nC. (not (not not ((not not (((4 * -2 * -1 * -3) == (10 + -10)) and ((0 * 20) < (8 % 10)))) or ((((-1 * -4 * -2 * 0) == (-5 + 8)) or ((1 ** 3) < (-10 * 9 + 2 * -4) < (-10 - -19))) or (秘鲁的货币是索尔。))))) and (((not ((铀的化学符号是He。) or ((美国的货币是美元。) and (氧气在常温下是液体。)))) and (not not (not not ((4 ** 2) > (2 ** 3))))) and (((美国位于北美洲。) or (not not (金在常温下是液体。)) or (柏林墙倒塌发生在1988年。)) or ((1921年是闰年。) or (水蒸气在常温下是气体。) or ((((6 * -17) <= (1 + -17)) or (第一部iPhone发布发生在2007年。)) and (月球自己发光。)))))\nD. not not (not (not not (not ((太阳绕地球运转。) or ((德国位于欧洲。) and (秘鲁的首都是加拉加斯。))))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 34496763,
"true_count": 2
},
"seed": 34496763,
"task_id": 634496763,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not ((0 + 14) < (-19 + -14) < (4 ** 2))
B. ((The chemical symbol for Manganese is Mn.) or ((The chemical symbol for Tin is Sn.) and (Mercury is the 6th planet from the Sun.))) and (((4 ** 1) > (-10 * 2 * -9 * 6)) or (Germany is in Antarctica.)) and ((((5 ** 3) < (20 - -15) < (-9 * -4)) or (The 2004 Olympics were held in Berlin.)) and ((Neptune is the 8th planet from the Sun.) or ((-16 * 19) <= (8 * -1))))
C. (not (((-15 - 14) < (3 + -8)) or ((-18 + 14) == (-4 * 0)))) or (Steam is a gas at room temperature.) or (((14 + -8) > (-8 * -6 - 10 * -8)) or (((19 - -4) >= (4 ** 3)) and (Mercury is the 1st planet from the Sun.)))
D. ((not not (The chemical symbol for Titanium is Ti.)) or (((2 * 7 + -4 * 5) == (-3 * -10 - 0 * 3)) and ((1 - 12) < (16 + -9)))) or (((The capital of Singapore is Manila.) and ((5 * -10 * 4 * -2) != (3 ** 2))) or ((A ant is a mammal.) or (The 1960 Olympics were held in Athens.)))
E. (not (((3 ** 3) == (13 % 6)) or ((39 % 4) == (7 * -2 - -3 * 0)))) or ((not not ((8 + 1) != (39 % 6))) or (not not (The 1928 Olympics were held in Amsterdam.)))
F. (Morocco is in Africa.) or (not not (Silver is a solid at room temperature.)) or (Brazil is in South America.)
G. ((not not (The 1920 Olympics were held in Mexico City.)) and (((4 ** 1) != (4 ** 3)) and ((8 * 13) == (-5 + -5)))) and ((not not ((-8 - -10) < (8 * 8 * -1 * -2))) or (((-10 - 9) >= (-17 + -20)) or ((-15 * 8) > (17 % 5))))
H. not ((20 - -8) > (2 - -2))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 22315814,
"true_count": 5
},
"question": "Consider the following logical expressions:\n\nA. not ((0 + 14) < (-19 + -14) < (4 ** 2))\nB. ((The chemical symbol for Manganese is Mn.) or ((The chemical symbol for Tin is Sn.) and (Mercury is the 6th planet from the Sun.))) and (((4 ** 1) > (-10 * 2 * -9 * 6)) or (Germany is in Antarctica.)) and ((((5 ** 3) < (20 - -15) < (-9 * -4)) or (The 2004 Olympics were held in Berlin.)) and ((Neptune is the 8th planet from the Sun.) or ((-16 * 19) <= (8 * -1))))\nC. (not (((-15 - 14) < (3 + -8)) or ((-18 + 14) == (-4 * 0)))) or (Steam is a gas at room temperature.) or (((14 + -8) > (-8 * -6 - 10 * -8)) or (((19 - -4) >= (4 ** 3)) and (Mercury is the 1st planet from the Sun.)))\nD. ((not not (The chemical symbol for Titanium is Ti.)) or (((2 * 7 + -4 * 5) == (-3 * -10 - 0 * 3)) and ((1 - 12) < (16 + -9)))) or (((The capital of Singapore is Manila.) and ((5 * -10 * 4 * -2) != (3 ** 2))) or ((A ant is a mammal.) or (The 1960 Olympics were held in Athens.)))\nE. (not (((3 ** 3) == (13 % 6)) or ((39 % 4) == (7 * -2 - -3 * 0)))) or ((not not ((8 + 1) != (39 % 6))) or (not not (The 1928 Olympics were held in Amsterdam.)))\nF. (Morocco is in Africa.) or (not not (Silver is a solid at room temperature.)) or (Brazil is in South America.)\nG. ((not not (The 1920 Olympics were held in Mexico City.)) and (((4 ** 1) != (4 ** 3)) and ((8 * 13) == (-5 + -5)))) and ((not not ((-8 - -10) < (8 * 8 * -1 * -2))) or (((-10 - 9) >= (-17 + -20)) or ((-15 * 8) > (17 % 5))))\nH. not ((20 - -8) > (2 - -2))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 22315814,
"true_count": 5
},
"seed": 22315814,
"task_id": 622315814,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (not ((((1 + -13) != (11 * 1)) or (Australia is in Asia.)) and (The chemical symbol for Platinum is Ca.))) or ((The Moon produces its own light.) or ((16 - -8) <= (7 * 7 * 1 * 5) <= (4 ** 1)) or (The 2000 Olympics were held in Montreal.))
B. (((not (The currency of Malaysia is the Ringgit.)) and (World War I ended occurred in 1918.)) and ((Venus is the 2nd planet from the Sun.) or ((Earth is the 6th planet from the Sun.) or (The currency of Philippines is the Peso.)))) or (not (((The currency of Japan is the Dollar.) or ((13 + 1) < (-6 * 1 * 3 * 1) < (4 ** 1))) and (((1 ** 1) == (-18 * 9)) or (South Korea is in Asia.))))
C. (((-8 * 2 - 6 * -6) >= (-4 - -4)) and ((((5 - -12) < (-10 * 0 - -2 * 4)) or (Saturn is the 6th planet from the Sun.)) or ((The chemical symbol for Chlorine is Cl.) and (Plants produce oxygen through photosynthesis.)))) or ((((The capital of Indonesia is Jakarta.) or (Mercury is the 1st planet from the Sun.)) and ((The currency of Poland is the Dong.) and (The currency of Poland is the Forint.))) or ((-10 + 16) <= (-17 * 9)))
D. ((The capital of South Korea is Seoul.) or (not ((19 + -20) <= (-4 + 15))) or ((The Great Wall of China was built in one year.) or ((-9 - -15) >= (12 * 13)))) and (((Argentina is in Africa.) or (The chemical symbol for Magnesium is Mg.)) or ((The chemical symbol for Silicon is Ca.) or ((-10 * -2 * -2 * -8) > (-2 * 2 + 9 * -7)))) and (not (not not ((479 is a Fibonacci number.) and ((48 % 3) >= (-15 * 7)))))
E. (((3 % 8) != (17 - -16)) and ((-7 * -9) >= (37 % 6))) or (((3 ** 2) == (17 * -20)) or ((The capital of Vietnam is Kyiv.) and ((-3 + -13) < (-8 * 1 * -3 * 8) < (0 * 8 * -1 * 2))))
F. (not (((Diamond is a solid at room temperature.) and (China is in Asia.)) or (not not ((-13 - 9) < (13 + -20) < (-2 * -6 - 2 * -6))))) or ((The currency of Egypt is the Pound.) and (The currency of Denmark is the Riyal.))
G. ((not ((The currency of Russia is the Krona.) and (The capital of Sweden is Bern.))) and ((5 ** 3) == (2 ** 2)) and (not not (not not ((11 % 2) != (3 * 17))))) or (((Steam is a liquid at room temperature.) and (not not ((2 ** 1) <= (2 % 4) <= (5 * -19)))) or ((not not (The currency of Brazil is the Real.)) and ((A penguin is a bird.) and (A frog has 10 legs.))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 41756805,
"true_count": 5
},
"question": "Consider the following logical expressions:\n\nA. (not ((((1 + -13) != (11 * 1)) or (Australia is in Asia.)) and (The chemical symbol for Platinum is Ca.))) or ((The Moon produces its own light.) or ((16 - -8) <= (7 * 7 * 1 * 5) <= (4 ** 1)) or (The 2000 Olympics were held in Montreal.))\nB. (((not (The currency of Malaysia is the Ringgit.)) and (World War I ended occurred in 1918.)) and ((Venus is the 2nd planet from the Sun.) or ((Earth is the 6th planet from the Sun.) or (The currency of Philippines is the Peso.)))) or (not (((The currency of Japan is the Dollar.) or ((13 + 1) < (-6 * 1 * 3 * 1) < (4 ** 1))) and (((1 ** 1) == (-18 * 9)) or (South Korea is in Asia.))))\nC. (((-8 * 2 - 6 * -6) >= (-4 - -4)) and ((((5 - -12) < (-10 * 0 - -2 * 4)) or (Saturn is the 6th planet from the Sun.)) or ((The chemical symbol for Chlorine is Cl.) and (Plants produce oxygen through photosynthesis.)))) or ((((The capital of Indonesia is Jakarta.) or (Mercury is the 1st planet from the Sun.)) and ((The currency of Poland is the Dong.) and (The currency of Poland is the Forint.))) or ((-10 + 16) <= (-17 * 9)))\nD. ((The capital of South Korea is Seoul.) or (not ((19 + -20) <= (-4 + 15))) or ((The Great Wall of China was built in one year.) or ((-9 - -15) >= (12 * 13)))) and (((Argentina is in Africa.) or (The chemical symbol for Magnesium is Mg.)) or ((The chemical symbol for Silicon is Ca.) or ((-10 * -2 * -2 * -8) > (-2 * 2 + 9 * -7)))) and (not (not not ((479 is a Fibonacci number.) and ((48 % 3) >= (-15 * 7)))))\nE. (((3 % 8) != (17 - -16)) and ((-7 * -9) >= (37 % 6))) or (((3 ** 2) == (17 * -20)) or ((The capital of Vietnam is Kyiv.) and ((-3 + -13) < (-8 * 1 * -3 * 8) < (0 * 8 * -1 * 2))))\nF. (not (((Diamond is a solid at room temperature.) and (China is in Asia.)) or (not not ((-13 - 9) < (13 + -20) < (-2 * -6 - 2 * -6))))) or ((The currency of Egypt is the Pound.) and (The currency of Denmark is the Riyal.))\nG. ((not ((The currency of Russia is the Krona.) and (The capital of Sweden is Bern.))) and ((5 ** 3) == (2 ** 2)) and (not not (not not ((11 % 2) != (3 * 17))))) or (((Steam is a liquid at room temperature.) and (not not ((2 ** 1) <= (2 % 4) <= (5 * -19)))) or ((not not (The currency of Brazil is the Real.)) and ((A penguin is a bird.) and (A frog has 10 legs.))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 41756805,
"true_count": 5
},
"seed": 41756805,
"task_id": 641756805,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not ((-1 - -16) >= (-3 + -3))
B. not (((10 - -9) <= (-10 * 14)) or (((-9 - -8) > (-9 * 14)) or (There are 30 days in February.)))
C. not ((28 % 1) > (-10 + -4))
D. (The currency of Hungary is the Forint.) or ((-12 + 9) <= (4 ** 2)) or (not (Humans have three lungs.))
E. not not ((((-10 - 10) >= (1 * 4 * -9 * -1)) or (The chemical symbol for Neon is Ne.)) or (((1 * 4 * 5 * 1) > (-16 - -7)) or ((-12 - 13) < (-5 * 6 + 1 * 0))))
F. not not ((1 + 9) > (-11 * -12))
G. ((not not (There are 30 days in June.)) and (not ((6 + 1) <= (-9 * 2)))) and (((The capital of India is New Delhi.) and (A bird has 0 legs.)) and (not (159 is an even number.)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 23084841,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. not not ((-1 - -16) >= (-3 + -3))\nB. not (((10 - -9) <= (-10 * 14)) or (((-9 - -8) > (-9 * 14)) or (There are 30 days in February.)))\nC. not ((28 % 1) > (-10 + -4))\nD. (The currency of Hungary is the Forint.) or ((-12 + 9) <= (4 ** 2)) or (not (Humans have three lungs.))\nE. not not ((((-10 - 10) >= (1 * 4 * -9 * -1)) or (The chemical symbol for Neon is Ne.)) or (((1 * 4 * 5 * 1) > (-16 - -7)) or ((-12 - 13) < (-5 * 6 + 1 * 0))))\nF. not not ((1 + 9) > (-11 * -12))\nG. ((not not (There are 30 days in June.)) and (not ((6 + 1) <= (-9 * 2)))) and (((The capital of India is New Delhi.) and (A bird has 0 legs.)) and (not (159 is an even number.)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 23084841,
"true_count": 3
},
"seed": 23084841,
"task_id": 623084841,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not not (((8 * -9 * -10 * -6) > (15 * 13)) and (Thailand is in Asia.))) or ((5 * 4 - -1 * 8) >= (5 ** 3))
B. (The chemical symbol for Iron is Fe.) and ((not (The capital of Spain is Madrid.)) and ((A cow has 8 legs.) and ((-2 - -11) > (-14 * -20))))
C. (Sound travels faster in a vacuum.) or ((9 * 3 + -4 * -6) > (-4 * 8 - 6 * -1))
D. not not ((5 + 1) > (-16 * -14))
E. ((18 * 9) == (5 * -17)) or ((The capital of Turkey is Ankara.) and ((-12 - 5) != (12 + -4))) or (Water boils at 100 degrees Celsius at sea level.)
F. (((The 2000 Olympics were held in Munich.) and (Helium is a solid at room temperature.)) and ((United States is in North America.) or (Mercury is the 1st planet from the Sun.))) or (((0 * 17) <= (3 ** 2)) or ((37 % 5) > (7 * 10))) or (not not (A fish has 6 legs.))
G. not not ((-19 + 19) < (-16 - 2))
H. not not ((not not ((44 % 10) != (33 % 10))) and (((1 - 1) <= (9 * -10 - -3 * 5) <= (9 + -7)) and (The chemical symbol for Oxygen is O.)))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 65172418,
"true_count": 3
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (not not (((8 * -9 * -10 * -6) > (15 * 13)) and (Thailand is in Asia.))) or ((5 * 4 - -1 * 8) >= (5 ** 3))\nB. (The chemical symbol for Iron is Fe.) and ((not (The capital of Spain is Madrid.)) and ((A cow has 8 legs.) and ((-2 - -11) > (-14 * -20))))\nC. (Sound travels faster in a vacuum.) or ((9 * 3 + -4 * -6) > (-4 * 8 - 6 * -1))\nD. not not ((5 + 1) > (-16 * -14))\nE. ((18 * 9) == (5 * -17)) or ((The capital of Turkey is Ankara.) and ((-12 - 5) != (12 + -4))) or (Water boils at 100 degrees Celsius at sea level.)\nF. (((The 2000 Olympics were held in Munich.) and (Helium is a solid at room temperature.)) and ((United States is in North America.) or (Mercury is the 1st planet from the Sun.))) or (((0 * 17) <= (3 ** 2)) or ((37 % 5) > (7 * 10))) or (not not (A fish has 6 legs.))\nG. not not ((-19 + 19) < (-16 - 2))\nH. not not ((not not ((44 % 10) != (33 % 10))) and (((1 - 1) <= (9 * -10 - -3 * 5) <= (9 + -7)) and (The chemical symbol for Oxygen is O.)))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 65172418,
"true_count": 3
},
"seed": 65172418,
"task_id": 665172418,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((-3 * 3 + 4 * -9) != (8 * 7 * -10 * -2)) or (not not ((2 ** 1) < (-4 * -10))) or (水星是距离太阳第1近的行星。)
B. (((瑞士的首都是墨西哥城。) or ((-6 + 3) == (18 * -15))) and ((捷克的货币是韩元。) and (以色列的货币是比索。))) or (((-8 * 15) > (7 * -2)) and ((1 ** 3) > (19 + 5))) or (((中国位于亚洲。) and ((-16 * -2) == (44 % 5))) or (not not ((-9 + -20) <= (5 % 9) <= (4 + -3))))
C. (not (not (木头在常温下是固体。))) and ((82大于28。) or (2007年是闰年。)) and (not not ((13 % 5) < (-3 - -9)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 76401501,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. ((-3 * 3 + 4 * -9) != (8 * 7 * -10 * -2)) or (not not ((2 ** 1) < (-4 * -10))) or (水星是距离太阳第1近的行星。)\nB. (((瑞士的首都是墨西哥城。) or ((-6 + 3) == (18 * -15))) and ((捷克的货币是韩元。) and (以色列的货币是比索。))) or (((-8 * 15) > (7 * -2)) and ((1 ** 3) > (19 + 5))) or (((中国位于亚洲。) and ((-16 * -2) == (44 % 5))) or (not not ((-9 + -20) <= (5 % 9) <= (4 + -3))))\nC. (not (not (木头在常温下是固体。))) and ((82大于28。) or (2007年是闰年。)) and (not not ((13 % 5) < (-3 - -9)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 76401501,
"true_count": 2
},
"seed": 76401501,
"task_id": 676401501,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. ((((-2 + -3) < (-8 + -19) < (1 ** 1)) or (not ((荷兰的首都是阿姆斯特丹。) or ((5 ** 1) < (5 ** 1) < (7 * -2))))) and ((not not ((九月有29天。) and (铜在常温下是固体。))) or ((not ((-16 - -8) >= (0 + -11))) and (铜在常温下是气体。)))) or (((not (not ((-3 * 7 - -2 * 1) <= (-13 - -9)))) or (现代奥运会首届举办发生在1894年。) or (泰坦尼克号沉没发生在1912年。)) and (not ((((-15 * 17) != (-16 + -5)) or (牛有10条腿。)) and (((9 + -7) <= (12 * 18) <= (48 % 9)) and ((-10 * 0 * -4 * -6) >= (5 % 5))))))
B. ((not ((-5 * 4) != (12 + -7))) and (((not (意大利位于欧洲。)) and (((14 - 1) < (2 * -5 + 2 * -6) < (12 - 3)) or ((-11 - 14) <= (18 + -13)))) and (not (油在常温下是固体。)))) and (not not (((11 - 12) <= (43 % 8)) or ((10 * 10 + -2 * 4) != (-14 * 2))))
C. not (((((第二次世界大战结束发生在1950年。) or (委内瑞拉的首都是内罗毕。)) and (三月有31天。)) or ((((-20 * 15) <= (2 ** 2)) or (印度尼西亚的首都是雅加达。)) or ((24 % 9) <= (2 ** 3)))) and (狗是哺乳动物。) and ((not (not not (1996年奥运会在赫尔辛基举办。))) or (((瑞士的货币是欧元。) and ((5 ** 3) < (-20 + -12))) or (泰国位于亚洲。))))
D. not not ((((秘鲁位于欧洲。) and (1980年奥运会在莫斯科举办。)) or ((4 * 3 * 3 * 10) == (-12 * -20))) or (((28能被10整除。) and ((-5 * -7 * 3 * 3) <= (-12 - -17))) or (((-19 + -1) <= (5 ** 3) <= (-18 - 0)) and (酒精在常温下是液体。))) or ((not not ((8 - -16) < (4 - 5))) or (((45 % 10) < (5 ** 3)) and ((84能被6整除。) and ((2 ** 1) >= (6 + 0))))))
E. (not ((((10 * -6 - 5 * 5) <= (1 ** 1)) and (not not ((-1 * -3 * -5 * 10) < (6 - 13) < (-13 - -6)))) or (144的平方根是12。))) or (((not ((氦气在常温下是气体。) or ((38 % 5) <= (-19 * -8) <= (4 - 17)))) or ((-16 * 10) == (3 ** 2))) or (((not not ((6 * 15) < (-12 * 8) < (-2 * 1 + -5 * -5))) or (((-11 - -13) == (-5 * 4 - -3 * -6)) and ((-2 * 9 - -2 * 7) <= (20 + 18)))) or ((not (匈牙利的货币是福林。)) or (((-14 + 4) <= (39 % 5)) or (铬的化学符号是Ti。)))))
F. not ((not ((5 ** 1) > (17 + -6))) or (not not ((-4 * 4 + 8 * 5) == (4 % 6))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"seed": 82248327,
"true_count": 2
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"question": "研究以下逻辑语句：\n\nA. ((((-2 + -3) < (-8 + -19) < (1 ** 1)) or (not ((荷兰的首都是阿姆斯特丹。) or ((5 ** 1) < (5 ** 1) < (7 * -2))))) and ((not not ((九月有29天。) and (铜在常温下是固体。))) or ((not ((-16 - -8) >= (0 + -11))) and (铜在常温下是气体。)))) or (((not (not ((-3 * 7 - -2 * 1) <= (-13 - -9)))) or (现代奥运会首届举办发生在1894年。) or (泰坦尼克号沉没发生在1912年。)) and (not ((((-15 * 17) != (-16 + -5)) or (牛有10条腿。)) and (((9 + -7) <= (12 * 18) <= (48 % 9)) and ((-10 * 0 * -4 * -6) >= (5 % 5))))))\nB. ((not ((-5 * 4) != (12 + -7))) and (((not (意大利位于欧洲。)) and (((14 - 1) < (2 * -5 + 2 * -6) < (12 - 3)) or ((-11 - 14) <= (18 + -13)))) and (not (油在常温下是固体。)))) and (not not (((11 - 12) <= (43 % 8)) or ((10 * 10 + -2 * 4) != (-14 * 2))))\nC. not (((((第二次世界大战结束发生在1950年。) or (委内瑞拉的首都是内罗毕。)) and (三月有31天。)) or ((((-20 * 15) <= (2 ** 2)) or (印度尼西亚的首都是雅加达。)) or ((24 % 9) <= (2 ** 3)))) and (狗是哺乳动物。) and ((not (not not (1996年奥运会在赫尔辛基举办。))) or (((瑞士的货币是欧元。) and ((5 ** 3) < (-20 + -12))) or (泰国位于亚洲。))))\nD. not not ((((秘鲁位于欧洲。) and (1980年奥运会在莫斯科举办。)) or ((4 * 3 * 3 * 10) == (-12 * -20))) or (((28能被10整除。) and ((-5 * -7 * 3 * 3) <= (-12 - -17))) or (((-19 + -1) <= (5 ** 3) <= (-18 - 0)) and (酒精在常温下是液体。))) or ((not not ((8 - -16) < (4 - 5))) or (((45 % 10) < (5 ** 3)) and ((84能被6整除。) and ((2 ** 1) >= (6 + 0))))))\nE. (not ((((10 * -6 - 5 * 5) <= (1 ** 1)) and (not not ((-1 * -3 * -5 * 10) < (6 - 13) < (-13 - -6)))) or (144的平方根是12。))) or (((not ((氦气在常温下是气体。) or ((38 % 5) <= (-19 * -8) <= (4 - 17)))) or ((-16 * 10) == (3 ** 2))) or (((not not ((6 * 15) < (-12 * 8) < (-2 * 1 + -5 * -5))) or (((-11 - -13) == (-5 * 4 - -3 * -6)) and ((-2 * 9 - -2 * 7) <= (20 + 18)))) or ((not (匈牙利的货币是福林。)) or (((-14 + 4) <= (39 % 5)) or (铬的化学符号是Ti。)))))\nF. not ((not ((5 ** 1) > (17 + -6))) or (not not ((-4 * 4 + 8 * 5) == (4 % 6))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 82248327,
"true_count": 2
},
"seed": 82248327,
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"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. 氮的化学符号是Hg。
B. 3大于61。
C. (((8 * 2 - 6 * 1) < (-4 - -16)) or ((-2 * 0) == (4 ** 3))) and ((鳟鱼是鱼类。) or ((14 - 3) <= (12 * 2)))
D. not not (((45 % 4) >= (0 - 20)) and (韩国位于亚洲。))
E. ((火星是距离太阳第4近的行星。) and (五月有30天。)) or ((第一部iPhone发布发生在2012年。) or (尼日利亚的首都是新加坡。))
F. (-4 * -1) < (-12 + -10) < (5 * 9 - -4 * -1)
G. ((美国位于北美洲。) and (柏林墙倒塌发生在1989年。)) or (not ((3 - -9) == (18 * -6)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "C,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
"num_options": 7,
"seed": 81286225,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. 氮的化学符号是Hg。\nB. 3大于61。\nC. (((8 * 2 - 6 * 1) < (-4 - -16)) or ((-2 * 0) == (4 ** 3))) and ((鳟鱼是鱼类。) or ((14 - 3) <= (12 * 2)))\nD. not not (((45 % 4) >= (0 - 20)) and (韩国位于亚洲。))\nE. ((火星是距离太阳第4近的行星。) and (五月有30天。)) or ((第一部iPhone发布发生在2012年。) or (尼日利亚的首都是新加坡。))\nF. (-4 * -1) < (-12 + -10) < (5 * 9 - -4 * -1)\nG. ((美国位于北美洲。) and (柏林墙倒塌发生在1989年。)) or (not ((3 - -9) == (18 * -6)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 81286225,
"true_count": 3
},
"seed": 81286225,
"task_id": 681286225,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not not (((五月有31天。) or (钻石在常温下是固体。)) and (((8 + -3) > (-2 - 18)) or (226是完全平方数。)))
B. not ((第一部iPhone发布发生在2007年。) and (305是斐波那契数。))
C. ((not ((-4 * 10) > (50 % 1))) and (((4 * 13) == (5 ** 2)) and ((-20 * 7) <= (19 - -15)))) or (((17 * -6) <= (0 - 9)) or (铅的化学符号是Pb。)) or ((not not (日本的货币是欧元。)) and (not not (1918年是闰年。)))
D. (钴的化学符号是Ag。) and ((((25 % 4) > (2 + 4)) and (2004年奥运会在雅典举办。)) or ((8 * -9 * -3 * 10) <= (-18 - -10)))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"seed": 1401538,
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},
"question": "下面是几个布尔表达式：\n\nA. not not (((五月有31天。) or (钻石在常温下是固体。)) and (((8 + -3) > (-2 - 18)) or (226是完全平方数。)))\nB. not ((第一部iPhone发布发生在2007年。) and (305是斐波那契数。))\nC. ((not ((-4 * 10) > (50 % 1))) and (((4 * 13) == (5 ** 2)) and ((-20 * 7) <= (19 - -15)))) or (((17 * -6) <= (0 - 9)) or (铅的化学符号是Pb。)) or ((not not (日本的货币是欧元。)) and (not not (1918年是闰年。)))\nD. (钴的化学符号是Ag。) and ((((25 % 4) > (2 + 4)) and (2004年奥运会在雅典举办。)) or ((8 * -9 * -3 * 10) <= (-18 - -10)))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 1401538,
"true_count": 3
},
"seed": 1401538,
"task_id": 601401538,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not ((((Mercury is the 1st planet from the Sun.) or (The currency of European Union is the Euro.)) and (((-8 * -6 + -4 * 9) > (16 + -16)) and (A day on Earth is 24 hours.))) or ((The currency of Switzerland is the Franc.) and ((12 + -3) >= (5 ** 3))) or (Plants produce oxygen through photosynthesis.))
B. ((((A kangaroo is a mammal.) and (The capital of Australia is Tokyo.)) or ((The currency of Denmark is the Krone.) or (The 1996 Olympics were held in Paris.))) or (not (The capital of Indonesia is Lima.)) or (Sound cannot travel through a vacuum.)) and (((The currency of Canada is the Dollar.) and (Wood is a solid at room temperature.)) or (not not ((10 * -6) < (4 - 10) < (12 + -9)))) and (not not (not not (The 1952 Olympics were held in Antwerp.)))
C. not ((((The currency of Argentina is the Peso.) and (26 is a prime number.)) and (not not ((10 - 7) <= (-15 * 9)))) and (not (The 1932 Olympics were held in Seoul.)))
D. not not ((234 is a perfect square.) and ((10 + -9) < (16 - -19) < (29 % 9)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
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"seed": 14440592,
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},
"question": "Study the following logical statements:\n\nA. not not ((((Mercury is the 1st planet from the Sun.) or (The currency of European Union is the Euro.)) and (((-8 * -6 + -4 * 9) > (16 + -16)) and (A day on Earth is 24 hours.))) or ((The currency of Switzerland is the Franc.) and ((12 + -3) >= (5 ** 3))) or (Plants produce oxygen through photosynthesis.))\nB. ((((A kangaroo is a mammal.) and (The capital of Australia is Tokyo.)) or ((The currency of Denmark is the Krone.) or (The 1996 Olympics were held in Paris.))) or (not (The capital of Indonesia is Lima.)) or (Sound cannot travel through a vacuum.)) and (((The currency of Canada is the Dollar.) and (Wood is a solid at room temperature.)) or (not not ((10 * -6) < (4 - 10) < (12 + -9)))) and (not not (not not (The 1952 Olympics were held in Antwerp.)))\nC. not ((((The currency of Argentina is the Peso.) and (26 is a prime number.)) and (not not ((10 - 7) <= (-15 * 9)))) and (not (The 1932 Olympics were held in Seoul.)))\nD. not not ((234 is a perfect square.) and ((10 + -9) < (16 - -19) < (29 % 9)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 14440592,
"true_count": 2
},
"seed": 14440592,
"task_id": 614440592,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not (The square root of 169 is 13.)
B. The 1964 Olympics were held in Tokyo.
C. ((-6 + 4) != (4 % 3)) or (The capital of Sweden is Ankara.)
D. (-6 - -9) <= (18 + 11) <= (5 - -6)
E. (The currency of Sweden is the Won.) or ((-20 * 2) < (-12 - -12))
F. (Saturn is the 6th planet from the Sun.) or (((-1 * -6 * 4 * 4) <= (7 * 0 * 3 * 9)) and (Electricity flows faster than light.))
G. (Venus is the 1st planet from the Sun.) or ((There are 31 days in September.) or (There are 30 days in November.))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 27590141,
"true_count": 5
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"question": "Below are several boolean expressions:\n\nA. not (The square root of 169 is 13.)\nB. The 1964 Olympics were held in Tokyo.\nC. ((-6 + 4) != (4 % 3)) or (The capital of Sweden is Ankara.)\nD. (-6 - -9) <= (18 + 11) <= (5 - -6)\nE. (The currency of Sweden is the Won.) or ((-20 * 2) < (-12 - -12))\nF. (Saturn is the 6th planet from the Sun.) or (((-1 * -6 * 4 * 4) <= (7 * 0 * 3 * 9)) and (Electricity flows faster than light.))\nG. (Venus is the 1st planet from the Sun.) or ((There are 31 days in September.) or (There are 30 days in November.))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 27590141,
"true_count": 5
},
"seed": 27590141,
"task_id": 627590141,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. ((((17 - -1) != (-3 - 8)) or (not (not not ((-10 * 1 + 9 * 4) < (-6 * -8 - -2 * 9))))) and (not not (氮气在常温下是气体。))) or ((((青蛙有4条腿。) or (not not (一月有31天。))) or ((人体有206块骨头。) or ((1 * -5) <= (-4 + 19) <= (4 ** 3))) or (((钙的化学符号是N。) or (澳大利亚的货币是澳元。)) and (((10 * -9 * -3 * 3) >= (-6 + 13)) or ((-3 + 2) > (-9 * -5 + 4 * 1))))) or ((-4 - -10) == (1 * 0)) or ((not not ((十二月有31天。) or (泰坦尼克号沉没发生在1922年。))) and (not (not not (瑞士的首都是巴黎。)))))
B. ((not (捷克的首都是布加勒斯特。)) or (not not (((64的平方根是1。) or ((-7 * 3 + -5 * 2) == (7 + 1))) or ((59能被3整除。) and (1936年奥运会在东京举办。))))) and ((土耳其的货币是里拉。) and ((((20 - -12) > (3 ** 3)) or (鱼有8条腿。)) or ((美国宣布独立发生在1776年。) and ((-20 - -16) != (6 * 2 + -9 * -9))))) and (not not ((not (not not ((11 - 14) <= (0 * 1 + -9 * 1)))) and (not not ((-5 + 8) <= (18 + -11) <= (4 + 17))) and ((-5 - -17) == (9 * -3 - -4 * 7))))
C. ((not not ((((-8 + -13) < (18 * 17)) and ((-18 - -7) != (20 + -6))) or ((南非位于非洲。) and ((-16 + -9) != (17 - 8))))) or (水星是距离太阳第2近的行星。) or ((狮子是哺乳动物。) and (not not ((5 - -20) > (-1 - 7))))) or ((not not ((-9 * 0 + 6 * -7) < (3 + -3))) and (not not (not not ((5 ** 1) <= (5 + 15))))) or ((not not ((19 - -8) >= (-19 + -8))) or (((5 + -20) >= (6 * 1)) and (1956年奥运会在墨尔本举办。) and ((2 * 18) != (41 % 6))))
D. not (not not (not not ((not not (德国位于欧洲。)) or ((氧的化学符号是O。) or (太平洋是最大的海洋。)))))
E. not not (((not (not ((5 ** 3) == (21 % 5)))) and ((16 + 3) == (-5 * -20))) or (((-2 - -1) != (11 + -6)) and ((13 * -18) < (20 - 9))))
F. not not ((((((16 * -1) <= (12 % 2)) or (越南的货币是奈拉。)) and (not ((-13 * -10) < (-4 + 10) < (-16 + 12)))) and ((青蛙有4条腿。) or ((-9 + 15) > (-8 * 4 * -7 * 1))) and ((4 * -11) < (9 + 16))) or (not not (哥伦比亚位于亚洲。)))
G. (((((1924年是闰年。) or ((0 * -17) <= (-2 - 5) <= (20 + -5))) or ((24 % 8) == (9 * -1 + -6 * 1))) or (((越南的货币是越南盾。) and (2012年奥运会在雅典举办。)) and (汞在常温下是液体。))) or ((-20 - -12) < (4 + 20)) or (((5 + -13) <= (17 % 5) <= (-7 - 14)) and (印度尼西亚位于非洲。) and (十二月有31天。))) or (not not (((16 - 1) > (6 + 12)) and (not ((-2 * 5 + 7 * 0) >= (6 * 7 + 8 * 10))))) or (not (((not (2029年是闰年。)) or (中国长城是在一年内建成的。)) and ((4 - 16) < (-13 * -4))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 81790629,
"true_count": 5
},
"question": "研究以下逻辑语句：\n\nA. ((((17 - -1) != (-3 - 8)) or (not (not not ((-10 * 1 + 9 * 4) < (-6 * -8 - -2 * 9))))) and (not not (氮气在常温下是气体。))) or ((((青蛙有4条腿。) or (not not (一月有31天。))) or ((人体有206块骨头。) or ((1 * -5) <= (-4 + 19) <= (4 ** 3))) or (((钙的化学符号是N。) or (澳大利亚的货币是澳元。)) and (((10 * -9 * -3 * 3) >= (-6 + 13)) or ((-3 + 2) > (-9 * -5 + 4 * 1))))) or ((-4 - -10) == (1 * 0)) or ((not not ((十二月有31天。) or (泰坦尼克号沉没发生在1922年。))) and (not (not not (瑞士的首都是巴黎。)))))\nB. ((not (捷克的首都是布加勒斯特。)) or (not not (((64的平方根是1。) or ((-7 * 3 + -5 * 2) == (7 + 1))) or ((59能被3整除。) and (1936年奥运会在东京举办。))))) and ((土耳其的货币是里拉。) and ((((20 - -12) > (3 ** 3)) or (鱼有8条腿。)) or ((美国宣布独立发生在1776年。) and ((-20 - -16) != (6 * 2 + -9 * -9))))) and (not not ((not (not not ((11 - 14) <= (0 * 1 + -9 * 1)))) and (not not ((-5 + 8) <= (18 + -11) <= (4 + 17))) and ((-5 - -17) == (9 * -3 - -4 * 7))))\nC. ((not not ((((-8 + -13) < (18 * 17)) and ((-18 - -7) != (20 + -6))) or ((南非位于非洲。) and ((-16 + -9) != (17 - 8))))) or (水星是距离太阳第2近的行星。) or ((狮子是哺乳动物。) and (not not ((5 - -20) > (-1 - 7))))) or ((not not ((-9 * 0 + 6 * -7) < (3 + -3))) and (not not (not not ((5 ** 1) <= (5 + 15))))) or ((not not ((19 - -8) >= (-19 + -8))) or (((5 + -20) >= (6 * 1)) and (1956年奥运会在墨尔本举办。) and ((2 * 18) != (41 % 6))))\nD. not (not not (not not ((not not (德国位于欧洲。)) or ((氧的化学符号是O。) or (太平洋是最大的海洋。)))))\nE. not not (((not (not ((5 ** 3) == (21 % 5)))) and ((16 + 3) == (-5 * -20))) or (((-2 - -1) != (11 + -6)) and ((13 * -18) < (20 - 9))))\nF. not not ((((((16 * -1) <= (12 % 2)) or (越南的货币是奈拉。)) and (not ((-13 * -10) < (-4 + 10) < (-16 + 12)))) and ((青蛙有4条腿。) or ((-9 + 15) > (-8 * 4 * -7 * 1))) and ((4 * -11) < (9 + 16))) or (not not (哥伦比亚位于亚洲。)))\nG. (((((1924年是闰年。) or ((0 * -17) <= (-2 - 5) <= (20 + -5))) or ((24 % 8) == (9 * -1 + -6 * 1))) or (((越南的货币是越南盾。) and (2012年奥运会在雅典举办。)) and (汞在常温下是液体。))) or ((-20 - -12) < (4 + 20)) or (((5 + -13) <= (17 % 5) <= (-7 - 14)) and (印度尼西亚位于非洲。) and (十二月有31天。))) or (not not (((16 - 1) > (6 + 12)) and (not ((-2 * 5 + 7 * 0) >= (6 * 7 + 8 * 10))))) or (not (((not (2029年是闰年。)) or (中国长城是在一年内建成的。)) and ((4 - 16) < (-13 * -4))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 81790629,
"true_count": 5
},
"seed": 81790629,
"task_id": 681790629,
"task_type": "boolean_expressions"
} |
logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. (((not ((((1 ** 1) >= (-8 * 7 - -7 * 6)) or (丹麦的首都是波哥大。)) and (not not ((-3 + -10) < (2 ** 3))))) and (((-14 * 7) == (-14 + 10)) and (not ((1956年奥运会在里约热内卢举办。) or ((-7 + -16) > (18 + 11)))))) and (not not (((not not (青蛙有8条腿。)) and (企鹅能飞翔。)) and (not ((瑞典的货币是里亚尔。) and (马来西亚的货币是林吉特。)))))) or (not not (not (not not (((乌克兰的首都是北京。) or (德国位于非洲。)) and (((1 * -5 + 10 * 9) >= (-6 * -2 * 3 * -4)) or ((29 % 9) < (5 * 8 * 2 * 0) < (4 ** 1)))))))
B. not not (not not (((((蝴蝶有2条腿。) and (钴的化学符号是Co。)) and ((10 % 1) >= (11 % 9))) and (金星是距离太阳第1近的行星。)) and (not ((((-12 - 14) != (-1 * 2 * 4 * 6)) or ((-1 - 1) >= (-16 - -16))) and (not ((-2 + 18) != (-1 - -19)))))))
C. not (not ((((not not ((1 - 4) <= (-6 * -12) <= (4 * -10 + -3 * -5))) or ((1900年奥运会在伦敦举办。) or (月球自己发光。))) and (not ((氖的化学符号是Cr。) and ((5 * 5 - -7 * 8) <= (-1 + -20))))) or (not (((1 ** 3) <= (-9 * 11)) or ((地球是距离太阳第3近的行星。) or (现代奥运会首届举办发生在1896年。))))))
D. not (not (((not not ((英国的货币是里拉。) and (法国大革命开始发生在1789年。))) and (沙特阿拉伯的首都是布宜诺斯艾利斯。)) or ((((一月有31天。) and (阿根廷位于南美洲。)) and ((土耳其的首都是北京。) and ((-7 + -3) < (14 - 5)))) or (not ((9 * -3 - 5 * -5) < (3 * -9 - -8 * -8) < (46 % 10))) or (泰国的货币是泰铢。))))
E. not not (not not (((((10 * -2) < (5 - 10)) and (((-13 + 12) == (-15 + -6)) and ((13 + 4) != (19 + -20)))) or (not not (印度尼西亚的首都是雅加达。)) or ((not not (鱼有8条腿。)) or (not not (地球是距离太阳第3近的行星。)))) and ((not not ((-12 + 3) <= (-9 - 8) <= (-4 + -16))) and ((印度的货币是泰铢。) or ((-1 - -17) == (-16 * -4))) and ((((20 + 17) == (15 + -19)) or ((5 * 9 + 4 * 2) != (-7 * 8 - 6 * -1))) or (not (69能被7整除。))))))
F. not not (not not (((not (((2 * 6) >= (-1 - 11)) or ((-11 * -3) == (7 - 11)))) and ((not not ((16 * 13) <= (48 % 9))) or ((德国位于大洋洲。) or (木星是距离太阳第5近的行星。)))) or (not ((((-12 - -11) < (4 * 4) < (0 * -1)) or ((0 - -14) >= (2 ** 1))) or ((比利时的首都是东京。) and ((-3 * 3 - 2 * -4) < (3 ** 1)))))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 31670210,
"true_count": 2
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. (((not ((((1 ** 1) >= (-8 * 7 - -7 * 6)) or (丹麦的首都是波哥大。)) and (not not ((-3 + -10) < (2 ** 3))))) and (((-14 * 7) == (-14 + 10)) and (not ((1956年奥运会在里约热内卢举办。) or ((-7 + -16) > (18 + 11)))))) and (not not (((not not (青蛙有8条腿。)) and (企鹅能飞翔。)) and (not ((瑞典的货币是里亚尔。) and (马来西亚的货币是林吉特。)))))) or (not not (not (not not (((乌克兰的首都是北京。) or (德国位于非洲。)) and (((1 * -5 + 10 * 9) >= (-6 * -2 * 3 * -4)) or ((29 % 9) < (5 * 8 * 2 * 0) < (4 ** 1)))))))\nB. not not (not not (((((蝴蝶有2条腿。) and (钴的化学符号是Co。)) and ((10 % 1) >= (11 % 9))) and (金星是距离太阳第1近的行星。)) and (not ((((-12 - 14) != (-1 * 2 * 4 * 6)) or ((-1 - 1) >= (-16 - -16))) and (not ((-2 + 18) != (-1 - -19)))))))\nC. not (not ((((not not ((1 - 4) <= (-6 * -12) <= (4 * -10 + -3 * -5))) or ((1900年奥运会在伦敦举办。) or (月球自己发光。))) and (not ((氖的化学符号是Cr。) and ((5 * 5 - -7 * 8) <= (-1 + -20))))) or (not (((1 ** 3) <= (-9 * 11)) or ((地球是距离太阳第3近的行星。) or (现代奥运会首届举办发生在1896年。))))))\nD. not (not (((not not ((英国的货币是里拉。) and (法国大革命开始发生在1789年。))) and (沙特阿拉伯的首都是布宜诺斯艾利斯。)) or ((((一月有31天。) and (阿根廷位于南美洲。)) and ((土耳其的首都是北京。) and ((-7 + -3) < (14 - 5)))) or (not ((9 * -3 - 5 * -5) < (3 * -9 - -8 * -8) < (46 % 10))) or (泰国的货币是泰铢。))))\nE. not not (not not (((((10 * -2) < (5 - 10)) and (((-13 + 12) == (-15 + -6)) and ((13 + 4) != (19 + -20)))) or (not not (印度尼西亚的首都是雅加达。)) or ((not not (鱼有8条腿。)) or (not not (地球是距离太阳第3近的行星。)))) and ((not not ((-12 + 3) <= (-9 - 8) <= (-4 + -16))) and ((印度的货币是泰铢。) or ((-1 - -17) == (-16 * -4))) and ((((20 + 17) == (15 + -19)) or ((5 * 9 + 4 * 2) != (-7 * 8 - 6 * -1))) or (not (69能被7整除。))))))\nF. not not (not not (((not (((2 * 6) >= (-1 - 11)) or ((-11 * -3) == (7 - 11)))) and ((not not ((16 * 13) <= (48 % 9))) or ((德国位于大洋洲。) or (木星是距离太阳第5近的行星。)))) or (not ((((-12 - -11) < (4 * 4) < (0 * -1)) or ((0 - -14) >= (2 ** 1))) or ((比利时的首都是东京。) and ((-3 * 3 - 2 * -4) < (3 ** 1)))))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 31670210,
"true_count": 2
},
"seed": 31670210,
"task_id": 631670210,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (-10 + -6) < (6 * -10 * 9 * -8) < (8 * 1)
B. not (not not (The capital of Spain is Seoul.))
C. ((The currency of Saudi Arabia is the Euro.) or (There are 28 days in July.)) and (not ((5 * -4 + 9 * 6) > (-4 * -4 + 4 * 5)))
D. ((18 * 2) < (15 - -6)) and ((Germany is in Europe.) or ((1 ** 1) > (-1 * -7 + -9 * -1)))
E. (Italy is in Europe.) and (((3 % 5) > (10 * 3 * 9 * -7)) or ((-7 - -5) == (15 + 9)))
F. not ((A chicken has 2 legs.) and ((-3 * 3 + 5 * -10) <= (9 * 9 - -9 * -3)))
G. (((4 * -8 - -4 * 8) <= (-14 * -11)) and ((-18 + 10) >= (16 - -6))) or ((The capital of Japan is Bucharest.) and (2010 is a leap year.))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 91363872,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. (-10 + -6) < (6 * -10 * 9 * -8) < (8 * 1)\nB. not (not not (The capital of Spain is Seoul.))\nC. ((The currency of Saudi Arabia is the Euro.) or (There are 28 days in July.)) and (not ((5 * -4 + 9 * 6) > (-4 * -4 + 4 * 5)))\nD. ((18 * 2) < (15 - -6)) and ((Germany is in Europe.) or ((1 ** 1) > (-1 * -7 + -9 * -1)))\nE. (Italy is in Europe.) and (((3 % 5) > (10 * 3 * 9 * -7)) or ((-7 - -5) == (15 + 9)))\nF. not ((A chicken has 2 legs.) and ((-3 * 3 + 5 * -10) <= (9 * 9 - -9 * -3)))\nG. (((4 * -8 - -4 * 8) <= (-14 * -11)) and ((-18 + 10) >= (16 - -6))) or ((The capital of Japan is Bucharest.) and (2010 is a leap year.))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 91363872,
"true_count": 2
},
"seed": 91363872,
"task_id": 691363872,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. 美国位于亚洲。
B. not not (((0 + -15) <= (-20 * -7)) and (土星是距离太阳第2近的行星。))
C. (((8 - -3) < (-16 * 12)) or ((18 * -14) > (8 * -10 * -2 * -7))) and (钛的化学符号是Al。)
D. (((7 - -18) > (33 % 10)) and ((-17 - 16) < (-12 - -18))) and ((5 * -13) < (-8 + 3))
E. (not (锡的化学符号是Sn。)) and (((-9 + -15) < (-14 + 0) < (17 + -19)) and (80能被2整除。))
F. 地球是距离太阳第3近的行星。
G. (5 + 17) != (0 * -9 + 0 * -1)
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "D,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 8184971,
"true_count": 3
},
"question": "研究以下逻辑语句：\n\nA. 美国位于亚洲。\nB. not not (((0 + -15) <= (-20 * -7)) and (土星是距离太阳第2近的行星。))\nC. (((8 - -3) < (-16 * 12)) or ((18 * -14) > (8 * -10 * -2 * -7))) and (钛的化学符号是Al。)\nD. (((7 - -18) > (33 % 10)) and ((-17 - 16) < (-12 - -18))) and ((5 * -13) < (-8 + 3))\nE. (not (锡的化学符号是Sn。)) and (((-9 + -15) < (-14 + 0) < (17 + -19)) and (80能被2整除。))\nF. 地球是距离太阳第3近的行星。\nG. (5 + 17) != (0 * -9 + 0 * -1)\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 8184971,
"true_count": 3
},
"seed": 8184971,
"task_id": 608184971,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not not (((-18 * -13) <= (0 + 18)) and ((17 + 20) <= (11 + -4) <= (-16 * -2)))) or (not not (1959 is a leap year.)) or ((Alcohol is a liquid at room temperature.) and (not (A fish has 10 legs.)))
B. (Mercury is the 1st planet from the Sun.) and (The capital of Russia is Moscow.)
C. (not ((United States is in Oceania.) and ((20 * -5) < (5 ** 1)))) and ((not not ((20 % 10) != (6 - -3))) or ((The 1928 Olympics were held in Berlin.) and ((8 * -6 * -6 * 1) > (18 * -13))))
D. ((6 + -12) > (3 * 0 + -6 * 0)) and ((-14 + -2) != (-4 * -10 * -1 * 4))
E. ((6 * -18) >= (0 * 0)) and (((10 + -1) != (-6 * 1 - -9 * -6)) and (((1 * -4 + -2 * -2) != (13 * -5)) or (The 1996 Olympics were held in Atlanta.)))
F. (((19 + -7) <= (1 ** 1)) and (Whales are fish.)) or (Mars is the 4th planet from the Sun.)
G. (not not (not not (2043 is a leap year.))) and (((26 is less than or equal to 85.) or ((-18 * -6) >= (48 % 4))) and (not (Spiders are insects.)))
H. not not ((not not (Earth is the 3rd planet from the Sun.)) and (not (Gold is a liquid at room temperature.)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 29048229,
"true_count": 5
},
"question": "Below are several boolean expressions:\n\nA. (not not (((-18 * -13) <= (0 + 18)) and ((17 + 20) <= (11 + -4) <= (-16 * -2)))) or (not not (1959 is a leap year.)) or ((Alcohol is a liquid at room temperature.) and (not (A fish has 10 legs.)))\nB. (Mercury is the 1st planet from the Sun.) and (The capital of Russia is Moscow.)\nC. (not ((United States is in Oceania.) and ((20 * -5) < (5 ** 1)))) and ((not not ((20 % 10) != (6 - -3))) or ((The 1928 Olympics were held in Berlin.) and ((8 * -6 * -6 * 1) > (18 * -13))))\nD. ((6 + -12) > (3 * 0 + -6 * 0)) and ((-14 + -2) != (-4 * -10 * -1 * 4))\nE. ((6 * -18) >= (0 * 0)) and (((10 + -1) != (-6 * 1 - -9 * -6)) and (((1 * -4 + -2 * -2) != (13 * -5)) or (The 1996 Olympics were held in Atlanta.)))\nF. (((19 + -7) <= (1 ** 1)) and (Whales are fish.)) or (Mars is the 4th planet from the Sun.)\nG. (not not (not not (2043 is a leap year.))) and (((26 is less than or equal to 85.) or ((-18 * -6) >= (48 % 4))) and (not (Spiders are insects.)))\nH. not not ((not not (Earth is the 3rd planet from the Sun.)) and (not (Gold is a liquid at room temperature.)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 29048229,
"true_count": 5
},
"seed": 29048229,
"task_id": 629048229,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (36 % 8) <= (-7 - -16) <= (19 * -14)
B. 铜的化学符号是Ag。
C. (18 * -20) <= (29 % 6) <= (18 - 6)
D. 1912年奥运会在雅典举办。
E. (((13 + 0) < (-14 * -2) < (49 % 5)) and ((3 ** 1) <= (4 ** 2) <= (-8 + -12))) or ((青蛙有4条腿。) or ((-20 - -4) >= (-3 * 6 * 9 * -4)))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 48637673,
"true_count": 2
},
"question": "评估以下每个表达式：\n\nA. (36 % 8) <= (-7 - -16) <= (19 * -14)\nB. 铜的化学符号是Ag。\nC. (18 * -20) <= (29 % 6) <= (18 - 6)\nD. 1912年奥运会在雅典举办。\nE. (((13 + 0) < (-14 * -2) < (49 % 5)) and ((3 ** 1) <= (4 ** 2) <= (-8 + -12))) or ((青蛙有4条腿。) or ((-20 - -4) >= (-3 * 6 * 9 * -4)))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 48637673,
"true_count": 2
},
"seed": 48637673,
"task_id": 648637673,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. 1921 is a leap year.
B. (((10 * -14) == (15 - 10)) or ((-5 + 3) > (10 * 0 * 9 * -10))) or (((-6 + -19) < (3 * 1) < (13 - 9)) and ((5 ** 1) > (8 * 1 + -3 * -2)))
C. (3 - -12) >= (5 ** 3)
D. The French Revolution began occurred in 1789.
E. ((The 1956 Olympics were held in Melbourne.) or ((-4 * 4) < (-17 - 4) < (7 * -14))) and (There are 30 days in September.)
F. ((2 ** 3) < (6 - 5)) or (((18 - 19) == (-10 * -3)) or ((-7 * 4) >= (-3 - -7)))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 90983261,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. 1921 is a leap year.\nB. (((10 * -14) == (15 - 10)) or ((-5 + 3) > (10 * 0 * 9 * -10))) or (((-6 + -19) < (3 * 1) < (13 - 9)) and ((5 ** 1) > (8 * 1 + -3 * -2)))\nC. (3 - -12) >= (5 ** 3)\nD. The French Revolution began occurred in 1789.\nE. ((The 1956 Olympics were held in Melbourne.) or ((-4 * 4) < (-17 - 4) < (7 * -14))) and (There are 30 days in September.)\nF. ((2 ** 3) < (6 - 5)) or (((18 - 19) == (-10 * -3)) or ((-7 * 4) >= (-3 - -7)))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 90983261,
"true_count": 2
},
"seed": 90983261,
"task_id": 690983261,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. There are 31 days in January.
B. not not ((24 % 5) <= (20 * 9) <= (3 % 9))
C. New Zealand is in North America.
D. not not ((The 1900 Olympics were held in Paris.) and (There are 31 days in November.))
E. (((-13 + 17) >= (19 + 9)) and ((16 - 17) <= (3 ** 3))) and (The currency of Malaysia is the Dollar.)
F. not (The chemical symbol for Silver is Si.)
G. (((7 * 7 * -5 * -4) == (17 % 7)) or (Sharks are mammals.)) or (((0 - 20) < (1 + -2)) and ((-2 * 4 + 5 * -2) == (-6 * 0 * -5 * 4)))
H. ((-16 * -2) > (12 + -16)) or ((13 + 18) < (19 - -14) < (-20 - 15))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 33434638,
"true_count": 3
},
"question": "Analyze these boolean expressions:\n\nA. There are 31 days in January.\nB. not not ((24 % 5) <= (20 * 9) <= (3 % 9))\nC. New Zealand is in North America.\nD. not not ((The 1900 Olympics were held in Paris.) and (There are 31 days in November.))\nE. (((-13 + 17) >= (19 + 9)) and ((16 - 17) <= (3 ** 3))) and (The currency of Malaysia is the Dollar.)\nF. not (The chemical symbol for Silver is Si.)\nG. (((7 * 7 * -5 * -4) == (17 % 7)) or (Sharks are mammals.)) or (((0 - 20) < (1 + -2)) and ((-2 * 4 + 5 * -2) == (-6 * 0 * -5 * 4)))\nH. ((-16 * -2) > (12 + -16)) or ((13 + 18) < (19 - -14) < (-20 - 15))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 33434638,
"true_count": 3
},
"seed": 33434638,
"task_id": 633434638,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (-7 * 8 + 1 * 6) < (-7 - -7) < (9 + 8)
B. (not not (马有4条腿。)) or ((智利的首都是圣地亚哥。) or (银的化学符号是Pt。))
C. not not (((-2 * 1 + -4 * 2) <= (2 + 18)) or (火星是距离太阳第4近的行星。))
D. (not not ((9 + 2) >= (-15 - -8))) and ((德国的首都是里斯本。) or ((9 * -8 * 2 * 7) < (-20 - -2)))
E. (西班牙的首都是惠灵顿。) and (not (铅的化学符号是K。))
F. (((-18 * 12) > (-5 + 19)) or ((-12 + -11) > (50 % 10))) or (not not (比利时的首都是布鲁塞尔。))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,B,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 16072769,
"true_count": 5
},
"question": "下面是几个布尔表达式：\n\nA. (-7 * 8 + 1 * 6) < (-7 - -7) < (9 + 8)\nB. (not not (马有4条腿。)) or ((智利的首都是圣地亚哥。) or (银的化学符号是Pt。))\nC. not not (((-2 * 1 + -4 * 2) <= (2 + 18)) or (火星是距离太阳第4近的行星。))\nD. (not not ((9 + 2) >= (-15 - -8))) and ((德国的首都是里斯本。) or ((9 * -8 * 2 * 7) < (-20 - -2)))\nE. (西班牙的首都是惠灵顿。) and (not (铅的化学符号是K。))\nF. (((-18 * 12) > (-5 + 19)) or ((-12 + -11) > (50 % 10))) or (not not (比利时的首都是布鲁塞尔。))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 16072769,
"true_count": 5
},
"seed": 16072769,
"task_id": 616072769,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not ((铁在常温下是液体。) or ((9 + -10) >= (-15 * 2)))
B. (((15 * 16) == (1 ** 1)) or ((-10 * -8 - 8 * -5) != (-1 - 10))) and (not (苏联解体发生在1992年。))
C. not not (泰国的首都是哈瓦那。)
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 62143132,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. not ((铁在常温下是液体。) or ((9 + -10) >= (-15 * 2)))\nB. (((15 * 16) == (1 ** 1)) or ((-10 * -8 - 8 * -5) != (-1 - 10))) and (not (苏联解体发生在1992年。))\nC. not not (泰国的首都是哈瓦那。)\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 62143132,
"true_count": 1
},
"seed": 62143132,
"task_id": 662143132,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not ((((-18 - 13) != (-19 - -15)) or (Venus is the 6th planet from the Sun.)) or (The 1928 Olympics were held in Amsterdam.))
B. not not (The chemical symbol for Magnesium is Hg.)
C. not (((A frog has 8 legs.) and ((4 ** 3) > (10 + 12))) or (not (Electricity flows faster than light.)))
D. not (The chemical symbol for Chlorine is O.)
E. ((15 + 9) >= (-15 * 0)) and ((Neptune is the 4th planet from the Sun.) or (not ((2 ** 2) <= (-6 * 1 + -8 * -4))))
F. not not ((-2 * 5) >= (-13 * 3))
G. ((((-5 * 18) >= (3 ** 2)) or ((5 + 19) != (17 + -18))) or (((34 % 1) >= (2 ** 3)) and (United States is in North America.))) or ((-19 - 1) < (-14 + 10)) or ((((8 * 4 * -7 * -6) == (2 ** 3)) or ((14 - 1) > (2 ** 2))) or ((48 % 4) <= (3 * 18)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,D,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 42993199,
"true_count": 4
},
"question": "Examine these expressions:\n\nA. not not ((((-18 - 13) != (-19 - -15)) or (Venus is the 6th planet from the Sun.)) or (The 1928 Olympics were held in Amsterdam.))\nB. not not (The chemical symbol for Magnesium is Hg.)\nC. not (((A frog has 8 legs.) and ((4 ** 3) > (10 + 12))) or (not (Electricity flows faster than light.)))\nD. not (The chemical symbol for Chlorine is O.)\nE. ((15 + 9) >= (-15 * 0)) and ((Neptune is the 4th planet from the Sun.) or (not ((2 ** 2) <= (-6 * 1 + -8 * -4))))\nF. not not ((-2 * 5) >= (-13 * 3))\nG. ((((-5 * 18) >= (3 ** 2)) or ((5 + 19) != (17 + -18))) or (((34 % 1) >= (2 ** 3)) and (United States is in North America.))) or ((-19 - 1) < (-14 + 10)) or ((((8 * 4 * -7 * -6) == (2 ** 3)) or ((14 - 1) > (2 ** 2))) or ((48 % 4) <= (3 * 18)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 42993199,
"true_count": 4
},
"seed": 42993199,
"task_id": 642993199,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not not (((The chemical symbol for Oxygen is N.) and ((48 % 4) != (-18 * 14))) or (not not ((-17 + 7) > (16 * -12))))
B. not ((44 % 2) >= (-6 - -10))
C. not not ((-5 + 19) <= (13 % 7) <= (10 + 12))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 4228339,
"true_count": 2
},
"question": "Consider the following logical expressions:\n\nA. not not (((The chemical symbol for Oxygen is N.) and ((48 % 4) != (-18 * 14))) or (not not ((-17 + 7) > (16 * -12))))\nB. not ((44 % 2) >= (-6 - -10))\nC. not not ((-5 + 19) <= (13 % 7) <= (10 + 12))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 4228339,
"true_count": 2
},
"seed": 4228339,
"task_id": 604228339,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((36 % 10) < (-4 * -9)) or (((-14 * -20) < (-6 * 8 + -2 * -6)) or ((There are 28 days in July.) or (A crab has 10 legs.)))
B. ((((-10 - -16) <= (-19 + -6)) or (Mars is the closest planet to the Sun.)) or (((-17 - 16) < (-5 - 15)) or (Spiders are insects.))) and (Sharks are mammals.) and ((not (18 is a Fibonacci number.)) or ((12 + -11) >= (16 - -15)))
C. ((not ((1 ** 2) <= (-11 * 10))) or ((Mercury is the 1st planet from the Sun.) or (The capital of Sweden is Stockholm.))) and ((30 % 10) > (-5 * 9))
D. (((-5 - 8) == (-18 * -16)) or (((1 * 4 + 7 * -3) < (-4 * -1)) or (The Moon orbits the Earth.))) and (((2008 is a leap year.) or (There are 30 days in September.)) or ((-2 - 8) <= (-4 - 4) <= (-3 * -10 + -6 * 7)))
E. ((1 ** 1) > (13 * 6)) and ((The capital of Netherlands is Abuja.) and ((-7 * 9 - -2 * -9) != (-12 * 8)))
F. ((((5 ** 2) <= (5 % 5) <= (-13 - 6)) or ((5 * -16) < (-12 + 16))) and (not not (Jupiter is the 5th planet from the Sun.))) and (Vietnam is in Asia.)
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 81593010,
"true_count": 4
},
"question": "Given the following boolean expressions:\n\nA. ((36 % 10) < (-4 * -9)) or (((-14 * -20) < (-6 * 8 + -2 * -6)) or ((There are 28 days in July.) or (A crab has 10 legs.)))\nB. ((((-10 - -16) <= (-19 + -6)) or (Mars is the closest planet to the Sun.)) or (((-17 - 16) < (-5 - 15)) or (Spiders are insects.))) and (Sharks are mammals.) and ((not (18 is a Fibonacci number.)) or ((12 + -11) >= (16 - -15)))\nC. ((not ((1 ** 2) <= (-11 * 10))) or ((Mercury is the 1st planet from the Sun.) or (The capital of Sweden is Stockholm.))) and ((30 % 10) > (-5 * 9))\nD. (((-5 - 8) == (-18 * -16)) or (((1 * 4 + 7 * -3) < (-4 * -1)) or (The Moon orbits the Earth.))) and (((2008 is a leap year.) or (There are 30 days in September.)) or ((-2 - 8) <= (-4 - 4) <= (-3 * -10 + -6 * 7)))\nE. ((1 ** 1) > (13 * 6)) and ((The capital of Netherlands is Abuja.) and ((-7 * 9 - -2 * -9) != (-12 * 8)))\nF. ((((5 ** 2) <= (5 % 5) <= (-13 - 6)) or ((5 * -16) < (-12 + 16))) and (not not (Jupiter is the 5th planet from the Sun.))) and (Vietnam is in Asia.)\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 81593010,
"true_count": 4
},
"seed": 81593010,
"task_id": 681593010,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not (((-5 * 2 + 0 * 1) > (29 % 6)) and (Mars is the 5th planet from the Sun.))
B. (France is in Africa.) and (((1 * 6 + 5 * -6) >= (0 - -2)) and (46 is less than or equal to 91.))
C. ((There are 30 days in September.) and (There are 29 days in May.)) or (10 is an even number.)
D. not ((10 * 5 + 0 * 8) == (15 - 3))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 27561094,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. not not (((-5 * 2 + 0 * 1) > (29 % 6)) and (Mars is the 5th planet from the Sun.))\nB. (France is in Africa.) and (((1 * 6 + 5 * -6) >= (0 - -2)) and (46 is less than or equal to 91.))\nC. ((There are 30 days in September.) and (There are 29 days in May.)) or (10 is an even number.)\nD. not ((10 * 5 + 0 * 8) == (15 - 3))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 27561094,
"true_count": 2
},
"seed": 27561094,
"task_id": 627561094,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. not ((not ((((4 * 20) == (-6 + 20)) or (墨西哥的货币是兹罗提。)) or ((智利位于南美洲。) and ((3 ** 3) >= (5 * -11))))) or (not not (((3 * 3 * -6 * -4) <= (10 - -16)) and (哥伦比亚的首都是布拉格。))))
B. ((not not (((-13 - 12) != (-2 * 10 - 4 * 1)) and (not not (南非的货币是欧元。)))) or (not (((水在常温下是液体。) or (1902年是闰年。)) and ((2008年奥运会在安特卫普举办。) and ((-6 * -14) >= (1 + -10)))))) and (((not (尼日利亚的货币是英镑。)) and ((((-17 + 5) <= (9 * -3 + 5 * 5)) or ((40 % 5) > (-7 * -10 - 3 * 0))) or ((马来西亚的货币是林吉特。) or ((8 + 15) < (-6 * 4))))) or (新加坡的首都是新加坡。) or (((((20 - -11) <= (1 ** 2) <= (-14 * 6)) or (金星是距离太阳第2近的行星。)) and ((智利位于南美洲。) and (哥伦比亚的货币是韩元。))) or ((-13 - 12) == (3 + 10))))
C. (((((1920年奥运会在安特卫普举办。) or (越南位于欧洲。)) or (汞的化学符号是Hg。)) and ((-6 - -5) <= (5 * -5 * 4 * 7))) and ((((瑞典的货币是美元。) and ((0 * -8 + -7 * -8) > (1 ** 2))) and ((-16 * 13) > (-4 * 4 + 7 * -6))) or (not ((5 ** 2) < (-18 + -7))))) and (not not (not not (((12 % 8) < (20 - 3)) or ((9 % 10) > (-10 * 7)))))
D. not not ((not not ((墨西哥位于大洋洲。) and (((4 - -5) <= (14 + -6)) and (猫是昆虫。)))) and ((not not ((79能被11整除。) and (地球绕太阳运转。))) and (((48 % 10) != (-4 + 17)) and (意大利位于欧洲。)) and (1948年奥运会在柏林举办。)))
E. (((铁在常温下是固体。) or (699是斐波那契数。)) or (not (not not ((中国的货币是人民币。) and ((-18 + 14) != (-12 + -3)))))) and (((尼日利亚的首都是莫斯科。) or (欧盟的货币是欧元。)) or (not not ((-15 - 14) <= (18 + 3))))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 44497050,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. not ((not ((((4 * 20) == (-6 + 20)) or (墨西哥的货币是兹罗提。)) or ((智利位于南美洲。) and ((3 ** 3) >= (5 * -11))))) or (not not (((3 * 3 * -6 * -4) <= (10 - -16)) and (哥伦比亚的首都是布拉格。))))\nB. ((not not (((-13 - 12) != (-2 * 10 - 4 * 1)) and (not not (南非的货币是欧元。)))) or (not (((水在常温下是液体。) or (1902年是闰年。)) and ((2008年奥运会在安特卫普举办。) and ((-6 * -14) >= (1 + -10)))))) and (((not (尼日利亚的货币是英镑。)) and ((((-17 + 5) <= (9 * -3 + 5 * 5)) or ((40 % 5) > (-7 * -10 - 3 * 0))) or ((马来西亚的货币是林吉特。) or ((8 + 15) < (-6 * 4))))) or (新加坡的首都是新加坡。) or (((((20 - -11) <= (1 ** 2) <= (-14 * 6)) or (金星是距离太阳第2近的行星。)) and ((智利位于南美洲。) and (哥伦比亚的货币是韩元。))) or ((-13 - 12) == (3 + 10))))\nC. (((((1920年奥运会在安特卫普举办。) or (越南位于欧洲。)) or (汞的化学符号是Hg。)) and ((-6 - -5) <= (5 * -5 * 4 * 7))) and ((((瑞典的货币是美元。) and ((0 * -8 + -7 * -8) > (1 ** 2))) and ((-16 * 13) > (-4 * 4 + 7 * -6))) or (not ((5 ** 2) < (-18 + -7))))) and (not not (not not (((12 % 8) < (20 - 3)) or ((9 % 10) > (-10 * 7)))))\nD. not not ((not not ((墨西哥位于大洋洲。) and (((4 - -5) <= (14 + -6)) and (猫是昆虫。)))) and ((not not ((79能被11整除。) and (地球绕太阳运转。))) and (((48 % 10) != (-4 + 17)) and (意大利位于欧洲。)) and (1948年奥运会在柏林举办。)))\nE. (((铁在常温下是固体。) or (699是斐波那契数。)) or (not (not not ((中国的货币是人民币。) and ((-18 + 14) != (-12 + -3)))))) and (((尼日利亚的首都是莫斯科。) or (欧盟的货币是欧元。)) or (not not ((-15 - 14) <= (18 + 3))))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 44497050,
"true_count": 3
},
"seed": 44497050,
"task_id": 644497050,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((not (((-4 * 5 * 5 * -7) <= (0 * 5 - -4 * -2) <= (6 + -4)) and (not (1904年奥运会在圣路易斯举办。)))) and ((not ((一月有28天。) and ((-14 + 10) < (1 * 7 + -7 * -8)))) and (((1952年奥运会在东京举办。) and (肯尼亚的首都是基辅。)) and ((莱特兄弟首次飞行发生在1902年。) and ((9 * 9) >= (2 - 10)))))) and ((not not ((5 ** 1) != (5 ** 2))) or ((((-20 - 3) <= (41 % 3) <= (-10 * 9 + 5 * 3)) and (((5 ** 2) == (0 + -11)) and ((46 % 6) > (-17 * -2)))) and (not not (铀的化学符号是Si。)) and ((((2 - -10) != (4 * 6 - -1 * 1)) or (蚂蚁有8条腿。)) and (1948年奥运会在伦敦举办。))))
B. (not not (not (美国宣布独立发生在1776年。))) and (((not (氯的化学符号是Fe。)) and ((not (俄罗斯的货币是卢布。)) or (731是斐波那契数。))) or (not (((鲸鱼是哺乳动物。) or ((9 * -4) <= (3 % 3))) and (((8 * 3 * 5 * -2) <= (-19 * -7) <= (20 - 14)) and (天王星是距离太阳第5近的行星。)))))
C. (not (not (not (not not (钠的化学符号是C。))))) and (((三文鱼是哺乳动物。) and (((-5 * -19) >= (-14 * 19)) or (秘鲁位于南美洲。))) or (((-3 * 3 + -2 * 9) > (17 - 3)) and (美国宣布独立发生在1781年。)) or ((((-17 - -8) <= (8 * -9 + 10 * -1)) or (1932年奥运会在雅典举办。)) and (not (沙特阿拉伯位于亚洲。)))) and (not not (not ((34 % 10) != (9 * -8 - -3 * 0))))
D. (((二氧化碳在常温下是固体。) or ((-20 - 11) <= (-10 * -2 - -4 * 2))) or (((16 % 10) < (-12 + -20)) and ((((37 % 3) != (-15 - 6)) and (以色列的货币是澳元。)) and (韩国的货币是克朗。)))) or (not ((韩国位于南美洲。) and (((3 ** 1) > (-4 * 2 + 1 * 0)) and ((5 ** 1) < (3 * -12))) and ((341是完全平方数。) and ((-1 * 8 - 0 * -1) == (18 + 17)))))
E. (not (((哥伦布到达美洲发生在1491年。) or (not not (1908年奥运会在亚特兰大举办。))) and ((49 % 1) <= (12 * -10)))) and (((1904年奥运会在亚特兰大举办。) and (not not ((地球绕太阳运转。) or (韩国位于亚洲。)))) or (((-19 + -18) <= (2 * -13)) or (not not (第二次世界大战结束发生在1944年。))) or (((土星是距离太阳第6近的行星。) and (((9 * -8 * 7 * 0) > (7 * -19)) and ((10 * -14) <= (7 * -5 - 3 * 7) <= (14 + 10)))) and ((((-13 - -13) >= (6 + 15)) and (2020年奥运会在雅典举办。)) and (not (74能被8整除。)))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 93853406,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. ((not (((-4 * 5 * 5 * -7) <= (0 * 5 - -4 * -2) <= (6 + -4)) and (not (1904年奥运会在圣路易斯举办。)))) and ((not ((一月有28天。) and ((-14 + 10) < (1 * 7 + -7 * -8)))) and (((1952年奥运会在东京举办。) and (肯尼亚的首都是基辅。)) and ((莱特兄弟首次飞行发生在1902年。) and ((9 * 9) >= (2 - 10)))))) and ((not not ((5 ** 1) != (5 ** 2))) or ((((-20 - 3) <= (41 % 3) <= (-10 * 9 + 5 * 3)) and (((5 ** 2) == (0 + -11)) and ((46 % 6) > (-17 * -2)))) and (not not (铀的化学符号是Si。)) and ((((2 - -10) != (4 * 6 - -1 * 1)) or (蚂蚁有8条腿。)) and (1948年奥运会在伦敦举办。))))\nB. (not not (not (美国宣布独立发生在1776年。))) and (((not (氯的化学符号是Fe。)) and ((not (俄罗斯的货币是卢布。)) or (731是斐波那契数。))) or (not (((鲸鱼是哺乳动物。) or ((9 * -4) <= (3 % 3))) and (((8 * 3 * 5 * -2) <= (-19 * -7) <= (20 - 14)) and (天王星是距离太阳第5近的行星。)))))\nC. (not (not (not (not not (钠的化学符号是C。))))) and (((三文鱼是哺乳动物。) and (((-5 * -19) >= (-14 * 19)) or (秘鲁位于南美洲。))) or (((-3 * 3 + -2 * 9) > (17 - 3)) and (美国宣布独立发生在1781年。)) or ((((-17 - -8) <= (8 * -9 + 10 * -1)) or (1932年奥运会在雅典举办。)) and (not (沙特阿拉伯位于亚洲。)))) and (not not (not ((34 % 10) != (9 * -8 - -3 * 0))))\nD. (((二氧化碳在常温下是固体。) or ((-20 - 11) <= (-10 * -2 - -4 * 2))) or (((16 % 10) < (-12 + -20)) and ((((37 % 3) != (-15 - 6)) and (以色列的货币是澳元。)) and (韩国的货币是克朗。)))) or (not ((韩国位于南美洲。) and (((3 ** 1) > (-4 * 2 + 1 * 0)) and ((5 ** 1) < (3 * -12))) and ((341是完全平方数。) and ((-1 * 8 - 0 * -1) == (18 + 17)))))\nE. (not (((哥伦布到达美洲发生在1491年。) or (not not (1908年奥运会在亚特兰大举办。))) and ((49 % 1) <= (12 * -10)))) and (((1904年奥运会在亚特兰大举办。) and (not not ((地球绕太阳运转。) or (韩国位于亚洲。)))) or (((-19 + -18) <= (2 * -13)) or (not not (第二次世界大战结束发生在1944年。))) or (((土星是距离太阳第6近的行星。) and (((9 * -8 * 7 * 0) > (7 * -19)) and ((10 * -14) <= (7 * -5 - 3 * 7) <= (14 + 10)))) and ((((-13 - -13) >= (6 + 15)) and (2020年奥运会在雅典举办。)) and (not (74能被8整除。)))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 93853406,
"true_count": 2
},
"seed": 93853406,
"task_id": 693853406,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((not not ((359是完全平方数。) and (二月有28天。))) or ((((德国位于大洋洲。) and ((-19 * -6) != (31 % 2))) and (not not (36的平方根是5。))) and (53是偶数。))) and ((not (((19 * -9) > (18 * 19)) or ((铜在常温下是固体。) and ((20 - -18) == (1 ** 2))))) or (not not (((六月有30天。) and (氧气对人类生存是必需的。)) and ((牛是哺乳动物。) or ((-1 * -7 * -2 * -3) > (-9 * 12))))))
B. ((not not ((氮的化学符号是N。) and ((12 * -15) == (8 * 1 * -10 * -8)))) or (not (not not ((1992年奥运会在巴塞罗那举办。) and ((8 * -1 - -5 * 4) <= (1 - 13) <= (4 * 5 - 4 * 3)))))) or (((((21 % 6) > (-18 + 8)) and (锰的化学符号是Mn。)) or (not not (not not (52能被5整除。)))) and ((南非的货币是兰特。) or (not not (美国宣布独立发生在1774年。)) or (not (((18 - -13) <= (-10 * 8 + -7 * -4) <= (0 * -7)) or ((1 ** 2) < (4 * 0) < (10 - 5))))))
C. (((((1928年奥运会在阿姆斯特丹举办。) and (墨西哥的货币是新西兰元。)) and ((地球是距离太阳第3近的行星。) and (氮气在常温下是气体。))) and ((77是质数。) or ((1 ** 2) >= (-5 * 8 + 9 * 6))) and ((20 * 19) < (-17 + -12))) or ((((氢的化学符号是H。) or (1959年是闰年。)) and ((9 % 9) <= (-9 + -15))) or (((29 % 2) == (-3 - 17)) or ((17 - -14) <= (-19 + -16))) or (((-4 * -5 * -7 * -4) < (10 % 6)) or ((2053年是闰年。) or ((7 * -15) >= (17 + -11)))))) or (((1912年奥运会在东京举办。) and (钴的化学符号是Ca。)) or (not (((金的化学符号是Au。) or (氦气在常温下是液体。)) or (氦的化学符号是He。))))
D. not ((not not ((巴西位于大洋洲。) and (not not ((3 ** 2) < (36 % 10))))) and ((铀的化学符号是Cr。) and (not not (((12 % 8) >= (1 % 10)) and ((11 - -4) > (48 % 3))))))
E. (((人体有206块骨头。) or (not (((2 ** 2) >= (9 + -2)) and (汞的化学符号是Hg。)))) and ((not not ((-13 * 16) == (-5 - 11))) or ((一月有31天。) and ((澳大利亚位于大洋洲。) and (钠的化学符号是Cu。))))) or (((铁在常温下是固体。) and (not not ((42 % 5) > (-14 * 14)))) and (not (not not (尼日利亚的货币是奈拉。)))) or ((not not (鳕鱼是哺乳动物。)) and ((not not (柏林墙倒塌发生在1989年。)) or ((汞在常温下是液体。) or (1996年是闰年。))) and (not not (not not ((钻石在常温下是液体。) or (乌龟是鸟类。)))))
F. not not ((not (新加坡的首都是新加坡。)) or ((1952年奥运会在伦敦举办。) and ((19 + 20) <= (6 - -13)) and (人类只使用了大脑的10%。)))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 87392843,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. ((not not ((359是完全平方数。) and (二月有28天。))) or ((((德国位于大洋洲。) and ((-19 * -6) != (31 % 2))) and (not not (36的平方根是5。))) and (53是偶数。))) and ((not (((19 * -9) > (18 * 19)) or ((铜在常温下是固体。) and ((20 - -18) == (1 ** 2))))) or (not not (((六月有30天。) and (氧气对人类生存是必需的。)) and ((牛是哺乳动物。) or ((-1 * -7 * -2 * -3) > (-9 * 12))))))\nB. ((not not ((氮的化学符号是N。) and ((12 * -15) == (8 * 1 * -10 * -8)))) or (not (not not ((1992年奥运会在巴塞罗那举办。) and ((8 * -1 - -5 * 4) <= (1 - 13) <= (4 * 5 - 4 * 3)))))) or (((((21 % 6) > (-18 + 8)) and (锰的化学符号是Mn。)) or (not not (not not (52能被5整除。)))) and ((南非的货币是兰特。) or (not not (美国宣布独立发生在1774年。)) or (not (((18 - -13) <= (-10 * 8 + -7 * -4) <= (0 * -7)) or ((1 ** 2) < (4 * 0) < (10 - 5))))))\nC. (((((1928年奥运会在阿姆斯特丹举办。) and (墨西哥的货币是新西兰元。)) and ((地球是距离太阳第3近的行星。) and (氮气在常温下是气体。))) and ((77是质数。) or ((1 ** 2) >= (-5 * 8 + 9 * 6))) and ((20 * 19) < (-17 + -12))) or ((((氢的化学符号是H。) or (1959年是闰年。)) and ((9 % 9) <= (-9 + -15))) or (((29 % 2) == (-3 - 17)) or ((17 - -14) <= (-19 + -16))) or (((-4 * -5 * -7 * -4) < (10 % 6)) or ((2053年是闰年。) or ((7 * -15) >= (17 + -11)))))) or (((1912年奥运会在东京举办。) and (钴的化学符号是Ca。)) or (not (((金的化学符号是Au。) or (氦气在常温下是液体。)) or (氦的化学符号是He。))))\nD. not ((not not ((巴西位于大洋洲。) and (not not ((3 ** 2) < (36 % 10))))) and ((铀的化学符号是Cr。) and (not not (((12 % 8) >= (1 % 10)) and ((11 - -4) > (48 % 3))))))\nE. (((人体有206块骨头。) or (not (((2 ** 2) >= (9 + -2)) and (汞的化学符号是Hg。)))) and ((not not ((-13 * 16) == (-5 - 11))) or ((一月有31天。) and ((澳大利亚位于大洋洲。) and (钠的化学符号是Cu。))))) or (((铁在常温下是固体。) and (not not ((42 % 5) > (-14 * 14)))) and (not (not not (尼日利亚的货币是奈拉。)))) or ((not not (鳕鱼是哺乳动物。)) and ((not not (柏林墙倒塌发生在1989年。)) or ((汞在常温下是液体。) or (1996年是闰年。))) and (not not (not not ((钻石在常温下是液体。) or (乌龟是鸟类。)))))\nF. not not ((not (新加坡的首都是新加坡。)) or ((1952年奥运会在伦敦举办。) and ((19 + 20) <= (6 - -13)) and (人类只使用了大脑的10%。)))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 87392843,
"true_count": 2
},
"seed": 87392843,
"task_id": 687392843,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (not (not not ((((-17 * 13) >= (8 + 20)) or ((-9 - 10) != (8 * 14))) or (((6 - -12) < (29 % 6)) and ((7 + 4) == (9 - 8)))))) and ((not (not (not (South Korea is in Asia.)))) or ((not (The chemical symbol for Aluminum is Al.)) and (((34 % 7) < (1 * 3 + -4 * 5)) or ((-20 * -9) != (38 % 9))) and (not (not not (A mosquito is an insect.)))))
B. not (not ((not (not not (The capital of Malaysia is Kuala Lumpur.))) or (A gecko is a reptile.) or (not not (((8 + -1) <= (47 % 2) <= (-11 + -19)) and (The currency of United States is the Peso.)))))
C. ((((1 - -15) == (16 - 12)) and ((57 is a prime number.) or ((Water is a liquid at room temperature.) or ((14 * 1) > (5 * -3))))) and ((((Lightning never strikes the same place twice.) and ((2 ** 1) < (7 * 4 - -9 * 2))) or ((-18 - 13) > (6 + -1))) and (not (not (The 1992 Olympics were held in Beijing.))))) or (not not (not not (((1969 is a leap year.) or (The capital of New Zealand is Wellington.)) or (not (Lightning never strikes the same place twice.)))))
D. not (not ((not ((-1 - -19) >= (14 % 5))) or (((-9 * 11) < (10 * -4 - 7 * 7)) and ((15 - 8) >= (29 % 2))) or (((Steam is a gas at room temperature.) or ((15 * 13) != (-13 + 12))) and (((-7 * -5 - 3 * 5) != (2 ** 1)) or (The currency of Thailand is the Dollar.)))))
E. (not not (((((-16 * 16) <= (9 * -9 - 0 * -10)) and ((15 - 2) == (-17 * 1))) or ((A grasshopper is an insect.) or ((10 % 8) <= (2 ** 2)))) and ((World War I ended occurred in 1918.) and (((20 * -1) == (15 % 8)) and (The chemical symbol for Zinc is Fe.))))) and ((not (The chemical symbol for Titanium is Hg.)) or ((The 1980 Olympics were held in Munich.) and ((1 * -10 * -10 * 1) == (7 * -9 * 6 * -4))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 30617487,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. (not (not not ((((-17 * 13) >= (8 + 20)) or ((-9 - 10) != (8 * 14))) or (((6 - -12) < (29 % 6)) and ((7 + 4) == (9 - 8)))))) and ((not (not (not (South Korea is in Asia.)))) or ((not (The chemical symbol for Aluminum is Al.)) and (((34 % 7) < (1 * 3 + -4 * 5)) or ((-20 * -9) != (38 % 9))) and (not (not not (A mosquito is an insect.)))))\nB. not (not ((not (not not (The capital of Malaysia is Kuala Lumpur.))) or (A gecko is a reptile.) or (not not (((8 + -1) <= (47 % 2) <= (-11 + -19)) and (The currency of United States is the Peso.)))))\nC. ((((1 - -15) == (16 - 12)) and ((57 is a prime number.) or ((Water is a liquid at room temperature.) or ((14 * 1) > (5 * -3))))) and ((((Lightning never strikes the same place twice.) and ((2 ** 1) < (7 * 4 - -9 * 2))) or ((-18 - 13) > (6 + -1))) and (not (not (The 1992 Olympics were held in Beijing.))))) or (not not (not not (((1969 is a leap year.) or (The capital of New Zealand is Wellington.)) or (not (Lightning never strikes the same place twice.)))))\nD. not (not ((not ((-1 - -19) >= (14 % 5))) or (((-9 * 11) < (10 * -4 - 7 * 7)) and ((15 - 8) >= (29 % 2))) or (((Steam is a gas at room temperature.) or ((15 * 13) != (-13 + 12))) and (((-7 * -5 - 3 * 5) != (2 ** 1)) or (The currency of Thailand is the Dollar.)))))\nE. (not not (((((-16 * 16) <= (9 * -9 - 0 * -10)) and ((15 - 2) == (-17 * 1))) or ((A grasshopper is an insect.) or ((10 % 8) <= (2 ** 2)))) and ((World War I ended occurred in 1918.) and (((20 * -1) == (15 % 8)) and (The chemical symbol for Zinc is Fe.))))) and ((not (The chemical symbol for Titanium is Hg.)) or ((The 1980 Olympics were held in Munich.) and ((1 * -10 * -10 * 1) == (7 * -9 * 6 * -4))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 30617487,
"true_count": 3
},
"seed": 30617487,
"task_id": 630617487,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (-13 + -2) < (3 ** 2) < (3 % 8)
B. not not (((36 % 5) <= (-8 * -1 + 2 * -6)) and ((17 - -17) <= (10 - -13)))
C. 氧气对人类生存是必需的。
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 87012078,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. (-13 + -2) < (3 ** 2) < (3 % 8)\nB. not not (((36 % 5) <= (-8 * -1 + 2 * -6)) and ((17 - -17) <= (10 - -13)))\nC. 氧气对人类生存是必需的。\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 87012078,
"true_count": 1
},
"seed": 87012078,
"task_id": 687012078,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (8 * 10 + -8 * 0) >= (1 ** 3)
B. (not ((-6 * -5 * 8 * 1) < (-6 * -1 + 8 * 4))) and ((光速约为每秒30万公里。) and ((8 * -2 * 2 * 1) <= (-1 - -20) <= (-18 + 13)))
C. not (氯的化学符号是Pb。)
D. ((17 + -11) != (3 ** 2)) and ((鲸鱼是鱼类。) and ((16 * 10) <= (-13 * 8)))
E. (1 ** 1) != (5 * -7 * -5 * 8)
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 60624339,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. (8 * 10 + -8 * 0) >= (1 ** 3)\nB. (not ((-6 * -5 * 8 * 1) < (-6 * -1 + 8 * 4))) and ((光速约为每秒30万公里。) and ((8 * -2 * 2 * 1) <= (-1 - -20) <= (-18 + 13)))\nC. not (氯的化学符号是Pb。)\nD. ((17 + -11) != (3 ** 2)) and ((鲸鱼是鱼类。) and ((16 * 10) <= (-13 * 8)))\nE. (1 ** 1) != (5 * -7 * -5 * 8)\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 60624339,
"true_count": 3
},
"seed": 60624339,
"task_id": 660624339,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not (((4 + 12) < (17 % 8) < (-10 * 1 * 4 * -8)) or (西班牙位于欧洲。))
B. (((3 ** 3) <= (-10 * -6 - 5 * 4)) and ((-4 - 16) < (0 + 18))) and ((土星是距离太阳第1近的行星。) or ((-3 - -16) > (10 - 10)))
C. not not (1948年奥运会在伦敦举办。)
D. (not not ((-10 * -12) != (1 * 13))) and (((17 - -7) <= (10 - 20)) or ((5 - -6) >= (5 - 0)))
E. 2099年是闰年。
F. ((12 - -4) <= (-15 - -12) <= (20 * -15)) and (((12 * 8) < (12 * -1) < (34 % 7)) or (沙特阿拉伯的货币是克朗。))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 22715846,
"true_count": 3
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not (((4 + 12) < (17 % 8) < (-10 * 1 * 4 * -8)) or (西班牙位于欧洲。))\nB. (((3 ** 3) <= (-10 * -6 - 5 * 4)) and ((-4 - 16) < (0 + 18))) and ((土星是距离太阳第1近的行星。) or ((-3 - -16) > (10 - 10)))\nC. not not (1948年奥运会在伦敦举办。)\nD. (not not ((-10 * -12) != (1 * 13))) and (((17 - -7) <= (10 - 20)) or ((5 - -6) >= (5 - 0)))\nE. 2099年是闰年。\nF. ((12 - -4) <= (-15 - -12) <= (20 * -15)) and (((12 * 8) < (12 * -1) < (34 % 7)) or (沙特阿拉伯的货币是克朗。))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 22715846,
"true_count": 3
},
"seed": 22715846,
"task_id": 622715846,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. not (((1928年奥运会在斯德哥尔摩举办。) or ((-20 - -20) >= (-4 + -7))) or (第二次世界大战结束发生在1955年。))
B. (((-16 - 16) < (-3 - -18)) or (not ((10 * -17) > (10 + 10)))) or ((18 - 7) != (6 + -6))
C. (not not ((火星是距离太阳最近的行星。) and ((32 % 6) < (-3 - -17)))) and (not ((-15 - -9) > (5 ** 3)))
D. ((9 * 17) >= (-9 * -9)) or ((5 ** 2) > (-5 * 1))
E. not not ((((3 * 9 - -2 * 1) >= (12 * -2)) and (沙特阿拉伯的首都是利雅得。)) and ((木星是距离太阳第5近的行星。) and (人体有206块骨头。)))
F. not not (墨西哥的货币是比索。)
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "B,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 76940381,
"true_count": 4
},
"question": "分析以下逻辑表达式：\n\nA. not (((1928年奥运会在斯德哥尔摩举办。) or ((-20 - -20) >= (-4 + -7))) or (第二次世界大战结束发生在1955年。))\nB. (((-16 - 16) < (-3 - -18)) or (not ((10 * -17) > (10 + 10)))) or ((18 - 7) != (6 + -6))\nC. (not not ((火星是距离太阳最近的行星。) and ((32 % 6) < (-3 - -17)))) and (not ((-15 - -9) > (5 ** 3)))\nD. ((9 * 17) >= (-9 * -9)) or ((5 ** 2) > (-5 * 1))\nE. not not ((((3 * 9 - -2 * 1) >= (12 * -2)) and (沙特阿拉伯的首都是利雅得。)) and ((木星是距离太阳第5近的行星。) and (人体有206块骨头。)))\nF. not not (墨西哥的货币是比索。)\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 76940381,
"true_count": 4
},
"seed": 76940381,
"task_id": 676940381,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. A dog has 4 legs.
B. 33 is less than or equal to 66.
C. The chemical symbol for Potassium is K.
D. (A chameleon is a reptile.) or (The first moon landing occurred in 1969.)
E. not (((9 * -8 * 1 * -2) == (5 * 11)) and (387 is a perfect square.))
F. (-1 - 8) >= (9 + 11)
G. 1974 is a leap year.
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 88095419,
"true_count": 5
},
"question": "Here are some boolean expressions to evaluate:\n\nA. A dog has 4 legs.\nB. 33 is less than or equal to 66.\nC. The chemical symbol for Potassium is K.\nD. (A chameleon is a reptile.) or (The first moon landing occurred in 1969.)\nE. not (((9 * -8 * 1 * -2) == (5 * 11)) and (387 is a perfect square.))\nF. (-1 - 8) >= (9 + 11)\nG. 1974 is a leap year.\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 88095419,
"true_count": 5
},
"seed": 88095419,
"task_id": 688095419,
"task_type": "boolean_expressions"
} |
logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. (龙虾有0条腿。) or (((-13 - -4) != (5 ** 3)) or ((-4 * 4) <= (-9 + -15) <= (5 % 4))) or ((((23 % 9) < (17 + 5)) or (海王星是距离太阳第8近的行星。)) and ((1 ** 1) < (0 * 3 * 1 * -2)))
B. (not ((2 ** 1) < (1 * -8 + -10 * 1) < (17 + -12))) or ((not not ((-18 + -10) <= (11 * -13) <= (34 % 2))) and ((0 * 1 + -7 * 8) == (15 + 11)))
C. (((水星是距离太阳第1近的行星。) or ((-6 + -1) < (-5 + 19))) and (((13 + 4) == (49 % 5)) and (1896年奥运会在墨西哥城举办。))) and (not not (锡的化学符号是S。)) and ((二月有30天。) and (((4 - 6) != (-9 + 2)) or (南极洲是最冷的大陆。)))
D. (美国宣布独立发生在1777年。) or ((瑞典的货币是比索。) and (not ((-4 * -8 - -5 * 10) <= (-17 * 19) <= (14 + -20))))
E. not (1896年奥运会在墨尔本举办。)
F. (not not ((第一部iPhone发布发生在2008年。) or ((13 - 15) != (-4 * 5)))) or (((铅的化学符号是Mn。) or (章鱼有6条腿。)) and (not not ((15 % 5) <= (-12 + 19) <= (8 - 1))))
G. not ((not (1917年是闰年。)) and (not ((5 + 16) > (-1 * 3))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A,B,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 41670463,
"true_count": 5
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. (龙虾有0条腿。) or (((-13 - -4) != (5 ** 3)) or ((-4 * 4) <= (-9 + -15) <= (5 % 4))) or ((((23 % 9) < (17 + 5)) or (海王星是距离太阳第8近的行星。)) and ((1 ** 1) < (0 * 3 * 1 * -2)))\nB. (not ((2 ** 1) < (1 * -8 + -10 * 1) < (17 + -12))) or ((not not ((-18 + -10) <= (11 * -13) <= (34 % 2))) and ((0 * 1 + -7 * 8) == (15 + 11)))\nC. (((水星是距离太阳第1近的行星。) or ((-6 + -1) < (-5 + 19))) and (((13 + 4) == (49 % 5)) and (1896年奥运会在墨西哥城举办。))) and (not not (锡的化学符号是S。)) and ((二月有30天。) and (((4 - 6) != (-9 + 2)) or (南极洲是最冷的大陆。)))\nD. (美国宣布独立发生在1777年。) or ((瑞典的货币是比索。) and (not ((-4 * -8 - -5 * 10) <= (-17 * 19) <= (14 + -20))))\nE. not (1896年奥运会在墨尔本举办。)\nF. (not not ((第一部iPhone发布发生在2008年。) or ((13 - 15) != (-4 * 5)))) or (((铅的化学符号是Mn。) or (章鱼有6条腿。)) and (not not ((15 % 5) <= (-12 + 19) <= (8 - 1))))\nG. not ((not (1917年是闰年。)) and (not ((5 + 16) > (-1 * 3))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 41670463,
"true_count": 5
},
"seed": 41670463,
"task_id": 641670463,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. Oxygen is necessary for human survival.
B. not not (not (not (A fly is a mammal.)))
C. ((not not ((not ((11 % 2) > (-2 * 8 * 6 * -3))) or (The currency of Argentina is the Peso.))) and (not ((((-15 + -11) <= (27 % 3)) or ((37 % 3) < (-9 + 5))) or (not not ((19 % 4) > (-19 * 16)))))) and ((not (not (((4 * 8 - -1 * -4) < (-11 - -15) < (6 * 6 * 10 * -5)) and (Oil is a solid at room temperature.)))) or ((not (not (Uranus is the 7th planet from the Sun.))) or ((-13 * -11) < (7 * -2 - 6 * -5))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 15175056,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. Oxygen is necessary for human survival.\nB. not not (not (not (A fly is a mammal.)))\nC. ((not not ((not ((11 % 2) > (-2 * 8 * 6 * -3))) or (The currency of Argentina is the Peso.))) and (not ((((-15 + -11) <= (27 % 3)) or ((37 % 3) < (-9 + 5))) or (not not ((19 % 4) > (-19 * 16)))))) and ((not (not (((4 * 8 - -1 * -4) < (-11 - -15) < (6 * 6 * 10 * -5)) and (Oil is a solid at room temperature.)))) or ((not (not (Uranus is the 7th planet from the Sun.))) or ((-13 * -11) < (7 * -2 - 6 * -5))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 15175056,
"true_count": 1
},
"seed": 15175056,
"task_id": 615175056,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (not not ((十二月有31天。) or ((以色列的货币是雷亚尔。) or (金在常温下是液体。)))) or (not not (not not (not not ((18 + 11) != (8 * -8 * -10 * -6)))))
B. not (((((-5 * -2 * 6 * 1) != (-6 * -1 + -9 * -4)) and ((-11 * 9) <= (10 * 8 * 0 * 7))) and ((1952年奥运会在赫尔辛基举办。) or ((1 * -9 - 1 * 3) == (-8 * -3 - 1 * -5)))) or (((21能被8整除。) or (鸭子有2条腿。)) and (41大于35。)))
C. not not ((not (钴的化学符号是Fe。)) and (not (((-1 + -13) > (18 + -15)) or ((-16 - -6) < (-2 * 2) < (-2 * 2 - 10 * -1)))))
D. (((-16 - 17) < (-17 + -19)) and ((30 % 1) < (-2 * 3 - 2 * 8)) and ((14 - 4) < (1 - -5))) or (((3 ** 1) < (8 - 11) < (30 % 7)) and (((-10 + 14) > (0 - -17)) and (1928年奥运会在阿姆斯特丹举办。))) or ((((氧气对人类生存是必需的。) and ((-9 * -3 * 3 * 2) != (2 * 6))) or ((孔雀是昆虫。) or (泰坦尼克号沉没发生在1913年。))) and (not ((大象有4条腿。) or ((0 * 8 + 8 * 0) != (2 % 1)))))
E. (not (not not (印度尼西亚位于亚洲。))) or ((((3 ** 2) == (13 + -7)) and (瑞士的货币是瑞士法郎。)) or ((墨西哥的首都是罗马。) or ((-15 - -8) != (-2 * 0)))) or (not (((8 + -1) == (11 % 10)) or (((-5 * 6 - 2 * -8) <= (5 ** 1)) and ((10 - -5) < (-2 * -9 * 8 * -10) < (-1 * -17)))))
F. (((-4 * 15) >= (-8 - 16)) or (柏林墙倒塌发生在1987年。) or (((173是偶数。) and ((-19 + 16) < (18 - -11))) and (人类首次登月发生在1969年。))) and ((铝的化学符号是Al。) and ((-9 * 9) <= (-4 * -6 * 0 * 10))) and (((1949年是闰年。) and ((37 % 7) < (-9 * -3 - -9 * 10))) or ((((14 - -9) >= (-5 * 4)) or ((-19 - 15) <= (-7 * -7) <= (-9 * 2 + 6 * -6))) or ((1956年奥运会在东京举办。) or ((-1 + 20) >= (-2 - -8)))))
G. (not not ((甲虫是昆虫。) and (((10 * 5 * -10 * 0) < (3 ** 1)) or (木头在常温下是固体。)))) and (not (铬的化学符号是Ni。))
H. ((金的化学符号是Au。) and ((-7 * 2 - 6 * 4) <= (-17 - -15) <= (2 - 11))) and (not (not not (((15 + -12) < (7 * -6 * 9 * 7)) and (水蒸气在常温下是固体。))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 8,
"seed": 2007914,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. (not not ((十二月有31天。) or ((以色列的货币是雷亚尔。) or (金在常温下是液体。)))) or (not not (not not (not not ((18 + 11) != (8 * -8 * -10 * -6)))))\nB. not (((((-5 * -2 * 6 * 1) != (-6 * -1 + -9 * -4)) and ((-11 * 9) <= (10 * 8 * 0 * 7))) and ((1952年奥运会在赫尔辛基举办。) or ((1 * -9 - 1 * 3) == (-8 * -3 - 1 * -5)))) or (((21能被8整除。) or (鸭子有2条腿。)) and (41大于35。)))\nC. not not ((not (钴的化学符号是Fe。)) and (not (((-1 + -13) > (18 + -15)) or ((-16 - -6) < (-2 * 2) < (-2 * 2 - 10 * -1)))))\nD. (((-16 - 17) < (-17 + -19)) and ((30 % 1) < (-2 * 3 - 2 * 8)) and ((14 - 4) < (1 - -5))) or (((3 ** 1) < (8 - 11) < (30 % 7)) and (((-10 + 14) > (0 - -17)) and (1928年奥运会在阿姆斯特丹举办。))) or ((((氧气对人类生存是必需的。) and ((-9 * -3 * 3 * 2) != (2 * 6))) or ((孔雀是昆虫。) or (泰坦尼克号沉没发生在1913年。))) and (not ((大象有4条腿。) or ((0 * 8 + 8 * 0) != (2 % 1)))))\nE. (not (not not (印度尼西亚位于亚洲。))) or ((((3 ** 2) == (13 + -7)) and (瑞士的货币是瑞士法郎。)) or ((墨西哥的首都是罗马。) or ((-15 - -8) != (-2 * 0)))) or (not (((8 + -1) == (11 % 10)) or (((-5 * 6 - 2 * -8) <= (5 ** 1)) and ((10 - -5) < (-2 * -9 * 8 * -10) < (-1 * -17)))))\nF. (((-4 * 15) >= (-8 - 16)) or (柏林墙倒塌发生在1987年。) or (((173是偶数。) and ((-19 + 16) < (18 - -11))) and (人类首次登月发生在1969年。))) and ((铝的化学符号是Al。) and ((-9 * 9) <= (-4 * -6 * 0 * 10))) and (((1949年是闰年。) and ((37 % 7) < (-9 * -3 - -9 * 10))) or ((((14 - -9) >= (-5 * 4)) or ((-19 - 15) <= (-7 * -7) <= (-9 * 2 + 6 * -6))) or ((1956年奥运会在东京举办。) or ((-1 + 20) >= (-2 - -8)))))\nG. (not not ((甲虫是昆虫。) and (((10 * 5 * -10 * 0) < (3 ** 1)) or (木头在常温下是固体。)))) and (not (铬的化学符号是Ni。))\nH. ((金的化学符号是Au。) and ((-7 * 2 - 6 * 4) <= (-17 - -15) <= (2 - 11))) and (not (not not (((15 + -12) < (7 * -6 * 9 * 7)) and (水蒸气在常温下是固体。))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 8,
"seed": 2007914,
"true_count": 3
},
"seed": 2007914,
"task_id": 602007914,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (not not ((((巴西的货币是人民币。) and (1932年奥运会在东京举办。)) and ((法国位于欧洲。) and ((3 + -16) < (-3 * 0 - 3 * 4)))) and ((2080年是闰年。) and (81的平方根是6。)) and (not not (((3 * 9 * 8 * 1) != (-14 - 12)) and ((-19 + -18) > (5 ** 1)))))) or (not not ((-9 * 8 + 6 * 8) != (-3 - -8))) or ((((not (1970年是闰年。)) and (not not ((2 - -14) < (18 - -17)))) or (((汞在常温下是气体。) and ((-16 * 6) != (-13 - 1))) and (not (螃蟹有10条腿。)))) and (not not (蜘蛛是昆虫。)))
B. (((not (镁的化学符号是N。)) or ((-9 + -8) <= (-9 * -2 * 4 * 10))) or (((19 * 12) > (6 - 13)) or (磷的化学符号是Co。)) or (not not (not not ((地球是距离太阳第3近的行星。) or ((-18 * 20) >= (10 + -20)))))) and (((木星是距离太阳第8近的行星。) or ((氦的化学符号是He。) or ((11 * -11) >= (7 % 10)))) or (((天王星是距离太阳第5近的行星。) or (not (哥伦布到达美洲发生在1492年。))) or (not not (墨西哥位于非洲。)) or (not (not (1964年奥运会在东京举办。)))))
C. ((((16 * -14) == (40 % 10)) and (not not (not not ((18 + -4) > (-17 - -9))))) and (((蚂蚁有6条腿。) and ((韩国的首都是布鲁塞尔。) or (十一月有30天。))) or ((not ((-7 - 5) < (9 % 10))) or (太阳绕地球运转。)))) or (((not (((7 * 5 * 9 * 1) != (-16 - 13)) or (空气在常温下是气体。))) or ((1968年奥运会在墨西哥城举办。) and ((15 % 1) < (1 * -6 + -1 * 2) < (33 % 4))) or (not (not not ((4 - -9) != (-3 * 1 - -7 * 9))))) or (((225的平方根是15。) and (委内瑞拉的首都是加拉加斯。)) and (not not (((0 * 6 - -10 * -10) != (8 * 20)) or (铂的化学符号是Ne。)))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 70853130,
"true_count": 3
},
"question": "评估以下每个表达式：\n\nA. (not not ((((巴西的货币是人民币。) and (1932年奥运会在东京举办。)) and ((法国位于欧洲。) and ((3 + -16) < (-3 * 0 - 3 * 4)))) and ((2080年是闰年。) and (81的平方根是6。)) and (not not (((3 * 9 * 8 * 1) != (-14 - 12)) and ((-19 + -18) > (5 ** 1)))))) or (not not ((-9 * 8 + 6 * 8) != (-3 - -8))) or ((((not (1970年是闰年。)) and (not not ((2 - -14) < (18 - -17)))) or (((汞在常温下是气体。) and ((-16 * 6) != (-13 - 1))) and (not (螃蟹有10条腿。)))) and (not not (蜘蛛是昆虫。)))\nB. (((not (镁的化学符号是N。)) or ((-9 + -8) <= (-9 * -2 * 4 * 10))) or (((19 * 12) > (6 - 13)) or (磷的化学符号是Co。)) or (not not (not not ((地球是距离太阳第3近的行星。) or ((-18 * 20) >= (10 + -20)))))) and (((木星是距离太阳第8近的行星。) or ((氦的化学符号是He。) or ((11 * -11) >= (7 % 10)))) or (((天王星是距离太阳第5近的行星。) or (not (哥伦布到达美洲发生在1492年。))) or (not not (墨西哥位于非洲。)) or (not (not (1964年奥运会在东京举办。)))))\nC. ((((16 * -14) == (40 % 10)) and (not not (not not ((18 + -4) > (-17 - -9))))) and (((蚂蚁有6条腿。) and ((韩国的首都是布鲁塞尔。) or (十一月有30天。))) or ((not ((-7 - 5) < (9 % 10))) or (太阳绕地球运转。)))) or (((not (((7 * 5 * 9 * 1) != (-16 - 13)) or (空气在常温下是气体。))) or ((1968年奥运会在墨西哥城举办。) and ((15 % 1) < (1 * -6 + -1 * 2) < (33 % 4))) or (not (not not ((4 - -9) != (-3 * 1 - -7 * 9))))) or (((225的平方根是15。) and (委内瑞拉的首都是加拉加斯。)) and (not not (((0 * 6 - -10 * -10) != (8 * 20)) or (铂的化学符号是Ne。)))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 70853130,
"true_count": 3
},
"seed": 70853130,
"task_id": 670853130,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not (((((-14 - -10) > (-16 - 17)) and (铅的化学符号是Sn。)) or (火星是距离太阳第4近的行星。)) or (((1907年是闰年。) or (哥伦比亚的货币是越南盾。)) or (not not ((16 + -5) != (-11 - -19)))))
B. (((-18 * 12) >= (0 + -9)) and (not (2008年奥运会在北京举办。))) or (鲸鱼是鱼类。) or ((((蜘蛛是昆虫。) and ((-2 * 19) > (5 - 18))) or (((-7 * -2) >= (7 - 11)) and ((15 - 13) <= (6 + 2)))) and (not (not ((-16 - 19) < (-7 * 5 * -1 * -3)))))
C. not (not not ((((8 * -10) != (7 * 9)) or (美国位于北美洲。)) and (((-4 * 8 * -10 * -6) < (-6 * 6 + 9 * 7)) and ((8 + -11) > (2 ** 2)))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 3,
"seed": 66587741,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. not (((((-14 - -10) > (-16 - 17)) and (铅的化学符号是Sn。)) or (火星是距离太阳第4近的行星。)) or (((1907年是闰年。) or (哥伦比亚的货币是越南盾。)) or (not not ((16 + -5) != (-11 - -19)))))\nB. (((-18 * 12) >= (0 + -9)) and (not (2008年奥运会在北京举办。))) or (鲸鱼是鱼类。) or ((((蜘蛛是昆虫。) and ((-2 * 19) > (5 - 18))) or (((-7 * -2) >= (7 - 11)) and ((15 - 13) <= (6 + 2)))) and (not (not ((-16 - 19) < (-7 * 5 * -1 * -3)))))\nC. not (not not ((((8 * -10) != (7 * 9)) or (美国位于北美洲。)) and (((-4 * 8 * -10 * -6) < (-6 * 6 + 9 * 7)) and ((8 + -11) > (2 ** 2)))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 3,
"seed": 66587741,
"true_count": 1
},
"seed": 66587741,
"task_id": 666587741,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. ((((5 ** 2) == (-4 * -5 - -2 * 10)) and ((not not (法国的首都是巴黎。)) or (((1 ** 3) < (2 ** 1)) and ((-4 - -16) < (8 * -17))))) or ((木星是距离太阳第3近的行星。) and ((-1 - 1) >= (3 * -14))) or (not ((((43 % 8) <= (6 + 18)) and ((1 * -4 + -7 * -3) > (-1 * 9 + -4 * 4))) and (哥伦布到达美洲发生在1492年。)))) or (not not ((not ((4 ** 1) != (-5 - 8))) and (((-14 + -9) >= (-8 * -3 + 8 * -2)) or (1988年奥运会在首尔举办。)))) or (not not (not not (((氦气在常温下是液体。) and (埃及的首都是开罗。)) and (鸭子有2条腿。))))
B. (not (not not (钛的化学符号是Ti。))) and ((((not not (2016年奥运会在东京举办。)) or (not not (太阳绕地球运转。))) or (蝴蝶有6条腿。)) or ((not (地球是距离太阳第3近的行星。)) or (莱特兄弟首次飞行发生在1898年。)) or (((3 * -5 - 3 * 0) <= (2 ** 1) <= (2 - 0)) or (第一部iPhone发布发生在2005年。) or (((-11 * 8) != (-4 * -9 * 10 * 7)) and (((12 - 14) > (1 * -1 - -2 * 9)) and (锌的化学符号是Cl。)))))
C. ((not not ((((-16 - -6) <= (5 - 4)) and (短吻鳄是爬行动物。)) and (((1 * 12) != (-16 - 12)) and (人类有三个肺。)))) or (((火星是距离太阳最近的行星。) or ((章鱼有8条腿。) or (2082年是闰年。))) or (not not (not ((-2 - -1) != (-19 + 0)))))) and (((((41是完全平方数。) and ((24 % 3) >= (1 ** 1))) or (((-4 * -2 - -5 * -1) >= (15 + -7)) and (75是质数。))) or ((2004年奥运会在雅典举办。) or (151是偶数。)) or ((not (铁在常温下是固体。)) and ((金星是距离太阳第1近的行星。) and (第一次世界大战开始发生在1924年。)))) and (not ((not not (铀的化学符号是U。)) or ((空气在常温下是气体。) or (南极洲是最冷的大陆。)))))
D. not ((((-1 * -6 - 7 * -9) < (18 - 18)) and ((not (3小于等于82。)) and (地球是距离太阳第4近的行星。))) and (金在常温下是固体。) and ((not not ((第一次世界大战开始发生在1915年。) and (天王星是距离太阳第7近的行星。))) and (not ((6 * -20) >= (-3 - 19)))))
E. (not not (((-3 * -4 - 6 * 3) <= (6 * 2) <= (14 - 15)) and (not not ((-1 * 20) >= (8 * 7 + 10 * 9))) and ((法国大革命开始发生在1791年。) or ((-1 + 11) == (0 - -20))))) or ((not not (((牛有4条腿。) and ((15 * -5) == (11 % 8))) and ((4 ** 2) <= (3 - 14)))) and ((((氧气在常温下是固体。) and ((25 % 4) <= (21 % 9) <= (-4 * 6 - 9 * 10))) or ((9 + 0) < (2 + -1) < (-16 * 16))) and (((2 ** 1) < (-19 * -18) < (-8 - -10)) and ((-10 * -12) < (0 * 19)))))
F. (not not (((not not (加拿大位于非洲。)) or (((2 + 19) <= (6 % 10)) and (空气在常温下是气体。))) or ((西班牙的首都是马德里。) or (not not (67是偶数。))))) or (((-8 + -16) != (-20 * 1)) or (not (蜘蛛有100条腿。)) or (((现代奥运会首届举办发生在1901年。) or (蝙蝠是瞎的。)) or (not not ((4 ** 2) != (9 - 2))))) or (not (not not (加拿大的首都是斯德哥尔摩。)))
G. not ((((2023年是闰年。) or ((地球上一天是24小时。) or (西班牙的首都是马德里。))) and (((4 * 7 + 7 * 10) >= (-7 * 8 + 7 * -10)) or (铬的化学符号是Au。))) or (not not ((not not ((14 - -12) <= (5 + -4))) or (((-2 - -17) == (17 % 3)) and (捷克的货币是克朗。)))))
H. (not not (not not ((-10 - -15) != (-20 - -7)))) and (((not ((蝴蝶是昆虫。) or ((3 - 10) != (2 + -5)))) and ((((-19 * -15) <= (2 + -18) <= (18 * 7)) and (铬的化学符号是Cu。)) and (((4 * 7 - 2 * -2) < (3 * 7 - 5 * 5) < (-5 - 2)) and (1972年奥运会在慕尼黑举办。)))) or (((((3 * -2 * 4 * -8) > (20 + 2)) or (火星是距离太阳第4近的行星。)) or ((墨西哥位于北美洲。) and (2034年是闰年。))) and ((((-5 * 10 * -7 * -9) > (4 + 9)) and ((-7 - -19) <= (-1 + 13) <= (3 + 20))) or (((-9 * -12) < (7 * -8 * 6 * 4) < (-2 * 6 + 4 * -6)) or ((45 % 5) >= (42 % 4))))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"question": "给定以下布尔表达式：\n\nA. ((((5 ** 2) == (-4 * -5 - -2 * 10)) and ((not not (法国的首都是巴黎。)) or (((1 ** 3) < (2 ** 1)) and ((-4 - -16) < (8 * -17))))) or ((木星是距离太阳第3近的行星。) and ((-1 - 1) >= (3 * -14))) or (not ((((43 % 8) <= (6 + 18)) and ((1 * -4 + -7 * -3) > (-1 * 9 + -4 * 4))) and (哥伦布到达美洲发生在1492年。)))) or (not not ((not ((4 ** 1) != (-5 - 8))) and (((-14 + -9) >= (-8 * -3 + 8 * -2)) or (1988年奥运会在首尔举办。)))) or (not not (not not (((氦气在常温下是液体。) and (埃及的首都是开罗。)) and (鸭子有2条腿。))))\nB. (not (not not (钛的化学符号是Ti。))) and ((((not not (2016年奥运会在东京举办。)) or (not not (太阳绕地球运转。))) or (蝴蝶有6条腿。)) or ((not (地球是距离太阳第3近的行星。)) or (莱特兄弟首次飞行发生在1898年。)) or (((3 * -5 - 3 * 0) <= (2 ** 1) <= (2 - 0)) or (第一部iPhone发布发生在2005年。) or (((-11 * 8) != (-4 * -9 * 10 * 7)) and (((12 - 14) > (1 * -1 - -2 * 9)) and (锌的化学符号是Cl。)))))\nC. ((not not ((((-16 - -6) <= (5 - 4)) and (短吻鳄是爬行动物。)) and (((1 * 12) != (-16 - 12)) and (人类有三个肺。)))) or (((火星是距离太阳最近的行星。) or ((章鱼有8条腿。) or (2082年是闰年。))) or (not not (not ((-2 - -1) != (-19 + 0)))))) and (((((41是完全平方数。) and ((24 % 3) >= (1 ** 1))) or (((-4 * -2 - -5 * -1) >= (15 + -7)) and (75是质数。))) or ((2004年奥运会在雅典举办。) or (151是偶数。)) or ((not (铁在常温下是固体。)) and ((金星是距离太阳第1近的行星。) and (第一次世界大战开始发生在1924年。)))) and (not ((not not (铀的化学符号是U。)) or ((空气在常温下是气体。) or (南极洲是最冷的大陆。)))))\nD. not ((((-1 * -6 - 7 * -9) < (18 - 18)) and ((not (3小于等于82。)) and (地球是距离太阳第4近的行星。))) and (金在常温下是固体。) and ((not not ((第一次世界大战开始发生在1915年。) and (天王星是距离太阳第7近的行星。))) and (not ((6 * -20) >= (-3 - 19)))))\nE. (not not (((-3 * -4 - 6 * 3) <= (6 * 2) <= (14 - 15)) and (not not ((-1 * 20) >= (8 * 7 + 10 * 9))) and ((法国大革命开始发生在1791年。) or ((-1 + 11) == (0 - -20))))) or ((not not (((牛有4条腿。) and ((15 * -5) == (11 % 8))) and ((4 ** 2) <= (3 - 14)))) and ((((氧气在常温下是固体。) and ((25 % 4) <= (21 % 9) <= (-4 * 6 - 9 * 10))) or ((9 + 0) < (2 + -1) < (-16 * 16))) and (((2 ** 1) < (-19 * -18) < (-8 - -10)) and ((-10 * -12) < (0 * 19)))))\nF. (not not (((not not (加拿大位于非洲。)) or (((2 + 19) <= (6 % 10)) and (空气在常温下是气体。))) or ((西班牙的首都是马德里。) or (not not (67是偶数。))))) or (((-8 + -16) != (-20 * 1)) or (not (蜘蛛有100条腿。)) or (((现代奥运会首届举办发生在1901年。) or (蝙蝠是瞎的。)) or (not not ((4 ** 2) != (9 - 2))))) or (not (not not (加拿大的首都是斯德哥尔摩。)))\nG. not ((((2023年是闰年。) or ((地球上一天是24小时。) or (西班牙的首都是马德里。))) and (((4 * 7 + 7 * 10) >= (-7 * 8 + 7 * -10)) or (铬的化学符号是Au。))) or (not not ((not not ((14 - -12) <= (5 + -4))) or (((-2 - -17) == (17 % 3)) and (捷克的货币是克朗。)))))\nH. (not not (not not ((-10 - -15) != (-20 - -7)))) and (((not ((蝴蝶是昆虫。) or ((3 - 10) != (2 + -5)))) and ((((-19 * -15) <= (2 + -18) <= (18 * 7)) and (铬的化学符号是Cu。)) and (((4 * 7 - 2 * -2) < (3 * 7 - 5 * 5) < (-5 - 2)) and (1972年奥运会在慕尼黑举办。)))) or (((((3 * -2 * 4 * -8) > (20 + 2)) or (火星是距离太阳第4近的行星。)) or ((墨西哥位于北美洲。) and (2034年是闰年。))) and ((((-5 * 10 * -7 * -9) > (4 + 9)) and ((-7 - -19) <= (-1 + 13) <= (3 + 20))) or (((-9 * -12) < (7 * -8 * 6 * 4) < (-2 * 6 + 4 * -6)) or ((45 % 5) >= (42 % 4))))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
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logic-v2 | Review these logical expressions:
A. ((((1 * -1 * 8 * 3) == (16 - 12)) and (Oxygen is necessary for human survival.)) and (((-4 * -10 * 6 * 1) <= (2 + 13) <= (-9 * -10 + 1 * 10)) and (The chemical symbol for Gold is Au.))) or (((18 * 2) < (-16 + -2)) or ((9 * 8 - 6 * 9) <= (-13 - -13))) or ((The currency of Philippines is the Dollar.) and ((The 2000 Olympics were held in Amsterdam.) or (A owl is a bird.)))
B. not ((not ((-17 + -17) < (-8 - 19))) or ((1942 is a leap year.) and (The chemical symbol for Silver is Ag.)))
C. (Saudi Arabia is in Asia.) or (not ((-19 - 17) > (-2 * 1)))
D. (not (The first iPhone was released occurred in 2007.)) and (France is in Europe.)
E. (not ((The capital of Ukraine is Kyiv.) and (The chemical symbol for Carbon is C.))) and (The square root of 64 is 15.) and ((-14 * -16) >= (-11 * -16))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"question": "Review these logical expressions:\n\nA. ((((1 * -1 * 8 * 3) == (16 - 12)) and (Oxygen is necessary for human survival.)) and (((-4 * -10 * 6 * 1) <= (2 + 13) <= (-9 * -10 + 1 * 10)) and (The chemical symbol for Gold is Au.))) or (((18 * 2) < (-16 + -2)) or ((9 * 8 - 6 * 9) <= (-13 - -13))) or ((The currency of Philippines is the Dollar.) and ((The 2000 Olympics were held in Amsterdam.) or (A owl is a bird.)))\nB. not ((not ((-17 + -17) < (-8 - 19))) or ((1942 is a leap year.) and (The chemical symbol for Silver is Ag.)))\nC. (Saudi Arabia is in Asia.) or (not ((-19 - 17) > (-2 * 1)))\nD. (not (The first iPhone was released occurred in 2007.)) and (France is in Europe.)\nE. (not ((The capital of Ukraine is Kyiv.) and (The chemical symbol for Carbon is C.))) and (The square root of 64 is 15.) and ((-14 * -16) >= (-11 * -16))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
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logic-v2 | 下面是几个布尔表达式：
A. ((not ((38 % 3) != (-5 * 18))) or (not not (土星是距离太阳第6近的行星。))) or ((((5 ** 3) < (7 * 0 + -6 * 6)) and (马有2条腿。)) and (not (钴的化学符号是Co。)))
B. ((1 ** 2) <= (34 % 2) <= (11 + -20)) or (((中国的首都是拉巴特。) and (金星是距离太阳第7近的行星。)) or ((海王星是距离太阳第8近的行星。) or (2078年是闰年。)))
C. (not (((8 % 4) <= (20 * 4)) and ((-5 * -3 * 1 * 3) > (11 - 2)))) or (地球上一天是24小时。) or ((((-19 - 8) == (2 + -5)) and ((2 ** 1) < (6 * -10 + -8 * -1))) or ((法国大革命开始发生在1799年。) and ((-9 * 1 * 10 * -7) < (1 * -14))))
D. ((not (铬的化学符号是Cr。)) and (not not ((8 + -2) < (-16 + -4)))) or (((柏林墙倒塌发生在1989年。) and ((7 * -8) < (4 ** 3) < (46 % 8))) and ((-4 * -8 * -5 * -1) >= (19 % 7)))
E. not not (((水在海平面上的沸点是100摄氏度。) or ((16 - -16) <= (-1 * 1 * -4 * 2) <= (5 * 6))) and (not (美国宣布独立发生在1776年。)))
F. not ((((16 - 5) > (-4 - 18)) and (秘鲁的首都是利马。)) or (((-15 + 6) < (-1 * 7) < (25 % 8)) and ((-14 + -19) >= (-5 * -7 + -2 * 7))))
G. ((((-1 + 2) <= (9 * -9 - 0 * 7)) and (蝙蝠是瞎的。)) and ((16 - 20) == (3 % 5))) or ((光速约为每秒30万公里。) and (澳大利亚的货币是澳元。)) or (986是斐波那契数。)
H. not not (not (((5 ** 3) > (-10 * 0 - -1 * -4)) and (西班牙位于欧洲。)))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
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"question": "下面是几个布尔表达式：\n\nA. ((not ((38 % 3) != (-5 * 18))) or (not not (土星是距离太阳第6近的行星。))) or ((((5 ** 3) < (7 * 0 + -6 * 6)) and (马有2条腿。)) and (not (钴的化学符号是Co。)))\nB. ((1 ** 2) <= (34 % 2) <= (11 + -20)) or (((中国的首都是拉巴特。) and (金星是距离太阳第7近的行星。)) or ((海王星是距离太阳第8近的行星。) or (2078年是闰年。)))\nC. (not (((8 % 4) <= (20 * 4)) and ((-5 * -3 * 1 * 3) > (11 - 2)))) or (地球上一天是24小时。) or ((((-19 - 8) == (2 + -5)) and ((2 ** 1) < (6 * -10 + -8 * -1))) or ((法国大革命开始发生在1799年。) and ((-9 * 1 * 10 * -7) < (1 * -14))))\nD. ((not (铬的化学符号是Cr。)) and (not not ((8 + -2) < (-16 + -4)))) or (((柏林墙倒塌发生在1989年。) and ((7 * -8) < (4 ** 3) < (46 % 8))) and ((-4 * -8 * -5 * -1) >= (19 % 7)))\nE. not not (((水在海平面上的沸点是100摄氏度。) or ((16 - -16) <= (-1 * 1 * -4 * 2) <= (5 * 6))) and (not (美国宣布独立发生在1776年。)))\nF. not ((((16 - 5) > (-4 - 18)) and (秘鲁的首都是利马。)) or (((-15 + 6) < (-1 * 7) < (25 % 8)) and ((-14 + -19) >= (-5 * -7 + -2 * 7))))\nG. ((((-1 + 2) <= (9 * -9 - 0 * 7)) and (蝙蝠是瞎的。)) and ((16 - 20) == (3 % 5))) or ((光速约为每秒30万公里。) and (澳大利亚的货币是澳元。)) or (986是斐波那契数。)\nH. not not (not (((5 ** 3) > (-10 * 0 - -1 * -4)) and (西班牙位于欧洲。)))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
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logic-v2 | Study the following logical statements:
A. ((not not ((35 % 2) == (1 - -10))) or (not (not not (not ((4 ** 1) == (25 % 5)))))) or (((There are 30 days in April.) or (not ((The currency of Czech Republic is the Koruna.) or (156 is an even number.)))) and (not (The 1960 Olympics were held in Rome.)))
B. not not (((not (not not (Wood is a solid at room temperature.))) or ((-4 - -2) <= (16 + 13) <= (-20 - 3)) or ((18 * -17) < (15 % 7))) or (Diamond is a gas at room temperature.) or (((not not ((5 * 9) < (6 * 7 * -9 * -4))) and (((2 ** 3) == (10 * 13)) or ((1 ** 3) >= (4 * -17)))) or (The French Revolution began occurred in 1789.)))
C. not not (((((The chemical symbol for Manganese is Co.) and ((1 ** 1) <= (5 ** 3))) and ((The currency of Argentina is the Peso.) and (Vietnam is in Asia.))) and (not (Steam is a liquid at room temperature.)) and (Oil is a liquid at room temperature.)) or (((4 ** 3) != (1 ** 3)) or ((The capital of Thailand is Singapore.) or (The currency of Thailand is the Rupiah.))) or (not ((21 % 7) == (0 * 20))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
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"question": "Study the following logical statements:\n\nA. ((not not ((35 % 2) == (1 - -10))) or (not (not not (not ((4 ** 1) == (25 % 5)))))) or (((There are 30 days in April.) or (not ((The currency of Czech Republic is the Koruna.) or (156 is an even number.)))) and (not (The 1960 Olympics were held in Rome.)))\nB. not not (((not (not not (Wood is a solid at room temperature.))) or ((-4 - -2) <= (16 + 13) <= (-20 - 3)) or ((18 * -17) < (15 % 7))) or (Diamond is a gas at room temperature.) or (((not not ((5 * 9) < (6 * 7 * -9 * -4))) and (((2 ** 3) == (10 * 13)) or ((1 ** 3) >= (4 * -17)))) or (The French Revolution began occurred in 1789.)))\nC. not not (((((The chemical symbol for Manganese is Co.) and ((1 ** 1) <= (5 ** 3))) and ((The currency of Argentina is the Peso.) and (Vietnam is in Asia.))) and (not (Steam is a liquid at room temperature.)) and (Oil is a liquid at room temperature.)) or (((4 ** 3) != (1 ** 3)) or ((The capital of Thailand is Singapore.) or (The currency of Thailand is the Rupiah.))) or (not ((21 % 7) == (0 * 20))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
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logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (((9 * 3 + 7 * -10) <= (-7 * 10 + -6 * -9) <= (-15 - -11)) or (((-19 + 17) >= (3 * 7)) and (There are 31 days in March.)) or (((1 - 12) < (-11 + 1)) or ((The Earth revolves around the Sun.) and (The 2004 Olympics were held in Athens.))))
B. ((India is in Asia.) and (((0 + 15) < (1 * 6)) or ((24 % 2) < (-15 - 1))) and (((7 + 12) < (-12 + -8)) or ((The currency of South Africa is the Rand.) or (The square root of 144 is 12.)))) or (not not (((Steam is a gas at room temperature.) or ((19 + -3) != (1 * -8 * 9 * -2))) or (((0 + 5) <= (-3 + 10)) or ((-10 + 8) >= (4 ** 2)))))
C. not (not not (not not ((10 * 2 * -9 * -6) == (3 ** 3))))
D. (((-5 - 11) == (2 * 3)) and (((84 is a prime number.) or ((-2 - 13) < (-5 - 2) < (19 * -2))) and (The capital of Chile is Santiago.))) or (not not (not (not (86 is an even number.))))
E. not ((Diamond is a solid at room temperature.) and ((18 - 15) == (9 - 16)))
F. (((The 2004 Olympics were held in Athens.) or (not ((27 % 10) <= (-1 + -11) <= (5 ** 3)))) or ((18 + -15) != (32 % 3))) or (((Brazil is in North America.) or ((The currency of Canada is the Rupiah.) and ((-6 - 15) != (20 % 7)))) and (((Air is a gas at room temperature.) and ((8 * 5 * -6 * -4) >= (33 % 2))) or (((-2 + -6) > (20 - 11)) or (The 1904 Olympics were held in St. Louis.))))
G. (((Egypt is in Asia.) or ((7 - 15) == (-1 * -2))) and (not (not (A salmon is a bird.)))) and ((((2 * -9 - -3 * 6) >= (0 + 3)) and (There are 30 days in September.)) and (((The capital of Sweden is Stockholm.) or (Mercury is the 2nd planet from the Sun.)) and ((1 ** 1) == (-20 + 19))))
H. not not (((14 - -4) != (11 * 2)) and ((not ((10 + -6) == (-14 + -19))) and (((25 % 9) != (12 - 18)) and ((-6 * -2 + -10 * 7) < (19 * -7)))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
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"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (((9 * 3 + 7 * -10) <= (-7 * 10 + -6 * -9) <= (-15 - -11)) or (((-19 + 17) >= (3 * 7)) and (There are 31 days in March.)) or (((1 - 12) < (-11 + 1)) or ((The Earth revolves around the Sun.) and (The 2004 Olympics were held in Athens.))))\nB. ((India is in Asia.) and (((0 + 15) < (1 * 6)) or ((24 % 2) < (-15 - 1))) and (((7 + 12) < (-12 + -8)) or ((The currency of South Africa is the Rand.) or (The square root of 144 is 12.)))) or (not not (((Steam is a gas at room temperature.) or ((19 + -3) != (1 * -8 * 9 * -2))) or (((0 + 5) <= (-3 + 10)) or ((-10 + 8) >= (4 ** 2)))))\nC. not (not not (not not ((10 * 2 * -9 * -6) == (3 ** 3))))\nD. (((-5 - 11) == (2 * 3)) and (((84 is a prime number.) or ((-2 - 13) < (-5 - 2) < (19 * -2))) and (The capital of Chile is Santiago.))) or (not not (not (not (86 is an even number.))))\nE. not ((Diamond is a solid at room temperature.) and ((18 - 15) == (9 - 16)))\nF. (((The 2004 Olympics were held in Athens.) or (not ((27 % 10) <= (-1 + -11) <= (5 ** 3)))) or ((18 + -15) != (32 % 3))) or (((Brazil is in North America.) or ((The currency of Canada is the Rupiah.) and ((-6 - 15) != (20 % 7)))) and (((Air is a gas at room temperature.) and ((8 * 5 * -6 * -4) >= (33 % 2))) or (((-2 + -6) > (20 - 11)) or (The 1904 Olympics were held in St. Louis.))))\nG. (((Egypt is in Asia.) or ((7 - 15) == (-1 * -2))) and (not (not (A salmon is a bird.)))) and ((((2 * -9 - -3 * 6) >= (0 + 3)) and (There are 30 days in September.)) and (((The capital of Sweden is Stockholm.) or (Mercury is the 2nd planet from the Sun.)) and ((1 ** 1) == (-20 + 19))))\nH. not not (((14 - -4) != (11 * 2)) and ((not ((10 + -6) == (-14 + -19))) and (((25 % 9) != (12 - 18)) and ((-6 * -2 + -10 * 7) < (19 * -7)))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
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"language": "en",
"num_options": 8,
"seed": 51482902,
"true_count": 6
},
"seed": 51482902,
"task_id": 651482902,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. ((not ((3 ** 2) >= (14 + -6))) and ((((13 * 20) >= (-8 * 11)) or (猫头鹰是鸟类。)) and ((水在常温下是气体。) and ((6 - -15) <= (-10 * -15))))) or ((人体有206块骨头。) and ((摩洛哥位于非洲。) or (墨西哥的首都是内罗毕。))) or (not not ((((8 + 2) > (3 ** 3)) and (2024年奥运会在阿姆斯特丹举办。)) or (墨西哥位于北美洲。)))
B. not not ((((企鹅能飞翔。) or (第一次世界大战结束发生在1923年。)) and (not not (158是奇数。))) and (not not (((17 * -12) >= (4 * 8 * 2 * -9)) and (第一次世界大战开始发生在1914年。))))
C. (((((1 ** 1) != (11 * 20)) or (沙特阿拉伯的首都是利雅得。)) or ((火烈鸟是鸟类。) and ((11 * 15) == (-16 * 10)))) and (哥伦布到达美洲发生在1492年。) and ((not not (金星是距离太阳第2近的行星。)) and (not ((-18 - -19) <= (2 * 1 + 8 * -10))))) or ((not not (((-5 * 6) != (-19 - 3)) or ((7 * -4 * 5 * -10) >= (-3 * 4)))) or (not not ((钛的化学符号是Ti。) and (马有0条腿。))))
D. not (not not ((((-7 * 0 + 3 * 2) <= (10 * 9 - -8 * -7)) or (25的平方根是5。)) or ((1914年是闰年。) or (镁的化学符号是Au。))))
E. (((((3 * 7 * -6 * -3) >= (11 + 4)) or (鸟有10条腿。)) and (1984年奥运会在洛杉矶举办。)) and (((马是哺乳动物。) or (新西兰的货币是克朗。)) or (not not (海王星是距离太阳第3近的行星。)))) or ((2024年奥运会在伦敦举办。) and (not not (not ((1 ** 2) < (-20 + -11) < (-4 - 18)))))
F. not ((66是斐波那契数。) or ((-20 * -7) <= (3 % 10)))
G. (((-2 + -2) < (-15 * 20) < (14 - 13)) and (not (钻石由碳元素组成。))) and (not ((地球是距离太阳第7近的行星。) and ((金星是距离太阳第3近的行星。) or ((2 - -17) >= (-6 + 18)))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 82255341,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. ((not ((3 ** 2) >= (14 + -6))) and ((((13 * 20) >= (-8 * 11)) or (猫头鹰是鸟类。)) and ((水在常温下是气体。) and ((6 - -15) <= (-10 * -15))))) or ((人体有206块骨头。) and ((摩洛哥位于非洲。) or (墨西哥的首都是内罗毕。))) or (not not ((((8 + 2) > (3 ** 3)) and (2024年奥运会在阿姆斯特丹举办。)) or (墨西哥位于北美洲。)))\nB. not not ((((企鹅能飞翔。) or (第一次世界大战结束发生在1923年。)) and (not not (158是奇数。))) and (not not (((17 * -12) >= (4 * 8 * 2 * -9)) and (第一次世界大战开始发生在1914年。))))\nC. (((((1 ** 1) != (11 * 20)) or (沙特阿拉伯的首都是利雅得。)) or ((火烈鸟是鸟类。) and ((11 * 15) == (-16 * 10)))) and (哥伦布到达美洲发生在1492年。) and ((not not (金星是距离太阳第2近的行星。)) and (not ((-18 - -19) <= (2 * 1 + 8 * -10))))) or ((not not (((-5 * 6) != (-19 - 3)) or ((7 * -4 * 5 * -10) >= (-3 * 4)))) or (not not ((钛的化学符号是Ti。) and (马有0条腿。))))\nD. not (not not ((((-7 * 0 + 3 * 2) <= (10 * 9 - -8 * -7)) or (25的平方根是5。)) or ((1914年是闰年。) or (镁的化学符号是Au。))))\nE. (((((3 * 7 * -6 * -3) >= (11 + 4)) or (鸟有10条腿。)) and (1984年奥运会在洛杉矶举办。)) and (((马是哺乳动物。) or (新西兰的货币是克朗。)) or (not not (海王星是距离太阳第3近的行星。)))) or ((2024年奥运会在伦敦举办。) and (not not (not ((1 ** 2) < (-20 + -11) < (-4 - 18)))))\nF. not ((66是斐波那契数。) or ((-20 * -7) <= (3 % 10)))\nG. (((-2 + -2) < (-15 * 20) < (14 - 13)) and (not (钻石由碳元素组成。))) and (not ((地球是距离太阳第7近的行星。) and ((金星是距离太阳第3近的行星。) or ((2 - -17) >= (-6 + 18)))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 82255341,
"true_count": 4
},
"seed": 82255341,
"task_id": 682255341,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not ((France is in Asia.) and (The currency of Japan is the Won.))
B. (not not ((137 is a perfect square.) or (There are 31 days in August.))) and ((not (Helium is a liquid at room temperature.)) and (((19 - 8) < (-3 * 2) < (-1 - 3)) or (The currency of Russia is the Franc.)))
C. (not not ((The chemical symbol for Lead is Pb.) or (1990 is a leap year.))) or (The chemical symbol for Copper is Zn.) or (((3 * -6 + 8 * 5) < (-7 + 15)) or ((The 1924 Olympics were held in Paris.) or ((12 * 1) < (-2 - -17) < (9 % 1))))
D. (not ((2015 is a leap year.) or (The Soviet Union dissolved occurred in 1991.))) or ((not not (The currency of Norway is the Krone.)) or ((Argentina is in South America.) or (The chemical symbol for Carbon is C.)))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 22110186,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. not not ((France is in Asia.) and (The currency of Japan is the Won.))\nB. (not not ((137 is a perfect square.) or (There are 31 days in August.))) and ((not (Helium is a liquid at room temperature.)) and (((19 - 8) < (-3 * 2) < (-1 - 3)) or (The currency of Russia is the Franc.)))\nC. (not not ((The chemical symbol for Lead is Pb.) or (1990 is a leap year.))) or (The chemical symbol for Copper is Zn.) or (((3 * -6 + 8 * 5) < (-7 + 15)) or ((The 1924 Olympics were held in Paris.) or ((12 * 1) < (-2 - -17) < (9 % 1))))\nD. (not ((2015 is a leap year.) or (The Soviet Union dissolved occurred in 1991.))) or ((not not (The currency of Norway is the Krone.)) or ((Argentina is in South America.) or (The chemical symbol for Carbon is C.)))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 22110186,
"true_count": 2
},
"seed": 22110186,
"task_id": 622110186,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not ((6 * 5 + 2 * -7) >= (3 * -8))
B. (-2 + -10) <= (5 ** 2)
C. 84 is divisible by 9.
D. not not (not (The chemical symbol for Nitrogen is N.))
E. (50 % 10) < (16 - -8)
F. not ((15 * 16) > (-10 + -10))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 96316593,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. not not ((6 * 5 + 2 * -7) >= (3 * -8))\nB. (-2 + -10) <= (5 ** 2)\nC. 84 is divisible by 9.\nD. not not (not (The chemical symbol for Nitrogen is N.))\nE. (50 % 10) < (16 - -8)\nF. not ((15 * 16) > (-10 + -10))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 96316593,
"true_count": 3
},
"seed": 96316593,
"task_id": 696316593,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not not (not (((not (The chemical symbol for Nickel is Cu.)) or (not (((-19 + 15) < (19 * 15) < (6 + 15)) or (A iguana is an insect.)))) and (not not (((The Soviet Union dissolved occurred in 1991.) and (Oxygen is a liquid at room temperature.)) or (((20 - -7) > (-3 - 18)) and (Italy is in North America.))))))
B. not not (not not ((not ((The chemical symbol for Potassium is Cl.) and ((-10 * 2) < (5 * 3 - 6 * -4)))) and ((((1 * 4 - -6 * -1) >= (18 % 1)) and (The chemical symbol for Manganese is C.)) or (((-6 * -16) == (-3 + -13)) or (Ice is a liquid at room temperature.))) and (((4 ** 1) >= (8 * 15)) and (not ((15 - 16) < (3 ** 1))) and ((3 % 5) > (-18 + -10)))))
C. not not ((not (not (2011 is a leap year.))) or (not not ((((Whales are fish.) or (The currency of Australia is the Koruna.)) and ((The currency of Indonesia is the Rupiah.) and (The United States declared independence occurred in 1776.))) and ((-1 * 3 * 4 * -4) > (-13 * 17)) and (A kangaroo has 2 legs.))))
D. not ((not (not not ((-2 * -1 + 9 * 2) <= (7 * 6)))) or (not not (not ((3 ** 3) >= (-7 * 9)))) or (((not ((The currency of Canada is the Won.) or (Bats are blind.))) or (not not (The chemical symbol for Tin is K.)) or (Neptune is the 8th planet from the Sun.)) and (((46 % 8) < (-7 + 2)) or ((not ((-10 * 11) <= (-7 * -4 + -6 * -3) <= (-10 + 3))) and (not not (The chemical symbol for Sulfur is S.))))))
E. not not (not ((((not ((4 - 0) > (1 - -11))) or ((The square root of 225 is 4.) and (Germany is in Europe.))) and ((not ((20 * 18) != (8 * 3 * 8 * 7))) and (((-18 + -9) >= (4 ** 2)) and ((6 * 0) < (-14 * -5) < (7 - -10))))) or ((The capital of Turkey is Ankara.) and (not (Colombia is in South America.))) or (not (The 2016 Olympics were held in Athens.))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 29594592,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. not not (not (((not (The chemical symbol for Nickel is Cu.)) or (not (((-19 + 15) < (19 * 15) < (6 + 15)) or (A iguana is an insect.)))) and (not not (((The Soviet Union dissolved occurred in 1991.) and (Oxygen is a liquid at room temperature.)) or (((20 - -7) > (-3 - 18)) and (Italy is in North America.))))))\nB. not not (not not ((not ((The chemical symbol for Potassium is Cl.) and ((-10 * 2) < (5 * 3 - 6 * -4)))) and ((((1 * 4 - -6 * -1) >= (18 % 1)) and (The chemical symbol for Manganese is C.)) or (((-6 * -16) == (-3 + -13)) or (Ice is a liquid at room temperature.))) and (((4 ** 1) >= (8 * 15)) and (not ((15 - 16) < (3 ** 1))) and ((3 % 5) > (-18 + -10)))))\nC. not not ((not (not (2011 is a leap year.))) or (not not ((((Whales are fish.) or (The currency of Australia is the Koruna.)) and ((The currency of Indonesia is the Rupiah.) and (The United States declared independence occurred in 1776.))) and ((-1 * 3 * 4 * -4) > (-13 * 17)) and (A kangaroo has 2 legs.))))\nD. not ((not (not not ((-2 * -1 + 9 * 2) <= (7 * 6)))) or (not not (not ((3 ** 3) >= (-7 * 9)))) or (((not ((The currency of Canada is the Won.) or (Bats are blind.))) or (not not (The chemical symbol for Tin is K.)) or (Neptune is the 8th planet from the Sun.)) and (((46 % 8) < (-7 + 2)) or ((not ((-10 * 11) <= (-7 * -4 + -6 * -3) <= (-10 + 3))) and (not not (The chemical symbol for Sulfur is S.))))))\nE. not not (not ((((not ((4 - 0) > (1 - -11))) or ((The square root of 225 is 4.) and (Germany is in Europe.))) and ((not ((20 * 18) != (8 * 3 * 8 * 7))) and (((-18 + -9) >= (4 ** 2)) and ((6 * 0) < (-14 * -5) < (7 - -10))))) or ((The capital of Turkey is Ankara.) and (not (Colombia is in South America.))) or (not (The 2016 Olympics were held in Athens.))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 29594592,
"true_count": 1
},
"seed": 29594592,
"task_id": 629594592,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not (not ((not not ((2 + -20) >= (6 + 20))) or (not (Air is a gas at room temperature.))))) and (((6 % 9) <= (19 * -17)) and (((-6 * 18) > (-3 * -3 + -4 * -2)) and ((-2 - 8) == (2 ** 3)))) and (not (not ((-18 * 15) != (9 + 6))))
B. (not (((A cat has 4 legs.) and ((The capital of Vietnam is Bucharest.) and (A carp is a fish.))) and (((The chemical symbol for Silver is Ag.) and ((1 ** 2) > (5 - -13))) or ((Ice is a gas at room temperature.) or ((-20 + -15) >= (14 * 3)))))) or ((not not ((2 - 18) != (14 * -9))) and ((((3 + 20) < (47 % 1)) and (not ((13 * -8) <= (-14 + 15)))) and (((Morocco is in Asia.) or (Australia is in Oceania.)) and (((35 % 1) == (16 % 6)) or ((5 ** 2) <= (14 * -20) <= (-4 - 10))))))
C. ((not (not (There are 30 days in March.))) or (not not ((10 * 3 * 9 * 1) != (4 ** 3)))) or ((The square root of 49 is 7.) and ((64 is less than or equal to 1.) and (Saturn is the 6th planet from the Sun.)) and ((3 ** 3) <= (10 * 0 - -10 * 8))) or (not not (not ((((8 * 5 * 9 * 7) < (12 * -17)) or ((-8 * 1 * 4 * -1) < (5 * -4))) and ((Japan is in Asia.) or ((-1 - -15) != (-18 + 6))))))
D. (not (not not (The currency of Australia is the Peso.))) or (not (not not (The currency of South Korea is the Won.)))
E. not ((((not not ((-7 * 10 - -2 * -6) <= (1 ** 3))) or ((The first moon landing occurred in 1969.) or ((20 * -6) >= (-13 * 2)))) and (((77 is divisible by 7.) and ((5 * -10 * -4 * 0) >= (10 % 3))) and (((14 + -6) == (30 % 6)) and ((6 * 2 + 2 * -8) <= (7 - 5))))) or (((not ((17 - -14) >= (-2 * 10 - 2 * 2))) and (((28 % 1) == (-5 - 3)) and ((-20 + -8) != (-12 * -15)))) and ((1 ** 1) != (5 + -7))))
F. not (((not ((Iron is a gas at room temperature.) and (2013 is a leap year.))) or (not not ((15 - -10) > (12 + 1))) or (not not (((3 ** 3) < (-10 - -16)) and (The Moon produces its own light.)))) and (The capital of Czech Republic is New Delhi.) and ((((1 * -10 * 0 * 7) != (13 - -13)) and ((The currency of China is the Dong.) or (The chemical symbol for Aluminum is Al.))) or (The 1908 Olympics were held in London.)))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "B,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 47335793,
"true_count": 5
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (not (not ((not not ((2 + -20) >= (6 + 20))) or (not (Air is a gas at room temperature.))))) and (((6 % 9) <= (19 * -17)) and (((-6 * 18) > (-3 * -3 + -4 * -2)) and ((-2 - 8) == (2 ** 3)))) and (not (not ((-18 * 15) != (9 + 6))))\nB. (not (((A cat has 4 legs.) and ((The capital of Vietnam is Bucharest.) and (A carp is a fish.))) and (((The chemical symbol for Silver is Ag.) and ((1 ** 2) > (5 - -13))) or ((Ice is a gas at room temperature.) or ((-20 + -15) >= (14 * 3)))))) or ((not not ((2 - 18) != (14 * -9))) and ((((3 + 20) < (47 % 1)) and (not ((13 * -8) <= (-14 + 15)))) and (((Morocco is in Asia.) or (Australia is in Oceania.)) and (((35 % 1) == (16 % 6)) or ((5 ** 2) <= (14 * -20) <= (-4 - 10))))))\nC. ((not (not (There are 30 days in March.))) or (not not ((10 * 3 * 9 * 1) != (4 ** 3)))) or ((The square root of 49 is 7.) and ((64 is less than or equal to 1.) and (Saturn is the 6th planet from the Sun.)) and ((3 ** 3) <= (10 * 0 - -10 * 8))) or (not not (not ((((8 * 5 * 9 * 7) < (12 * -17)) or ((-8 * 1 * 4 * -1) < (5 * -4))) and ((Japan is in Asia.) or ((-1 - -15) != (-18 + 6))))))\nD. (not (not not (The currency of Australia is the Peso.))) or (not (not not (The currency of South Korea is the Won.)))\nE. not ((((not not ((-7 * 10 - -2 * -6) <= (1 ** 3))) or ((The first moon landing occurred in 1969.) or ((20 * -6) >= (-13 * 2)))) and (((77 is divisible by 7.) and ((5 * -10 * -4 * 0) >= (10 % 3))) and (((14 + -6) == (30 % 6)) and ((6 * 2 + 2 * -8) <= (7 - 5))))) or (((not ((17 - -14) >= (-2 * 10 - 2 * 2))) and (((28 % 1) == (-5 - 3)) and ((-20 + -8) != (-12 * -15)))) and ((1 ** 1) != (5 + -7))))\nF. not (((not ((Iron is a gas at room temperature.) and (2013 is a leap year.))) or (not not ((15 - -10) > (12 + 1))) or (not not (((3 ** 3) < (-10 - -16)) and (The Moon produces its own light.)))) and (The capital of Czech Republic is New Delhi.) and ((((1 * -10 * 0 * 7) != (13 - -13)) and ((The currency of China is the Dong.) or (The chemical symbol for Aluminum is Al.))) or (The 1908 Olympics were held in London.)))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 47335793,
"true_count": 5
},
"seed": 47335793,
"task_id": 647335793,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not not (((not not (((11 % 4) == (-17 - -5)) and ((13 + -11) >= (3 ** 2)))) and (Mercury is a solid at room temperature.)) or (((The currency of Argentina is the Krona.) or ((-7 * 6) < (-9 * 15) < (-7 - 5))) or (((3 + 16) <= (1 * -1 * -9 * -2) <= (6 * 20)) or (Gold is a gas at room temperature.))) or ((((2 ** 1) > (10 * -1 + 0 * -1)) or (not not (Neptune is the 8th planet from the Sun.))) or (not (29 is a prime number.))))
B. (not not (not not (The capital of Turkey is Prague.))) or (((The 2016 Olympics were held in Los Angeles.) and ((-2 + 8) < (1 - -15))) or ((((The capital of Hungary is Beijing.) or (Carbon dioxide is a solid at room temperature.)) and (not not (The capital of Indonesia is Jakarta.))) and (((-4 * -3 * 8 * -9) >= (3 % 10)) and (The 1948 Olympics were held in London.)) and ((2 ** 1) == (4 * 2 - 6 * -7))))
C. not not (not ((((3 + -4) == (3 ** 1)) or (not not (The chemical symbol for Calcium is Ca.))) and (The capital of Portugal is Bucharest.)))
D. not (not not ((Copper is a gas at room temperature.) and (not (Gold is a solid at room temperature.)) and ((((10 * -7) > (17 * 9)) or ((16 + -5) <= (2 + -13))) and (The human body has 150 bones.))))
E. (not not (not not ((not (India is in South America.)) and ((12 - 17) <= (17 * 4))))) or (not not ((not not (Sound travels faster in a vacuum.)) or (not not (not (2062 is a leap year.)))))
F. ((not (The currency of Norway is the Peso.)) or (((not not (The 1904 Olympics were held in Tokyo.)) or ((The 1904 Olympics were held in St. Louis.) or (137 is an even number.))) or ((not not (There are 31 days in February.)) and (World War II ended occurred in 1945.)))) or (not (not not ((not not ((19 - 10) > (11 + -1))) or (((-19 * 11) > (-9 * 16)) or ((-9 + 18) <= (-7 + 20))))))
G. not (not ((not (((20 - 13) == (11 - -12)) and ((-8 - 4) != (-11 * 3)))) or ((((2 ** 1) >= (6 * -8 - 1 * 10)) and ((14 - -5) < (2 + -1) < (-7 * 10 + -1 * 10))) or (not ((2 ** 3) <= (5 * 0 * 2 * -6))))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,C,D,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 15474752,
"true_count": 6
},
"question": "Review these logical expressions:\n\nA. not not (((not not (((11 % 4) == (-17 - -5)) and ((13 + -11) >= (3 ** 2)))) and (Mercury is a solid at room temperature.)) or (((The currency of Argentina is the Krona.) or ((-7 * 6) < (-9 * 15) < (-7 - 5))) or (((3 + 16) <= (1 * -1 * -9 * -2) <= (6 * 20)) or (Gold is a gas at room temperature.))) or ((((2 ** 1) > (10 * -1 + 0 * -1)) or (not not (Neptune is the 8th planet from the Sun.))) or (not (29 is a prime number.))))\nB. (not not (not not (The capital of Turkey is Prague.))) or (((The 2016 Olympics were held in Los Angeles.) and ((-2 + 8) < (1 - -15))) or ((((The capital of Hungary is Beijing.) or (Carbon dioxide is a solid at room temperature.)) and (not not (The capital of Indonesia is Jakarta.))) and (((-4 * -3 * 8 * -9) >= (3 % 10)) and (The 1948 Olympics were held in London.)) and ((2 ** 1) == (4 * 2 - 6 * -7))))\nC. not not (not ((((3 + -4) == (3 ** 1)) or (not not (The chemical symbol for Calcium is Ca.))) and (The capital of Portugal is Bucharest.)))\nD. not (not not ((Copper is a gas at room temperature.) and (not (Gold is a solid at room temperature.)) and ((((10 * -7) > (17 * 9)) or ((16 + -5) <= (2 + -13))) and (The human body has 150 bones.))))\nE. (not not (not not ((not (India is in South America.)) and ((12 - 17) <= (17 * 4))))) or (not not ((not not (Sound travels faster in a vacuum.)) or (not not (not (2062 is a leap year.)))))\nF. ((not (The currency of Norway is the Peso.)) or (((not not (The 1904 Olympics were held in Tokyo.)) or ((The 1904 Olympics were held in St. Louis.) or (137 is an even number.))) or ((not not (There are 31 days in February.)) and (World War II ended occurred in 1945.)))) or (not (not not ((not not ((19 - 10) > (11 + -1))) or (((-19 * 11) > (-9 * 16)) or ((-9 + 18) <= (-7 + 20))))))\nG. not (not ((not (((20 - 13) == (11 - -12)) and ((-8 - 4) != (-11 * 3)))) or ((((2 ** 1) >= (6 * -8 - 1 * 10)) and ((14 - -5) < (2 + -1) < (-7 * 10 + -1 * 10))) or (not ((2 ** 3) <= (5 * 0 * 2 * -6))))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
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"language": "en",
"num_options": 7,
"seed": 15474752,
"true_count": 6
},
"seed": 15474752,
"task_id": 615474752,
"task_type": "boolean_expressions"
} |
logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. not (not not (金星是距离太阳第2近的行星。))
B. 氧气对人类生存是必需的。
C. 第二次世界大战开始发生在1938年。
D. ((闪电不会两次击中同一个地方。) and (尼日利亚的货币是里亚尔。)) or ((水蒸气在常温下是气体。) and (韩国的首都是柏林。))
E. ((光速约为每秒30万公里。) and ((13 + -18) >= (0 + 0))) or ((人体有150块骨头。) and (钾的化学符号是K。))
F. ((8是偶数。) and ((-6 * 4 - 2 * 4) > (34 % 3))) and (not (肯尼亚的首都是内罗毕。))
G. not ((24 % 8) == (-19 + 20))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
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"difficulty": 1,
"gpt_response": "",
"metadata": {
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"seed": 50651545,
"true_count": 2
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"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. not (not not (金星是距离太阳第2近的行星。))\nB. 氧气对人类生存是必需的。\nC. 第二次世界大战开始发生在1938年。\nD. ((闪电不会两次击中同一个地方。) and (尼日利亚的货币是里亚尔。)) or ((水蒸气在常温下是气体。) and (韩国的首都是柏林。))\nE. ((光速约为每秒30万公里。) and ((13 + -18) >= (0 + 0))) or ((人体有150块骨头。) and (钾的化学符号是K。))\nF. ((8是偶数。) and ((-6 * 4 - 2 * 4) > (34 % 3))) and (not (肯尼亚的首都是内罗毕。))\nG. not ((24 % 8) == (-19 + 20))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 50651545,
"true_count": 2
},
"seed": 50651545,
"task_id": 650651545,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (not ((((not (The 2020 Olympics were held in Tokyo.)) or (The speed of light is approximately 300,000 km/s.)) or (((3 ** 2) >= (-10 + -13)) and (37 is a prime number.)) or (((38 % 2) != (-10 - -20)) and ((-18 + -17) > (17 * 17)))) and (not not (not (51 is divisible by 12.)))))
B. not not (((not not (not (not not ((6 - 10) >= (-16 + -5))))) or (not not ((4 ** 2) > (4 + -13)))) or (not not ((not not ((72 is a Fibonacci number.) and ((-5 * -6) > (-19 - -1)))) or (((-4 * 3 + -5 * 2) > (8 * 7)) and (The capital of Egypt is Cairo.)) or (not (((-3 + 18) <= (3 * 6 + 0 * -8) <= (-16 * -6)) or (A mouse is a fish.))))))
C. not not ((not (not ((5 ** 2) > (1 ** 2)))) and (not ((not ((Copper is a liquid at room temperature.) and (World War I ended occurred in 1918.))) or ((((-13 - 16) < (-7 * 10 * -7 * 1)) and (A day on Earth is 24 hours.)) or (not not (The chemical symbol for Oxygen is O.))))))
D. not (((not (not (not not ((-10 * 19) > (49 % 9))))) or (not not (not not ((Germany is in Europe.) and ((-10 * 3 - 8 * 10) != (8 + 4)))))) or ((not (13 is greater than 66.)) or (not not (((United Kingdom is in Europe.) and (The currency of Argentina is the Peso.)) or (not ((-17 - 18) >= (15 % 4)))))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
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"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not ((((not (The 2020 Olympics were held in Tokyo.)) or (The speed of light is approximately 300,000 km/s.)) or (((3 ** 2) >= (-10 + -13)) and (37 is a prime number.)) or (((38 % 2) != (-10 - -20)) and ((-18 + -17) > (17 * 17)))) and (not not (not (51 is divisible by 12.)))))\nB. not not (((not not (not (not not ((6 - 10) >= (-16 + -5))))) or (not not ((4 ** 2) > (4 + -13)))) or (not not ((not not ((72 is a Fibonacci number.) and ((-5 * -6) > (-19 - -1)))) or (((-4 * 3 + -5 * 2) > (8 * 7)) and (The capital of Egypt is Cairo.)) or (not (((-3 + 18) <= (3 * 6 + 0 * -8) <= (-16 * -6)) or (A mouse is a fish.))))))\nC. not not ((not (not ((5 ** 2) > (1 ** 2)))) and (not ((not ((Copper is a liquid at room temperature.) and (World War I ended occurred in 1918.))) or ((((-13 - 16) < (-7 * 10 * -7 * 1)) and (A day on Earth is 24 hours.)) or (not not (The chemical symbol for Oxygen is O.))))))\nD. not (((not (not (not not ((-10 * 19) > (49 % 9))))) or (not not (not not ((Germany is in Europe.) and ((-10 * 3 - 8 * 10) != (8 + 4)))))) or ((not (13 is greater than 66.)) or (not not (((United Kingdom is in Europe.) and (The currency of Argentina is the Peso.)) or (not ((-17 - 18) >= (15 % 4)))))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 56609439,
"true_count": 2
},
"seed": 56609439,
"task_id": 656609439,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. ((((-9 - -3) > (-4 - -6)) or (((6 * -3 + -5 * -4) == (-1 + 10)) and (二氧化碳在常温下是气体。))) or (((8 * -2 + 3 * 1) > (2 - 3)) and (not not ((-20 + 19) > (6 * -5 - -7 * 5))))) and ((2 * -16) != (-14 * -5)) and (not ((-19 - -4) < (3 * -7 * -4 * -1)))
B. ((((2 * -15) <= (2 + -17) <= (-18 + 1)) or (((-7 - -19) != (29 % 10)) and (天王星是距离太阳第7近的行星。))) or (((鸭子有2条腿。) and ((-3 * 1 + -3 * -8) < (11 * -8))) and ((2085年是闰年。) or ((-12 * 12) == (-8 * 10 * 5 * -9))))) and ((((0 + -13) > (-5 + 3)) and (not (第二次世界大战开始发生在1939年。))) or (not (not ((29 % 8) <= (17 * 4)))))
C. ((not not (((10 - 16) != (20 * 8)) and ((2 * 9) < (-10 + 6) < (-18 + -9)))) and (not not (((1 * 9 + -3 * 6) == (4 * -3 + 7 * 4)) and ((-13 - 15) >= (13 * -18))))) and (not not ((地球是距离太阳第7近的行星。) or ((-2 + -19) > (2 * -20)))) and ((not ((土星是距离太阳第6近的行星。) or ((-14 * -3) >= (15 + -4)))) or (not not ((9 * -14) <= (4 ** 3))))
D. (((not (泰坦尼克号沉没发生在1912年。)) and ((第二次世界大战结束发生在1945年。) or (新加坡的货币是新加坡元。))) and (((-9 * 0 + 7 * 1) >= (13 - -13)) and ((9 * -7) > (11 - -2))) and ((-14 - -15) <= (-1 + -9) <= (7 * 17))) and (((2016年奥运会在里约热内卢举办。) or ((6 * 13) < (0 * 3) < (-5 - 7))) and (((-8 * 3 * 8 * 10) < (25 % 4) < (14 * 6)) and (大象是哺乳动物。))) and ((2067年是闰年。) or (伦敦大火发生在1656年。))
E. ((瑞典的货币是欧元。) and ((-10 + 9) > (-8 * -3)) and (((0 * 4 - -5 * -5) <= (12 * -9)) or ((-2 * -9 - 5 * 3) == (16 * -6)))) or ((南非的货币是里亚尔。) or (((11 - -1) < (4 + -19) < (-5 + 0)) and (莱特兄弟首次飞行发生在1903年。))) or (not ((3 * 19) > (-1 * -8 * 8 * 4)))
F. ((((-2 + -13) <= (-3 + -12)) and (not ((20 - -19) < (2 * 13)))) or (蚂蚁是昆虫。)) and (((not not ((-18 + 9) != (-17 * 2))) or (((-17 - -2) <= (3 ** 2)) and (人类首次登月发生在1970年。))) and (not (钛的化学符号是Ni。)) and ((not (法国大革命开始发生在1789年。)) and (not not ((8 + -11) <= (-10 * -15)))))
G. ((((1960年奥运会在罗马举办。) and (1994年是闰年。)) and (not not (1904年奥运会在雅典举办。))) and (not not (not (比利时的首都是伯尔尼。)))) or (not ((((12 * 10) >= (15 * 5)) or (锡的化学符号是Ag。)) and (not (1908年奥运会在伦敦举办。))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
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"answer": "B,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
"num_options": 7,
"seed": 14502894,
"true_count": 3
},
"question": "审视以下逻辑表达式：\n\nA. ((((-9 - -3) > (-4 - -6)) or (((6 * -3 + -5 * -4) == (-1 + 10)) and (二氧化碳在常温下是气体。))) or (((8 * -2 + 3 * 1) > (2 - 3)) and (not not ((-20 + 19) > (6 * -5 - -7 * 5))))) and ((2 * -16) != (-14 * -5)) and (not ((-19 - -4) < (3 * -7 * -4 * -1)))\nB. ((((2 * -15) <= (2 + -17) <= (-18 + 1)) or (((-7 - -19) != (29 % 10)) and (天王星是距离太阳第7近的行星。))) or (((鸭子有2条腿。) and ((-3 * 1 + -3 * -8) < (11 * -8))) and ((2085年是闰年。) or ((-12 * 12) == (-8 * 10 * 5 * -9))))) and ((((0 + -13) > (-5 + 3)) and (not (第二次世界大战开始发生在1939年。))) or (not (not ((29 % 8) <= (17 * 4)))))\nC. ((not not (((10 - 16) != (20 * 8)) and ((2 * 9) < (-10 + 6) < (-18 + -9)))) and (not not (((1 * 9 + -3 * 6) == (4 * -3 + 7 * 4)) and ((-13 - 15) >= (13 * -18))))) and (not not ((地球是距离太阳第7近的行星。) or ((-2 + -19) > (2 * -20)))) and ((not ((土星是距离太阳第6近的行星。) or ((-14 * -3) >= (15 + -4)))) or (not not ((9 * -14) <= (4 ** 3))))\nD. (((not (泰坦尼克号沉没发生在1912年。)) and ((第二次世界大战结束发生在1945年。) or (新加坡的货币是新加坡元。))) and (((-9 * 0 + 7 * 1) >= (13 - -13)) and ((9 * -7) > (11 - -2))) and ((-14 - -15) <= (-1 + -9) <= (7 * 17))) and (((2016年奥运会在里约热内卢举办。) or ((6 * 13) < (0 * 3) < (-5 - 7))) and (((-8 * 3 * 8 * 10) < (25 % 4) < (14 * 6)) and (大象是哺乳动物。))) and ((2067年是闰年。) or (伦敦大火发生在1656年。))\nE. ((瑞典的货币是欧元。) and ((-10 + 9) > (-8 * -3)) and (((0 * 4 - -5 * -5) <= (12 * -9)) or ((-2 * -9 - 5 * 3) == (16 * -6)))) or ((南非的货币是里亚尔。) or (((11 - -1) < (4 + -19) < (-5 + 0)) and (莱特兄弟首次飞行发生在1903年。))) or (not ((3 * 19) > (-1 * -8 * 8 * 4)))\nF. ((((-2 + -13) <= (-3 + -12)) and (not ((20 - -19) < (2 * 13)))) or (蚂蚁是昆虫。)) and (((not not ((-18 + 9) != (-17 * 2))) or (((-17 - -2) <= (3 ** 2)) and (人类首次登月发生在1970年。))) and (not (钛的化学符号是Ni。)) and ((not (法国大革命开始发生在1789年。)) and (not not ((8 + -11) <= (-10 * -15)))))\nG. ((((1960年奥运会在罗马举办。) and (1994年是闰年。)) and (not not (1904年奥运会在雅典举办。))) and (not not (not (比利时的首都是伯尔尼。)))) or (not ((((12 * 10) >= (15 * 5)) or (锡的化学符号是Ag。)) and (not (1908年奥运会在伦敦举办。))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
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"language": "cn",
"num_options": 7,
"seed": 14502894,
"true_count": 3
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"seed": 14502894,
"task_id": 614502894,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (((((-19 - 11) == (-5 + 19)) and (地球是距离太阳第3近的行星。)) or ((2007年是闰年。) and (76是质数。))) and ((西班牙位于欧洲。) or (not (地球是距离太阳第6近的行星。)))) or (not not (not ((3 ** 1) != (2 * -17)))) or (not not (((16 + 8) < (-6 * 4) < (9 - 8)) and ((33 % 5) != (6 * 2 * 3 * 0))))
B. (((((-1 * 3 + -8 * 10) > (2 ** 3)) or ((-1 * -10 * -9 * -5) != (-20 + -2))) and (哥伦比亚的首都是雅加达。)) and ((氢的化学符号是H。) or ((现代奥运会首届举办发生在1896年。) and (1996年奥运会在亚特兰大举办。)))) and ((印度位于亚洲。) or (((29 % 10) <= (0 * 7 - 5 * 5)) and (65是质数。))) and (not (((42是质数。) or ((4 - -5) < (-19 * -1))) and ((沙特阿拉伯的首都是加拉加斯。) and ((4 * 1 - 2 * 8) >= (37 % 7)))))
C. not (not (((铀的化学符号是U。) and (木头在常温下是液体。)) or (not ((-2 + 14) != (14 * 12)))))
D. not ((((铂的化学符号是Mn。) and (马来西亚的货币是兹罗提。)) or (((3 * -4 * -3 * 9) < (-18 + -2) < (-20 + -4)) and ((-4 * -20) != (-19 + 6)))) and ((火星是距离太阳最近的行星。) and ((8 * -9 + -9 * -10) < (-1 - -4))) and (((第二次世界大战结束发生在1945年。) and ((1 ** 3) <= (29 % 6) <= (5 * 7 + 10 * -8))) and (((2 ** 1) == (-6 + 1)) and ((6 * -3 - 3 * 4) > (3 * 12)))))
E. ((((现代奥运会首届举办发生在1896年。) and ((1 ** 1) <= (-17 * -8))) or ((-1 - 2) < (-5 * 6 * 0 * 5) < (16 * -14))) and (((9 - 15) != (19 - 18)) and ((泰国的首都是新德里。) or ((-11 + -14) > (17 - 18))))) or (((2 * 7 - -6 * 7) <= (8 % 2) <= (-11 - -3)) and ((钙的化学符号是Sn。) and (第二次世界大战开始发生在1939年。))) or ((((-7 * -7) == (20 + -9)) and (not not (俄罗斯位于欧洲。))) and ((1936年奥运会在蒙特利尔举办。) or ((18 * -14) <= (25 % 6))) and ((柏林墙倒塌发生在1999年。) or (((3 * -7 * -9 * 9) >= (43 % 8)) and ((14 + 2) > (9 * 11)))))
F. not not ((水星是距离太阳第2近的行星。) or ((((35 % 6) != (-3 + 8)) and (2089年是闰年。)) or (((7 + -5) == (10 * 9 + -7 * 1)) or (金星是距离太阳第2近的行星。))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
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"answer": "D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"question": "审视以下逻辑表达式：\n\nA. (((((-19 - 11) == (-5 + 19)) and (地球是距离太阳第3近的行星。)) or ((2007年是闰年。) and (76是质数。))) and ((西班牙位于欧洲。) or (not (地球是距离太阳第6近的行星。)))) or (not not (not ((3 ** 1) != (2 * -17)))) or (not not (((16 + 8) < (-6 * 4) < (9 - 8)) and ((33 % 5) != (6 * 2 * 3 * 0))))\nB. (((((-1 * 3 + -8 * 10) > (2 ** 3)) or ((-1 * -10 * -9 * -5) != (-20 + -2))) and (哥伦比亚的首都是雅加达。)) and ((氢的化学符号是H。) or ((现代奥运会首届举办发生在1896年。) and (1996年奥运会在亚特兰大举办。)))) and ((印度位于亚洲。) or (((29 % 10) <= (0 * 7 - 5 * 5)) and (65是质数。))) and (not (((42是质数。) or ((4 - -5) < (-19 * -1))) and ((沙特阿拉伯的首都是加拉加斯。) and ((4 * 1 - 2 * 8) >= (37 % 7)))))\nC. not (not (((铀的化学符号是U。) and (木头在常温下是液体。)) or (not ((-2 + 14) != (14 * 12)))))\nD. not ((((铂的化学符号是Mn。) and (马来西亚的货币是兹罗提。)) or (((3 * -4 * -3 * 9) < (-18 + -2) < (-20 + -4)) and ((-4 * -20) != (-19 + 6)))) and ((火星是距离太阳最近的行星。) and ((8 * -9 + -9 * -10) < (-1 - -4))) and (((第二次世界大战结束发生在1945年。) and ((1 ** 3) <= (29 % 6) <= (5 * 7 + 10 * -8))) and (((2 ** 1) == (-6 + 1)) and ((6 * -3 - 3 * 4) > (3 * 12)))))\nE. ((((现代奥运会首届举办发生在1896年。) and ((1 ** 1) <= (-17 * -8))) or ((-1 - 2) < (-5 * 6 * 0 * 5) < (16 * -14))) and (((9 - 15) != (19 - 18)) and ((泰国的首都是新德里。) or ((-11 + -14) > (17 - 18))))) or (((2 * 7 - -6 * 7) <= (8 % 2) <= (-11 - -3)) and ((钙的化学符号是Sn。) and (第二次世界大战开始发生在1939年。))) or ((((-7 * -7) == (20 + -9)) and (not not (俄罗斯位于欧洲。))) and ((1936年奥运会在蒙特利尔举办。) or ((18 * -14) <= (25 % 6))) and ((柏林墙倒塌发生在1999年。) or (((3 * -7 * -9 * 9) >= (43 % 8)) and ((14 + 2) > (9 * 11)))))\nF. not not ((水星是距离太阳第2近的行星。) or ((((35 % 6) != (-3 + 8)) and (2089年是闰年。)) or (((7 + -5) == (10 * 9 + -7 * 1)) or (金星是距离太阳第2近的行星。))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
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"language": "cn",
"num_options": 6,
"seed": 31467958,
"true_count": 2
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"seed": 31467958,
"task_id": 631467958,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (((not not (not not (not not ((5 ** 3) > (-17 - -9))))) or (((1986年是闰年。) and (not not (第二次世界大战开始发生在1939年。))) and ((1960年是闰年。) and (印度位于亚洲。)) and (丹麦的货币是埃及镑。))) or (not ((((壁虎是爬行动物。) or (1924年奥运会在雅典举办。)) and (not not ((9 * 1 - -5 * -2) < (8 * 7 * -6 * -4)))) or ((-7 - -16) != (24 % 4))))) or (not not (not not ((not not ((-1 + -15) != (19 + 17))) and (硫的化学符号是S。))))
B. not ((not (((((-5 * -11) < (-1 * 0 * 2 * 4)) or ((17 - -11) < (-5 - 17))) and (瑞典的首都是斯德哥尔摩。)) or ((2087年是闰年。) or (韩国位于欧洲。)) or (马来西亚的首都是吉隆坡。))) and ((((柏林墙倒塌发生在1991年。) and ((-6 * 8 * -4 * -8) != (-3 * 13))) and (not not ((-3 - -6) == (-3 * 5 - -4 * -8)))) or (not not ((西班牙位于欧洲。) or (铅的化学符号是Al。)))) and (not ((八月有31天。) and (((8 + 3) < (2 * 3)) or (蜜蜂是昆虫。)) and (摩洛哥位于欧洲。))))
C. (not (not not (not (磷的化学符号是Sn。)))) or (not not ((not (not not (not (1984年奥运会在赫尔辛基举办。)))) and (((-10 * -13) < (12 - -1)) and (not not (金星是距离太阳第3近的行星。)) and (((15 + -2) >= (10 * -6 - -8 * -7)) and (not (欧盟的货币是欧元。))))))
D. not ((not not (not not (86是质数。))) or (not ((酒精在常温下是液体。) or (((12 % 7) > (-16 * 6)) or ((-4 * 8 * -8 * 1) != (-12 * -10))))) or (not not (((-10 - 18) >= (20 % 7)) or (韩国的首都是利雅得。))))
E. not ((((not (not not (金在常温下是液体。))) and (((7 + -1) <= (15 % 8) <= (-7 + -5)) and (not not ((1 ** 1) > (19 - -15))))) or (not (not not (锌的化学符号是Mg。)))) and (((not (((12 % 5) > (16 * 5)) or (现代奥运会首届举办发生在1896年。))) or (((3 - 4) < (-7 * -7 + -6 * -8)) or (金在常温下是气体。)) or (((12 + 14) <= (32 % 7) <= (7 * -9 + -6 * 10)) or (((-7 * -12) >= (8 * 2 - -2 * -4)) or (意大利位于欧洲。)))) or ((not (法国大革命开始发生在1789年。)) or ((-6 + 14) == (21 % 8)))))
F. ((not (not not (捷克的货币是克朗。))) or ((((0 * -3 - 6 * -8) >= (20 - 6)) and (1964年奥运会在东京举办。) and ((not not (126是偶数。)) and ((8 * 5 - 8 * 1) >= (2 ** 3)))) or ((法国大革命开始发生在1789年。) or (not not (not not (1924年是闰年。)))))) or (not ((not not (not (not not ((9 + 9) <= (13 - -14))))) or ((((-2 - 16) != (-1 - -15)) and ((-14 + 16) < (-6 - -2))) or ((89是质数。) or (波兰的首都是伯尔尼。))) or ((not ((人类有2条腿。) and ((15 + 8) > (-19 + -2)))) or (哥伦布到达美洲发生在1494年。))))
G. not (((not ((-16 + -7) == (-15 * 2))) or (not (not not (2002年是闰年。))) or ((埃及的货币是埃及镑。) and (not not ((-14 - -9) >= (-6 * -6))) and ((((46 % 4) == (27 % 10)) or ((-5 + 13) == (-12 - -4))) and ((植物通过光合作用产生氧气。) or (二月有28天。))))) or (not (((((-18 + -15) < (-7 * -10)) and ((-17 * 11) > (-6 - -20))) and (((-16 + 5) > (17 * 12)) or (1924年奥运会在阿姆斯特丹举办。))) or ((-3 * -9 - -7 * -3) < (-13 + -2) < (-1 - 7)))))
H. not ((not (((((8 + -4) != (16 - 12)) and ((25 % 8) != (-11 * -10))) or ((2004年奥运会在雅典举办。) or ((-5 * 5 - 1 * -1) > (-2 - 7)))) and (not ((十二月有31天。) and (美国宣布独立发生在1776年。))))) and ((((((-3 * -1 * -6 * 8) != (5 + -9)) or ((3 ** 1) > (14 + 19))) or (not (磷的化学符号是P。))) and (((-6 * 5 + 0 * 4) <= (-10 * -1) <= (0 * 7)) and (阿根廷位于南美洲。)) and (not not (((3 ** 3) <= (2 + -7) <= (13 * 12)) and (麻雀是鸟类。)))) or (not ((1 * -3 - 2 * 3) >= (-4 - -9)))))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
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"question": "分析以下逻辑表达式：\n\nA. (((not not (not not (not not ((5 ** 3) > (-17 - -9))))) or (((1986年是闰年。) and (not not (第二次世界大战开始发生在1939年。))) and ((1960年是闰年。) and (印度位于亚洲。)) and (丹麦的货币是埃及镑。))) or (not ((((壁虎是爬行动物。) or (1924年奥运会在雅典举办。)) and (not not ((9 * 1 - -5 * -2) < (8 * 7 * -6 * -4)))) or ((-7 - -16) != (24 % 4))))) or (not not (not not ((not not ((-1 + -15) != (19 + 17))) and (硫的化学符号是S。))))\nB. not ((not (((((-5 * -11) < (-1 * 0 * 2 * 4)) or ((17 - -11) < (-5 - 17))) and (瑞典的首都是斯德哥尔摩。)) or ((2087年是闰年。) or (韩国位于欧洲。)) or (马来西亚的首都是吉隆坡。))) and ((((柏林墙倒塌发生在1991年。) and ((-6 * 8 * -4 * -8) != (-3 * 13))) and (not not ((-3 - -6) == (-3 * 5 - -4 * -8)))) or (not not ((西班牙位于欧洲。) or (铅的化学符号是Al。)))) and (not ((八月有31天。) and (((8 + 3) < (2 * 3)) or (蜜蜂是昆虫。)) and (摩洛哥位于欧洲。))))\nC. (not (not not (not (磷的化学符号是Sn。)))) or (not not ((not (not not (not (1984年奥运会在赫尔辛基举办。)))) and (((-10 * -13) < (12 - -1)) and (not not (金星是距离太阳第3近的行星。)) and (((15 + -2) >= (10 * -6 - -8 * -7)) and (not (欧盟的货币是欧元。))))))\nD. not ((not not (not not (86是质数。))) or (not ((酒精在常温下是液体。) or (((12 % 7) > (-16 * 6)) or ((-4 * 8 * -8 * 1) != (-12 * -10))))) or (not not (((-10 - 18) >= (20 % 7)) or (韩国的首都是利雅得。))))\nE. not ((((not (not not (金在常温下是液体。))) and (((7 + -1) <= (15 % 8) <= (-7 + -5)) and (not not ((1 ** 1) > (19 - -15))))) or (not (not not (锌的化学符号是Mg。)))) and (((not (((12 % 5) > (16 * 5)) or (现代奥运会首届举办发生在1896年。))) or (((3 - 4) < (-7 * -7 + -6 * -8)) or (金在常温下是气体。)) or (((12 + 14) <= (32 % 7) <= (7 * -9 + -6 * 10)) or (((-7 * -12) >= (8 * 2 - -2 * -4)) or (意大利位于欧洲。)))) or ((not (法国大革命开始发生在1789年。)) or ((-6 + 14) == (21 % 8)))))\nF. ((not (not not (捷克的货币是克朗。))) or ((((0 * -3 - 6 * -8) >= (20 - 6)) and (1964年奥运会在东京举办。) and ((not not (126是偶数。)) and ((8 * 5 - 8 * 1) >= (2 ** 3)))) or ((法国大革命开始发生在1789年。) or (not not (not not (1924年是闰年。)))))) or (not ((not not (not (not not ((9 + 9) <= (13 - -14))))) or ((((-2 - 16) != (-1 - -15)) and ((-14 + 16) < (-6 - -2))) or ((89是质数。) or (波兰的首都是伯尔尼。))) or ((not ((人类有2条腿。) and ((15 + 8) > (-19 + -2)))) or (哥伦布到达美洲发生在1494年。))))\nG. not (((not ((-16 + -7) == (-15 * 2))) or (not (not not (2002年是闰年。))) or ((埃及的货币是埃及镑。) and (not not ((-14 - -9) >= (-6 * -6))) and ((((46 % 4) == (27 % 10)) or ((-5 + 13) == (-12 - -4))) and ((植物通过光合作用产生氧气。) or (二月有28天。))))) or (not (((((-18 + -15) < (-7 * -10)) and ((-17 * 11) > (-6 - -20))) and (((-16 + 5) > (17 * 12)) or (1924年奥运会在阿姆斯特丹举办。))) or ((-3 * -9 - -7 * -3) < (-13 + -2) < (-1 - 7)))))\nH. not ((not (((((8 + -4) != (16 - 12)) and ((25 % 8) != (-11 * -10))) or ((2004年奥运会在雅典举办。) or ((-5 * 5 - 1 * -1) > (-2 - 7)))) and (not ((十二月有31天。) and (美国宣布独立发生在1776年。))))) and ((((((-3 * -1 * -6 * 8) != (5 + -9)) or ((3 ** 1) > (14 + 19))) or (not (磷的化学符号是P。))) and (((-6 * 5 + 0 * 4) <= (-10 * -1) <= (0 * 7)) and (阿根廷位于南美洲。)) and (not not (((3 ** 3) <= (2 + -7) <= (13 * 12)) and (麻雀是鸟类。)))) or (not ((1 * -3 - 2 * 3) >= (-4 - -9)))))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
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logic-v2 | 评估以下每个表达式：
A. ((((-10 - 13) < (-9 * 15) < (12 * 7)) and (第一部iPhone发布发生在2007年。)) or ((15 + -17) > (9 * -8 + -9 * -10))) or (((-1 * 7 * 8 * 0) >= (9 * -5)) or (马来西亚的货币是林吉特。))
B. not not ((-2 * 17) > (2 ** 2))
C. (钻石由碳元素组成。) and ((((4 ** 3) <= (0 * 15)) and (85是奇数。)) or ((银在常温下是液体。) or (地球是距离太阳第7近的行星。)))
D. (not (not not (68小于等于69。))) or ((((46 % 10) < (-15 * -10)) or ((-10 - 12) <= (14 * -7))) or (not (摩洛哥的首都是利雅得。)))
E. ((1 * 0) > (1 ** 1)) or (((19 - -15) == (-2 - 10)) and ((-1 + -3) <= (15 * 11))) or (not not (not (泰国位于亚洲。)))
F. ((not not (植物通过光合作用产生氧气。)) or ((76小于等于14。) or (90小于等于21。))) and ((印度尼西亚位于北美洲。) and (水星是距离太阳第1近的行星。)) and (not not (((-20 + -2) <= (3 * -1 + 8 * -7)) and ((19 * -4) <= (10 - 6))))
G. ((哥伦比亚的货币是兹罗提。) or ((美国位于北美洲。) and (欧盟的货币是加元。))) and ((-12 * -6) < (5 * -3 * 7 * 2))
H. ((-12 - -6) >= (20 * -10)) and ((-12 - 9) >= (0 * -5 * -6 * -3))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
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"answer": "A,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"question": "评估以下每个表达式：\n\nA. ((((-10 - 13) < (-9 * 15) < (12 * 7)) and (第一部iPhone发布发生在2007年。)) or ((15 + -17) > (9 * -8 + -9 * -10))) or (((-1 * 7 * 8 * 0) >= (9 * -5)) or (马来西亚的货币是林吉特。))\nB. not not ((-2 * 17) > (2 ** 2))\nC. (钻石由碳元素组成。) and ((((4 ** 3) <= (0 * 15)) and (85是奇数。)) or ((银在常温下是液体。) or (地球是距离太阳第7近的行星。)))\nD. (not (not not (68小于等于69。))) or ((((46 % 10) < (-15 * -10)) or ((-10 - 12) <= (14 * -7))) or (not (摩洛哥的首都是利雅得。)))\nE. ((1 * 0) > (1 ** 1)) or (((19 - -15) == (-2 - 10)) and ((-1 + -3) <= (15 * 11))) or (not not (not (泰国位于亚洲。)))\nF. ((not not (植物通过光合作用产生氧气。)) or ((76小于等于14。) or (90小于等于21。))) and ((印度尼西亚位于北美洲。) and (水星是距离太阳第1近的行星。)) and (not not (((-20 + -2) <= (3 * -1 + 8 * -7)) and ((19 * -4) <= (10 - 6))))\nG. ((哥伦比亚的货币是兹罗提。) or ((美国位于北美洲。) and (欧盟的货币是加元。))) and ((-12 * -6) < (5 * -3 * 7 * 2))\nH. ((-12 - -6) >= (20 * -10)) and ((-12 - 9) >= (0 * -5 * -6 * -3))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 49470212,
"true_count": 2
},
"seed": 49470212,
"task_id": 649470212,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (((not not (((14 - 10) > (15 + -20)) or (36的平方根是6。))) or ((-17 + 10) > (-5 * -1))) or ((((19 - 13) == (-4 * -6)) and (((14 * 8) == (15 + 1)) and (铜在常温下是固体。))) or (((越南位于北美洲。) and ((9 - -11) <= (-6 * 5 * -2 * -2) <= (14 + -14))) and (((32 % 8) > (19 - 15)) or ((5 % 9) != (-19 + -12)))))) and ((((1 ** 1) < (44 % 8)) or (((蜻蜓是昆虫。) and (钾的化学符号是K。)) or (蚂蚁是昆虫。))) or (not ((not ((-4 * -6 - 0 * 8) <= (-13 * 5))) or (not (韩国位于亚洲。)))))
B. ((not not (not not (((-18 - 0) > (-6 * 2)) and (2003年是闰年。)))) or (((-13 + 13) == (-14 - 18)) or ((巴西位于南美洲。) and ((匈牙利的首都是布达佩斯。) and (钻石在常温下是气体。))))) and (((植物通过光合作用产生氧气。) and (澳大利亚的货币是雷亚尔。)) or (not (not not (((1 * -10 + 2 * -7) >= (2 * 6 + 6 * 8)) or ((38 % 7) < (-1 * 0))))))
C. ((not ((6 + -10) < (15 * -2) < (-2 + -2))) or (((not (金星是距离太阳第2近的行星。)) or ((第二次世界大战结束发生在1955年。) or (水蒸气在常温下是固体。))) and (not not (((10 * 5 + 10 * 0) > (1 * -9 * 6 * -3)) and (酒精在常温下是气体。))))) or (not (((第二次世界大战结束发生在1945年。) and (鲨鱼是哺乳动物。)) or (((太阳绕地球运转。) or (46是偶数。)) and (法国位于欧洲。))))
D. (not (not ((-15 - -2) > (17 + 20)))) or ((((6 - 15) > (4 + 19)) and (马来西亚的货币是瑞士法郎。) and (not (((-15 - 13) != (-13 + 10)) or (279是完全平方数。)))) or ((not not (((-14 - -12) <= (7 % 1)) or (1936年奥运会在柏林举办。))) or (not not ((硫的化学符号是Ti。) or ((15 % 9) >= (3 + -16))))))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
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"question": "这里有一些需要评估的布尔表达式：\n\nA. (((not not (((14 - 10) > (15 + -20)) or (36的平方根是6。))) or ((-17 + 10) > (-5 * -1))) or ((((19 - 13) == (-4 * -6)) and (((14 * 8) == (15 + 1)) and (铜在常温下是固体。))) or (((越南位于北美洲。) and ((9 - -11) <= (-6 * 5 * -2 * -2) <= (14 + -14))) and (((32 % 8) > (19 - 15)) or ((5 % 9) != (-19 + -12)))))) and ((((1 ** 1) < (44 % 8)) or (((蜻蜓是昆虫。) and (钾的化学符号是K。)) or (蚂蚁是昆虫。))) or (not ((not ((-4 * -6 - 0 * 8) <= (-13 * 5))) or (not (韩国位于亚洲。)))))\nB. ((not not (not not (((-18 - 0) > (-6 * 2)) and (2003年是闰年。)))) or (((-13 + 13) == (-14 - 18)) or ((巴西位于南美洲。) and ((匈牙利的首都是布达佩斯。) and (钻石在常温下是气体。))))) and (((植物通过光合作用产生氧气。) and (澳大利亚的货币是雷亚尔。)) or (not (not not (((1 * -10 + 2 * -7) >= (2 * 6 + 6 * 8)) or ((38 % 7) < (-1 * 0))))))\nC. ((not ((6 + -10) < (15 * -2) < (-2 + -2))) or (((not (金星是距离太阳第2近的行星。)) or ((第二次世界大战结束发生在1955年。) or (水蒸气在常温下是固体。))) and (not not (((10 * 5 + 10 * 0) > (1 * -9 * 6 * -3)) and (酒精在常温下是气体。))))) or (not (((第二次世界大战结束发生在1945年。) and (鲨鱼是哺乳动物。)) or (((太阳绕地球运转。) or (46是偶数。)) and (法国位于欧洲。))))\nD. (not (not ((-15 - -2) > (17 + 20)))) or ((((6 - 15) > (4 + 19)) and (马来西亚的货币是瑞士法郎。) and (not (((-15 - 13) != (-13 + 10)) or (279是完全平方数。)))) or ((not not (((-14 - -12) <= (7 % 1)) or (1936年奥运会在柏林举办。))) or (not not ((硫的化学符号是Ti。) or ((15 % 9) >= (3 + -16))))))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
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logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. not not ((((牛有2条腿。) or ((0 - 0) == (-10 + 0))) or ((马有8条腿。) or ((木头在常温下是气体。) and ((18 - 13) < (10 + -5)))) or ((((6 + 19) < (5 ** 3)) and ((29能被4整除。) or ((-15 + -4) == (27 % 7)))) and ((6 - -9) > (-8 * 6 - 9 * -3)))) and (((not ((柏林墙倒塌发生在1989年。) or (太阳绕地球运转。))) and (((尼日利亚的货币是卢布。) and ((41 % 7) != (1 * 9 - 5 * 2))) and ((八月有31天。) or (哥伦比亚的货币是比索。)))) or (not (not not ((智利的首都是圣地亚哥。) and (二月有29天。))))))
B. not not (not not (((not ((19 + 15) != (-12 + -17))) and ((地球上一天是24小时。) and (((-13 + 18) > (8 + 1)) or (蝴蝶有6条腿。)))) or (((光速比声速快。) or (金星是距离太阳第4近的行星。)) or (not (印度位于非洲。))) or ((((俄罗斯位于欧洲。) or (67是质数。)) and (天王星是距离太阳第3近的行星。)) and (not not ((17 % 1) >= (-16 * -12))) and (not ((-9 - -12) != (-8 + 20))))))
C. not ((not not (((((-6 * 6) > (10 * -9 * 0 * -10)) and (鱼有100条腿。)) and (not not ((-2 * -10) != (3 * -10 - 10 * 2)))) or (((1的平方根是9。) or (柏林墙倒塌发生在1991年。)) or ((柏林墙倒塌发生在1989年。) or ((-8 - -11) <= (11 + 3)))))) and (not not ((not not (((49 % 8) != (3 - 9)) or (委内瑞拉的首都是曼谷。))) or (鳄鱼是昆虫。) or (not not ((镍的化学符号是K。) or (1971年是闰年。))))))
D. not ((not not (not not (((意大利位于北美洲。) and ((7 + 13) > (-19 - 20))) and (not ((9 - -17) > (2 * 4)))))) and ((((not ((-9 + -13) > (9 + -7))) or (埃及的首都是吉隆坡。)) and ((109是偶数。) or ((挪威的首都是布拉格。) or ((4 ** 1) <= (-20 + -10))))) and (not not (not (not (鬣蜥是爬行动物。))))))
E. not (not not (not (((-3 - 17) <= (-19 + 10)) or (((新加坡的货币是卢布。) or ((2 + 11) == (30 % 6))) and (三月有31天。)))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
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"answer": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"true_count": 3
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"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. not not ((((牛有2条腿。) or ((0 - 0) == (-10 + 0))) or ((马有8条腿。) or ((木头在常温下是气体。) and ((18 - 13) < (10 + -5)))) or ((((6 + 19) < (5 ** 3)) and ((29能被4整除。) or ((-15 + -4) == (27 % 7)))) and ((6 - -9) > (-8 * 6 - 9 * -3)))) and (((not ((柏林墙倒塌发生在1989年。) or (太阳绕地球运转。))) and (((尼日利亚的货币是卢布。) and ((41 % 7) != (1 * 9 - 5 * 2))) and ((八月有31天。) or (哥伦比亚的货币是比索。)))) or (not (not not ((智利的首都是圣地亚哥。) and (二月有29天。))))))\nB. not not (not not (((not ((19 + 15) != (-12 + -17))) and ((地球上一天是24小时。) and (((-13 + 18) > (8 + 1)) or (蝴蝶有6条腿。)))) or (((光速比声速快。) or (金星是距离太阳第4近的行星。)) or (not (印度位于非洲。))) or ((((俄罗斯位于欧洲。) or (67是质数。)) and (天王星是距离太阳第3近的行星。)) and (not not ((17 % 1) >= (-16 * -12))) and (not ((-9 - -12) != (-8 + 20))))))\nC. not ((not not (((((-6 * 6) > (10 * -9 * 0 * -10)) and (鱼有100条腿。)) and (not not ((-2 * -10) != (3 * -10 - 10 * 2)))) or (((1的平方根是9。) or (柏林墙倒塌发生在1991年。)) or ((柏林墙倒塌发生在1989年。) or ((-8 - -11) <= (11 + 3)))))) and (not not ((not not (((49 % 8) != (3 - 9)) or (委内瑞拉的首都是曼谷。))) or (鳄鱼是昆虫。) or (not not ((镍的化学符号是K。) or (1971年是闰年。))))))\nD. not ((not not (not not (((意大利位于北美洲。) and ((7 + 13) > (-19 - 20))) and (not ((9 - -17) > (2 * 4)))))) and ((((not ((-9 + -13) > (9 + -7))) or (埃及的首都是吉隆坡。)) and ((109是偶数。) or ((挪威的首都是布拉格。) or ((4 ** 1) <= (-20 + -10))))) and (not not (not (not (鬣蜥是爬行动物。))))))\nE. not (not not (not (((-3 - 17) <= (-19 + 10)) or (((新加坡的货币是卢布。) or ((2 + 11) == (30 % 6))) and (三月有31天。)))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
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} |
logic-v2 | Below are several boolean expressions:
A. not (not not ((A lobster has 10 legs.) and (((-1 * 19) <= (1 + -3)) and (Diamond is a liquid at room temperature.)) and (((1 - -19) <= (9 * 6 * -3 * 5)) or ((15 * -8) <= (-16 - -2) <= (-3 + -3)))))
B. (not ((not (((4 ** 1) == (-4 - 17)) or ((7 - 8) > (3 - -10)))) and ((10 * -8 - -5 * 4) >= (-9 * 3 * -9 * -6)) and (There are 31 days in December.))) and (not (not ((2 ** 3) < (1 ** 3) < (2 ** 3))))
C. (((((The chemical symbol for Silver is Ag.) and (Iron is a solid at room temperature.)) and (((16 - -11) == (-19 * -15)) or ((2 + -17) < (13 % 8)))) or (not (not not ((-8 * -14) > (5 ** 3))))) or (not (A chicken has 2 legs.))) or (not (((16 - 11) <= (-5 + -20) <= (19 - -13)) and (2067 is a leap year.)))
D. (not not (not not (((Morocco is in Africa.) and ((9 - -4) <= (5 * -6 + 3 * -6))) or (((3 + -7) <= (50 % 1)) or (The currency of Canada is the Sol.))))) and ((not not (not ((4 ** 2) < (6 - -18)))) and ((5 ** 1) < (20 - -4) < (-17 * -6)) and ((The 1992 Olympics were held in Stockholm.) or (((27 % 9) <= (32 % 10) <= (14 - 4)) and (850 is a Fibonacci number.)))) and (not ((The chemical symbol for Manganese is Mn.) and (A ant has 4 legs.)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
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"question": "Below are several boolean expressions:\n\nA. not (not not ((A lobster has 10 legs.) and (((-1 * 19) <= (1 + -3)) and (Diamond is a liquid at room temperature.)) and (((1 - -19) <= (9 * 6 * -3 * 5)) or ((15 * -8) <= (-16 - -2) <= (-3 + -3)))))\nB. (not ((not (((4 ** 1) == (-4 - 17)) or ((7 - 8) > (3 - -10)))) and ((10 * -8 - -5 * 4) >= (-9 * 3 * -9 * -6)) and (There are 31 days in December.))) and (not (not ((2 ** 3) < (1 ** 3) < (2 ** 3))))\nC. (((((The chemical symbol for Silver is Ag.) and (Iron is a solid at room temperature.)) and (((16 - -11) == (-19 * -15)) or ((2 + -17) < (13 % 8)))) or (not (not not ((-8 * -14) > (5 ** 3))))) or (not (A chicken has 2 legs.))) or (not (((16 - 11) <= (-5 + -20) <= (19 - -13)) and (2067 is a leap year.)))\nD. (not not (not not (((Morocco is in Africa.) and ((9 - -4) <= (5 * -6 + 3 * -6))) or (((3 + -7) <= (50 % 1)) or (The currency of Canada is the Sol.))))) and ((not not (not ((4 ** 2) < (6 - -18)))) and ((5 ** 1) < (20 - -4) < (-17 * -6)) and ((The 1992 Olympics were held in Stockholm.) or (((27 % 9) <= (32 % 10) <= (14 - 4)) and (850 is a Fibonacci number.)))) and (not ((The chemical symbol for Manganese is Mn.) and (A ant has 4 legs.)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
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logic-v2 | Review these logical expressions:
A. not not (((not not (((-4 * 3) != (-15 + -9)) or (The 1984 Olympics were held in Atlanta.))) or ((32 % 7) == (20 - -10))) and ((((The capital of Sweden is Amsterdam.) or (The currency of European Union is the Ruble.)) and ((The capital of Netherlands is Amsterdam.) or ((9 * -10) != (8 - -2)))) and (The currency of Colombia is the Peso.)))
B. not not ((not (((10 + 12) > (3 - -11)) or (Neptune is the 6th planet from the Sun.))) and (((((4 * 8) >= (8 - 17)) and (2082 is a leap year.)) or ((Japan is in Asia.) or ((-8 + 2) < (7 - 7)))) and ((-11 * 2) > (-7 * 3 * 3 * -1))))
C. not not (not not ((((97 is a prime number.) and ((7 - -3) > (8 - -4))) or ((18 * 20) > (-20 * 16))) or ((Oxygen is necessary for human survival.) and ((17 - -14) == (12 % 6))) or ((-18 * 15) >= (42 % 10))))
D. ((not not ((Penguins can fly.) or (not ((-20 - -17) <= (2 * -9 + -7 * -9))))) and (not (The 1952 Olympics were held in Mexico City.)) and ((Japan is in North America.) and ((4 * -10) < (23 % 3)))) or (not not ((not (Humans have three lungs.)) and (((12 - -4) <= (20 % 6)) or (((6 * 3 * 4 * 6) == (-9 - 6)) or (United States is in North America.)))))
E. ((not not (The 1964 Olympics were held in Los Angeles.)) or ((((The chemical symbol for Cobalt is K.) or (Light travels faster than sound.)) or (not ((-18 + 0) != (9 * -3 + -5 * 7)))) and (((A horse has 4 legs.) or (The 2012 Olympics were held in Beijing.)) and (not (There are 31 days in March.))))) and (not (((9 - 4) < (10 * -7 + -7 * 8)) and (((9 * -9 + -6 * -2) > (-16 - 16)) or ((Copper is a solid at room temperature.) or (Venus is the 8th planet from the Sun.)))))
F. ((not ((10 * 8) >= (-10 * -9 + -9 * -1))) and ((-8 * -2 + -7 * -2) > (-7 + -18)) and ((not ((The chemical symbol for Carbon is C.) or ((-5 - -7) > (-10 + 5)))) and ((not (64 is a prime number.)) or ((South Africa is in Africa.) or ((1 ** 1) != (4 ** 2)))))) or (((World War I ended occurred in 1918.) or (29 is an odd number.)) and ((not not ((-19 + 3) <= (9 * 6))) or (not ((-9 * 11) > (-5 + -10)))) and (not not (((-7 + -18) != (19 + 6)) and (not not ((11 * 18) == (11 + 6))))))
G. (not not (((6 - 18) < (-12 - -19)) and ((((-2 - 4) > (-12 * -4)) or (The 1924 Olympics were held in Moscow.)) or ((0 * -20) >= (-9 - -12))))) or (not (((13 + -13) <= (-18 - -7)) or (not not (A kangaroo has 2 legs.)) or ((-14 - 13) <= (-6 * 5 - 8 * -9))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"question": "Review these logical expressions:\n\nA. not not (((not not (((-4 * 3) != (-15 + -9)) or (The 1984 Olympics were held in Atlanta.))) or ((32 % 7) == (20 - -10))) and ((((The capital of Sweden is Amsterdam.) or (The currency of European Union is the Ruble.)) and ((The capital of Netherlands is Amsterdam.) or ((9 * -10) != (8 - -2)))) and (The currency of Colombia is the Peso.)))\nB. not not ((not (((10 + 12) > (3 - -11)) or (Neptune is the 6th planet from the Sun.))) and (((((4 * 8) >= (8 - 17)) and (2082 is a leap year.)) or ((Japan is in Asia.) or ((-8 + 2) < (7 - 7)))) and ((-11 * 2) > (-7 * 3 * 3 * -1))))\nC. not not (not not ((((97 is a prime number.) and ((7 - -3) > (8 - -4))) or ((18 * 20) > (-20 * 16))) or ((Oxygen is necessary for human survival.) and ((17 - -14) == (12 % 6))) or ((-18 * 15) >= (42 % 10))))\nD. ((not not ((Penguins can fly.) or (not ((-20 - -17) <= (2 * -9 + -7 * -9))))) and (not (The 1952 Olympics were held in Mexico City.)) and ((Japan is in North America.) and ((4 * -10) < (23 % 3)))) or (not not ((not (Humans have three lungs.)) and (((12 - -4) <= (20 % 6)) or (((6 * 3 * 4 * 6) == (-9 - 6)) or (United States is in North America.)))))\nE. ((not not (The 1964 Olympics were held in Los Angeles.)) or ((((The chemical symbol for Cobalt is K.) or (Light travels faster than sound.)) or (not ((-18 + 0) != (9 * -3 + -5 * 7)))) and (((A horse has 4 legs.) or (The 2012 Olympics were held in Beijing.)) and (not (There are 31 days in March.))))) and (not (((9 - 4) < (10 * -7 + -7 * 8)) and (((9 * -9 + -6 * -2) > (-16 - 16)) or ((Copper is a solid at room temperature.) or (Venus is the 8th planet from the Sun.)))))\nF. ((not ((10 * 8) >= (-10 * -9 + -9 * -1))) and ((-8 * -2 + -7 * -2) > (-7 + -18)) and ((not ((The chemical symbol for Carbon is C.) or ((-5 - -7) > (-10 + 5)))) and ((not (64 is a prime number.)) or ((South Africa is in Africa.) or ((1 ** 1) != (4 ** 2)))))) or (((World War I ended occurred in 1918.) or (29 is an odd number.)) and ((not not ((-19 + 3) <= (9 * 6))) or (not ((-9 * 11) > (-5 + -10)))) and (not not (((-7 + -18) != (19 + 6)) and (not not ((11 * 18) == (11 + 6))))))\nG. (not not (((6 - 18) < (-12 - -19)) and ((((-2 - 4) > (-12 * -4)) or (The 1924 Olympics were held in Moscow.)) or ((0 * -20) >= (-9 - -12))))) or (not (((13 + -13) <= (-18 - -7)) or (not not (A kangaroo has 2 legs.)) or ((-14 - 13) <= (-6 * 5 - 8 * -9))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
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logic-v2 | 检验这些表达式：
A. not not (((挪威的货币是比索。) and (铜的化学符号是Cu。)) and ((第二次世界大战结束发生在1945年。) and (1896年奥运会在雅典举办。)))
B. not not ((not not ((5 ** 3) > (10 - 15))) and ((4 ** 3) < (8 * 9 + -6 * -1)))
C. not (人类有三个肺。)
D. ((((-7 * -3) <= (-7 + 15)) and ((29 % 5) < (-7 - 2) < (9 - -6))) or ((伦敦大火发生在1666年。) or ((47 % 5) <= (-10 * 3 + -9 * -2) <= (9 * -9 + 4 * 4)))) or ((not (金在常温下是固体。)) or (((-1 + 2) < (7 * -10 - 6 * -9) < (-10 * 10 - -5 * -7)) or ((20 + -1) < (-8 * -3 + 4 * -3) < (5 + 17))))
E. (not ((海豚是哺乳动物。) or (土星是距离太阳第4近的行星。))) and ((942是斐波那契数。) and (((11 * -12) < (2 ** 2)) and ((17 - 9) == (10 + -11))))
F. not (((铜在常温下是气体。) and (1904年奥运会在圣路易斯举办。)) and (((31 % 1) > (10 * -2 + -10 * 4)) or (二月有31天。)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C,D,F",
"difficulty": 1,
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"question": "检验这些表达式：\n\nA. not not (((挪威的货币是比索。) and (铜的化学符号是Cu。)) and ((第二次世界大战结束发生在1945年。) and (1896年奥运会在雅典举办。)))\nB. not not ((not not ((5 ** 3) > (10 - 15))) and ((4 ** 3) < (8 * 9 + -6 * -1)))\nC. not (人类有三个肺。)\nD. ((((-7 * -3) <= (-7 + 15)) and ((29 % 5) < (-7 - 2) < (9 - -6))) or ((伦敦大火发生在1666年。) or ((47 % 5) <= (-10 * 3 + -9 * -2) <= (9 * -9 + 4 * 4)))) or ((not (金在常温下是固体。)) or (((-1 + 2) < (7 * -10 - 6 * -9) < (-10 * 10 - -5 * -7)) or ((20 + -1) < (-8 * -3 + 4 * -3) < (5 + 17))))\nE. (not ((海豚是哺乳动物。) or (土星是距离太阳第4近的行星。))) and ((942是斐波那契数。) and (((11 * -12) < (2 ** 2)) and ((17 - 9) == (10 + -11))))\nF. not (((铜在常温下是气体。) and (1904年奥运会在圣路易斯举办。)) and (((31 % 1) > (10 * -2 + -10 * 4)) or (二月有31天。)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
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"language": "cn",
"num_options": 6,
"seed": 17129823,
"true_count": 4
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"seed": 17129823,
"task_id": 617129823,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. (Oil is a liquid at room temperature.) and ((not (There are 30 days in October.)) or ((-12 - 9) >= (3 % 10)))
B. not (Jupiter is the 5th planet from the Sun.)
C. (((The 2020 Olympics were held in Tokyo.) and (A kangaroo has 2 legs.)) or (not ((3 ** 3) != (37 % 4)))) and (not not ((46 % 2) != (-10 - -11))) and ((not ((-20 * -12) != (-8 * 12))) and ((There are 31 days in March.) and (The 1896 Olympics were held in Melbourne.)))
D. (not (((12 * 11) != (3 * 8 - 4 * -3)) and (World War I began occurred in 1914.))) or (not ((Christopher Columbus reached America occurred in 1492.) or ((-2 + -13) < (-9 - -11))))
E. ((((-12 + -8) <= (-5 * 9 * -5 * -3) <= (-16 + 18)) or (The capital of Australia is Nairobi.)) or (((3 - 16) >= (8 * 8 * 8 * -8)) and ((-5 * -9) <= (19 + -1)))) or ((((-16 * 16) > (-16 + -18)) or (Canada is in North America.)) and (((-14 + 11) > (6 + 0)) and ((-1 * 10 - 2 * -8) <= (-7 * 16))))
F. ((18 * -4) <= (13 + -14)) and ((Mercury is a liquid at room temperature.) or ((1 ** 1) < (-9 * 4 + 1 * -10))) and ((20 * -7) < (2 + 1) < (2 ** 1))
G. (not ((The capital of Belgium is Brussels.) or (The capital of Nigeria is Bangkok.))) and ((-4 * 3) != (5 + 15))
H. ((not ((14 - 15) > (4 ** 2))) or (((7 + 5) == (-8 + -3)) and ((17 + 12) <= (3 * 5 - 6 * 4)))) and (not not (The 1936 Olympics were held in Berlin.)) and (2098 is a leap year.)
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
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"answer": "A",
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"question": "Examine these expressions:\n\nA. (Oil is a liquid at room temperature.) and ((not (There are 30 days in October.)) or ((-12 - 9) >= (3 % 10)))\nB. not (Jupiter is the 5th planet from the Sun.)\nC. (((The 2020 Olympics were held in Tokyo.) and (A kangaroo has 2 legs.)) or (not ((3 ** 3) != (37 % 4)))) and (not not ((46 % 2) != (-10 - -11))) and ((not ((-20 * -12) != (-8 * 12))) and ((There are 31 days in March.) and (The 1896 Olympics were held in Melbourne.)))\nD. (not (((12 * 11) != (3 * 8 - 4 * -3)) and (World War I began occurred in 1914.))) or (not ((Christopher Columbus reached America occurred in 1492.) or ((-2 + -13) < (-9 - -11))))\nE. ((((-12 + -8) <= (-5 * 9 * -5 * -3) <= (-16 + 18)) or (The capital of Australia is Nairobi.)) or (((3 - 16) >= (8 * 8 * 8 * -8)) and ((-5 * -9) <= (19 + -1)))) or ((((-16 * 16) > (-16 + -18)) or (Canada is in North America.)) and (((-14 + 11) > (6 + 0)) and ((-1 * 10 - 2 * -8) <= (-7 * 16))))\nF. ((18 * -4) <= (13 + -14)) and ((Mercury is a liquid at room temperature.) or ((1 ** 1) < (-9 * 4 + 1 * -10))) and ((20 * -7) < (2 + 1) < (2 ** 1))\nG. (not ((The capital of Belgium is Brussels.) or (The capital of Nigeria is Bangkok.))) and ((-4 * 3) != (5 + 15))\nH. ((not ((14 - 15) > (4 ** 2))) or (((7 + 5) == (-8 + -3)) and ((17 + 12) <= (3 * 5 - 6 * 4)))) and (not not (The 1936 Olympics were held in Berlin.)) and (2098 is a leap year.)\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
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"language": "en",
"num_options": 8,
"seed": 47388480,
"true_count": 1
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"seed": 47388480,
"task_id": 647388480,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not (((1905年是闰年。) or (水星是距离太阳第3近的行星。)) or (((4 - -7) <= (-18 * -4)) and (汞的化学符号是Fe。)))
B. (锡的化学符号是Au。) or (not not (not ((16 * 0) > (-2 * 0))))
C. not not ((((0 * -12) == (-9 * 5 - -7 * 6)) or ((9 * -1 * -2 * 4) <= (5 ** 1))) and ((8 * 0 + -6 * 1) == (-11 - -10)))
D. not ((八月有31天。) and ((-14 - -6) < (3 ** 2)))
E. ((-14 * 20) != (40 % 4)) and (((-8 * 3 * 0 * 3) >= (5 ** 2)) and (((-8 + 8) < (4 ** 1) < (-6 - -17)) and ((45 % 10) > (-4 - 9))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
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"answer": "A,B",
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"question": "审视以下逻辑表达式：\n\nA. not (((1905年是闰年。) or (水星是距离太阳第3近的行星。)) or (((4 - -7) <= (-18 * -4)) and (汞的化学符号是Fe。)))\nB. (锡的化学符号是Au。) or (not not (not ((16 * 0) > (-2 * 0))))\nC. not not ((((0 * -12) == (-9 * 5 - -7 * 6)) or ((9 * -1 * -2 * 4) <= (5 ** 1))) and ((8 * 0 + -6 * 1) == (-11 - -10)))\nD. not ((八月有31天。) and ((-14 - -6) < (3 ** 2)))\nE. ((-14 * 20) != (40 % 4)) and (((-8 * 3 * 0 * 3) >= (5 ** 2)) and (((-8 + 8) < (4 ** 1) < (-6 - -17)) and ((45 % 10) > (-4 - 9))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
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"language": "cn",
"num_options": 5,
"seed": 58033490,
"true_count": 2
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"seed": 58033490,
"task_id": 658033490,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not not (not (not (not ((not (哥伦比亚的首都是赫尔辛基。)) and (水星是距离太阳第7近的行星。)))))
B. not not (not ((((13 + -2) >= (1 ** 1)) or ((695是斐波那契数。) and (声音在真空中传播更快。)) or (not (((10 * -20) != (16 - -15)) and (印度尼西亚位于南极洲。)))) or (not ((-10 - 2) > (-9 + 17)))))
C. ((not ((not not ((印度尼西亚位于大洋洲。) or ((4 ** 1) > (16 * -20)))) or ((not (太平洋是最大的海洋。)) or ((-6 - 10) <= (1 * -10 * 10 * -2) <= (-12 - 7))))) and (not not (not ((not not (尼日利亚的货币是奈拉。)) or (((16 % 1) == (2 * 6)) and (2068年是闰年。)))))) or ((not (not not (氧的化学符号是O。))) or ((not not (((1980年奥运会在莫斯科举办。) or (356是完全平方数。)) or ((新西兰位于大洋洲。) and ((-3 * 3 - -5 * -9) == (-11 + 14))))) and (not not (not not (第一次世界大战开始发生在1914年。)))))
D. (not not (not not (not (钻石在常温下是固体。)))) or (not ((((-6 * -3) > (6 * -11)) or (((-9 + 10) < (-4 * -8)) or (((6 + 3) <= (8 * 1 - -7 * 2) <= (10 * -18)) and (2034年是闰年。)))) and (not not (((-6 * -5 - -3 * 6) > (18 % 6)) or (氢的化学符号是Ag。))) and (((八月有31天。) or (((-10 * 0 - -7 * -9) < (2 ** 1) < (1 ** 1)) or ((-3 * -1) >= (20 - -17)))) or (((1956年奥运会在赫尔辛基举办。) or ((-3 * 7 - 0 * -7) == (8 * 1 * -8 * -10))) or ((冰在常温下是固体。) or ((11 - -10) == (8 - -19)))))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"answer": "A,C",
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"metadata": {
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"language": "cn",
"num_options": 4,
"seed": 15378888,
"true_count": 2
},
"question": "给定以下布尔表达式：\n\nA. not not (not (not (not ((not (哥伦比亚的首都是赫尔辛基。)) and (水星是距离太阳第7近的行星。)))))\nB. not not (not ((((13 + -2) >= (1 ** 1)) or ((695是斐波那契数。) and (声音在真空中传播更快。)) or (not (((10 * -20) != (16 - -15)) and (印度尼西亚位于南极洲。)))) or (not ((-10 - 2) > (-9 + 17)))))\nC. ((not ((not not ((印度尼西亚位于大洋洲。) or ((4 ** 1) > (16 * -20)))) or ((not (太平洋是最大的海洋。)) or ((-6 - 10) <= (1 * -10 * 10 * -2) <= (-12 - 7))))) and (not not (not ((not not (尼日利亚的货币是奈拉。)) or (((16 % 1) == (2 * 6)) and (2068年是闰年。)))))) or ((not (not not (氧的化学符号是O。))) or ((not not (((1980年奥运会在莫斯科举办。) or (356是完全平方数。)) or ((新西兰位于大洋洲。) and ((-3 * 3 - -5 * -9) == (-11 + 14))))) and (not not (not not (第一次世界大战开始发生在1914年。)))))\nD. (not not (not not (not (钻石在常温下是固体。)))) or (not ((((-6 * -3) > (6 * -11)) or (((-9 + 10) < (-4 * -8)) or (((6 + 3) <= (8 * 1 - -7 * 2) <= (10 * -18)) and (2034年是闰年。)))) and (not not (((-6 * -5 - -3 * 6) > (18 % 6)) or (氢的化学符号是Ag。))) and (((八月有31天。) or (((-10 * 0 - -7 * -9) < (2 ** 1) < (1 ** 1)) or ((-3 * -1) >= (20 - -17)))) or (((1956年奥运会在赫尔辛基举办。) or ((-3 * 7 - 0 * -7) == (8 * 1 * -8 * -10))) or ((冰在常温下是固体。) or ((11 - -10) == (8 - -19)))))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 15378888,
"true_count": 2
},
"seed": 15378888,
"task_id": 615378888,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((金星是距离太阳第2近的行星。) or (澳大利亚位于大洋洲。)) or ((金的化学符号是Ag。) and (水星是距离太阳第1近的行星。))) or (not not (六月有28天。))
B. not (印度的货币是克朗。)
C. not (not not ((蚊子是哺乳动物。) or (氧的化学符号是Pt。)))
D. not not ((14 + 15) < (3 * -10))
E. ((-7 * 18) <= (10 + 14) <= (10 * -2)) or (25能被9整除。) or (((电流比光速更快。) or (2016年奥运会在里约热内卢举办。)) or ((空气在常温下是液体。) or (瑞典的货币是克朗。)))
F. ((水在常温下是液体。) or (((13 - -5) >= (43 % 6)) and ((10 * -6) <= (-13 + 8)))) and (((木星是距离太阳第5近的行星。) or ((-1 * -10 - 3 * 8) == (-1 * -15))) or (not not ((35 % 9) > (1 - -6))))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,B,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 2699037,
"true_count": 5
},
"question": "考虑以下布尔表达式：\n\nA. (((金星是距离太阳第2近的行星。) or (澳大利亚位于大洋洲。)) or ((金的化学符号是Ag。) and (水星是距离太阳第1近的行星。))) or (not not (六月有28天。))\nB. not (印度的货币是克朗。)\nC. not (not not ((蚊子是哺乳动物。) or (氧的化学符号是Pt。)))\nD. not not ((14 + 15) < (3 * -10))\nE. ((-7 * 18) <= (10 + 14) <= (10 * -2)) or (25能被9整除。) or (((电流比光速更快。) or (2016年奥运会在里约热内卢举办。)) or ((空气在常温下是液体。) or (瑞典的货币是克朗。)))\nF. ((水在常温下是液体。) or (((13 - -5) >= (43 % 6)) and ((10 * -6) <= (-13 + 8)))) and (((木星是距离太阳第5近的行星。) or ((-1 * -10 - 3 * 8) == (-1 * -15))) or (not not ((35 % 9) > (1 - -6))))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 2699037,
"true_count": 5
},
"seed": 2699037,
"task_id": 602699037,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. ((氮的化学符号是N。) and (蝙蝠是瞎的。)) or (not ((not not (75能被5整除。)) and (((-3 * -5 + -9 * 0) > (5 ** 2)) and ((7 + -4) != (-11 - 17)))))
B. not not ((not not (第一次世界大战开始发生在1915年。)) and (not ((10 * 7 + 6 * -7) >= (-8 + -14))))
C. (not (((-6 - 13) <= (5 * 0 - -9 * 5) <= (1 * -17)) and (not not (113是完全平方数。)))) or (((((6 * -3 + 3 * 6) <= (-7 * -11)) and ((4 ** 3) < (-8 - -2))) or (((-9 - 16) < (2 % 1)) and ((20 % 5) < (7 - -2)))) or ((大象有4条腿。) and (not not ((2 + -18) <= (9 % 1)))))
D. not (((not (1964年奥运会在东京举办。)) and (((20 - 9) <= (5 ** 2)) and (人类有2条腿。))) or (not ((-10 * 5 + -4 * 5) <= (18 + -9))) or ((-20 + 4) == (-3 * -9)))
E. (not not ((((1 ** 2) < (3 * -8 - 8 * 8)) and ((7 * -3 + -5 * -3) >= (25 % 8))) or ((氮的化学符号是N。) and ((0 * 0) <= (0 - -15))))) and ((瑞士的首都是伯尔尼。) or (not ((16 * -11) <= (5 ** 2))))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 5560898,
"true_count": 4
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"question": "考虑以下布尔表达式：\n\nA. ((氮的化学符号是N。) and (蝙蝠是瞎的。)) or (not ((not not (75能被5整除。)) and (((-3 * -5 + -9 * 0) > (5 ** 2)) and ((7 + -4) != (-11 - 17)))))\nB. not not ((not not (第一次世界大战开始发生在1915年。)) and (not ((10 * 7 + 6 * -7) >= (-8 + -14))))\nC. (not (((-6 - 13) <= (5 * 0 - -9 * 5) <= (1 * -17)) and (not not (113是完全平方数。)))) or (((((6 * -3 + 3 * 6) <= (-7 * -11)) and ((4 ** 3) < (-8 - -2))) or (((-9 - 16) < (2 % 1)) and ((20 % 5) < (7 - -2)))) or ((大象有4条腿。) and (not not ((2 + -18) <= (9 % 1)))))\nD. not (((not (1964年奥运会在东京举办。)) and (((20 - 9) <= (5 ** 2)) and (人类有2条腿。))) or (not ((-10 * 5 + -4 * 5) <= (18 + -9))) or ((-20 + 4) == (-3 * -9)))\nE. (not not ((((1 ** 2) < (3 * -8 - 8 * 8)) and ((7 * -3 + -5 * -3) >= (25 % 8))) or ((氮的化学符号是N。) and ((0 * 0) <= (0 - -15))))) and ((瑞士的首都是伯尔尼。) or (not ((16 * -11) <= (5 ** 2))))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 5560898,
"true_count": 4
},
"seed": 5560898,
"task_id": 605560898,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (not (not not ((-8 + 18) >= (-16 * 11)))) and (((not ((-17 - -6) > (7 * 9))) or ((12 + -16) < (-12 * -15) < (-19 - -2))) or (not ((0 * 9) != (20 * -17))) or ((3 % 2) == (5 - 0))) and (((not ((-7 * -7 - 3 * 7) >= (12 - 16))) and (not not (七月有31天。)) and (委内瑞拉的首都是巴西利亚。)) or (not not (((-9 + 0) == (10 * 1 - 9 * 2)) or (not not ((-6 * 10 + 5 * -4) == (16 - 19))))))
B. ((not not (not (澳大利亚的货币是澳元。))) and (((17 - 9) > (5 ** 2)) or (not not (((-4 * 4) != (42 % 6)) and (牛是哺乳动物。))))) and ((((-6 * 7 * 1 * 1) <= (-1 * 2 * -3 * 2)) or (蚂蚁是昆虫。)) or (not not ((-5 + -13) <= (-13 - -1))) or (((印度尼西亚位于大洋洲。) or (氮气在常温下是气体。)) or ((鬣蜥是爬行动物。) and (第一次世界大战结束发生在1918年。)))) and (not ((((第一次世界大战开始发生在1914年。) or ((7 % 8) <= (-2 * 15))) and (美国宣布独立发生在1778年。)) and ((not not (越南的货币是越南盾。)) or (((32 % 1) <= (-7 - 4) <= (2 ** 1)) and ((5 ** 1) < (-4 * -8 + 7 * 10) < (7 + 3))))))
C. ((not not ((18 + 11) <= (2 + 3))) or (((not not (古巴的首都是北京。)) or ((-5 * 9 + -9 * 0) < (7 * -2 * -5 * -3))) or ((5 * 9 * -7 * -7) < (-9 - 8) < (4 ** 1)) or (not ((海王星是距离太阳第3近的行星。) and (火星是距离太阳第4近的行星。))))) and (not (((丹麦的货币是卢布。) or (not not ((9 * -14) <= (9 - -15)))) or ((2 * 6 - -4 * -2) < (37 % 9))))
D. ((not not ((not (三月有30天。)) and ((1905年是闰年。) or ((-4 + -17) <= (-20 * -4) <= (0 * 4 + -6 * -4))))) or (not (螃蟹有8条腿。))) and (not (not not ((not not ((5 + 15) <= (13 - 1) <= (12 + -14))) and (not not (锰的化学符号是P。)))))
E. ((((7 % 3) > (-3 + -1)) or ((-12 * -1) < (2 - -15) < (13 - -14))) and (((火星是距离太阳第4近的行星。) or (((-1 * 2 * -8 * 1) <= (3 ** 3)) and ((-9 * 5 - 5 * 5) < (-5 + 2) < (-5 + -2)))) or (not not (((-19 * -4) > (-18 * -20)) or (天王星是距离太阳第7近的行星。))))) and (not not (not not ((322是完全平方数。) and (((-8 * -10 + -8 * 2) <= (-4 * 7)) and ((-8 - 13) > (1 ** 2))))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 44470671,
"true_count": 1
},
"question": "检验这些表达式：\n\nA. (not (not not ((-8 + 18) >= (-16 * 11)))) and (((not ((-17 - -6) > (7 * 9))) or ((12 + -16) < (-12 * -15) < (-19 - -2))) or (not ((0 * 9) != (20 * -17))) or ((3 % 2) == (5 - 0))) and (((not ((-7 * -7 - 3 * 7) >= (12 - 16))) and (not not (七月有31天。)) and (委内瑞拉的首都是巴西利亚。)) or (not not (((-9 + 0) == (10 * 1 - 9 * 2)) or (not not ((-6 * 10 + 5 * -4) == (16 - 19))))))\nB. ((not not (not (澳大利亚的货币是澳元。))) and (((17 - 9) > (5 ** 2)) or (not not (((-4 * 4) != (42 % 6)) and (牛是哺乳动物。))))) and ((((-6 * 7 * 1 * 1) <= (-1 * 2 * -3 * 2)) or (蚂蚁是昆虫。)) or (not not ((-5 + -13) <= (-13 - -1))) or (((印度尼西亚位于大洋洲。) or (氮气在常温下是气体。)) or ((鬣蜥是爬行动物。) and (第一次世界大战结束发生在1918年。)))) and (not ((((第一次世界大战开始发生在1914年。) or ((7 % 8) <= (-2 * 15))) and (美国宣布独立发生在1778年。)) and ((not not (越南的货币是越南盾。)) or (((32 % 1) <= (-7 - 4) <= (2 ** 1)) and ((5 ** 1) < (-4 * -8 + 7 * 10) < (7 + 3))))))\nC. ((not not ((18 + 11) <= (2 + 3))) or (((not not (古巴的首都是北京。)) or ((-5 * 9 + -9 * 0) < (7 * -2 * -5 * -3))) or ((5 * 9 * -7 * -7) < (-9 - 8) < (4 ** 1)) or (not ((海王星是距离太阳第3近的行星。) and (火星是距离太阳第4近的行星。))))) and (not (((丹麦的货币是卢布。) or (not not ((9 * -14) <= (9 - -15)))) or ((2 * 6 - -4 * -2) < (37 % 9))))\nD. ((not not ((not (三月有30天。)) and ((1905年是闰年。) or ((-4 + -17) <= (-20 * -4) <= (0 * 4 + -6 * -4))))) or (not (螃蟹有8条腿。))) and (not (not not ((not not ((5 + 15) <= (13 - 1) <= (12 + -14))) and (not not (锰的化学符号是P。)))))\nE. ((((7 % 3) > (-3 + -1)) or ((-12 * -1) < (2 - -15) < (13 - -14))) and (((火星是距离太阳第4近的行星。) or (((-1 * 2 * -8 * 1) <= (3 ** 3)) and ((-9 * 5 - 5 * 5) < (-5 + 2) < (-5 + -2)))) or (not not (((-19 * -4) > (-18 * -20)) or (天王星是距离太阳第7近的行星。))))) and (not not (not not ((322是完全平方数。) and (((-8 * -10 + -8 * 2) <= (-4 * 7)) and ((-8 - 13) > (1 ** 2))))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 44470671,
"true_count": 1
},
"seed": 44470671,
"task_id": 644470671,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not ((not (not not ((not not ((7 * 14) <= (9 + -3))) or ((2012年奥运会在首尔举办。) or ((0 * 5 + -5 * -10) < (15 - -15)))))) or ((not not (not not (苏联解体发生在1993年。))) or (not (韩国的货币是韩元。)) or ((4 * 2 + -9 * -8) != (19 + 9))) or (not not (((-4 - 4) < (-9 + -7)) and ((2061年是闰年。) and ((3 ** 1) < (3 + -14) < (-5 * -2 * 1 * -1))) and (((意大利的首都是维也纳。) or ((20 - 10) >= (5 - 8))) and ((-9 * -3) <= (-1 * -2 + 0 * -5) <= (17 - 1))))))
B. (not not (((((10 % 1) >= (-10 * -8 - 2 * 10)) or (not not (1972年奥运会在慕尼黑举办。))) and ((14 % 4) > (-17 - -20))) or ((1956年奥运会在慕尼黑举办。) or ((乌克兰的首都是基辅。) and (铁的化学符号是Au。))) or (not not (十月有28天。)))) or (not ((((((2 * -10) < (-2 - 14)) and (358是完全平方数。)) and (蝴蝶有100条腿。)) or ((not (马有4条腿。)) or (not (泰国位于亚洲。)))) or (((not (钠的化学符号是Na。)) and ((油在常温下是液体。) or ((10 * 1) <= (15 - -1)))) or (not (1956年奥运会在首尔举办。)) or ((((3 ** 3) <= (9 * 10 - 0 * 3)) or ((15 + -20) == (-17 - 4))) or (氮的化学符号是N。)))))
C. ((((((-15 - -14) >= (5 * -17)) or (((-3 * -10 - -5 * -2) <= (-12 + -11) <= (3 + 5)) or (酒精在常温下是气体。))) and (((3 * 16) < (-11 - 9)) or ((14 + -14) < (-17 * -19) < (9 * 16)))) and (not ((-4 + 5) == (19 + 5)))) and (((not ((钻石在常温下是固体。) or (第一部iPhone发布发生在2007年。))) or (碳的化学符号是He。)) and ((((-1 * -8 - -2 * 10) >= (-19 + 9)) and (not ((11 - -15) <= (0 * 19)))) and (not not (三月有31天。)) and ((13 - -13) <= (18 - -19))))) and (not not (not not ((加拿大位于欧洲。) and (not not ((俄罗斯位于南美洲。) and (192是奇数。))))))
D. not ((not not (((捷克的货币是兹罗提。) and (not ((-12 + -17) <= (-4 - 4)))) and (越南的货币是越南盾。))) or (((((-4 * 0 - -4 * -10) == (-5 * 16)) and (not ((16 + -12) == (13 * 11)))) or (((12 + 9) <= (6 % 4) <= (2 * 2 - 5 * -6)) or (not ((17 * -2) < (-8 * 19))))) or ((油在常温下是液体。) and ((((-12 * 16) < (22 % 4)) and ((-9 * 7 - -7 * 7) >= (3 * -7))) or (not not ((6 * 4 * -8 * -5) == (-10 * 2)))))))
E. not (not not (((((闪电不会两次击中同一个地方。) and ((19 - -12) <= (-11 * -5) <= (6 * 8 * -2 * 0))) and ((1935年是闰年。) and ((25 % 9) > (19 - 15)))) or (硅的化学符号是Si。)) and (not (氮气在常温下是液体。))))
F. not not (not not (((((挪威的货币是人民币。) or (肯尼亚位于非洲。)) or ((第一次世界大战开始发生在1912年。) or (阿根廷位于南美洲。))) or (((章鱼有8条腿。) or ((20 + -11) >= (-18 - 6))) or (not not ((15 - -7) < (-12 * -19))))) or (not not (冰的密度比液态水小。))))
G. (((not (not not (not not (鳟鱼是鸟类。)))) and ((not ((27大于9。) or (2000年奥运会在悉尼举办。))) or ((-12 - 14) <= (5 ** 3)) or (((钠的化学符号是S。) and (1947年是闰年。)) or ((1 ** 3) != (3 * -7 * 10 * -1))))) or (((声音在真空中传播更快。) and (239是斐波那契数。) and ((14 * -5) != (5 ** 1))) and (not not ((0 * -5) == (-15 + 4))))) and (not not (not ((not (((-4 * 5 - -6 * 6) != (-12 * -3)) and ((-4 * 7 - 4 * -1) <= (11 - -14)))) and (铬的化学符号是C。))))
H. not ((((1920年奥运会在东京举办。) and (蜘蛛是昆虫。)) or ((2018年是闰年。) and ((秘鲁位于南极洲。) or (100是斐波那契数。))) or (((((-11 + 6) <= (1 ** 3)) or (第一部iPhone发布发生在2007年。)) or (not (西班牙位于欧洲。))) and (((-5 * 4) > (-10 * -3 * 8 * 4)) and (not not (582是斐波那契数。))))) and (((not not (中国的首都是北京。)) and ((1 ** 3) <= (1 % 3) <= (13 + -11))) and (水星是距离太阳第2近的行星。) and ((2000年奥运会在蒙特利尔举办。) and (not (青蛙有10条腿。)))) and (not not (((not not ((44 % 3) >= (-16 + 9))) or ((水蒸气在常温下是气体。) or (人体有150块骨头。))) and ((-9 + 6) <= (16 - 11)))))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "F,G,H",
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"gpt_response": "",
"metadata": {
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"language": "cn",
"num_options": 8,
"seed": 1827144,
"true_count": 3
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"question": "这里有一些需要评估的布尔表达式：\n\nA. not ((not (not not ((not not ((7 * 14) <= (9 + -3))) or ((2012年奥运会在首尔举办。) or ((0 * 5 + -5 * -10) < (15 - -15)))))) or ((not not (not not (苏联解体发生在1993年。))) or (not (韩国的货币是韩元。)) or ((4 * 2 + -9 * -8) != (19 + 9))) or (not not (((-4 - 4) < (-9 + -7)) and ((2061年是闰年。) and ((3 ** 1) < (3 + -14) < (-5 * -2 * 1 * -1))) and (((意大利的首都是维也纳。) or ((20 - 10) >= (5 - 8))) and ((-9 * -3) <= (-1 * -2 + 0 * -5) <= (17 - 1))))))\nB. (not not (((((10 % 1) >= (-10 * -8 - 2 * 10)) or (not not (1972年奥运会在慕尼黑举办。))) and ((14 % 4) > (-17 - -20))) or ((1956年奥运会在慕尼黑举办。) or ((乌克兰的首都是基辅。) and (铁的化学符号是Au。))) or (not not (十月有28天。)))) or (not ((((((2 * -10) < (-2 - 14)) and (358是完全平方数。)) and (蝴蝶有100条腿。)) or ((not (马有4条腿。)) or (not (泰国位于亚洲。)))) or (((not (钠的化学符号是Na。)) and ((油在常温下是液体。) or ((10 * 1) <= (15 - -1)))) or (not (1956年奥运会在首尔举办。)) or ((((3 ** 3) <= (9 * 10 - 0 * 3)) or ((15 + -20) == (-17 - 4))) or (氮的化学符号是N。)))))\nC. ((((((-15 - -14) >= (5 * -17)) or (((-3 * -10 - -5 * -2) <= (-12 + -11) <= (3 + 5)) or (酒精在常温下是气体。))) and (((3 * 16) < (-11 - 9)) or ((14 + -14) < (-17 * -19) < (9 * 16)))) and (not ((-4 + 5) == (19 + 5)))) and (((not ((钻石在常温下是固体。) or (第一部iPhone发布发生在2007年。))) or (碳的化学符号是He。)) and ((((-1 * -8 - -2 * 10) >= (-19 + 9)) and (not ((11 - -15) <= (0 * 19)))) and (not not (三月有31天。)) and ((13 - -13) <= (18 - -19))))) and (not not (not not ((加拿大位于欧洲。) and (not not ((俄罗斯位于南美洲。) and (192是奇数。))))))\nD. not ((not not (((捷克的货币是兹罗提。) and (not ((-12 + -17) <= (-4 - 4)))) and (越南的货币是越南盾。))) or (((((-4 * 0 - -4 * -10) == (-5 * 16)) and (not ((16 + -12) == (13 * 11)))) or (((12 + 9) <= (6 % 4) <= (2 * 2 - 5 * -6)) or (not ((17 * -2) < (-8 * 19))))) or ((油在常温下是液体。) and ((((-12 * 16) < (22 % 4)) and ((-9 * 7 - -7 * 7) >= (3 * -7))) or (not not ((6 * 4 * -8 * -5) == (-10 * 2)))))))\nE. not (not not (((((闪电不会两次击中同一个地方。) and ((19 - -12) <= (-11 * -5) <= (6 * 8 * -2 * 0))) and ((1935年是闰年。) and ((25 % 9) > (19 - 15)))) or (硅的化学符号是Si。)) and (not (氮气在常温下是液体。))))\nF. not not (not not (((((挪威的货币是人民币。) or (肯尼亚位于非洲。)) or ((第一次世界大战开始发生在1912年。) or (阿根廷位于南美洲。))) or (((章鱼有8条腿。) or ((20 + -11) >= (-18 - 6))) or (not not ((15 - -7) < (-12 * -19))))) or (not not (冰的密度比液态水小。))))\nG. (((not (not not (not not (鳟鱼是鸟类。)))) and ((not ((27大于9。) or (2000年奥运会在悉尼举办。))) or ((-12 - 14) <= (5 ** 3)) or (((钠的化学符号是S。) and (1947年是闰年。)) or ((1 ** 3) != (3 * -7 * 10 * -1))))) or (((声音在真空中传播更快。) and (239是斐波那契数。) and ((14 * -5) != (5 ** 1))) and (not not ((0 * -5) == (-15 + 4))))) and (not not (not ((not (((-4 * 5 - -6 * 6) != (-12 * -3)) and ((-4 * 7 - 4 * -1) <= (11 - -14)))) and (铬的化学符号是C。))))\nH. not ((((1920年奥运会在东京举办。) and (蜘蛛是昆虫。)) or ((2018年是闰年。) and ((秘鲁位于南极洲。) or (100是斐波那契数。))) or (((((-11 + 6) <= (1 ** 3)) or (第一部iPhone发布发生在2007年。)) or (not (西班牙位于欧洲。))) and (((-5 * 4) > (-10 * -3 * 8 * 4)) and (not not (582是斐波那契数。))))) and (((not not (中国的首都是北京。)) and ((1 ** 3) <= (1 % 3) <= (13 + -11))) and (水星是距离太阳第2近的行星。) and ((2000年奥运会在蒙特利尔举办。) and (not (青蛙有10条腿。)))) and (not not (((not not ((44 % 3) >= (-16 + 9))) or ((水蒸气在常温下是气体。) or (人体有150块骨头。))) and ((-9 + 6) <= (16 - 11)))))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
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logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. ((not (((-16 - 15) <= (-4 * 1 - 5 * -1) <= (-12 + 8)) or (((-17 + -8) > (-8 * -10 - 0 * 10)) or (加拿大的货币是加元。)))) or (not not ((马是哺乳动物。) or (新西兰的货币是比索。))) or (not not ((((-8 * -5) > (-14 + -3)) or ((0 * -13) != (5 ** 3))) or (捷克的货币是克朗。)))) and (not ((((10 + 3) <= (6 * 2 + 4 * 5) <= (-8 - -9)) and (not not (欧盟的货币是欧元。))) and (not not ((铬的化学符号是Pb。) and (37小于等于92。)))))
B. ((not not (not not (not not (企鹅能飞翔。)))) and ((天王星是距离太阳第3近的行星。) and ((中国的货币是人民币。) and (2016年奥运会在里约热内卢举办。)) and ((((5 ** 1) <= (-18 + 19)) and (中国的货币是人民币。)) and (人类有2条腿。)))) or (((((4 % 9) == (2 ** 1)) and (伦敦大火发生在1666年。)) and (金在常温下是固体。)) and (金在常温下是液体。)) or ((((俄罗斯位于欧洲。) or ((冰在常温下是液体。) and (七月有31天。))) or ((波兰的货币是里拉。) or (埃及的货币是福林。))) and (not not (not not (((32 % 10) < (16 - -3)) or (月球绕地球运转。)))))
C. not not (((水星是距离太阳第7近的行星。) and (not (水在海平面上的沸点是100摄氏度。)) and ((not not (捷克的首都是布鲁塞尔。)) and (((-12 + -20) > (-13 * -6)) or ((10 * -1 * -6 * -5) != (-8 + 18))))) and (((((-15 - -14) < (-10 - 6)) or (爱尔兰的首都是阿姆斯特丹。)) and ((地球是距离太阳第3近的行星。) and ((-8 * -6 + 4 * 6) <= (10 * -1 - -8 * -10)))) and ((-10 * -6) <= (-6 * 9 - 4 * -8))))
D. not not ((not not (1900年奥运会在东京举办。)) or (((现代奥运会首届举办发生在1898年。) or ((10 + -17) <= (8 - -10))) and ((-16 * -20) >= (5 ** 1))))
E. not not (((not (((9 * -10) < (1 ** 2) < (-7 * -8 - -7 * -10)) and (水星是距离太阳第5近的行星。))) or (钻石由碳元素组成。)) or (not ((5 * 3) == (-2 - -3))))
F. ((((not not ((4 * 1 + -2 * -2) < (-8 * -10 - 5 * 8) < (14 - -6))) and (not ((25 % 10) == (-9 - 9)))) or ((蝴蝶有6条腿。) and (44小于等于80。)) or (三月有29天。)) or (((5 - 5) < (2 * -4 * 1 * 10) < (12 * -1)) and (乌鸦是昆虫。) and (水星是距离太阳第2近的行星。))) and (((((1 ** 1) > (-18 * 9)) and (((49 % 9) < (-4 * 3 - 6 * 10) < (4 * 1)) or (新西兰的首都是惠灵顿。))) and ((中国的货币是雷亚尔。) and (37大于90。)) and ((not ((3 ** 1) > (-8 * -20))) or (新西兰位于亚洲。))) and ((铁在常温下是固体。) or (not not ((变色龙是爬行动物。) or (2012年奥运会在伦敦举办。)))))
G. (((not (1896年奥运会在雅典举办。)) or ((((-4 - 20) < (6 - -8)) or (2011年是闰年。)) or ((5 * 0 + 0 * 0) <= (18 * -18) <= (10 + 2)))) or (not not ((9 - 8) > (-14 - 5)))) and (not ((((人体有206块骨头。) and ((-14 + -9) < (14 + 16) < (2 ** 1))) and (((17 + 15) <= (19 * 19)) and (1900年奥运会在安特卫普举办。))) and (((空气在常温下是气体。) and (智利位于南美洲。)) and ((-14 + -12) >= (4 ** 1)))))
H. ((not (((海王星是距离太阳第7近的行星。) and (中国的首都是北京。)) or (not (1956年奥运会在墨尔本举办。)))) or (韩国的首都是首尔。) or (not not (((鳄鱼是爬行动物。) or ((10 * 10 - 1 * -1) < (20 - -11))) or ((哥伦比亚的首都是新德里。) or ((7 - -6) == (5 - -11)))))) or (not not (81的平方根是9。)) or ((((6 * 3 * 9 * -8) != (-19 - -19)) and (not not (越南位于大洋洲。)) and (not not (2008年奥运会在北京举办。))) and (not not ((64能被3整除。) and ((-10 * 3 - -6 * 4) > (1 * 0 * 10 * -6)))) and ((鳄鱼是爬行动物。) or ((木星是距离太阳第5近的行星。) and (2021年是闰年。)) or ((10 + -20) != (10 - 5))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
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"difficulty": 1,
"gpt_response": "",
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"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. ((not (((-16 - 15) <= (-4 * 1 - 5 * -1) <= (-12 + 8)) or (((-17 + -8) > (-8 * -10 - 0 * 10)) or (加拿大的货币是加元。)))) or (not not ((马是哺乳动物。) or (新西兰的货币是比索。))) or (not not ((((-8 * -5) > (-14 + -3)) or ((0 * -13) != (5 ** 3))) or (捷克的货币是克朗。)))) and (not ((((10 + 3) <= (6 * 2 + 4 * 5) <= (-8 - -9)) and (not not (欧盟的货币是欧元。))) and (not not ((铬的化学符号是Pb。) and (37小于等于92。)))))\nB. ((not not (not not (not not (企鹅能飞翔。)))) and ((天王星是距离太阳第3近的行星。) and ((中国的货币是人民币。) and (2016年奥运会在里约热内卢举办。)) and ((((5 ** 1) <= (-18 + 19)) and (中国的货币是人民币。)) and (人类有2条腿。)))) or (((((4 % 9) == (2 ** 1)) and (伦敦大火发生在1666年。)) and (金在常温下是固体。)) and (金在常温下是液体。)) or ((((俄罗斯位于欧洲。) or ((冰在常温下是液体。) and (七月有31天。))) or ((波兰的货币是里拉。) or (埃及的货币是福林。))) and (not not (not not (((32 % 10) < (16 - -3)) or (月球绕地球运转。)))))\nC. not not (((水星是距离太阳第7近的行星。) and (not (水在海平面上的沸点是100摄氏度。)) and ((not not (捷克的首都是布鲁塞尔。)) and (((-12 + -20) > (-13 * -6)) or ((10 * -1 * -6 * -5) != (-8 + 18))))) and (((((-15 - -14) < (-10 - 6)) or (爱尔兰的首都是阿姆斯特丹。)) and ((地球是距离太阳第3近的行星。) and ((-8 * -6 + 4 * 6) <= (10 * -1 - -8 * -10)))) and ((-10 * -6) <= (-6 * 9 - 4 * -8))))\nD. not not ((not not (1900年奥运会在东京举办。)) or (((现代奥运会首届举办发生在1898年。) or ((10 + -17) <= (8 - -10))) and ((-16 * -20) >= (5 ** 1))))\nE. not not (((not (((9 * -10) < (1 ** 2) < (-7 * -8 - -7 * -10)) and (水星是距离太阳第5近的行星。))) or (钻石由碳元素组成。)) or (not ((5 * 3) == (-2 - -3))))\nF. ((((not not ((4 * 1 + -2 * -2) < (-8 * -10 - 5 * 8) < (14 - -6))) and (not ((25 % 10) == (-9 - 9)))) or ((蝴蝶有6条腿。) and (44小于等于80。)) or (三月有29天。)) or (((5 - 5) < (2 * -4 * 1 * 10) < (12 * -1)) and (乌鸦是昆虫。) and (水星是距离太阳第2近的行星。))) and (((((1 ** 1) > (-18 * 9)) and (((49 % 9) < (-4 * 3 - 6 * 10) < (4 * 1)) or (新西兰的首都是惠灵顿。))) and ((中国的货币是雷亚尔。) and (37大于90。)) and ((not ((3 ** 1) > (-8 * -20))) or (新西兰位于亚洲。))) and ((铁在常温下是固体。) or (not not ((变色龙是爬行动物。) or (2012年奥运会在伦敦举办。)))))\nG. (((not (1896年奥运会在雅典举办。)) or ((((-4 - 20) < (6 - -8)) or (2011年是闰年。)) or ((5 * 0 + 0 * 0) <= (18 * -18) <= (10 + 2)))) or (not not ((9 - 8) > (-14 - 5)))) and (not ((((人体有206块骨头。) and ((-14 + -9) < (14 + 16) < (2 ** 1))) and (((17 + 15) <= (19 * 19)) and (1900年奥运会在安特卫普举办。))) and (((空气在常温下是气体。) and (智利位于南美洲。)) and ((-14 + -12) >= (4 ** 1)))))\nH. ((not (((海王星是距离太阳第7近的行星。) and (中国的首都是北京。)) or (not (1956年奥运会在墨尔本举办。)))) or (韩国的首都是首尔。) or (not not (((鳄鱼是爬行动物。) or ((10 * 10 - 1 * -1) < (20 - -11))) or ((哥伦比亚的首都是新德里。) or ((7 - -6) == (5 - -11)))))) or (not not (81的平方根是9。)) or ((((6 * 3 * 9 * -8) != (-19 - -19)) and (not not (越南位于大洋洲。)) and (not not (2008年奥运会在北京举办。))) and (not not ((64能被3整除。) and ((-10 * 3 - -6 * 4) > (1 * 0 * 10 * -6)))) and ((鳄鱼是爬行动物。) or ((木星是距离太阳第5近的行星。) and (2021年是闰年。)) or ((10 + -20) != (10 - 5))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
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"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (not not ((not not (The Pacific Ocean is the largest ocean.)) and (not ((-3 - 17) == (3 * -3 - 2 * -7)))))
B. (not ((((-18 - 1) <= (4 - -6)) or ((3 % 6) == (-2 * -10 + 0 * 7))) or ((-2 * -1 + -4 * 9) < (8 * 5 + -9 * 4)))) and (The chemical symbol for Chlorine is Cl.) and (not not (((Spain is in Europe.) or (143 is an odd number.)) and (not not ((-6 - -14) >= (-11 + -5)))))
C. not not (((-6 * -5 - -3 * -10) >= (2 ** 3)) or (Italy is in Antarctica.))
D. not (not (Diamond is a solid at room temperature.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
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"answer": "A,D",
"difficulty": 1,
"gpt_response": "",
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"language": "en",
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"question": "Examine these expressions:\n\nA. not not (not not ((not not (The Pacific Ocean is the largest ocean.)) and (not ((-3 - 17) == (3 * -3 - 2 * -7)))))\nB. (not ((((-18 - 1) <= (4 - -6)) or ((3 % 6) == (-2 * -10 + 0 * 7))) or ((-2 * -1 + -4 * 9) < (8 * 5 + -9 * 4)))) and (The chemical symbol for Chlorine is Cl.) and (not not (((Spain is in Europe.) or (143 is an odd number.)) and (not not ((-6 - -14) >= (-11 + -5)))))\nC. not not (((-6 * -5 - -3 * -10) >= (2 ** 3)) or (Italy is in Antarctica.))\nD. not (not (Diamond is a solid at room temperature.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 15224935,
"true_count": 2
},
"seed": 15224935,
"task_id": 615224935,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (((8 * -2 - -4 * 3) <= (12 - -3) <= (8 * 7 - 1 * 1)) or (法国大革命开始发生在1789年。)) and (((4 ** 2) == (-2 + 15)) and ((-9 + 14) <= (-19 - -6)))
B. not not (钻石由碳元素组成。)
C. (((-15 + 18) <= (14 * 17)) or ((-2 - -10) >= (40 % 1))) and (((5 ** 1) < (5 ** 3)) or (氖的化学符号是Ne。))
D. (4 * 6 * 8 * -9) < (16 + -20)
E. ((土星是距离太阳第6近的行星。) and (鳕鱼是爬行动物。)) or (not (1956年奥运会在墨尔本举办。))
F. (((9 + -8) == (-5 * -9 - 6 * -6)) or (二月有29天。)) and ((-10 * -5 * 10 * 0) > (5 - 4))
G. (9 + 9) >= (6 * 0 + 5 * 10)
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
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"question": "研究以下逻辑语句：\n\nA. (((8 * -2 - -4 * 3) <= (12 - -3) <= (8 * 7 - 1 * 1)) or (法国大革命开始发生在1789年。)) and (((4 ** 2) == (-2 + 15)) and ((-9 + 14) <= (-19 - -6)))\nB. not not (钻石由碳元素组成。)\nC. (((-15 + 18) <= (14 * 17)) or ((-2 - -10) >= (40 % 1))) and (((5 ** 1) < (5 ** 3)) or (氖的化学符号是Ne。))\nD. (4 * 6 * 8 * -9) < (16 + -20)\nE. ((土星是距离太阳第6近的行星。) and (鳕鱼是爬行动物。)) or (not (1956年奥运会在墨尔本举办。))\nF. (((9 + -8) == (-5 * -9 - 6 * -6)) or (二月有29天。)) and ((-10 * -5 * 10 * 0) > (5 - 4))\nG. (9 + 9) >= (6 * 0 + 5 * 10)\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 78635159,
"true_count": 3
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"seed": 78635159,
"task_id": 678635159,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (not (1977 is a leap year.))
B. (not not (((25 % 10) <= (5 * -3) <= (1 - 17)) and ((The square root of 64 is 3.) or (The capital of Turkey is Ankara.)))) or (not not (((The square root of 81 is 9.) or (1998 is a leap year.)) or (not not (The 1896 Olympics were held in Mexico City.))))
C. (((not (Water is a liquid at room temperature.)) and ((The capital of Turkey is Ankara.) or ((-19 + 16) > (3 + -4)))) or (not not ((A crab has 6 legs.) or (The 2024 Olympics were held in Barcelona.)))) and (((-20 * -20) <= (3 + -4)) or (not (((11 - -14) != (6 + -16)) and (16 is divisible by 10.))))
D. ((((Diamonds are made of carbon.) and ((16 + -16) != (3 * 1 - 0 * 3))) and ((1 ** 1) == (-14 + -20))) or (((17 + -18) <= (12 - 9)) or (The 1936 Olympics were held in Sydney.)) or ((((-9 + 16) < (3 + -8)) and ((-11 + -11) > (-10 + -5))) and ((The capital of Canada is Ottawa.) or ((-6 * 2 * 1 * 2) < (7 * 2 - 0 * -2))))) and ((not ((Nitrogen is a liquid at room temperature.) and (The capital of Japan is Tokyo.))) or ((not not ((2 + 0) < (5 ** 1) < (-11 + -3))) or ((-6 * 0 + 7 * -10) < (4 ** 3))))
E. (((not not (A cow is a mammal.)) or (The 2000 Olympics were held in Beijing.)) and ((Russia is in Europe.) and (((-10 + 3) > (3 ** 1)) or (Saturn is the 6th planet from the Sun.)))) and (((Mars is the closest planet to the Sun.) or (not (The chemical symbol for Mercury is Cu.))) or (not ((12 * -1) < (-4 * 12))) or (not (((14 - 7) <= (1 ** 3) <= (9 - 18)) or (Humans have three lungs.))))
F. ((not ((The speed of light is approximately 300,000 km/s.) or (The chemical symbol for Manganese is S.))) or (not not (not not (The 2008 Olympics were held in Antwerp.)))) or ((Alcohol is a liquid at room temperature.) and (not (not not ((15 % 3) >= (-1 - -9)))))
G. (((((-3 * -3 * -3 * -6) == (7 * 9 + -3 * -3)) or ((-10 + 15) > (1 + 6))) or ((A herring is a reptile.) or ((-15 * -9) <= (-4 * 9 * -3 * -4)))) or ((((5 % 10) < (6 + -8)) and ((24 % 3) <= (18 - -9) <= (23 % 3))) or ((The 1960 Olympics were held in Paris.) and (The chemical symbol for Titanium is Ti.)))) and (Oxygen is a gas at room temperature.) and (((((4 * -14) <= (2 * -6 + 10 * 0)) and ((14 % 4) > (-10 - 9))) and (not not (Neptune is the 8th planet from the Sun.))) and ((2 * -5) == (3 % 7)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "B,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 60339169,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not (1977 is a leap year.))\nB. (not not (((25 % 10) <= (5 * -3) <= (1 - 17)) and ((The square root of 64 is 3.) or (The capital of Turkey is Ankara.)))) or (not not (((The square root of 81 is 9.) or (1998 is a leap year.)) or (not not (The 1896 Olympics were held in Mexico City.))))\nC. (((not (Water is a liquid at room temperature.)) and ((The capital of Turkey is Ankara.) or ((-19 + 16) > (3 + -4)))) or (not not ((A crab has 6 legs.) or (The 2024 Olympics were held in Barcelona.)))) and (((-20 * -20) <= (3 + -4)) or (not (((11 - -14) != (6 + -16)) and (16 is divisible by 10.))))\nD. ((((Diamonds are made of carbon.) and ((16 + -16) != (3 * 1 - 0 * 3))) and ((1 ** 1) == (-14 + -20))) or (((17 + -18) <= (12 - 9)) or (The 1936 Olympics were held in Sydney.)) or ((((-9 + 16) < (3 + -8)) and ((-11 + -11) > (-10 + -5))) and ((The capital of Canada is Ottawa.) or ((-6 * 2 * 1 * 2) < (7 * 2 - 0 * -2))))) and ((not ((Nitrogen is a liquid at room temperature.) and (The capital of Japan is Tokyo.))) or ((not not ((2 + 0) < (5 ** 1) < (-11 + -3))) or ((-6 * 0 + 7 * -10) < (4 ** 3))))\nE. (((not not (A cow is a mammal.)) or (The 2000 Olympics were held in Beijing.)) and ((Russia is in Europe.) and (((-10 + 3) > (3 ** 1)) or (Saturn is the 6th planet from the Sun.)))) and (((Mars is the closest planet to the Sun.) or (not (The chemical symbol for Mercury is Cu.))) or (not ((12 * -1) < (-4 * 12))) or (not (((14 - 7) <= (1 ** 3) <= (9 - 18)) or (Humans have three lungs.))))\nF. ((not ((The speed of light is approximately 300,000 km/s.) or (The chemical symbol for Manganese is S.))) or (not not (not not (The 2008 Olympics were held in Antwerp.)))) or ((Alcohol is a liquid at room temperature.) and (not (not not ((15 % 3) >= (-1 - -9)))))\nG. (((((-3 * -3 * -3 * -6) == (7 * 9 + -3 * -3)) or ((-10 + 15) > (1 + 6))) or ((A herring is a reptile.) or ((-15 * -9) <= (-4 * 9 * -3 * -4)))) or ((((5 % 10) < (6 + -8)) and ((24 % 3) <= (18 - -9) <= (23 % 3))) or ((The 1960 Olympics were held in Paris.) and (The chemical symbol for Titanium is Ti.)))) and (Oxygen is a gas at room temperature.) and (((((4 * -14) <= (2 * -6 + 10 * 0)) and ((14 % 4) > (-10 - 9))) and (not not (Neptune is the 8th planet from the Sun.))) and ((2 * -5) == (3 % 7)))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 60339169,
"true_count": 4
},
"seed": 60339169,
"task_id": 660339169,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not (288 is a Fibonacci number.)
B. (16 + -13) >= (-5 * -6 * 0 * -7)
C. not (((-3 + 8) < (1 + -7)) and ((-7 * -4) != (31 % 2)))
D. (A day on Earth is 24 hours.) and (The Earth revolves around the Sun.)
E. ((Thailand is in South America.) or ((4 * 2 * 0 * -7) < (-17 * -7))) and (Nitrogen is a gas at room temperature.)
F. (((2 * -1 * 1 * -10) != (1 * 0)) and (A iguana is an insect.)) or (not not (Neptune is the 1st planet from the Sun.))
G. The 1992 Olympics were held in Los Angeles.
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 41200226,
"true_count": 5
},
"question": "Examine these expressions:\n\nA. not (288 is a Fibonacci number.)\nB. (16 + -13) >= (-5 * -6 * 0 * -7)\nC. not (((-3 + 8) < (1 + -7)) and ((-7 * -4) != (31 % 2)))\nD. (A day on Earth is 24 hours.) and (The Earth revolves around the Sun.)\nE. ((Thailand is in South America.) or ((4 * 2 * 0 * -7) < (-17 * -7))) and (Nitrogen is a gas at room temperature.)\nF. (((2 * -1 * 1 * -10) != (1 * 0)) and (A iguana is an insect.)) or (not not (Neptune is the 1st planet from the Sun.))\nG. The 1992 Olympics were held in Los Angeles.\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 41200226,
"true_count": 5
},
"seed": 41200226,
"task_id": 641200226,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not not ((Oil is a solid at room temperature.) and (((5 ** 3) <= (-3 + 8)) and ((7 * -8) <= (23 % 9) <= (-20 - 9))))
B. ((8 * 5 * 9 * 1) > (6 - -1)) or (not ((-19 - -14) > (9 - -14))) or (The 1996 Olympics were held in Atlanta.)
C. ((not ((18 + -1) > (9 * 5 + 3 * -7))) and (((-12 * 3) > (48 % 8)) and (Ice is a liquid at room temperature.))) or ((((19 + 18) >= (-4 * 0 - 1 * 10)) and (Diamond is a solid at room temperature.)) and (Sharks are mammals.))
D. (not not ((Earth is the 3rd planet from the Sun.) and ((12 - -16) < (-20 + 2) < (13 % 2)))) and ((not not ((4 - 17) <= (18 * -17))) and ((698 is a Fibonacci number.) and ((-6 * -6 - 9 * 3) > (22 % 8))))
E. ((-4 * -6 + -5 * 10) < (-8 * 3 - -1 * -8)) or ((The 2024 Olympics were held in London.) and (((7 * -3) != (0 - 0)) and (The human body has 150 bones.)))
F. ((9 - -2) == (10 * 2 * -6 * -8)) or (not (not ((15 - 10) > (-6 * 7 * -7 * 3))))
G. not not ((Uranus is the 7th planet from the Sun.) and ((Copper is a solid at room temperature.) and (The 1976 Olympics were held in Montreal.)))
H. not ((not not ((3 + -20) > (-14 + 7))) and ((A chicken has 100 legs.) and (The currency of New Zealand is the Riyal.)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "B,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 44294101,
"true_count": 3
},
"question": "Review these logical expressions:\n\nA. not not ((Oil is a solid at room temperature.) and (((5 ** 3) <= (-3 + 8)) and ((7 * -8) <= (23 % 9) <= (-20 - 9))))\nB. ((8 * 5 * 9 * 1) > (6 - -1)) or (not ((-19 - -14) > (9 - -14))) or (The 1996 Olympics were held in Atlanta.)\nC. ((not ((18 + -1) > (9 * 5 + 3 * -7))) and (((-12 * 3) > (48 % 8)) and (Ice is a liquid at room temperature.))) or ((((19 + 18) >= (-4 * 0 - 1 * 10)) and (Diamond is a solid at room temperature.)) and (Sharks are mammals.))\nD. (not not ((Earth is the 3rd planet from the Sun.) and ((12 - -16) < (-20 + 2) < (13 % 2)))) and ((not not ((4 - 17) <= (18 * -17))) and ((698 is a Fibonacci number.) and ((-6 * -6 - 9 * 3) > (22 % 8))))\nE. ((-4 * -6 + -5 * 10) < (-8 * 3 - -1 * -8)) or ((The 2024 Olympics were held in London.) and (((7 * -3) != (0 - 0)) and (The human body has 150 bones.)))\nF. ((9 - -2) == (10 * 2 * -6 * -8)) or (not (not ((15 - 10) > (-6 * 7 * -7 * 3))))\nG. not not ((Uranus is the 7th planet from the Sun.) and ((Copper is a solid at room temperature.) and (The 1976 Olympics were held in Montreal.)))\nH. not ((not not ((3 + -20) > (-14 + 7))) and ((A chicken has 100 legs.) and (The currency of New Zealand is the Riyal.)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 44294101,
"true_count": 3
},
"seed": 44294101,
"task_id": 644294101,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not ((((Alcohol is a liquid at room temperature.) and (The currency of United States is the Dollar.)) and ((The currency of Hungary is the Real.) or (Alcohol is a liquid at room temperature.))) and ((Uranus is the 7th planet from the Sun.) and (The 1996 Olympics were held in Mexico City.)))
B. (((Sound cannot travel through a vacuum.) and ((The chemical symbol for Hydrogen is S.) or (Oxygen is necessary for human survival.))) or (not ((The 1984 Olympics were held in Stockholm.) or ((-8 + -12) < (-17 - 18))))) and ((not (((-4 * -8 - -3 * -6) < (8 * 10 + -4 * 6)) or (United States is in North America.))) and (2002 is a leap year.))
C. ((((The capital of Denmark is Copenhagen.) or (The Soviet Union dissolved occurred in 1991.)) and ((9 * -16) > (-20 * -12))) or ((not ((2 * -11) < (19 + -12) < (4 ** 1))) or ((The Earth revolves around the Sun.) and (Alcohol is a gas at room temperature.)))) and (((3 - 1) <= (0 - 20)) and ((((-15 - -16) == (5 ** 3)) and ((7 - 16) <= (5 * -5) <= (-9 * -12))) and ((Uranus is the 4th planet from the Sun.) and (Copper is a solid at room temperature.))))
D. (((not not ((0 * 5 * 6 * -9) != (-12 - -3))) or ((3 ** 1) == (12 - -1))) or ((-7 * 2) != (10 * -8 * -7 * 9))) or ((not not (A bee is a mammal.)) and ((8 * 10) == (19 * 9))) or (((Saturn is the 1st planet from the Sun.) or (((12 % 2) > (-6 * 0 * 8 * -4)) or ((1 * 2) <= (7 * 8 + -4 * -1) <= (-8 * 7 * 10 * 7)))) or ((((-10 + -16) == (41 % 3)) or ((-18 + 18) <= (8 * -7))) or (((-14 + 16) == (2 ** 3)) and ((21 % 2) == (9 * -6 - -8 * -7)))))
E. (((188 is an even number.) or ((Indonesia is in Asia.) or ((6 * -1 - -2 * -3) <= (-7 * -3 * 3 * -5)))) or (((13 - 16) <= (8 * -10) <= (6 + -8)) or (A elephant has 6 legs.)) or (The Great Fire of London occurred in 1666.)) and ((not not (not not (A lizard is an insect.))) and ((2 ** 2) == (16 + -15)))
F. ((((2 ** 1) < (-19 - -3)) or ((Penguins can fly.) and ((5 ** 1) < (3 ** 3)))) or (not not (Carbon dioxide is a solid at room temperature.)) or ((not ((16 + -11) >= (4 ** 3))) and (The chemical symbol for Tin is Co.))) or (((not not (A alligator is a reptile.)) or (((31 % 2) != (-8 * 5 + -10 * -10)) and (38 is less than or equal to 80.))) or (A gecko is a reptile.))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 6253959,
"true_count": 3
},
"question": "Review these logical expressions:\n\nA. not ((((Alcohol is a liquid at room temperature.) and (The currency of United States is the Dollar.)) and ((The currency of Hungary is the Real.) or (Alcohol is a liquid at room temperature.))) and ((Uranus is the 7th planet from the Sun.) and (The 1996 Olympics were held in Mexico City.)))\nB. (((Sound cannot travel through a vacuum.) and ((The chemical symbol for Hydrogen is S.) or (Oxygen is necessary for human survival.))) or (not ((The 1984 Olympics were held in Stockholm.) or ((-8 + -12) < (-17 - 18))))) and ((not (((-4 * -8 - -3 * -6) < (8 * 10 + -4 * 6)) or (United States is in North America.))) and (2002 is a leap year.))\nC. ((((The capital of Denmark is Copenhagen.) or (The Soviet Union dissolved occurred in 1991.)) and ((9 * -16) > (-20 * -12))) or ((not ((2 * -11) < (19 + -12) < (4 ** 1))) or ((The Earth revolves around the Sun.) and (Alcohol is a gas at room temperature.)))) and (((3 - 1) <= (0 - 20)) and ((((-15 - -16) == (5 ** 3)) and ((7 - 16) <= (5 * -5) <= (-9 * -12))) and ((Uranus is the 4th planet from the Sun.) and (Copper is a solid at room temperature.))))\nD. (((not not ((0 * 5 * 6 * -9) != (-12 - -3))) or ((3 ** 1) == (12 - -1))) or ((-7 * 2) != (10 * -8 * -7 * 9))) or ((not not (A bee is a mammal.)) and ((8 * 10) == (19 * 9))) or (((Saturn is the 1st planet from the Sun.) or (((12 % 2) > (-6 * 0 * 8 * -4)) or ((1 * 2) <= (7 * 8 + -4 * -1) <= (-8 * 7 * 10 * 7)))) or ((((-10 + -16) == (41 % 3)) or ((-18 + 18) <= (8 * -7))) or (((-14 + 16) == (2 ** 3)) and ((21 % 2) == (9 * -6 - -8 * -7)))))\nE. (((188 is an even number.) or ((Indonesia is in Asia.) or ((6 * -1 - -2 * -3) <= (-7 * -3 * 3 * -5)))) or (((13 - 16) <= (8 * -10) <= (6 + -8)) or (A elephant has 6 legs.)) or (The Great Fire of London occurred in 1666.)) and ((not not (not not (A lizard is an insect.))) and ((2 ** 2) == (16 + -15)))\nF. ((((2 ** 1) < (-19 - -3)) or ((Penguins can fly.) and ((5 ** 1) < (3 ** 3)))) or (not not (Carbon dioxide is a solid at room temperature.)) or ((not ((16 + -11) >= (4 ** 3))) and (The chemical symbol for Tin is Co.))) or (((not not (A alligator is a reptile.)) or (((31 % 2) != (-8 * 5 + -10 * -10)) and (38 is less than or equal to 80.))) or (A gecko is a reptile.))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 6253959,
"true_count": 3
},
"seed": 6253959,
"task_id": 606253959,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not (not (95 is divisible by 5.))
B. (((-6 - -13) != (-2 + -10)) and ((11 * 7) <= (-8 * -6 * 5 * -6))) and (The capital of Belgium is Brussels.)
C. Nigeria is in South America.
D. not not (((13 * -4) != (3 * 6 * -7 * -8)) or (Mars is the 1st planet from the Sun.))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 66234007,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. not (not (95 is divisible by 5.))\nB. (((-6 - -13) != (-2 + -10)) and ((11 * 7) <= (-8 * -6 * 5 * -6))) and (The capital of Belgium is Brussels.)\nC. Nigeria is in South America.\nD. not not (((13 * -4) != (3 * 6 * -7 * -8)) or (Mars is the 1st planet from the Sun.))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 66234007,
"true_count": 2
},
"seed": 66234007,
"task_id": 666234007,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not ((((not ((16 + 4) < (-9 - -11) < (10 + 20))) or ((2036 is a leap year.) or ((Bats are blind.) and (The capital of Thailand is New Delhi.)))) and (not (not (not not (The chemical symbol for Sulfur is S.))))) or (not not ((not (((-2 + 6) <= (0 * 5) <= (6 - -14)) or (43 is a prime number.))) and ((There are 31 days in May.) or (not not (Lightning never strikes the same place twice.))))))
B. not ((not not (((not (The capital of Morocco is Paris.)) and ((-5 * -7 + -2 * 2) >= (9 + -4))) and ((-11 - 2) == (7 * -2 * 4 * 7)))) or (not (((not not (Whales are fish.)) or ((France is in Europe.) and ((-14 - -3) >= (-19 * 12)))) or (not (((-6 * -7 + -3 * -7) <= (5 * 0 - 5 * -7) <= (3 * 18)) or ((3 * -3 * -8 * 2) <= (47 % 9) <= (1 * 13)))))))
C. not not ((not (not ((14 % 8) > (-1 * -4 - 9 * 8)))) or (not ((-11 - -8) < (5 * -10))) or (((1990 is a leap year.) or (not ((8 * 4 + 5 * -2) == (-1 + -13)))) or (not (((16 + 12) <= (2 ** 2)) and (The 2024 Olympics were held in Amsterdam.))) or (not ((((20 - 12) == (1 ** 1)) and (The chemical symbol for Nickel is Ni.)) or (not ((13 - -12) <= (3 + 20)))))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 51062056,
"true_count": 2
},
"question": "Below are several boolean expressions:\n\nA. not ((((not ((16 + 4) < (-9 - -11) < (10 + 20))) or ((2036 is a leap year.) or ((Bats are blind.) and (The capital of Thailand is New Delhi.)))) and (not (not (not not (The chemical symbol for Sulfur is S.))))) or (not not ((not (((-2 + 6) <= (0 * 5) <= (6 - -14)) or (43 is a prime number.))) and ((There are 31 days in May.) or (not not (Lightning never strikes the same place twice.))))))\nB. not ((not not (((not (The capital of Morocco is Paris.)) and ((-5 * -7 + -2 * 2) >= (9 + -4))) and ((-11 - 2) == (7 * -2 * 4 * 7)))) or (not (((not not (Whales are fish.)) or ((France is in Europe.) and ((-14 - -3) >= (-19 * 12)))) or (not (((-6 * -7 + -3 * -7) <= (5 * 0 - 5 * -7) <= (3 * 18)) or ((3 * -3 * -8 * 2) <= (47 % 9) <= (1 * 13)))))))\nC. not not ((not (not ((14 % 8) > (-1 * -4 - 9 * 8)))) or (not ((-11 - -8) < (5 * -10))) or (((1990 is a leap year.) or (not ((8 * 4 + 5 * -2) == (-1 + -13)))) or (not (((16 + 12) <= (2 ** 2)) and (The 2024 Olympics were held in Amsterdam.))) or (not ((((20 - 12) == (1 ** 1)) and (The chemical symbol for Nickel is Ni.)) or (not ((13 - -12) <= (3 + 20)))))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 51062056,
"true_count": 2
},
"seed": 51062056,
"task_id": 651062056,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. Diamonds are made of carbon.
B. not not (not (The capital of Singapore is Singapore.))
C. ((Venus is the 2nd planet from the Sun.) and (Spiders are insects.)) and (not (The capital of Portugal is Lisbon.))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 37670815,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. Diamonds are made of carbon.\nB. not not (not (The capital of Singapore is Singapore.))\nC. ((Venus is the 2nd planet from the Sun.) and (Spiders are insects.)) and (not (The capital of Portugal is Lisbon.))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 37670815,
"true_count": 1
},
"seed": 37670815,
"task_id": 637670815,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. not not (((8 + -3) > (30 % 2)) and ((越南的货币是索尔。) or (马来西亚的货币是林吉特。)))
B. (2074年是闰年。) and (not (澳大利亚的货币是澳元。))
C. not not (((伦敦大火发生在1668年。) or (大象有4条腿。)) or (not ((9 % 8) <= (2 - -2) <= (1 * 8 + -1 * -2))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 1688210,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. not not (((8 + -3) > (30 % 2)) and ((越南的货币是索尔。) or (马来西亚的货币是林吉特。)))\nB. (2074年是闰年。) and (not (澳大利亚的货币是澳元。))\nC. not not (((伦敦大火发生在1668年。) or (大象有4条腿。)) or (not ((9 % 8) <= (2 - -2) <= (1 * 8 + -1 * -2))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 1688210,
"true_count": 2
},
"seed": 1688210,
"task_id": 601688210,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (not ((((5 * 14) <= (14 % 10) <= (-15 - 6)) or (Steam is a gas at room temperature.)) or ((8 % 5) >= (16 * -14)))) and (((2089 is a leap year.) or ((11 is greater than 98.) or (The capital of Ireland is Dublin.))) or (not (not not ((-11 - 12) != (5 * 15)))))
B. ((((3 + 7) < (5 ** 3)) or (((4 ** 3) <= (0 * 2 - 3 * -5)) or ((2 * -2 - -1 * -4) <= (4 ** 3)))) and ((2 ** 1) < (14 + -14))) or (((((-20 * 6) != (14 * -10)) and ((23 % 9) < (3 - 8))) and (not ((-16 - -3) == (-1 - 2)))) and ((10 * 3 + -8 * 6) > (-9 * 10 * -5 * -2)))
C. (not (((The chemical symbol for Silver is Ag.) or ((4 * 6 - 5 * 0) >= (32 % 7))) or ((Uranus is the 3rd planet from the Sun.) and ((3 * -9 + -7 * -8) < (38 % 7))))) and (((((-14 + 17) <= (45 % 3) <= (19 + 12)) and ((-4 * 9 - -10 * -3) <= (1 ** 2))) and (The human body has 150 bones.)) or ((A butterfly is an insect.) and (1930 is a leap year.)) or ((The currency of European Union is the Euro.) or (not not (Sound travels faster in a vacuum.))))
D. The human body has 206 bones.
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 87140201,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. (not ((((5 * 14) <= (14 % 10) <= (-15 - 6)) or (Steam is a gas at room temperature.)) or ((8 % 5) >= (16 * -14)))) and (((2089 is a leap year.) or ((11 is greater than 98.) or (The capital of Ireland is Dublin.))) or (not (not not ((-11 - 12) != (5 * 15)))))\nB. ((((3 + 7) < (5 ** 3)) or (((4 ** 3) <= (0 * 2 - 3 * -5)) or ((2 * -2 - -1 * -4) <= (4 ** 3)))) and ((2 ** 1) < (14 + -14))) or (((((-20 * 6) != (14 * -10)) and ((23 % 9) < (3 - 8))) and (not ((-16 - -3) == (-1 - 2)))) and ((10 * 3 + -8 * 6) > (-9 * 10 * -5 * -2)))\nC. (not (((The chemical symbol for Silver is Ag.) or ((4 * 6 - 5 * 0) >= (32 % 7))) or ((Uranus is the 3rd planet from the Sun.) and ((3 * -9 + -7 * -8) < (38 % 7))))) and (((((-14 + 17) <= (45 % 3) <= (19 + 12)) and ((-4 * 9 - -10 * -3) <= (1 ** 2))) and (The human body has 150 bones.)) or ((A butterfly is an insect.) and (1930 is a leap year.)) or ((The currency of European Union is the Euro.) or (not not (Sound travels faster in a vacuum.))))\nD. The human body has 206 bones.\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 87140201,
"true_count": 1
},
"seed": 87140201,
"task_id": 687140201,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((not not ((5 is less than or equal to 95.) or (The Soviet Union dissolved occurred in 1991.))) or ((-12 * 1) <= (9 + -19) <= (6 - -11))) and ((4 - 15) > (-3 * -14)) and (not not (not (Indonesia is in Asia.)))
B. (((-18 + 20) < (-4 * 9 - -10 * 3)) or (The chemical symbol for Neon is Ne.) or ((The capital of Romania is Rabat.) or (not not ((4 - 18) != (4 ** 2))))) and ((not (Gold is a solid at room temperature.)) and (not ((The currency of India is the Rupee.) or (Sound travels faster in a vacuum.))))
C. (not ((not (Helium is a gas at room temperature.)) and (Japan is in Asia.))) and ((((-2 * 0 - 5 * 2) != (7 + 6)) and ((-7 * 3 - -1 * -6) != (3 ** 3))) or ((-4 + -11) != (-7 - -14))) and (((not (Russia is in Europe.)) and (not (World War II ended occurred in 1945.))) and ((There are 31 days in January.) or (79 is divisible by 9.)) and ((The Moon orbits the Earth.) and ((10 + -14) >= (2 ** 3))))
D. ((The currency of Australia is the Dong.) or ((1 ** 2) < (-3 * -14) < (20 % 1))) and (not not ((2056 is a leap year.) and ((The capital of Mexico is Athens.) and ((-2 * -9) < (15 - -8) < (-17 * 17)))))
E. ((((0 + 10) > (5 ** 3)) and (((8 * -14) >= (-13 * 12)) or (1993 is a leap year.))) or (not (((6 - 5) == (2 ** 2)) and (Water boils at 100 degrees Celsius at sea level.)))) and ((The currency of Nigeria is the Dollar.) or (not not ((The square root of 36 is 6.) or ((12 * 19) < (-11 * -19) < (5 * -11)))))
F. ((The chemical symbol for Oxygen is Cr.) and ((-6 * 1) >= (49 % 7))) and (not not (((5 * -8) != (18 - 10)) or (((40 % 3) <= (5 * 2 * 6 * 10)) or (2035 is a leap year.))))
G. not (not ((-14 - -9) < (16 % 9) < (1 * -20)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 98305083,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. ((not not ((5 is less than or equal to 95.) or (The Soviet Union dissolved occurred in 1991.))) or ((-12 * 1) <= (9 + -19) <= (6 - -11))) and ((4 - 15) > (-3 * -14)) and (not not (not (Indonesia is in Asia.)))\nB. (((-18 + 20) < (-4 * 9 - -10 * 3)) or (The chemical symbol for Neon is Ne.) or ((The capital of Romania is Rabat.) or (not not ((4 - 18) != (4 ** 2))))) and ((not (Gold is a solid at room temperature.)) and (not ((The currency of India is the Rupee.) or (Sound travels faster in a vacuum.))))\nC. (not ((not (Helium is a gas at room temperature.)) and (Japan is in Asia.))) and ((((-2 * 0 - 5 * 2) != (7 + 6)) and ((-7 * 3 - -1 * -6) != (3 ** 3))) or ((-4 + -11) != (-7 - -14))) and (((not (Russia is in Europe.)) and (not (World War II ended occurred in 1945.))) and ((There are 31 days in January.) or (79 is divisible by 9.)) and ((The Moon orbits the Earth.) and ((10 + -14) >= (2 ** 3))))\nD. ((The currency of Australia is the Dong.) or ((1 ** 2) < (-3 * -14) < (20 % 1))) and (not not ((2056 is a leap year.) and ((The capital of Mexico is Athens.) and ((-2 * -9) < (15 - -8) < (-17 * 17)))))\nE. ((((0 + 10) > (5 ** 3)) and (((8 * -14) >= (-13 * 12)) or (1993 is a leap year.))) or (not (((6 - 5) == (2 ** 2)) and (Water boils at 100 degrees Celsius at sea level.)))) and ((The currency of Nigeria is the Dollar.) or (not not ((The square root of 36 is 6.) or ((12 * 19) < (-11 * -19) < (5 * -11)))))\nF. ((The chemical symbol for Oxygen is Cr.) and ((-6 * 1) >= (49 % 7))) and (not not (((5 * -8) != (18 - 10)) or (((40 % 3) <= (5 * 2 * 6 * 10)) or (2035 is a leap year.))))\nG. not (not ((-14 - -9) < (16 % 9) < (1 * -20)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 98305083,
"true_count": 1
},
"seed": 98305083,
"task_id": 698305083,
"task_type": "boolean_expressions"
} |
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