env stringclasses 1
value | prompt stringlengths 85 3.69k | extra dict |
|---|---|---|
logic-v2 | Study the following logical statements:
A. ((3 ** 2) < (-5 * -17)) or (((-12 * -8) > (5 + 9)) and (Mars is the 4th planet from the Sun.)) or ((((-1 * 10 - -7 * 10) != (2 ** 3)) or ((17 * 17) <= (3 + -5) <= (15 - 7))) and (not (The capital of Australia is Stockholm.)))
B. not ((-10 * 1) < (8 * 2 - -4 * -6))
C. ((not (The capital of South Korea is Copenhagen.)) and (((1 * -7 - -4 * 9) <= (-14 + -3)) or ((5 ** 1) <= (4 ** 3)))) or (A duck has 2 legs.)
D. (((Wood is a liquid at room temperature.) or (The square root of 144 is 12.)) or (not not (Christopher Columbus reached America occurred in 1492.))) or (not not (((-19 + 2) <= (0 * -6 + 1 * 5)) or (China is in Asia.)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 49444156,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. ((3 ** 2) < (-5 * -17)) or (((-12 * -8) > (5 + 9)) and (Mars is the 4th planet from the Sun.)) or ((((-1 * 10 - -7 * 10) != (2 ** 3)) or ((17 * 17) <= (3 + -5) <= (15 - 7))) and (not (The capital of Australia is Stockholm.)))\nB. not ((-10 * 1) < (8 * 2 - -4 * -6))\nC. ((not (The capital of South Korea is Copenhagen.)) and (((1 * -7 - -4 * 9) <= (-14 + -3)) or ((5 ** 1) <= (4 ** 3)))) or (A duck has 2 legs.)\nD. (((Wood is a liquid at room temperature.) or (The square root of 144 is 12.)) or (not not (Christopher Columbus reached America occurred in 1492.))) or (not not (((-19 + 2) <= (0 * -6 + 1 * 5)) or (China is in Asia.)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 49444156,
"true_count": 3
},
"seed": 49444156,
"task_id": 649444156,
"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. (1 % 7) > (5 - 12)
B. (-2 * 7 * -10 * -5) <= (29 % 10)
C. (-1 * 1 - -10 * 5) > (8 * -4 - 6 * 8)
D. 1960年奥运会在巴塞罗那举办。
E. 氯的化学符号是Cl。
F. ((17 - -8) != (1 ** 3)) and ((越南的首都是雅典。) and ((-8 - 20) >= (-1 - -11)))
G. 地球绕太阳运转。
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,C,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 5523101,
"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. (1 % 7) > (5 - 12)\nB. (-2 * 7 * -10 * -5) <= (29 % 10)\nC. (-1 * 1 - -10 * 5) > (8 * -4 - 6 * 8)\nD. 1960年奥运会在巴塞罗那举办。\nE. 氯的化学符号是Cl。\nF. ((17 - -8) != (1 ** 3)) and ((越南的首都是雅典。) and ((-8 - 20) >= (-1 - -11)))\nG. 地球绕太阳运转。\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": 5523101,
"true_count": 5
},
"seed": 5523101,
"task_id": 605523101,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((((not ((-9 * -10) > (16 - 2))) and ((四月有29天。) and ((2 * -9 + 5 * -6) == (4 ** 1)))) or (((2004年奥运会在墨尔本举办。) or ((-15 + 10) != (-10 - 6))) and ((九月有30天。) or (2004年奥运会在雅典举办。)))) and ((4 ** 3) > (7 * -6 + -7 * -2)) and (((1 % 4) != (3 + 12)) or ((2012年奥运会在东京举办。) or (not not (蛇有0条腿。))))) and (((((三月有29天。) or (1904年奥运会在圣路易斯举办。)) and (((3 ** 3) > (-15 * 18)) and ((10 * 4 * 6 * 4) < (7 * -8 + -3 * 0)))) or (八月有29天。)) or (not not (not not ((-7 * -4 + -4 * 7) >= (14 - -3)))))
B. ((not (七月有31天。)) and ((not (墨西哥的首都是新德里。)) or ((((-2 + -10) == (-14 * 2)) and (企鹅能飞翔。)) or (not not (智利的首都是圣地亚哥。))))) and (not ((泰国的货币是泰铢。) or (((钻石在常温下是气体。) or (2004年奥运会在伦敦举办。)) or ((锡的化学符号是Sn。) or ((-4 * 8 - -2 * 9) >= (1 * -1 - 6 * -9))))))
C. (not (((土星是距离太阳第7近的行星。) and ((墨西哥的货币是新西兰元。) or (1920年奥运会在安特卫普举办。))) or (墨西哥位于非洲。) or (((-5 - -12) == (-5 * -10 - -6 * -5)) or (not not ((42 % 2) != (-6 * -1 - 9 * -5)))))) or (not ((((1 * 8 * -7 * -3) == (14 - 16)) and (not not (光速比声速快。))) or (not ((-8 + -4) > (-14 - 12)))))
D. (((氧气对人类生存是必需的。) or ((-1 - 18) >= (4 + -8))) and ((蜘蛛是昆虫。) or (not not ((英国位于北美洲。) and (1904年奥运会在圣路易斯举办。))))) or ((83小于等于45。) or (硅的化学符号是Ag。) or ((-6 - -1) <= (-12 * -12) <= (17 * 19))) or (((((-10 * -1 - -8 * 3) != (9 - 12)) or (章鱼有8条腿。)) and ((瑞士的货币是瑞士法郎。) and (火星是距离太阳第4近的行星。)) and ((not not ((-11 + 6) < (8 * 13) < (3 ** 1))) and (硫的化学符号是S。))) or ((铅的化学符号是Pb。) and (((5 ** 1) >= (-7 * 1)) and (木头在常温下是液体。)) and ((13能被3整除。) or (((-10 - 17) > (-10 * -17)) or (变色龙是爬行动物。)))))
E. not (((((锰的化学符号是Mn。) or ((-16 * -9) < (2 ** 1))) or ((174是偶数。) and (印度的首都是马德里。))) or (not not (蛇有0条腿。))) and (not ((-6 * -18) != (10 + -1))))
F. (((not (木星是距离太阳第8近的行星。)) and (not not (528是斐波那契数。))) or ((((34 % 7) < (-19 + -5)) and ((-11 * 13) <= (1 ** 1) <= (-7 * 10))) or (酒精在常温下是液体。))) and (not not (((not not (澳大利亚位于亚洲。)) and ((18小于等于71。) or (柏林墙倒塌发生在1989年。))) or (((鸡有2条腿。) and (人体有206块骨头。)) and ((1912年奥运会在斯德哥尔摩举办。) and ((16 - 15) >= (5 * -1 - 9 * 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": "C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 62022021,
"true_count": 4
},
"question": "分析以下逻辑表达式：\n\nA. ((((not ((-9 * -10) > (16 - 2))) and ((四月有29天。) and ((2 * -9 + 5 * -6) == (4 ** 1)))) or (((2004年奥运会在墨尔本举办。) or ((-15 + 10) != (-10 - 6))) and ((九月有30天。) or (2004年奥运会在雅典举办。)))) and ((4 ** 3) > (7 * -6 + -7 * -2)) and (((1 % 4) != (3 + 12)) or ((2012年奥运会在东京举办。) or (not not (蛇有0条腿。))))) and (((((三月有29天。) or (1904年奥运会在圣路易斯举办。)) and (((3 ** 3) > (-15 * 18)) and ((10 * 4 * 6 * 4) < (7 * -8 + -3 * 0)))) or (八月有29天。)) or (not not (not not ((-7 * -4 + -4 * 7) >= (14 - -3)))))\nB. ((not (七月有31天。)) and ((not (墨西哥的首都是新德里。)) or ((((-2 + -10) == (-14 * 2)) and (企鹅能飞翔。)) or (not not (智利的首都是圣地亚哥。))))) and (not ((泰国的货币是泰铢。) or (((钻石在常温下是气体。) or (2004年奥运会在伦敦举办。)) or ((锡的化学符号是Sn。) or ((-4 * 8 - -2 * 9) >= (1 * -1 - 6 * -9))))))\nC. (not (((土星是距离太阳第7近的行星。) and ((墨西哥的货币是新西兰元。) or (1920年奥运会在安特卫普举办。))) or (墨西哥位于非洲。) or (((-5 - -12) == (-5 * -10 - -6 * -5)) or (not not ((42 % 2) != (-6 * -1 - 9 * -5)))))) or (not ((((1 * 8 * -7 * -3) == (14 - 16)) and (not not (光速比声速快。))) or (not ((-8 + -4) > (-14 - 12)))))\nD. (((氧气对人类生存是必需的。) or ((-1 - 18) >= (4 + -8))) and ((蜘蛛是昆虫。) or (not not ((英国位于北美洲。) and (1904年奥运会在圣路易斯举办。))))) or ((83小于等于45。) or (硅的化学符号是Ag。) or ((-6 - -1) <= (-12 * -12) <= (17 * 19))) or (((((-10 * -1 - -8 * 3) != (9 - 12)) or (章鱼有8条腿。)) and ((瑞士的货币是瑞士法郎。) and (火星是距离太阳第4近的行星。)) and ((not not ((-11 + 6) < (8 * 13) < (3 ** 1))) and (硫的化学符号是S。))) or ((铅的化学符号是Pb。) and (((5 ** 1) >= (-7 * 1)) and (木头在常温下是液体。)) and ((13能被3整除。) or (((-10 - 17) > (-10 * -17)) or (变色龙是爬行动物。)))))\nE. not (((((锰的化学符号是Mn。) or ((-16 * -9) < (2 ** 1))) or ((174是偶数。) and (印度的首都是马德里。))) or (not not (蛇有0条腿。))) and (not ((-6 * -18) != (10 + -1))))\nF. (((not (木星是距离太阳第8近的行星。)) and (not not (528是斐波那契数。))) or ((((34 % 7) < (-19 + -5)) and ((-11 * 13) <= (1 ** 1) <= (-7 * 10))) or (酒精在常温下是液体。))) and (not not (((not not (澳大利亚位于亚洲。)) and ((18小于等于71。) or (柏林墙倒塌发生在1989年。))) or (((鸡有2条腿。) and (人体有206块骨头。)) and ((1912年奥运会在斯德哥尔摩举办。) and ((16 - 15) >= (5 * -1 - 9 * 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": 62022021,
"true_count": 4
},
"seed": 62022021,
"task_id": 662022021,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (not not ((((10 * 6 * 6 * -6) <= (20 % 5)) or ((19 + -3) > (13 + -13))) or (氧气在常温下是气体。) or ((6 * -3 * 10 * -4) == (44 % 6)))) and ((((not not ((-7 - 19) == (10 * -7 + -1 * -9))) or (not not ((6 - 15) > (-2 * 2 * -4 * -5)))) or (not not (((9 * 10 + 4 * 0) == (8 * -5 * 9 * 6)) and (11能被2整除。)))) or (((((11 * -9) < (33 % 2) < (-7 * -4)) and ((-19 + 18) < (11 * -19))) or (((3 - 18) <= (-10 * 18)) and (二氧化碳在常温下是气体。))) and (not ((-19 - 12) > (-7 - -15))) and (not not ((4 ** 1) >= (18 * -3)))))
B. not (((not ((1948年是闰年。) and (七月有31天。))) or (((大象有4条腿。) and (人类只使用了大脑的10%。)) or (((4 % 4) <= (9 * 5 - -5 * 2)) or (智利位于南美洲。)))) or ((((90小于等于71。) or (铜在常温下是固体。)) and (((-7 * 13) < (-12 - -19) < (1 * 0 + 2 * -8)) or (水在海平面上的沸点是100摄氏度。))) or ((not not ((11 % 9) <= (-3 + -11))) and (not not (六月有31天。)))))
C. (((((巴西的首都是安卡拉。) and (225的平方根是9。)) or (((3 ** 1) < (1 * 10 + -4 * -2) < (19 * 2)) and ((-16 * -3) != (-5 * 10 + -8 * -4)))) or (((法国位于南美洲。) or (天王星是距离太阳第7近的行星。)) and (not (印度尼西亚位于北美洲。)))) or (((-14 + 16) < (3 * 7 * 8 * -8) < (3 ** 1)) and (沙特阿拉伯的首都是里斯本。))) or ((((((-15 - 8) != (-8 * 10 - 2 * 6)) or (火星是距离太阳第7近的行星。)) and ((-12 - 4) < (3 ** 2))) and ((3 * 18) >= (49 % 6))) and ((((南非的货币是美元。) or ((-6 + 14) == (-1 * 3))) or ((美国宣布独立发生在1777年。) or (越南位于非洲。))) and (木头在常温下是固体。)))
D. not ((((金星是距离太阳第2近的行星。) and ((泰国位于非洲。) and (1896年奥运会在雅典举办。))) or ((not not ((17 + 3) <= (14 * 8) <= (18 + 0))) or ((伦敦大火发生在1666年。) and (银在常温下是固体。)))) and ((电流比光速更快。) and (((9 - -2) != (-19 + -9)) and (四月有30天。)) and (((肯尼亚位于非洲。) or ((2 - 1) < (4 ** 2))) and (not not (沙特阿拉伯位于亚洲。)))))
E. not ((((9 - -9) == (0 - -6)) and (not (1972年奥运会在亚特兰大举办。))) and ((19 - -4) < (7 * 12) < (5 + -15)) and (((not not ((-14 - 18) > (2 ** 1))) or (((-7 - 13) != (-6 + -15)) and ((17 - 3) <= (20 % 10)))) or (not (2000年是闰年。)) or ((3 ** 3) == (-3 * -5 + 9 * -4))))
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,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 18616808,
"true_count": 4
},
"question": "检验这些表达式：\n\nA. (not not ((((10 * 6 * 6 * -6) <= (20 % 5)) or ((19 + -3) > (13 + -13))) or (氧气在常温下是气体。) or ((6 * -3 * 10 * -4) == (44 % 6)))) and ((((not not ((-7 - 19) == (10 * -7 + -1 * -9))) or (not not ((6 - 15) > (-2 * 2 * -4 * -5)))) or (not not (((9 * 10 + 4 * 0) == (8 * -5 * 9 * 6)) and (11能被2整除。)))) or (((((11 * -9) < (33 % 2) < (-7 * -4)) and ((-19 + 18) < (11 * -19))) or (((3 - 18) <= (-10 * 18)) and (二氧化碳在常温下是气体。))) and (not ((-19 - 12) > (-7 - -15))) and (not not ((4 ** 1) >= (18 * -3)))))\nB. not (((not ((1948年是闰年。) and (七月有31天。))) or (((大象有4条腿。) and (人类只使用了大脑的10%。)) or (((4 % 4) <= (9 * 5 - -5 * 2)) or (智利位于南美洲。)))) or ((((90小于等于71。) or (铜在常温下是固体。)) and (((-7 * 13) < (-12 - -19) < (1 * 0 + 2 * -8)) or (水在海平面上的沸点是100摄氏度。))) or ((not not ((11 % 9) <= (-3 + -11))) and (not not (六月有31天。)))))\nC. (((((巴西的首都是安卡拉。) and (225的平方根是9。)) or (((3 ** 1) < (1 * 10 + -4 * -2) < (19 * 2)) and ((-16 * -3) != (-5 * 10 + -8 * -4)))) or (((法国位于南美洲。) or (天王星是距离太阳第7近的行星。)) and (not (印度尼西亚位于北美洲。)))) or (((-14 + 16) < (3 * 7 * 8 * -8) < (3 ** 1)) and (沙特阿拉伯的首都是里斯本。))) or ((((((-15 - 8) != (-8 * 10 - 2 * 6)) or (火星是距离太阳第7近的行星。)) and ((-12 - 4) < (3 ** 2))) and ((3 * 18) >= (49 % 6))) and ((((南非的货币是美元。) or ((-6 + 14) == (-1 * 3))) or ((美国宣布独立发生在1777年。) or (越南位于非洲。))) and (木头在常温下是固体。)))\nD. not ((((金星是距离太阳第2近的行星。) and ((泰国位于非洲。) and (1896年奥运会在雅典举办。))) or ((not not ((17 + 3) <= (14 * 8) <= (18 + 0))) or ((伦敦大火发生在1666年。) and (银在常温下是固体。)))) and ((电流比光速更快。) and (((9 - -2) != (-19 + -9)) and (四月有30天。)) and (((肯尼亚位于非洲。) or ((2 - 1) < (4 ** 2))) and (not not (沙特阿拉伯位于亚洲。)))))\nE. not ((((9 - -9) == (0 - -6)) and (not (1972年奥运会在亚特兰大举办。))) and ((19 - -4) < (7 * 12) < (5 + -15)) and (((not not ((-14 - 18) > (2 ** 1))) or (((-7 - 13) != (-6 + -15)) and ((17 - 3) <= (20 % 10)))) or (not (2000年是闰年。)) or ((3 ** 3) == (-3 * -5 + 9 * -4))))\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": 18616808,
"true_count": 4
},
"seed": 18616808,
"task_id": 618616808,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not not ((3 ** 3) > (5 + -2))
B. (not not (There are 28 days in November.)) or (not ((1 - -9) > (3 * 4 - -5 * 9)))
C. ((2 ** 2) < (-20 - 10) < (-4 * -3 - -10 * -8)) or (The chemical symbol for Mercury is Zn.)
D. (not not ((The capital of Poland is Warsaw.) and ((-16 * 11) == (4 ** 2)))) and ((-19 * -17) >= (15 * 13))
E. (not not (((-6 * 5) == (1 ** 3)) and ((-4 + 14) < (16 * 8)))) and (The capital of Ukraine is Kyiv.) and ((not (Carbon dioxide is a gas at room temperature.)) or ((2 * 13) == (12 + 5)))
F. not not (((The chemical symbol for Chlorine is Cl.) or (The currency of China is the Yuan.)) and (((2 ** 2) >= (-10 + -10)) or ((4 + -14) >= (20 + -12))))
G. (not ((Wood is a solid at room temperature.) or (Wood is a gas at room temperature.))) or ((Japan is in North America.) and (A ant has 100 legs.))
H. (((2 is an even number.) and ((15 * 7) > (29 % 7))) and ((43 % 5) < (6 * 7 * -5 * 10))) or ((47 is divisible by 9.) or (Sound cannot travel through a vacuum.)) or (((Steam is a gas at room temperature.) and (Mercury is the 1st planet from the Sun.)) and (((2 + 17) == (4 ** 3)) and (The currency of Brazil is the Real.)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 25237161,
"true_count": 4
},
"question": "Below are several boolean expressions:\n\nA. not not ((3 ** 3) > (5 + -2))\nB. (not not (There are 28 days in November.)) or (not ((1 - -9) > (3 * 4 - -5 * 9)))\nC. ((2 ** 2) < (-20 - 10) < (-4 * -3 - -10 * -8)) or (The chemical symbol for Mercury is Zn.)\nD. (not not ((The capital of Poland is Warsaw.) and ((-16 * 11) == (4 ** 2)))) and ((-19 * -17) >= (15 * 13))\nE. (not not (((-6 * 5) == (1 ** 3)) and ((-4 + 14) < (16 * 8)))) and (The capital of Ukraine is Kyiv.) and ((not (Carbon dioxide is a gas at room temperature.)) or ((2 * 13) == (12 + 5)))\nF. not not (((The chemical symbol for Chlorine is Cl.) or (The currency of China is the Yuan.)) and (((2 ** 2) >= (-10 + -10)) or ((4 + -14) >= (20 + -12))))\nG. (not ((Wood is a solid at room temperature.) or (Wood is a gas at room temperature.))) or ((Japan is in North America.) and (A ant has 100 legs.))\nH. (((2 is an even number.) and ((15 * 7) > (29 % 7))) and ((43 % 5) < (6 * 7 * -5 * 10))) or ((47 is divisible by 9.) or (Sound cannot travel through a vacuum.)) or (((Steam is a gas at room temperature.) and (Mercury is the 1st planet from the Sun.)) and (((2 + 17) == (4 ** 3)) and (The currency of Brazil is the Real.)))\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": 25237161,
"true_count": 4
},
"seed": 25237161,
"task_id": 625237161,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (((((冰在常温下是固体。) and (36的平方根是9。)) and ((鲸鱼是鱼类。) or ((4 ** 1) <= (4 * -19)))) or (土星是距离太阳第6近的行星。) or (1927年是闰年。)) or (not not (not not ((蚱蜢是昆虫。) or (氢的化学符号是H。))))) or ((((1 * -15) > (0 - 10)) and (巴西的货币是埃及镑。)) and (not not (水蒸气在常温下是气体。)) and ((((鲸鱼是鱼类。) or (爱尔兰的首都是都柏林。)) and (not not (地球绕太阳运转。))) or (not (not not (狗有4条腿。)))))
B. (((锰的化学符号是Hg。) or ((硫的化学符号是Sn。) or ((-8 * -8 * -10 * 5) <= (-8 + 12)))) or ((not (铝的化学符号是H。)) or (not (not not (中国位于北美洲。))))) and ((((2 ** 1) == (3 + -1)) and ((((-8 * 8 + 9 * 8) <= (4 ** 1) <= (9 * 3)) or ((34 % 9) >= (-14 - -5))) or ((4 ** 1) <= (-4 * 5)))) or (((莱特兄弟首次飞行发生在1898年。) and (48是质数。)) and (not ((-17 - -8) <= (7 + 3) <= (3 - -7)))) or ((((-5 * -4 - 6 * 4) != (-15 + 14)) or ((1896年奥运会在雅典举办。) or ((-3 * -20) <= (0 * 4)))) and (秘鲁的货币是兰特。)))
C. not (((鲸鱼是鱼类。) or (not (((4 ** 2) <= (3 * -9 - -2 * -10)) and (第一次世界大战结束发生在1917年。)))) and (((-13 + 18) <= (10 + 0) <= (1 - 10)) or (not (91是质数。))))
D. not not (not not ((not ((8 + 11) <= (-5 + -11))) and (16能被10整除。) and ((not not (碳的化学符号是C。)) and (1901年是闰年。))))
E. (not ((((1960年奥运会在安特卫普举办。) or (奥地利的首都是开罗。)) or (地球是距离太阳第8近的行星。)) or ((((3 ** 3) == (-9 * -9 * 8 * 1)) and (氢的化学符号是Fe。)) and (光速比声速快。)))) and ((((((-1 * 14) < (4 ** 3) < (-19 - -17)) and (美国宣布独立发生在1776年。)) or ((芬兰的首都是赫尔辛基。) or (4大于90。))) or (二月有29天。) or (not (not not ((-2 - -16) >= (-10 * 6 + 3 * 8))))) or ((43 % 6) <= (-6 * -2)) or ((((鸟有2条腿。) and ((-20 - 16) < (-8 * 8 + -4 * 6) < (-1 + 2))) or (not not ((14 * -14) == (7 - 11)))) or (not not ((-1 - -2) >= (48 % 2)))))
F. (not not ((((-1 + -7) >= (4 + -19)) or (酒精在常温下是固体。)) or (((十二月有31天。) and ((7 - -20) == (-7 + 0))) and ((15 * 18) != (1 * -14))))) or ((((((-14 * -10) <= (-1 * -7 - 2 * 3)) or (哥伦比亚的首都是波哥大。)) and (木星是距离太阳第5近的行星。)) and (泰坦尼克号沉没发生在1912年。)) or (((碳的化学符号是C。) and (((13 * 0) >= (1 * 12)) and (哥伦比亚的货币是比索。))) or ((((2 ** 2) < (-18 * 16) < (3 * -1 - -2 * 3)) or (2000年奥运会在巴黎举办。)) and (not not ((34 % 5) != (9 - -11))))))
G. not (not ((not not ((48 % 8) < (40 % 4) < (-2 + 2))) or (not not (((-13 + -6) <= (-8 - -8) <= (-3 - 8)) or ((-6 - -4) == (5 ** 3))))))
H. not ((not (二氧化碳在常温下是气体。)) and ((((14 + -8) <= (7 + 0) <= (-7 - 0)) and (((11 - -14) == (13 - 3)) or ((1 ** 3) > (6 * -8 - -9 * 6)))) or (55能被4整除。) or (((哥伦布到达美洲发生在1497年。) and (金在常温下是固体。)) or (天王星是距离太阳第7近的行星。))))
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。 | {
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"question": "研究以下逻辑语句：\n\nA. (((((冰在常温下是固体。) and (36的平方根是9。)) and ((鲸鱼是鱼类。) or ((4 ** 1) <= (4 * -19)))) or (土星是距离太阳第6近的行星。) or (1927年是闰年。)) or (not not (not not ((蚱蜢是昆虫。) or (氢的化学符号是H。))))) or ((((1 * -15) > (0 - 10)) and (巴西的货币是埃及镑。)) and (not not (水蒸气在常温下是气体。)) and ((((鲸鱼是鱼类。) or (爱尔兰的首都是都柏林。)) and (not not (地球绕太阳运转。))) or (not (not not (狗有4条腿。)))))\nB. (((锰的化学符号是Hg。) or ((硫的化学符号是Sn。) or ((-8 * -8 * -10 * 5) <= (-8 + 12)))) or ((not (铝的化学符号是H。)) or (not (not not (中国位于北美洲。))))) and ((((2 ** 1) == (3 + -1)) and ((((-8 * 8 + 9 * 8) <= (4 ** 1) <= (9 * 3)) or ((34 % 9) >= (-14 - -5))) or ((4 ** 1) <= (-4 * 5)))) or (((莱特兄弟首次飞行发生在1898年。) and (48是质数。)) and (not ((-17 - -8) <= (7 + 3) <= (3 - -7)))) or ((((-5 * -4 - 6 * 4) != (-15 + 14)) or ((1896年奥运会在雅典举办。) or ((-3 * -20) <= (0 * 4)))) and (秘鲁的货币是兰特。)))\nC. not (((鲸鱼是鱼类。) or (not (((4 ** 2) <= (3 * -9 - -2 * -10)) and (第一次世界大战结束发生在1917年。)))) and (((-13 + 18) <= (10 + 0) <= (1 - 10)) or (not (91是质数。))))\nD. not not (not not ((not ((8 + 11) <= (-5 + -11))) and (16能被10整除。) and ((not not (碳的化学符号是C。)) and (1901年是闰年。))))\nE. (not ((((1960年奥运会在安特卫普举办。) or (奥地利的首都是开罗。)) or (地球是距离太阳第8近的行星。)) or ((((3 ** 3) == (-9 * -9 * 8 * 1)) and (氢的化学符号是Fe。)) and (光速比声速快。)))) and ((((((-1 * 14) < (4 ** 3) < (-19 - -17)) and (美国宣布独立发生在1776年。)) or ((芬兰的首都是赫尔辛基。) or (4大于90。))) or (二月有29天。) or (not (not not ((-2 - -16) >= (-10 * 6 + 3 * 8))))) or ((43 % 6) <= (-6 * -2)) or ((((鸟有2条腿。) and ((-20 - 16) < (-8 * 8 + -4 * 6) < (-1 + 2))) or (not not ((14 * -14) == (7 - 11)))) or (not not ((-1 - -2) >= (48 % 2)))))\nF. (not not ((((-1 + -7) >= (4 + -19)) or (酒精在常温下是固体。)) or (((十二月有31天。) and ((7 - -20) == (-7 + 0))) and ((15 * 18) != (1 * -14))))) or ((((((-14 * -10) <= (-1 * -7 - 2 * 3)) or (哥伦比亚的首都是波哥大。)) and (木星是距离太阳第5近的行星。)) and (泰坦尼克号沉没发生在1912年。)) or (((碳的化学符号是C。) and (((13 * 0) >= (1 * 12)) and (哥伦比亚的货币是比索。))) or ((((2 ** 2) < (-18 * 16) < (3 * -1 - -2 * 3)) or (2000年奥运会在巴黎举办。)) and (not not ((34 % 5) != (9 - -11))))))\nG. not (not ((not not ((48 % 8) < (40 % 4) < (-2 + 2))) or (not not (((-13 + -6) <= (-8 - -8) <= (-3 - 8)) or ((-6 - -4) == (5 ** 3))))))\nH. not ((not (二氧化碳在常温下是气体。)) and ((((14 + -8) <= (7 + 0) <= (-7 - 0)) and (((11 - -14) == (13 - 3)) or ((1 ** 3) > (6 * -8 - -9 * 6)))) or (55能被4整除。) or (((哥伦布到达美洲发生在1497年。) and (金在常温下是固体。)) or (天王星是距离太阳第7近的行星。))))\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。"
},
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"task_type": "boolean_expressions"
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logic-v2 | 检验这些表达式：
A. (not not (not (((-11 * 6) >= (10 * 7)) and ((4 - 10) != (-18 - -13))))) and (not not ((-11 - 12) >= (47 % 4))) and ((1972年奥运会在慕尼黑举办。) or (((35 % 4) <= (3 ** 2)) and ((3 * 4) != (-20 - -10))) or ((澳大利亚位于亚洲。) and (not ((2 ** 3) != (-13 - -1)))))
B. not ((氢的化学符号是Mg。) or (((5 + -14) == (11 - -2)) and (中国位于亚洲。)) or (not not ((水在常温下是液体。) and (孔雀是鸟类。))))
C. (not not ((80大于99。) and (not ((-8 * -2 + 3 * 3) == (18 - 18))))) and (not ((((8 * -8 + -1 * 4) < (-11 + -19)) and ((-5 * -1 + -9 * 6) > (-2 * 8 - -3 * -8))) and ((墨西哥位于南极洲。) or (秘鲁的首都是利马。))))
D. ((not not (not not ((1 ** 2) <= (5 * 7)))) or (((铜的化学符号是He。) and (九月有28天。)) or ((韩国位于大洋洲。) and (1968年奥运会在墨西哥城举办。)))) and (not not (((5 ** 3) < (22 % 5)) or ((-2 * 2 + 10 * 9) != (2 ** 2)))) and (not (not (((10 * -7 - -7 * -5) != (-1 * 1 - -10 * 0)) and (九月有31天。))))
E. not (((-13 + -14) != (15 - 19)) and (老鼠是哺乳动物。))
F. not (not ((((-7 * 1 * 5 * 8) == (-8 - -14)) or (1928年是闰年。)) and ((印度尼西亚位于亚洲。) and ((-20 * -19) != (9 + 14)))))
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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"difficulty": 1,
"gpt_response": "",
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"language": "cn",
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"question": "检验这些表达式：\n\nA. (not not (not (((-11 * 6) >= (10 * 7)) and ((4 - 10) != (-18 - -13))))) and (not not ((-11 - 12) >= (47 % 4))) and ((1972年奥运会在慕尼黑举办。) or (((35 % 4) <= (3 ** 2)) and ((3 * 4) != (-20 - -10))) or ((澳大利亚位于亚洲。) and (not ((2 ** 3) != (-13 - -1)))))\nB. not ((氢的化学符号是Mg。) or (((5 + -14) == (11 - -2)) and (中国位于亚洲。)) or (not not ((水在常温下是液体。) and (孔雀是鸟类。))))\nC. (not not ((80大于99。) and (not ((-8 * -2 + 3 * 3) == (18 - 18))))) and (not ((((8 * -8 + -1 * 4) < (-11 + -19)) and ((-5 * -1 + -9 * 6) > (-2 * 8 - -3 * -8))) and ((墨西哥位于南极洲。) or (秘鲁的首都是利马。))))\nD. ((not not (not not ((1 ** 2) <= (5 * 7)))) or (((铜的化学符号是He。) and (九月有28天。)) or ((韩国位于大洋洲。) and (1968年奥运会在墨西哥城举办。)))) and (not not (((5 ** 3) < (22 % 5)) or ((-2 * 2 + 10 * 9) != (2 ** 2)))) and (not (not (((10 * -7 - -7 * -5) != (-1 * 1 - -10 * 0)) and (九月有31天。))))\nE. not (((-13 + -14) != (15 - 19)) and (老鼠是哺乳动物。))\nF. not (not ((((-7 * 1 * 5 * 8) == (-8 - -14)) or (1928年是闰年。)) and ((印度尼西亚位于亚洲。) and ((-20 * -19) != (9 + 14)))))\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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"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 33728216,
"true_count": 1
},
"seed": 33728216,
"task_id": 633728216,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. not not (((((新西兰的首都是阿布贾。) and ((1909年是闰年。) and (91大于39。))) or ((35 % 4) < (5 ** 1) < (0 * 2 + 5 * -7))) or ((1908年奥运会在巴黎举办。) and (not not ((12 + 0) >= (7 + -5))) and (((2012年奥运会在墨西哥城举办。) and ((-7 + 8) < (1 % 9) < (1 * 10 + -9 * 1))) or (((10 - -18) <= (-4 * -8 + 4 * -5) <= (31 % 2)) and ((22 % 6) > (-2 * -5 - 7 * 1)))))) and (((1923年是闰年。) and (((10 * -6 * -6 * 9) > (-4 * -4 - 10 * -7)) or (not not (第二次世界大战开始发生在1934年。)))) or (not not ((氮气在常温下是气体。) and ((-18 + 2) != (9 * 6 * 4 * -5))))))
B. not (not not (((((154是完全平方数。) or (水蒸气在常温下是固体。)) and (176是偶数。)) and ((尼日利亚位于南极洲。) or ((铂的化学符号是P。) and ((9 * -19) >= (12 + 19))))) and (((not ((-20 - 4) > (40 % 5))) or (酒精在常温下是液体。)) or ((哥伦布到达美洲发生在1492年。) and (not not ((-8 * 7 - -7 * 0) < (8 * -7 - -1 * 5)))))))
C. not not ((not ((水星是距离太阳第8近的行星。) or (not not ((1972年奥运会在慕尼黑举办。) and ((-15 + -8) <= (-4 + 0)))))) and (not (((4 ** 3) <= (15 % 9)) and (鬣蜥是昆虫。))) and ((((硫的化学符号是S。) or ((-7 * 3 + -10 * -2) < (3 - -19))) and ((((-5 * 10 + -6 * 5) <= (8 * -8 - 6 * 0) <= (1 ** 1)) or ((34 % 5) == (10 - 8))) or (not (印度位于亚洲。)))) or (((((1 ** 3) >= (-17 + 0)) or (铁在常温下是固体。)) or ((7 * -4 - 9 * 5) <= (-12 - -8) <= (-17 * -15))) and ((not (锰的化学符号是Mn。)) and (氮气在常温下是固体。)))))
D. not not (not not ((not not ((not (十一月有30天。)) and ((印度尼西亚位于亚洲。) and ((40 % 3) <= (1 * 20))))) or (not ((-5 + 7) != (12 % 2)))))
E. (not not ((((-19 + -2) != (-20 - -11)) and (((鱼有8条腿。) or ((1 * -1 - -1 * -6) <= (5 ** 3) <= (1 + 14))) and (not not (蜘蛛有2条腿。)))) or (((((10 - 20) == (-17 * 17)) and (大象有4条腿。)) and (肯尼亚位于非洲。)) and (((1 - -7) >= (8 * -1 - 8 * -9)) and (1908年奥运会在伦敦举办。)) and (not (((14 % 8) > (-8 * -10)) and ((2 % 3) >= (2 ** 1))))))) and ((not ((莱特兄弟首次飞行发生在1903年。) or (人类只使用了大脑的10%。))) or (not not ((not not (not not (151是偶数。))) or (((六月有28天。) or (水星是距离太阳第1近的行星。)) and (not not ((-13 - 0) >= (0 - -17)))))))
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。 | {
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"answer": "B",
"difficulty": 1,
"gpt_response": "",
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"question": "考虑以下布尔表达式：\n\nA. not not (((((新西兰的首都是阿布贾。) and ((1909年是闰年。) and (91大于39。))) or ((35 % 4) < (5 ** 1) < (0 * 2 + 5 * -7))) or ((1908年奥运会在巴黎举办。) and (not not ((12 + 0) >= (7 + -5))) and (((2012年奥运会在墨西哥城举办。) and ((-7 + 8) < (1 % 9) < (1 * 10 + -9 * 1))) or (((10 - -18) <= (-4 * -8 + 4 * -5) <= (31 % 2)) and ((22 % 6) > (-2 * -5 - 7 * 1)))))) and (((1923年是闰年。) and (((10 * -6 * -6 * 9) > (-4 * -4 - 10 * -7)) or (not not (第二次世界大战开始发生在1934年。)))) or (not not ((氮气在常温下是气体。) and ((-18 + 2) != (9 * 6 * 4 * -5))))))\nB. not (not not (((((154是完全平方数。) or (水蒸气在常温下是固体。)) and (176是偶数。)) and ((尼日利亚位于南极洲。) or ((铂的化学符号是P。) and ((9 * -19) >= (12 + 19))))) and (((not ((-20 - 4) > (40 % 5))) or (酒精在常温下是液体。)) or ((哥伦布到达美洲发生在1492年。) and (not not ((-8 * 7 - -7 * 0) < (8 * -7 - -1 * 5)))))))\nC. not not ((not ((水星是距离太阳第8近的行星。) or (not not ((1972年奥运会在慕尼黑举办。) and ((-15 + -8) <= (-4 + 0)))))) and (not (((4 ** 3) <= (15 % 9)) and (鬣蜥是昆虫。))) and ((((硫的化学符号是S。) or ((-7 * 3 + -10 * -2) < (3 - -19))) and ((((-5 * 10 + -6 * 5) <= (8 * -8 - 6 * 0) <= (1 ** 1)) or ((34 % 5) == (10 - 8))) or (not (印度位于亚洲。)))) or (((((1 ** 3) >= (-17 + 0)) or (铁在常温下是固体。)) or ((7 * -4 - 9 * 5) <= (-12 - -8) <= (-17 * -15))) and ((not (锰的化学符号是Mn。)) and (氮气在常温下是固体。)))))\nD. not not (not not ((not not ((not (十一月有30天。)) and ((印度尼西亚位于亚洲。) and ((40 % 3) <= (1 * 20))))) or (not ((-5 + 7) != (12 % 2)))))\nE. (not not ((((-19 + -2) != (-20 - -11)) and (((鱼有8条腿。) or ((1 * -1 - -1 * -6) <= (5 ** 3) <= (1 + 14))) and (not not (蜘蛛有2条腿。)))) or (((((10 - 20) == (-17 * 17)) and (大象有4条腿。)) and (肯尼亚位于非洲。)) and (((1 - -7) >= (8 * -1 - 8 * -9)) and (1908年奥运会在伦敦举办。)) and (not (((14 % 8) > (-8 * -10)) and ((2 % 3) >= (2 ** 1))))))) and ((not ((莱特兄弟首次飞行发生在1903年。) or (人类只使用了大脑的10%。))) or (not not ((not not (not not (151是偶数。))) or (((六月有28天。) or (水星是距离太阳第1近的行星。)) and (not not ((-13 - 0) >= (0 - -17)))))))\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。"
},
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"language": "cn",
"num_options": 5,
"seed": 24009413,
"true_count": 1
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"seed": 24009413,
"task_id": 624009413,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. 鲤鱼是鱼类。
B. ((欧盟的货币是欧元。) and (水星是距离太阳第7近的行星。)) and ((匈牙利的货币是福林。) and ((-14 + 5) != (6 * -8)))
C. ((匈牙利的货币是福林。) or (火星是距离太阳第4近的行星。)) or (((-7 + 18) >= (16 - -12)) and (泰国位于亚洲。))
D. ((1924年奥运会在悉尼举办。) and ((-8 * 4 * -5 * 8) != (2 * 8 - -4 * -9))) or (not (1948年奥运会在东京举办。))
E. 地球绕太阳运转。
F. ((1964年奥运会在北京举办。) or (蜻蜓是哺乳动物。)) and (not not (鸟有2条腿。))
G. ((第一次世界大战开始发生在1912年。) or ((1 * 8 + -8 * -8) >= (17 + -20))) and ((50 % 6) != (-8 - 12))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,C,D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"seed": 65219805,
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"question": "审视以下逻辑表达式：\n\nA. 鲤鱼是鱼类。\nB. ((欧盟的货币是欧元。) and (水星是距离太阳第7近的行星。)) and ((匈牙利的货币是福林。) and ((-14 + 5) != (6 * -8)))\nC. ((匈牙利的货币是福林。) or (火星是距离太阳第4近的行星。)) or (((-7 + 18) >= (16 - -12)) and (泰国位于亚洲。))\nD. ((1924年奥运会在悉尼举办。) and ((-8 * 4 * -5 * 8) != (2 * 8 - -4 * -9))) or (not (1948年奥运会在东京举办。))\nE. 地球绕太阳运转。\nF. ((1964年奥运会在北京举办。) or (蜻蜓是哺乳动物。)) and (not not (鸟有2条腿。))\nG. ((第一次世界大战开始发生在1912年。) or ((1 * 8 + -8 * -8) >= (17 + -20))) and ((50 % 6) != (-8 - 12))\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": 7,
"seed": 65219805,
"true_count": 5
},
"seed": 65219805,
"task_id": 665219805,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. The currency of Nigeria is the Naira.
B. ((124 is an odd number.) or ((0 * -2 - -4 * -7) >= (35 % 8))) or ((2003 is a leap year.) or (The 1936 Olympics were held in Berlin.))
C. Argentina is in South America.
D. ((The currency of Norway is the Won.) or ((-11 - -14) < (-13 + 8))) or ((The chemical symbol for Nickel is Ni.) and (The currency of Canada is the Forint.))
E. ((4 + -13) < (18 * -16)) or (Argentina is in Europe.)
F. (((7 - 13) < (14 + 5) < (-19 - 8)) or ((20 - 15) < (14 * 4))) and (((-7 * -5 + -7 * 9) != (-4 - 1)) and ((4 - -16) <= (10 * -2 + 2 * 0) <= (5 ** 2)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 42682400,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. The currency of Nigeria is the Naira.\nB. ((124 is an odd number.) or ((0 * -2 - -4 * -7) >= (35 % 8))) or ((2003 is a leap year.) or (The 1936 Olympics were held in Berlin.))\nC. Argentina is in South America.\nD. ((The currency of Norway is the Won.) or ((-11 - -14) < (-13 + 8))) or ((The chemical symbol for Nickel is Ni.) and (The currency of Canada is the Forint.))\nE. ((4 + -13) < (18 * -16)) or (Argentina is in Europe.)\nF. (((7 - 13) < (14 + 5) < (-19 - 8)) or ((20 - 15) < (14 * 4))) and (((-7 * -5 + -7 * 9) != (-4 - 1)) and ((4 - -16) <= (10 * -2 + 2 * 0) <= (5 ** 2)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 42682400,
"true_count": 3
},
"seed": 42682400,
"task_id": 642682400,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (not not (not ((蛇是爬行动物。) and (((2 * 1 * 3 * -2) == (7 * -14)) and (钻石在常温下是固体。))))) or (not not ((((冰在常温下是气体。) or (巴西位于南美洲。)) or (((17 + -7) <= (-4 * 2)) or ((8 * -4 - -4 * -9) >= (5 - -11)))) and ((not not ((1 ** 2) == (-4 * 8 * 7 * -6))) and (not not (菲律宾的货币是比索。)))))
B. (((not (八月有29天。)) and (not not (蚂蚁有0条腿。)) and ((not not (十一月有30天。)) or (((-8 * 13) < (-5 * 5 - -3 * 10) < (-6 * 5 + -6 * -4)) or (铝的化学符号是Al。)))) or (((not (植物通过光合作用产生氧气。)) and ((墨西哥的首都是哈瓦那。) and ((4 ** 3) > (-1 - 17)))) and ((-4 - 12) > (4 % 1)))) and (not not (地球上一天是24小时。)) and (not (((35 % 8) <= (-10 * 9 - -8 * -6)) or ((not (鸟有2条腿。)) or ((鲸鱼是鱼类。) and (德国位于欧洲。)))))
C. not ((((not (52能被9整除。)) or (not not ((16 + 5) < (-8 - 3) < (5 + 4)))) or ((-2 * 17) <= (1 * -5 + -4 * -4)) or (not (((7 - 4) <= (19 - -6)) and (1932年奥运会在洛杉矶举办。)))) and (not (木星是距离太阳第5近的行星。)))
D. not (not (not (((泰国位于亚洲。) or ((7 - 0) == (3 + 0))) or (not (南非的货币是兰特。)))))
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,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 40716937,
"true_count": 2
},
"question": "下面是几个布尔表达式：\n\nA. (not not (not ((蛇是爬行动物。) and (((2 * 1 * 3 * -2) == (7 * -14)) and (钻石在常温下是固体。))))) or (not not ((((冰在常温下是气体。) or (巴西位于南美洲。)) or (((17 + -7) <= (-4 * 2)) or ((8 * -4 - -4 * -9) >= (5 - -11)))) and ((not not ((1 ** 2) == (-4 * 8 * 7 * -6))) and (not not (菲律宾的货币是比索。)))))\nB. (((not (八月有29天。)) and (not not (蚂蚁有0条腿。)) and ((not not (十一月有30天。)) or (((-8 * 13) < (-5 * 5 - -3 * 10) < (-6 * 5 + -6 * -4)) or (铝的化学符号是Al。)))) or (((not (植物通过光合作用产生氧气。)) and ((墨西哥的首都是哈瓦那。) and ((4 ** 3) > (-1 - 17)))) and ((-4 - 12) > (4 % 1)))) and (not not (地球上一天是24小时。)) and (not (((35 % 8) <= (-10 * 9 - -8 * -6)) or ((not (鸟有2条腿。)) or ((鲸鱼是鱼类。) and (德国位于欧洲。)))))\nC. not ((((not (52能被9整除。)) or (not not ((16 + 5) < (-8 - 3) < (5 + 4)))) or ((-2 * 17) <= (1 * -5 + -4 * -4)) or (not (((7 - 4) <= (19 - -6)) and (1932年奥运会在洛杉矶举办。)))) and (not (木星是距离太阳第5近的行星。)))\nD. not (not (not (((泰国位于亚洲。) or ((7 - 0) == (3 + 0))) or (not (南非的货币是兰特。)))))\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": 5,
"language": "cn",
"num_options": 4,
"seed": 40716937,
"true_count": 2
},
"seed": 40716937,
"task_id": 640716937,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not ((4 % 3) > (-15 - -10)))
B. ((not not ((10 * 8 - 5 * -6) <= (46 % 2))) or (((3 ** 2) >= (-8 - 12)) and ((-8 + 6) != (-5 * -6 - -6 * -9))) or ((not (Mercury is the 1st planet from the Sun.)) and (Electricity flows faster than light.))) or (((-8 + -3) != (-14 + 1)) and (The currency of Colombia is the Ruble.))
C. not (((Steam is a gas at room temperature.) and (((4 ** 3) > (6 * -3 + 0 * 10)) or ((-7 + 20) <= (5 * -5 * -8 * 6)))) and (not ((The currency of Norway is the Krone.) or (Germany is in Asia.))))
D. not not (not ((((5 ** 3) == (10 * 6 * -7 * -6)) or ((13 % 5) >= (6 * -5 * 7 * 3))) and (((16 * -7) <= (7 + -19) <= (38 % 9)) and (91 is divisible by 3.))))
E. ((The capital of Greece is Brussels.) or (2070 is a leap year.)) and ((Nigeria is in Africa.) or ((Neptune is the 8th planet from the Sun.) or ((398 is a Fibonacci number.) and ((1 - 8) == (-11 + -16)))))
F. (not not ((((1 ** 2) <= (5 ** 3)) or ((7 * 8 - 8 * 3) < (-3 * -6 * 9 * -2))) or (South Africa is in Africa.))) and ((Wood is a solid at room temperature.) and (((-6 * 1) <= (-7 + 13) <= (5 * 0 * 2 * 3)) or ((Whales are fish.) or (The capital of Portugal is Lisbon.))))
G. (not (not not (The capital of Italy is Rome.))) and (not not (not (The chemical symbol for Helium is He.)))
H. (((A ant has 100 legs.) and (((17 + 13) > (10 * -6 * -10 * 6)) or (The capital of Colombia is Rabat.))) and (not (((19 - -13) <= (28 % 3)) and ((17 - -15) > (4 % 6))))) or ((((The chemical symbol for Lead is Pt.) and (The currency of China is the Yuan.)) and (Brazil is in South America.)) and (not (((14 - 10) > (-1 + -10)) or (129 is an even number.))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 89878934,
"true_count": 5
},
"question": "Evaluate each expression below:\n\nA. not (not ((4 % 3) > (-15 - -10)))\nB. ((not not ((10 * 8 - 5 * -6) <= (46 % 2))) or (((3 ** 2) >= (-8 - 12)) and ((-8 + 6) != (-5 * -6 - -6 * -9))) or ((not (Mercury is the 1st planet from the Sun.)) and (Electricity flows faster than light.))) or (((-8 + -3) != (-14 + 1)) and (The currency of Colombia is the Ruble.))\nC. not (((Steam is a gas at room temperature.) and (((4 ** 3) > (6 * -3 + 0 * 10)) or ((-7 + 20) <= (5 * -5 * -8 * 6)))) and (not ((The currency of Norway is the Krone.) or (Germany is in Asia.))))\nD. not not (not ((((5 ** 3) == (10 * 6 * -7 * -6)) or ((13 % 5) >= (6 * -5 * 7 * 3))) and (((16 * -7) <= (7 + -19) <= (38 % 9)) and (91 is divisible by 3.))))\nE. ((The capital of Greece is Brussels.) or (2070 is a leap year.)) and ((Nigeria is in Africa.) or ((Neptune is the 8th planet from the Sun.) or ((398 is a Fibonacci number.) and ((1 - 8) == (-11 + -16)))))\nF. (not not ((((1 ** 2) <= (5 ** 3)) or ((7 * 8 - 8 * 3) < (-3 * -6 * 9 * -2))) or (South Africa is in Africa.))) and ((Wood is a solid at room temperature.) and (((-6 * 1) <= (-7 + 13) <= (5 * 0 * 2 * 3)) or ((Whales are fish.) or (The capital of Portugal is Lisbon.))))\nG. (not (not not (The capital of Italy is Rome.))) and (not not (not (The chemical symbol for Helium is He.)))\nH. (((A ant has 100 legs.) and (((17 + 13) > (10 * -6 * -10 * 6)) or (The capital of Colombia is Rabat.))) and (not (((19 - -13) <= (28 % 3)) and ((17 - -15) > (4 % 6))))) or ((((The chemical symbol for Lead is Pt.) and (The currency of China is the Yuan.)) and (Brazil is in South America.)) and (not (((14 - 10) > (-1 + -10)) or (129 is an even number.))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 89878934,
"true_count": 5
},
"seed": 89878934,
"task_id": 689878934,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (not ((1908年奥运会在伦敦举办。) or ((汞的化学符号是Mg。) or (氯的化学符号是Ca。)) or ((not (银的化学符号是He。)) and (((8 - -8) <= (14 + 8)) or (1896年奥运会在巴黎举办。))))) or (((not (not not (50能被6整除。))) and ((4 ** 3) > (-19 + 18))) or ((土耳其的货币是索尔。) or ((((17 % 2) >= (-16 - 12)) and (蚂蚁有2条腿。)) or (93小于等于98。))))
B. (not not ((((新西兰的货币是奈拉。) and ((-17 + -11) == (14 * 5))) or (澳大利亚位于大洋洲。)) or ((not not (海王星是距离太阳第2近的行星。)) or (not not ((-17 + 2) >= (5 ** 3)))))) and (((((-8 + 10) < (3 ** 2) < (-6 * -8)) and (not not ((11 * -16) < (-1 * 8 - 6 * 1) < (-11 * -5)))) and ((-18 - -15) <= (-5 * 9 * -9 * -6)) and (not ((越南的货币是越南盾。) or (西班牙位于南极洲。)))) and (not not (俄罗斯的货币是卢布。)))
C. (((九月有30天。) or (not ((4 + 6) <= (5 ** 1) <= (2 - -10)))) and ((not (闪电不会两次击中同一个地方。)) or ((5 * 15) < (9 * 7)))) and ((((13 - -12) >= (6 + -6)) and (not not (海王星是距离太阳第3近的行星。))) or (not not (not (not not ((15 - 19) <= (7 * -3 * 1 * -8))))))
D. not not (((猪有10条腿。) and (((43 % 2) <= (24 % 4)) or (not not ((4 * 9 - -10 * 5) == (-18 * -13))))) or (not ((莱特兄弟首次飞行发生在1908年。) and (2000年奥运会在悉尼举办。))) or ((not not ((金在常温下是固体。) or ((2 ** 1) < (-4 * -5 - -7 * -2) < (3 ** 1)))) and (not ((-11 * 5) < (-11 + -20) < (3 + 20))) and ((not not ((-10 - 18) >= (2 ** 1))) or (not (冰的密度比液态水小。)))))
E. not ((not not (荷兰的首都是阿姆斯特丹。)) and (((((8 + -18) != (4 + -17)) and (鸭子有2条腿。)) or (not (尼日利亚的货币是奈拉。))) or (((-5 * 3) == (2 * -2 * 1 * -6)) or (氮气在常温下是固体。)) or ((-3 + 15) > (12 * 6))))
F. (((1982年是闰年。) and ((-10 - 0) > (6 * 6 - -4 * -7))) and ((not not (法国大革命开始发生在1794年。)) or (((天王星是距离太阳第7近的行星。) and ((-9 - 14) > (-7 * -8 * -5 * -10))) and (((-13 + -17) >= (6 - -20)) or (火星是距离太阳第4近的行星。))))) or ((not (((77是质数。) or ((18 + 15) != (-19 - 18))) and (not not (尼日利亚位于非洲。)))) and ((摩洛哥的首都是伯尔尼。) or (((11 - 18) != (4 * -13)) or ((12 * -20) <= (-5 * -9 - 4 * -4) <= (-19 + 2)))) and (not (土星是距离太阳第6近的行星。)))
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,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 75864450,
"true_count": 2
},
"question": "下面是几个布尔表达式：\n\nA. (not ((1908年奥运会在伦敦举办。) or ((汞的化学符号是Mg。) or (氯的化学符号是Ca。)) or ((not (银的化学符号是He。)) and (((8 - -8) <= (14 + 8)) or (1896年奥运会在巴黎举办。))))) or (((not (not not (50能被6整除。))) and ((4 ** 3) > (-19 + 18))) or ((土耳其的货币是索尔。) or ((((17 % 2) >= (-16 - 12)) and (蚂蚁有2条腿。)) or (93小于等于98。))))\nB. (not not ((((新西兰的货币是奈拉。) and ((-17 + -11) == (14 * 5))) or (澳大利亚位于大洋洲。)) or ((not not (海王星是距离太阳第2近的行星。)) or (not not ((-17 + 2) >= (5 ** 3)))))) and (((((-8 + 10) < (3 ** 2) < (-6 * -8)) and (not not ((11 * -16) < (-1 * 8 - 6 * 1) < (-11 * -5)))) and ((-18 - -15) <= (-5 * 9 * -9 * -6)) and (not ((越南的货币是越南盾。) or (西班牙位于南极洲。)))) and (not not (俄罗斯的货币是卢布。)))\nC. (((九月有30天。) or (not ((4 + 6) <= (5 ** 1) <= (2 - -10)))) and ((not (闪电不会两次击中同一个地方。)) or ((5 * 15) < (9 * 7)))) and ((((13 - -12) >= (6 + -6)) and (not not (海王星是距离太阳第3近的行星。))) or (not not (not (not not ((15 - 19) <= (7 * -3 * 1 * -8))))))\nD. not not (((猪有10条腿。) and (((43 % 2) <= (24 % 4)) or (not not ((4 * 9 - -10 * 5) == (-18 * -13))))) or (not ((莱特兄弟首次飞行发生在1908年。) and (2000年奥运会在悉尼举办。))) or ((not not ((金在常温下是固体。) or ((2 ** 1) < (-4 * -5 - -7 * -2) < (3 ** 1)))) and (not ((-11 * 5) < (-11 + -20) < (3 + 20))) and ((not not ((-10 - 18) >= (2 ** 1))) or (not (冰的密度比液态水小。)))))\nE. not ((not not (荷兰的首都是阿姆斯特丹。)) and (((((8 + -18) != (4 + -17)) and (鸭子有2条腿。)) or (not (尼日利亚的货币是奈拉。))) or (((-5 * 3) == (2 * -2 * 1 * -6)) or (氮气在常温下是固体。)) or ((-3 + 15) > (12 * 6))))\nF. (((1982年是闰年。) and ((-10 - 0) > (6 * 6 - -4 * -7))) and ((not not (法国大革命开始发生在1794年。)) or (((天王星是距离太阳第7近的行星。) and ((-9 - 14) > (-7 * -8 * -5 * -10))) and (((-13 + -17) >= (6 - -20)) or (火星是距离太阳第4近的行星。))))) or ((not (((77是质数。) or ((18 + 15) != (-19 - 18))) and (not not (尼日利亚位于非洲。)))) and ((摩洛哥的首都是伯尔尼。) or (((11 - 18) != (4 * -13)) or ((12 * -20) <= (-5 * -9 - 4 * -4) <= (-19 + 2)))) and (not (土星是距离太阳第6近的行星。)))\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": 5,
"language": "cn",
"num_options": 6,
"seed": 75864450,
"true_count": 2
},
"seed": 75864450,
"task_id": 675864450,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not ((not (Steam is a gas at room temperature.)) and ((-17 * -19) < (6 % 9)))
B. ((16 - 13) == (19 - -2)) and (((-11 - 11) < (7 * 4 - -7 * 6)) and (7 is an odd number.)) and ((((-14 - -18) <= (9 * -8 * 2 * 10) <= (15 % 6)) or (1993 is a leap year.)) and ((The chemical symbol for Helium is Ca.) or (The currency of Japan is the Krona.)))
C. not not ((not not (The square root of 1 is 1.)) or (The chemical symbol for Mercury is H.))
D. ((-6 * -7 - 1 * -1) < (13 + 13) < (10 * -2 - 8 * 8)) and (not not (not ((-1 * 3 + -10 * -1) < (3 + 13))))
E. not not (((2078 is a leap year.) or (There are 31 days in August.)) and ((The first Olympic Games of modern era occurred in 1896.) and ((4 - 3) <= (13 * -16) <= (2 * -1 + 4 * 9))))
F. (Uranus is the 2nd planet from the Sun.) and (((14 + -2) <= (4 * 3 - 5 * -5)) and ((-7 * 0 - -5 * 9) >= (-16 - 0)))
G. not (not not (Gold is a solid at room temperature.))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 95555060,
"true_count": 2
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not ((not (Steam is a gas at room temperature.)) and ((-17 * -19) < (6 % 9)))\nB. ((16 - 13) == (19 - -2)) and (((-11 - 11) < (7 * 4 - -7 * 6)) and (7 is an odd number.)) and ((((-14 - -18) <= (9 * -8 * 2 * 10) <= (15 % 6)) or (1993 is a leap year.)) and ((The chemical symbol for Helium is Ca.) or (The currency of Japan is the Krona.)))\nC. not not ((not not (The square root of 1 is 1.)) or (The chemical symbol for Mercury is H.))\nD. ((-6 * -7 - 1 * -1) < (13 + 13) < (10 * -2 - 8 * 8)) and (not not (not ((-1 * 3 + -10 * -1) < (3 + 13))))\nE. not not (((2078 is a leap year.) or (There are 31 days in August.)) and ((The first Olympic Games of modern era occurred in 1896.) and ((4 - 3) <= (13 * -16) <= (2 * -1 + 4 * 9))))\nF. (Uranus is the 2nd planet from the Sun.) and (((14 + -2) <= (4 * 3 - 5 * -5)) and ((-7 * 0 - -5 * 9) >= (-16 - 0)))\nG. not (not not (Gold is a solid at room temperature.))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 95555060,
"true_count": 2
},
"seed": 95555060,
"task_id": 695555060,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not ((19 - 8) != (-14 + -16))
B. not (((There are 31 days in July.) and (Italy is in Europe.)) and (((5 ** 2) > (-17 + 3)) and ((-16 + 14) != (4 ** 2))))
C. not not ((9 * 6) > (3 * -7 * 4 * -10))
D. ((3 + -19) <= (33 % 2)) and (((The currency of Vietnam is the Dong.) and ((14 + -4) < (16 * 10))) and ((Saturn is the 7th planet from the Sun.) or (The 1976 Olympics were held in Montreal.)))
E. not not (not not (The capital of Peru is Moscow.))
F. (Antarctica is the coldest continent.) and (((21 is a perfect square.) and (1902 is a leap year.)) or ((South Korea is in Asia.) or (The 1920 Olympics were held in Seoul.)))
G. not (not ((A bird has 0 legs.) or (46 is an odd number.)))
H. not ((5 - -1) != (38 % 5))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 85684092,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. not ((19 - 8) != (-14 + -16))\nB. not (((There are 31 days in July.) and (Italy is in Europe.)) and (((5 ** 2) > (-17 + 3)) and ((-16 + 14) != (4 ** 2))))\nC. not not ((9 * 6) > (3 * -7 * 4 * -10))\nD. ((3 + -19) <= (33 % 2)) and (((The currency of Vietnam is the Dong.) and ((14 + -4) < (16 * 10))) and ((Saturn is the 7th planet from the Sun.) or (The 1976 Olympics were held in Montreal.)))\nE. not not (not not (The capital of Peru is Moscow.))\nF. (Antarctica is the coldest continent.) and (((21 is a perfect square.) and (1902 is a leap year.)) or ((South Korea is in Asia.) or (The 1920 Olympics were held in Seoul.)))\nG. not (not ((A bird has 0 legs.) or (46 is an odd number.)))\nH. not ((5 - -1) != (38 % 5))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 85684092,
"true_count": 2
},
"seed": 85684092,
"task_id": 685684092,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. ((The capital of Malaysia is Prague.) and (A dog has 8 legs.)) or (not (((9 + 1) > (9 % 4)) or ((The capital of Indonesia is Santiago.) or ((-7 - 15) == (4 * -20)))))
B. not not (((((6 * 3 - 3 * 3) >= (2 + -16)) and (Indonesia is in Asia.)) and (not not (The capital of Singapore is Kyiv.))) and ((not (Alcohol is a liquid at room temperature.)) and ((15 + 15) != (5 % 5))))
C. not not ((((The chemical symbol for Tin is Sn.) or ((7 * 4 * 9 * 5) > (5 ** 1))) and ((19 % 5) <= (-17 - 5))) and (not (The capital of Vietnam is Budapest.)))
D. (not ((-10 * -10 * 10 * 6) < (-17 + -12) < (9 % 8))) and ((((The chemical symbol for Neon is Ne.) or (A spider has 10 legs.)) or (592 is a Fibonacci number.)) or ((not not (The currency of Brazil is the Real.)) and ((-20 - 10) >= (50 % 8))))
E. not not (not not ((not (The currency of South Africa is the Ringgit.)) and ((The chemical symbol for Carbon is S.) or (The human body has 206 bones.))))
F. not (((9 + 14) < (-19 - 3)) or (A turtle is an insect.) or (not ((Chile is in Oceania.) or (Carbon dioxide is a liquid at room temperature.))))
G. (((not not ((34 % 9) < (-5 + 0))) and ((A ant is an insect.) or (The 1932 Olympics were held in Melbourne.))) and ((The 1964 Olympics were held in Tokyo.) and ((2 * -1 + -9 * 9) <= (-14 - -1))) and (not (There are 30 days in November.))) or ((not not (not not (1931 is a leap year.))) or ((World War II began occurred in 1939.) and (A duck has 4 legs.)))
H. not not ((Venus is the 6th planet from the Sun.) and (The currency of Turkey is the Lira.))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 3569472,
"true_count": 2
},
"question": "Consider the following logical expressions:\n\nA. ((The capital of Malaysia is Prague.) and (A dog has 8 legs.)) or (not (((9 + 1) > (9 % 4)) or ((The capital of Indonesia is Santiago.) or ((-7 - 15) == (4 * -20)))))\nB. not not (((((6 * 3 - 3 * 3) >= (2 + -16)) and (Indonesia is in Asia.)) and (not not (The capital of Singapore is Kyiv.))) and ((not (Alcohol is a liquid at room temperature.)) and ((15 + 15) != (5 % 5))))\nC. not not ((((The chemical symbol for Tin is Sn.) or ((7 * 4 * 9 * 5) > (5 ** 1))) and ((19 % 5) <= (-17 - 5))) and (not (The capital of Vietnam is Budapest.)))\nD. (not ((-10 * -10 * 10 * 6) < (-17 + -12) < (9 % 8))) and ((((The chemical symbol for Neon is Ne.) or (A spider has 10 legs.)) or (592 is a Fibonacci number.)) or ((not not (The currency of Brazil is the Real.)) and ((-20 - 10) >= (50 % 8))))\nE. not not (not not ((not (The currency of South Africa is the Ringgit.)) and ((The chemical symbol for Carbon is S.) or (The human body has 206 bones.))))\nF. not (((9 + 14) < (-19 - 3)) or (A turtle is an insect.) or (not ((Chile is in Oceania.) or (Carbon dioxide is a liquid at room temperature.))))\nG. (((not not ((34 % 9) < (-5 + 0))) and ((A ant is an insect.) or (The 1932 Olympics were held in Melbourne.))) and ((The 1964 Olympics were held in Tokyo.) and ((2 * -1 + -9 * 9) <= (-14 - -1))) and (not (There are 30 days in November.))) or ((not not (not not (1931 is a leap year.))) or ((World War II began occurred in 1939.) and (A duck has 4 legs.)))\nH. not not ((Venus is the 6th planet from the Sun.) and (The currency of Turkey is the Lira.))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 3569472,
"true_count": 2
},
"seed": 3569472,
"task_id": 603569472,
"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 (38是质数。))
B. (((not not ((3 ** 1) < (-1 * -9 - 4 * -9) < (0 * -16))) or ((第二次世界大战开始发生在1939年。) or ((7 * -16) > (-20 * 7)))) or (现代奥运会首届举办发生在1896年。)) and (not ((4 * -1 + 8 * -9) == (7 * -5 * 1 * 8)))
C. ((((2016年奥运会在柏林举办。) or ((3 ** 2) == (14 - -19))) or (((-9 - -14) != (-4 * 9)) or ((-6 * 5 - 2 * 6) != (-9 - -20)))) and (not not ((90是偶数。) and (十一月有29天。)))) or (((((-12 - -20) > (4 * -1 - 0 * 0)) or (罗马尼亚的首都是布加勒斯特。)) and (((3 * 2 - 8 * -9) > (-18 * 20)) or (18能被12整除。))) or (((-3 * -5 + -3 * 0) >= (-2 * -6 * 5 * -10)) and (泰国位于非洲。)))
D. not (not not (马来西亚的货币是林吉特。))
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,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 31536146,
"true_count": 3
},
"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 (38是质数。))\nB. (((not not ((3 ** 1) < (-1 * -9 - 4 * -9) < (0 * -16))) or ((第二次世界大战开始发生在1939年。) or ((7 * -16) > (-20 * 7)))) or (现代奥运会首届举办发生在1896年。)) and (not ((4 * -1 + 8 * -9) == (7 * -5 * 1 * 8)))\nC. ((((2016年奥运会在柏林举办。) or ((3 ** 2) == (14 - -19))) or (((-9 - -14) != (-4 * 9)) or ((-6 * 5 - 2 * 6) != (-9 - -20)))) and (not not ((90是偶数。) and (十一月有29天。)))) or (((((-12 - -20) > (4 * -1 - 0 * 0)) or (罗马尼亚的首都是布加勒斯特。)) and (((3 * 2 - 8 * -9) > (-18 * 20)) or (18能被12整除。))) or (((-3 * -5 + -3 * 0) >= (-2 * -6 * 5 * -10)) and (泰国位于非洲。)))\nD. not (not not (马来西亚的货币是林吉特。))\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": 4,
"language": "cn",
"num_options": 4,
"seed": 31536146,
"true_count": 3
},
"seed": 31536146,
"task_id": 631536146,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (43 % 4) > (-3 + -4)
B. 澳大利亚的货币是澳元。
C. 1984年奥运会在东京举办。
D. (((14 - -14) < (7 + -10) < (-2 + -9)) and ((-10 + 4) == (-7 * 2))) and ((葡萄牙的首都是波哥大。) and ((7 * -6 * 9 * 0) <= (-15 * -15)))
E. (((1 * 7 - 2 * -10) > (48 % 3)) and (光速约为每秒30万公里。)) or (not not (1920年奥运会在安特卫普举办。))
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,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 79351284,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. (43 % 4) > (-3 + -4)\nB. 澳大利亚的货币是澳元。\nC. 1984年奥运会在东京举办。\nD. (((14 - -14) < (7 + -10) < (-2 + -9)) and ((-10 + 4) == (-7 * 2))) and ((葡萄牙的首都是波哥大。) and ((7 * -6 * 9 * 0) <= (-15 * -15)))\nE. (((1 * 7 - 2 * -10) > (48 % 3)) and (光速约为每秒30万公里。)) or (not not (1920年奥运会在安特卫普举办。))\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": 5,
"seed": 79351284,
"true_count": 3
},
"seed": 79351284,
"task_id": 679351284,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not not (((5 % 9) < (-4 - -9) < (-7 * 4 + 5 * 4)) or ((-18 + 14) != (-5 - -7)))
B. (-3 - -16) >= (5 ** 3)
C. (not (1920年奥运会在洛杉矶举办。)) or (油在常温下是液体。)
D. (((14 - -11) == (-13 * -20)) or (哥伦布到达美洲发生在1482年。)) and (菲律宾的货币是比索。)
E. ((9 * 1 + 4 * -4) <= (7 % 9)) or (not not (地球是距离太阳第3近的行星。))
F. (not ((4 ** 2) > (5 * -10 + -8 * 4))) and ((-13 * -17) < (1 ** 1) < (-11 + -20))
G. not (阿根廷的首都是内罗毕。)
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,C,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 97398319,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. not not (((5 % 9) < (-4 - -9) < (-7 * 4 + 5 * 4)) or ((-18 + 14) != (-5 - -7)))\nB. (-3 - -16) >= (5 ** 3)\nC. (not (1920年奥运会在洛杉矶举办。)) or (油在常温下是液体。)\nD. (((14 - -11) == (-13 * -20)) or (哥伦布到达美洲发生在1482年。)) and (菲律宾的货币是比索。)\nE. ((9 * 1 + 4 * -4) <= (7 % 9)) or (not not (地球是距离太阳第3近的行星。))\nF. (not ((4 ** 2) > (5 * -10 + -8 * 4))) and ((-13 * -17) < (1 ** 1) < (-11 + -20))\nG. not (阿根廷的首都是内罗毕。)\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": 7,
"seed": 97398319,
"true_count": 4
},
"seed": 97398319,
"task_id": 697398319,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. ((((Saturn is the 6th planet from the Sun.) and ((9 + -15) <= (12 * 0))) and ((17 * -2) == (1 - -17))) and ((((-14 * 1) >= (2 * 1 - 0 * 8)) and (The square root of 9 is 3.)) or ((2 ** 2) == (39 % 7)))) or (not ((Water is a liquid at room temperature.) or (There are 30 days in November.))) or (((4 ** 2) < (-12 + 12)) or ((((-14 + 13) > (-6 + -14)) or (A bat is an insect.)) and ((8 * -5 * -8 * 10) < (-15 * 16) < (5 - 19))))
B. ((not ((6 * -8 + 8 * -2) >= (4 * -2 * 0 * -10))) or (Nitrogen is a liquid at room temperature.)) and (((9 * -8 * 8 * 1) > (32 % 3)) and ((-9 * -6 * -2 * 5) != (2 * 9 + 10 * 5)))
C. not not (not not (((The chemical symbol for Chromium is Au.) or (Carbon dioxide is a gas at room temperature.)) or (not ((-4 * -3 + 4 * 2) >= (5 ** 1)))))
D. (not ((The currency of Colombia is the Peso.) or (not not (The 1972 Olympics were held in Athens.)))) or (((-5 * 4 - -2 * -6) < (-15 * 5)) and (not not (There are 31 days in January.))) or ((26 is greater than 19.) and (((9 + 10) > (2 ** 1)) or (Bats are blind.)) and (A crab has 10 legs.))
E. not (((not (Thailand is in Asia.)) and ((Mercury is the 1st planet from the Sun.) and ((-13 - 12) < (-1 - 12) < (8 - 6)))) and (((3 + -11) != (9 - 6)) and ((The capital of Morocco is Rabat.) and ((13 + -8) <= (1 - -6) <= (5 ** 1)))))
F. ((The currency of United States is the Krona.) or (not ((19 - 13) >= (3 ** 3)))) and ((((A trout is a reptile.) or (Air is a gas at room temperature.)) and ((South Korea is in Asia.) or ((1 * 18) > (11 + 3)))) and ((3 * 9 * 3 * -4) >= (6 * -9)) and (not (not not (The square root of 121 is 1.))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 13586197,
"true_count": 3
},
"question": "Here are some boolean expressions to evaluate:\n\nA. ((((Saturn is the 6th planet from the Sun.) and ((9 + -15) <= (12 * 0))) and ((17 * -2) == (1 - -17))) and ((((-14 * 1) >= (2 * 1 - 0 * 8)) and (The square root of 9 is 3.)) or ((2 ** 2) == (39 % 7)))) or (not ((Water is a liquid at room temperature.) or (There are 30 days in November.))) or (((4 ** 2) < (-12 + 12)) or ((((-14 + 13) > (-6 + -14)) or (A bat is an insect.)) and ((8 * -5 * -8 * 10) < (-15 * 16) < (5 - 19))))\nB. ((not ((6 * -8 + 8 * -2) >= (4 * -2 * 0 * -10))) or (Nitrogen is a liquid at room temperature.)) and (((9 * -8 * 8 * 1) > (32 % 3)) and ((-9 * -6 * -2 * 5) != (2 * 9 + 10 * 5)))\nC. not not (not not (((The chemical symbol for Chromium is Au.) or (Carbon dioxide is a gas at room temperature.)) or (not ((-4 * -3 + 4 * 2) >= (5 ** 1)))))\nD. (not ((The currency of Colombia is the Peso.) or (not not (The 1972 Olympics were held in Athens.)))) or (((-5 * 4 - -2 * -6) < (-15 * 5)) and (not not (There are 31 days in January.))) or ((26 is greater than 19.) and (((9 + 10) > (2 ** 1)) or (Bats are blind.)) and (A crab has 10 legs.))\nE. not (((not (Thailand is in Asia.)) and ((Mercury is the 1st planet from the Sun.) and ((-13 - 12) < (-1 - 12) < (8 - 6)))) and (((3 + -11) != (9 - 6)) and ((The capital of Morocco is Rabat.) and ((13 + -8) <= (1 - -6) <= (5 ** 1)))))\nF. ((The currency of United States is the Krona.) or (not ((19 - 13) >= (3 ** 3)))) and ((((A trout is a reptile.) or (Air is a gas at room temperature.)) and ((South Korea is in Asia.) or ((1 * 18) > (11 + 3)))) and ((3 * 9 * 3 * -4) >= (6 * -9)) and (not (not not (The square root of 121 is 1.))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 13586197,
"true_count": 3
},
"seed": 13586197,
"task_id": 613586197,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not ((not not ((7 + 10) != (2 * -16))) and (not not (Australia is in Oceania.)))
B. (There are 30 days in June.) or (not (not not (The 1980 Olympics were held in Moscow.)))
C. (not not (not ((19 % 4) <= (18 - 19)))) and ((((-10 * 17) < (-15 * -12) < (-6 * 13)) and (78 is less than or equal to 84.)) or (((1 - -18) <= (-17 * 8)) or ((-12 * -10) != (11 + 10))))
D. not not (not ((The capital of Indonesia is Abuja.) and (Lightning never strikes the same place twice.)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 47648548,
"true_count": 3
},
"question": "Review these logical expressions:\n\nA. not ((not not ((7 + 10) != (2 * -16))) and (not not (Australia is in Oceania.)))\nB. (There are 30 days in June.) or (not (not not (The 1980 Olympics were held in Moscow.)))\nC. (not not (not ((19 % 4) <= (18 - 19)))) and ((((-10 * 17) < (-15 * -12) < (-6 * 13)) and (78 is less than or equal to 84.)) or (((1 - -18) <= (-17 * 8)) or ((-12 * -10) != (11 + 10))))\nD. not not (not ((The capital of Indonesia is Abuja.) and (Lightning never strikes the same place twice.)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 47648548,
"true_count": 3
},
"seed": 47648548,
"task_id": 647648548,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not not ((((19 + 7) < (-10 + 16)) and (A tuna is a bird.)) and ((2060 is a leap year.) or ((8 * -9 - -9 * -4) <= (-9 * -9 + 7 * -3))))
B. not not ((1 ** 2) <= (7 + 1) <= (-8 * 9 * 8 * 9))
C. not (((Helium is a solid at room temperature.) or (A human has 8 legs.)) and (not ((-14 - 17) < (11 + 3))))
D. (not ((5 * 8 - -8 * 2) > (3 ** 3))) or (not (((8 - 13) > (18 - -18)) and (The currency of Czech Republic is the Lira.)))
E. not not ((1 * 2 * 3 * 6) < (-10 + 3))
F. (((3 + 13) < (3 ** 3)) and (((2 * 3) <= (3 ** 2)) or (The 1988 Olympics were held in Rome.))) or (((-6 * -14) == (13 * -1)) or (not (There are 30 days in November.)))
G. (not (Saturn is the 5th planet from the Sun.)) and ((The 1996 Olympics were held in Helsinki.) and ((-12 + -9) < (4 ** 2))) and (not (The 1976 Olympics were held in Montreal.))
H. ((The currency of Norway is the Dollar.) or (not not (55 is greater than 57.))) and (not (not not ((7 * 16) > (35 % 10))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 57007252,
"true_count": 3
},
"question": "Review these logical expressions:\n\nA. not not ((((19 + 7) < (-10 + 16)) and (A tuna is a bird.)) and ((2060 is a leap year.) or ((8 * -9 - -9 * -4) <= (-9 * -9 + 7 * -3))))\nB. not not ((1 ** 2) <= (7 + 1) <= (-8 * 9 * 8 * 9))\nC. not (((Helium is a solid at room temperature.) or (A human has 8 legs.)) and (not ((-14 - 17) < (11 + 3))))\nD. (not ((5 * 8 - -8 * 2) > (3 ** 3))) or (not (((8 - 13) > (18 - -18)) and (The currency of Czech Republic is the Lira.)))\nE. not not ((1 * 2 * 3 * 6) < (-10 + 3))\nF. (((3 + 13) < (3 ** 3)) and (((2 * 3) <= (3 ** 2)) or (The 1988 Olympics were held in Rome.))) or (((-6 * -14) == (13 * -1)) or (not (There are 30 days in November.)))\nG. (not (Saturn is the 5th planet from the Sun.)) and ((The 1996 Olympics were held in Helsinki.) and ((-12 + -9) < (4 ** 2))) and (not (The 1976 Olympics were held in Montreal.))\nH. ((The currency of Norway is the Dollar.) or (not not (55 is greater than 57.))) and (not (not not ((7 * 16) > (35 % 10))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 57007252,
"true_count": 3
},
"seed": 57007252,
"task_id": 657007252,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not (((欧盟的货币是泰铢。) or (英国位于非洲。)) and (((5 + 11) > (-15 + 9)) and (60是质数。)))
B. not ((((3 ** 3) <= (-8 - 20)) or (479是斐波那契数。)) and (((-8 * 6 * 9 * 8) <= (3 + 9)) and ((-8 * 0 - 6 * 8) < (1 ** 2))))
C. (((-1 * 15) <= (20 - 5)) and (not not ((3 ** 1) <= (-4 * -10 * -7 * -2)))) and ((-16 - -3) == (9 + 9))
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": 3,
"language": "cn",
"num_options": 3,
"seed": 61732816,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. not not (((欧盟的货币是泰铢。) or (英国位于非洲。)) and (((5 + 11) > (-15 + 9)) and (60是质数。)))\nB. not ((((3 ** 3) <= (-8 - 20)) or (479是斐波那契数。)) and (((-8 * 6 * 9 * 8) <= (3 + 9)) and ((-8 * 0 - 6 * 8) < (1 ** 2))))\nC. (((-1 * 15) <= (20 - 5)) and (not not ((3 ** 1) <= (-4 * -10 * -7 * -2)))) and ((-16 - -3) == (9 + 9))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 61732816,
"true_count": 1
},
"seed": 61732816,
"task_id": 661732816,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not (not (not (((not ((-1 * 8) < (-12 - 3))) or (((3 ** 3) >= (-1 - -9)) and (The capital of Australia is Canberra.))) or (((There are 31 days in December.) and ((20 - -15) < (-20 + -20) < (-1 * 9 * -1 * 0))) or (((18 + 4) > (-18 - 20)) or (209 is a Fibonacci number.))))))
B. not not (not (not (not not (The 2016 Olympics were held in Tokyo.))))
C. not not (not not ((not (not (A butterfly has 2 legs.))) and (not (((1 ** 1) != (0 + -20)) or (Earth is the 3rd planet from the Sun.))) and (not ((not not (The currency of Australia is the Dollar.)) and (((14 * -12) < (-2 * 16) < (36 % 10)) and ((0 * -19) == (36 % 7)))))))
D. not (not not ((not ((((4 ** 3) <= (5 ** 3)) or (The currency of Japan is the Real.)) and ((-18 * -20) != (3 ** 1)))) and ((not not ((-11 + -11) < (-7 * 3 + 5 * -7) < (1 ** 2))) and (((-17 - -14) == (-7 - -10)) and ((-1 * -16) >= (-10 * 3 - -4 * 4)))) and (not ((Sharks are mammals.) or (The 1968 Olympics were held in London.)))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 58565997,
"true_count": 1
},
"question": "Examine these expressions:\n\nA. not (not (not (((not ((-1 * 8) < (-12 - 3))) or (((3 ** 3) >= (-1 - -9)) and (The capital of Australia is Canberra.))) or (((There are 31 days in December.) and ((20 - -15) < (-20 + -20) < (-1 * 9 * -1 * 0))) or (((18 + 4) > (-18 - 20)) or (209 is a Fibonacci number.))))))\nB. not not (not (not (not not (The 2016 Olympics were held in Tokyo.))))\nC. not not (not not ((not (not (A butterfly has 2 legs.))) and (not (((1 ** 1) != (0 + -20)) or (Earth is the 3rd planet from the Sun.))) and (not ((not not (The currency of Australia is the Dollar.)) and (((14 * -12) < (-2 * 16) < (36 % 10)) and ((0 * -19) == (36 % 7)))))))\nD. not (not not ((not ((((4 ** 3) <= (5 ** 3)) or (The currency of Japan is the Real.)) and ((-18 * -20) != (3 ** 1)))) and ((not not ((-11 + -11) < (-7 * 3 + 5 * -7) < (1 ** 2))) and (((-17 - -14) == (-7 - -10)) and ((-1 * -16) >= (-10 * 3 - -4 * 4)))) and (not ((Sharks are mammals.) or (The 1968 Olympics were held in London.)))))\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": 4,
"seed": 58565997,
"true_count": 1
},
"seed": 58565997,
"task_id": 658565997,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. ((not ((not not ((-1 * 14) >= (-2 * 7 - -5 * 10))) and ((12 + 17) != (-2 * -7 * 3 * -4)))) or (not not (((The capital of Czech Republic is Bern.) or ((2 * 4) < (6 * -11))) or (((2 ** 3) < (2 * 20)) or (Mercury is the 3rd planet from the Sun.))))) or (not not ((9 - -20) == (-11 - -18))) or (not not ((not not (The 2012 Olympics were held in London.)) or ((Alcohol is a liquid at room temperature.) or ((8 * 7 - 7 * 5) <= (-5 + 5))) or (not (Brazil is in South America.))))
B. ((not (not not ((The square root of 64 is 2.) and ((20 - 0) <= (37 % 8) <= (8 * -4 + 10 * 9))))) and (not not (not ((A lobster has 10 legs.) or ((9 * 5 * 4 * -2) >= (0 * 3 + -8 * 5)))))) or ((((not not (There are 31 days in July.)) and (Germany is in Europe.)) and (not (((1 + 11) < (11 - 12)) or ((-4 - 2) == (-14 + 5))))) and (((Jupiter is the 5th planet from the Sun.) and ((The square root of 225 is 15.) and ((18 - -5) == (3 ** 3)))) or (not (2042 is a leap year.))))
C. not not ((not not (not (not not (The chemical symbol for Phosphorus is C.)))) or (((not not ((-2 * 5) > (-3 + -3))) and (((3 + -12) <= (-5 * -1 + -10 * 2) <= (9 * -6)) or ((50 % 9) >= (-9 * 15)))) or ((The square root of 4 is 2.) or ((0 - -11) == (-6 * 1 - 2 * 2))) or (((Iron is a solid at room temperature.) and (2050 is a leap year.)) or (((16 * -19) == (16 - 7)) or (The currency of Denmark is the Krone.)))))
D. not (not ((not not (Diamond is a gas at room temperature.)) or ((There are 31 days in January.) and (((13 * -13) == (5 + 18)) or ((6 * -3 - 9 * -9) == (-7 * -9 * 10 * -6))))))
E. ((not (not (((4 + 16) == (2 ** 3)) and ((-15 * 11) > (1 * 1 - -5 * 8))))) or ((((-14 - -19) != (9 * 15)) and (((6 * -2 + -4 * -9) > (1 ** 1)) and ((2 + -7) <= (3 ** 2)))) and (((14 + 17) < (19 + 11) < (10 * 5 * 4 * 3)) and (((4 * 0) < (-9 + 18) < (10 * 1 - 9 * 2)) and ((2 + 7) >= (49 % 9)))))) and ((((-5 * 6 - -2 * -1) >= (4 ** 1)) and (not (Nigeria is in Africa.))) and (not not (((-18 + -8) == (-1 * 13)) or (((7 * -4) >= (-9 - 5)) and ((50 % 1) >= (1 - -15))))))
F. not (not (((A pig has 6 legs.) or ((The capital of Saudi Arabia is Riyadh.) and ((1 ** 3) > (3 - -10)))) or (not (((50 % 2) < (5 ** 2)) and (The currency of Peru is the Dollar.)))))
G. not ((not not (not ((Saturn is the 6th planet from the Sun.) and (The first airplane flight by the Wright Brothers occurred in 1903.)))) and ((Australia is in North America.) and ((2008 is a leap year.) or ((-1 - 16) < (0 * 7 - 3 * -1))) and ((-6 * -19) < (-2 * -6 - -7 * 5))))
H. (not not (not not ((not (The currency of Israel is the Shekel.)) or ((-1 * 3 + 7 * -7) >= (-17 + 11))))) and ((not (The human body has 150 bones.)) or (((((-14 - 1) > (1 ** 3)) and (A chicken has 2 legs.)) or ((9 * -5 - 9 * 4) <= (-1 * -13))) and ((((-6 * -13) > (6 * -13)) or (The chemical symbol for Chromium is Cr.)) and (The chemical symbol for Oxygen is K.))))
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,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "en",
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"seed": 73155948,
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"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. ((not ((not not ((-1 * 14) >= (-2 * 7 - -5 * 10))) and ((12 + 17) != (-2 * -7 * 3 * -4)))) or (not not (((The capital of Czech Republic is Bern.) or ((2 * 4) < (6 * -11))) or (((2 ** 3) < (2 * 20)) or (Mercury is the 3rd planet from the Sun.))))) or (not not ((9 - -20) == (-11 - -18))) or (not not ((not not (The 2012 Olympics were held in London.)) or ((Alcohol is a liquid at room temperature.) or ((8 * 7 - 7 * 5) <= (-5 + 5))) or (not (Brazil is in South America.))))\nB. ((not (not not ((The square root of 64 is 2.) and ((20 - 0) <= (37 % 8) <= (8 * -4 + 10 * 9))))) and (not not (not ((A lobster has 10 legs.) or ((9 * 5 * 4 * -2) >= (0 * 3 + -8 * 5)))))) or ((((not not (There are 31 days in July.)) and (Germany is in Europe.)) and (not (((1 + 11) < (11 - 12)) or ((-4 - 2) == (-14 + 5))))) and (((Jupiter is the 5th planet from the Sun.) and ((The square root of 225 is 15.) and ((18 - -5) == (3 ** 3)))) or (not (2042 is a leap year.))))\nC. not not ((not not (not (not not (The chemical symbol for Phosphorus is C.)))) or (((not not ((-2 * 5) > (-3 + -3))) and (((3 + -12) <= (-5 * -1 + -10 * 2) <= (9 * -6)) or ((50 % 9) >= (-9 * 15)))) or ((The square root of 4 is 2.) or ((0 - -11) == (-6 * 1 - 2 * 2))) or (((Iron is a solid at room temperature.) and (2050 is a leap year.)) or (((16 * -19) == (16 - 7)) or (The currency of Denmark is the Krone.)))))\nD. not (not ((not not (Diamond is a gas at room temperature.)) or ((There are 31 days in January.) and (((13 * -13) == (5 + 18)) or ((6 * -3 - 9 * -9) == (-7 * -9 * 10 * -6))))))\nE. ((not (not (((4 + 16) == (2 ** 3)) and ((-15 * 11) > (1 * 1 - -5 * 8))))) or ((((-14 - -19) != (9 * 15)) and (((6 * -2 + -4 * -9) > (1 ** 1)) and ((2 + -7) <= (3 ** 2)))) and (((14 + 17) < (19 + 11) < (10 * 5 * 4 * 3)) and (((4 * 0) < (-9 + 18) < (10 * 1 - 9 * 2)) and ((2 + 7) >= (49 % 9)))))) and ((((-5 * 6 - -2 * -1) >= (4 ** 1)) and (not (Nigeria is in Africa.))) and (not not (((-18 + -8) == (-1 * 13)) or (((7 * -4) >= (-9 - 5)) and ((50 % 1) >= (1 - -15))))))\nF. not (not (((A pig has 6 legs.) or ((The capital of Saudi Arabia is Riyadh.) and ((1 ** 3) > (3 - -10)))) or (not (((50 % 2) < (5 ** 2)) and (The currency of Peru is the Dollar.)))))\nG. not ((not not (not ((Saturn is the 6th planet from the Sun.) and (The first airplane flight by the Wright Brothers occurred in 1903.)))) and ((Australia is in North America.) and ((2008 is a leap year.) or ((-1 - 16) < (0 * 7 - 3 * -1))) and ((-6 * -19) < (-2 * -6 - -7 * 5))))\nH. (not not (not not ((not (The currency of Israel is the Shekel.)) or ((-1 * 3 + 7 * -7) >= (-17 + 11))))) and ((not (The human body has 150 bones.)) or (((((-14 - 1) > (1 ** 3)) and (A chicken has 2 legs.)) or ((9 * -5 - 9 * 4) <= (-1 * -13))) and ((((-6 * -13) > (6 * -13)) or (The chemical symbol for Chromium is Cr.)) and (The chemical symbol for Oxygen is K.))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 73155948,
"true_count": 5
},
"seed": 73155948,
"task_id": 673155948,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (not not ((not (((哥伦布到达美洲发生在1487年。) or (211是完全平方数。)) or ((-13 * 8) > (-7 * -3 - -10 * 6)))) and (((not not (蟑螂是昆虫。)) or (((4 ** 2) > (-9 * 3)) or ((-12 + 0) == (19 % 10)))) and (((水在常温下是液体。) or (第二次世界大战结束发生在1945年。)) and ((-9 - 10) <= (5 % 10)))))) and (not not (not (not not (not not (not ((12 - 18) < (3 ** 3)))))))
B. not ((not ((not not (not not ((17 - -10) != (2 + -11)))) and (((汞在常温下是液体。) or ((4 ** 1) < (13 * -1))) and ((挪威的首都是新加坡。) and ((-2 - 11) < (2 ** 1)))))) and (((((-1 * 10) < (-11 - -3)) and (三文鱼是鱼类。)) and (not not ((1 + 3) <= (8 - -7) <= (0 * 8)))) and ((-11 + -4) < (35 % 9) < (15 + 12))) and ((not (南极洲是最冷的大陆。)) or ((not ((锡的化学符号是Sn。) or ((5 - 19) <= (-1 * -6 + 9 * -8)))) and (not ((1 % 1) <= (-6 * -5 - -7 * 2) <= (16 - 10))) and (not (not (捷克的首都是罗马。))))))
C. not not (((((0 + -1) >= (3 + 9)) and ((2 * 13) <= (8 * -8))) and ((肯尼亚位于北美洲。) or (((13 + 4) >= (0 * -9 - -6 * 4)) or (欧盟的货币是欧元。))) and (not (not not ((碳的化学符号是C。) and (以色列的货币是谢克尔。))))) or ((((((20 - -18) > (-5 - -12)) or (十二月有31天。)) and (not not ((20 + 17) > (3 * -9 * 3 * -7)))) and ((5 ** 1) >= (4 ** 3)) and (((波兰的货币是兹罗提。) and (金在常温下是固体。)) and ((28 % 4) < (2 ** 1) < (-10 * -9 + 4 * 8)))) and (not ((((-10 - -17) > (3 ** 1)) and ((8 * 4 - -7 * -8) <= (-20 - 3))) or (not (埃及位于南极洲。))))))
D. not not (not (not not ((not not (阿根廷位于南极洲。)) or (((-13 * 5) != (5 ** 3)) and ((4 ** 1) <= (5 ** 1) <= (49 % 8))) or (((2 + -3) <= (-7 * 20)) or (not ((5 * 10 + -2 * -6) > (43 % 5)))))))
E. not not (((((-18 - -18) <= (-10 - 8)) or ((-12 * 4) == (-4 - 18))) or (not ((((4 - 20) != (-5 * 8 - 2 * 6)) and ((-7 * -7 - -9 * -6) <= (3 * 6 + -3 * 5))) or (not (匈牙利的货币是福林。))))) and (not not (not (二氧化碳在常温下是气体。))) and (((2068年是闰年。) and (((-2 + 1) >= (2 ** 1)) and ((9 * 5 - 8 * 9) > (-7 - -1))) and ((((8 % 3) >= (16 + -1)) and (2034年是闰年。)) or (not (鲸鱼是鱼类。)))) and ((not ((新西兰的货币是新西兰元。) or (二氧化碳在常温下是液体。))) and (not not ((0 * 12) == (7 + -12))) and ((504是斐波那契数。) and (not (88是奇数。))))))
F. (not ((not ((not (猫是哺乳动物。)) and ((人类有三个肺。) and ((-19 - -11) <= (-12 + 14) <= (6 % 10))))) or (冰的密度比液态水小。) or (not not (not not ((俄罗斯位于亚洲。) and (一月有28天。)))))) or (((((-15 * -1) <= (-2 * 6 + 1 * -2)) or (not (汞在常温下是固体。))) and (第一次世界大战结束发生在1917年。)) and (not (二氧化碳在常温下是气体。))) or ((not ((not (not ((4 ** 1) == (10 * 20)))) or (海王星是距离太阳第8近的行星。))) and (((((四月有30天。) and (77能被8整除。)) and (((6 + -2) == (13 + 1)) or (氧气在常温下是液体。))) and (法国位于北美洲。)) or (not not ((-11 - 7) > (-6 + -16)))))
G. not not ((not not ((not not (not (壁虎是哺乳动物。))) or (瑞士的首都是伯尔尼。))) or ((十二月有28天。) or (not not ((9 - 12) == (9 * 16))) or (((钻石由碳元素组成。) or (法国位于欧洲。)) and (not not (现代奥运会首届举办发生在1901年。)))) or (not (not not ((-1 - 20) <= (2 * -15)))))
H. (not ((not ((not not (金星是距离太阳第2近的行星。)) and ((法国大革命开始发生在1789年。) and ((-4 * -3 + 8 * 7) < (39 % 8))))) or (not (92大于4。)))) or (not not (((((蚂蚁是昆虫。) or ((20 * 3) != (11 * -11))) and (((3 + -14) > (15 - -8)) or (52是质数。))) or (((-11 * -3) == (-17 - -9)) and (((11 - -9) < (17 - -14)) and ((-4 - -3) >= (11 * 15))))) and ((not not (泰国的首都是利雅得。)) and (((-11 - 19) >= (-18 - 14)) and ((28 % 9) == (-7 * -19)))) and ((智利位于南美洲。) or ((((3 * 7) <= (5 % 5)) or (2024年奥运会在巴黎举办。)) or ((64的平方根是8。) or (地球绕太阳运转。))))))
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,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 64109563,
"true_count": 4
},
"question": "考虑以下布尔表达式：\n\nA. (not not ((not (((哥伦布到达美洲发生在1487年。) or (211是完全平方数。)) or ((-13 * 8) > (-7 * -3 - -10 * 6)))) and (((not not (蟑螂是昆虫。)) or (((4 ** 2) > (-9 * 3)) or ((-12 + 0) == (19 % 10)))) and (((水在常温下是液体。) or (第二次世界大战结束发生在1945年。)) and ((-9 - 10) <= (5 % 10)))))) and (not not (not (not not (not not (not ((12 - 18) < (3 ** 3)))))))\nB. not ((not ((not not (not not ((17 - -10) != (2 + -11)))) and (((汞在常温下是液体。) or ((4 ** 1) < (13 * -1))) and ((挪威的首都是新加坡。) and ((-2 - 11) < (2 ** 1)))))) and (((((-1 * 10) < (-11 - -3)) and (三文鱼是鱼类。)) and (not not ((1 + 3) <= (8 - -7) <= (0 * 8)))) and ((-11 + -4) < (35 % 9) < (15 + 12))) and ((not (南极洲是最冷的大陆。)) or ((not ((锡的化学符号是Sn。) or ((5 - 19) <= (-1 * -6 + 9 * -8)))) and (not ((1 % 1) <= (-6 * -5 - -7 * 2) <= (16 - 10))) and (not (not (捷克的首都是罗马。))))))\nC. not not (((((0 + -1) >= (3 + 9)) and ((2 * 13) <= (8 * -8))) and ((肯尼亚位于北美洲。) or (((13 + 4) >= (0 * -9 - -6 * 4)) or (欧盟的货币是欧元。))) and (not (not not ((碳的化学符号是C。) and (以色列的货币是谢克尔。))))) or ((((((20 - -18) > (-5 - -12)) or (十二月有31天。)) and (not not ((20 + 17) > (3 * -9 * 3 * -7)))) and ((5 ** 1) >= (4 ** 3)) and (((波兰的货币是兹罗提。) and (金在常温下是固体。)) and ((28 % 4) < (2 ** 1) < (-10 * -9 + 4 * 8)))) and (not ((((-10 - -17) > (3 ** 1)) and ((8 * 4 - -7 * -8) <= (-20 - 3))) or (not (埃及位于南极洲。))))))\nD. not not (not (not not ((not not (阿根廷位于南极洲。)) or (((-13 * 5) != (5 ** 3)) and ((4 ** 1) <= (5 ** 1) <= (49 % 8))) or (((2 + -3) <= (-7 * 20)) or (not ((5 * 10 + -2 * -6) > (43 % 5)))))))\nE. not not (((((-18 - -18) <= (-10 - 8)) or ((-12 * 4) == (-4 - 18))) or (not ((((4 - 20) != (-5 * 8 - 2 * 6)) and ((-7 * -7 - -9 * -6) <= (3 * 6 + -3 * 5))) or (not (匈牙利的货币是福林。))))) and (not not (not (二氧化碳在常温下是气体。))) and (((2068年是闰年。) and (((-2 + 1) >= (2 ** 1)) and ((9 * 5 - 8 * 9) > (-7 - -1))) and ((((8 % 3) >= (16 + -1)) and (2034年是闰年。)) or (not (鲸鱼是鱼类。)))) and ((not ((新西兰的货币是新西兰元。) or (二氧化碳在常温下是液体。))) and (not not ((0 * 12) == (7 + -12))) and ((504是斐波那契数。) and (not (88是奇数。))))))\nF. (not ((not ((not (猫是哺乳动物。)) and ((人类有三个肺。) and ((-19 - -11) <= (-12 + 14) <= (6 % 10))))) or (冰的密度比液态水小。) or (not not (not not ((俄罗斯位于亚洲。) and (一月有28天。)))))) or (((((-15 * -1) <= (-2 * 6 + 1 * -2)) or (not (汞在常温下是固体。))) and (第一次世界大战结束发生在1917年。)) and (not (二氧化碳在常温下是气体。))) or ((not ((not (not ((4 ** 1) == (10 * 20)))) or (海王星是距离太阳第8近的行星。))) and (((((四月有30天。) and (77能被8整除。)) and (((6 + -2) == (13 + 1)) or (氧气在常温下是液体。))) and (法国位于北美洲。)) or (not not ((-11 - 7) > (-6 + -16)))))\nG. not not ((not not ((not not (not (壁虎是哺乳动物。))) or (瑞士的首都是伯尔尼。))) or ((十二月有28天。) or (not not ((9 - 12) == (9 * 16))) or (((钻石由碳元素组成。) or (法国位于欧洲。)) and (not not (现代奥运会首届举办发生在1901年。)))) or (not (not not ((-1 - 20) <= (2 * -15)))))\nH. (not ((not ((not not (金星是距离太阳第2近的行星。)) and ((法国大革命开始发生在1789年。) and ((-4 * -3 + 8 * 7) < (39 % 8))))) or (not (92大于4。)))) or (not not (((((蚂蚁是昆虫。) or ((20 * 3) != (11 * -11))) and (((3 + -14) > (15 - -8)) or (52是质数。))) or (((-11 * -3) == (-17 - -9)) and (((11 - -9) < (17 - -14)) and ((-4 - -3) >= (11 * 15))))) and ((not not (泰国的首都是利雅得。)) and (((-11 - 19) >= (-18 - 14)) and ((28 % 9) == (-7 * -19)))) and ((智利位于南美洲。) or ((((3 * 7) <= (5 % 5)) or (2024年奥运会在巴黎举办。)) or ((64的平方根是8。) or (地球绕太阳运转。))))))\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": {
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"language": "cn",
"num_options": 8,
"seed": 64109563,
"true_count": 4
},
"seed": 64109563,
"task_id": 664109563,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. ((((7 * -2 * -10 * 4) <= (-3 * -4 + 9 * 4)) or (10是质数。)) and ((瑞士的首都是内罗毕。) and (1928年是闰年。))) or ((not not (1984年奥运会在东京举办。)) and ((17 - 16) <= (12 % 4)))
B. not not (((-19 + 3) <= (-11 - 7)) and ((-19 * -2) != (50 % 2)))
C. ((((-11 * 7) < (-18 + 2)) or ((5 - -20) == (4 ** 2))) or (not not (土星是距离太阳第6近的行星。))) or (not ((人体有206块骨头。) or (氧气在常温下是固体。)))
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": 3,
"language": "cn",
"num_options": 3,
"seed": 7806041,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. ((((7 * -2 * -10 * 4) <= (-3 * -4 + 9 * 4)) or (10是质数。)) and ((瑞士的首都是内罗毕。) and (1928年是闰年。))) or ((not not (1984年奥运会在东京举办。)) and ((17 - 16) <= (12 % 4)))\nB. not not (((-19 + 3) <= (-11 - 7)) and ((-19 * -2) != (50 % 2)))\nC. ((((-11 * 7) < (-18 + 2)) or ((5 - -20) == (4 ** 2))) or (not not (土星是距离太阳第6近的行星。))) or (not ((人体有206块骨头。) or (氧气在常温下是固体。)))\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": 3,
"seed": 7806041,
"true_count": 1
},
"seed": 7806041,
"task_id": 607806041,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. ((锰的化学符号是Zn。) or ((3 % 10) >= (-4 - 4))) or (not not (伦敦大火发生在1664年。))
B. (((-16 + -5) == (6 + -14)) or (袋鼠有4条腿。)) or ((马有2条腿。) and ((20 % 1) != (-2 - -2)))
C. not not (not (1980年奥运会在莫斯科举办。))
D. (10 * -5 * -5 * -9) >= (17 * 10)
E. not ((火星是距离太阳最近的行星。) or ((14 - -4) != (5 - 8)))
F. (not ((16 + -3) == (34 % 6))) and ((一月有31天。) and (2019年是闰年。))
G. ((加拿大的货币是兰特。) or ((-14 * -11) < (0 * -6 - -8 * 1))) or (六月有30天。)
H. (((-17 - -3) < (-5 - 15)) or ((17 * -18) >= (-17 - -3))) and ((蝙蝠是瞎的。) and ((31 % 8) >= (1 * 9 * 10 * 8)))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 92541232,
"true_count": 2
},
"question": "评估以下每个表达式：\n\nA. ((锰的化学符号是Zn。) or ((3 % 10) >= (-4 - 4))) or (not not (伦敦大火发生在1664年。))\nB. (((-16 + -5) == (6 + -14)) or (袋鼠有4条腿。)) or ((马有2条腿。) and ((20 % 1) != (-2 - -2)))\nC. not not (not (1980年奥运会在莫斯科举办。))\nD. (10 * -5 * -5 * -9) >= (17 * 10)\nE. not ((火星是距离太阳最近的行星。) or ((14 - -4) != (5 - 8)))\nF. (not ((16 + -3) == (34 % 6))) and ((一月有31天。) and (2019年是闰年。))\nG. ((加拿大的货币是兰特。) or ((-14 * -11) < (0 * -6 - -8 * 1))) or (六月有30天。)\nH. (((-17 - -3) < (-5 - 15)) or ((17 * -18) >= (-17 - -3))) and ((蝙蝠是瞎的。) and ((31 % 8) >= (1 * 9 * 10 * 8)))\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": 8,
"seed": 92541232,
"true_count": 2
},
"seed": 92541232,
"task_id": 692541232,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not ((not not (1942年是闰年。)) or (not ((-14 - 3) < (14 * 8))))
B. ((钛的化学符号是Na。) or ((锌的化学符号是P。) or ((9 * -8 + 6 * 8) > (18 + 9)))) or ((2024年奥运会在巴黎举办。) and ((木头在常温下是气体。) or (巴西位于欧洲。)))
C. not (not not (((23 % 7) > (16 - 17)) or (德国位于欧洲。)))
D. ((((6 * -8 + 6 * 2) != (-8 - -15)) or (日本的首都是东京。)) or (not (九月有31天。))) and (((-5 - 16) <= (16 - -14) <= (-20 - 14)) and (铁在常温下是液体。))
E. (猫有8条腿。) and ((((-7 - 9) < (-5 * 0 * -8 * -5)) and (2004年奥运会在雅典举办。)) and (((8 * -4 + -9 * 1) >= (-14 + 1)) and (菲律宾的货币是兹罗提。)))
F. (50是完全平方数。) or ((46 % 10) <= (-10 * 16) <= (-7 + 19))
G. not not ((not (袋鼠有10条腿。)) and (狗有4条腿。))
H. (303是斐波那契数。) or ((((5 ** 3) >= (-4 + 5)) or ((5 - -4) >= (8 * -17))) and ((-6 - -13) == (2 ** 2)))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 65888296,
"true_count": 2
},
"question": "评估以下每个表达式：\n\nA. not ((not not (1942年是闰年。)) or (not ((-14 - 3) < (14 * 8))))\nB. ((钛的化学符号是Na。) or ((锌的化学符号是P。) or ((9 * -8 + 6 * 8) > (18 + 9)))) or ((2024年奥运会在巴黎举办。) and ((木头在常温下是气体。) or (巴西位于欧洲。)))\nC. not (not not (((23 % 7) > (16 - 17)) or (德国位于欧洲。)))\nD. ((((6 * -8 + 6 * 2) != (-8 - -15)) or (日本的首都是东京。)) or (not (九月有31天。))) and (((-5 - 16) <= (16 - -14) <= (-20 - 14)) and (铁在常温下是液体。))\nE. (猫有8条腿。) and ((((-7 - 9) < (-5 * 0 * -8 * -5)) and (2004年奥运会在雅典举办。)) and (((8 * -4 + -9 * 1) >= (-14 + 1)) and (菲律宾的货币是兹罗提。)))\nF. (50是完全平方数。) or ((46 % 10) <= (-10 * 16) <= (-7 + 19))\nG. not not ((not (袋鼠有10条腿。)) and (狗有4条腿。))\nH. (303是斐波那契数。) or ((((5 ** 3) >= (-4 + 5)) or ((5 - -4) >= (8 * -17))) and ((-6 - -13) == (2 ** 2)))\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": 65888296,
"true_count": 2
},
"seed": 65888296,
"task_id": 665888296,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((((11 + 19) < (7 + 13)) or (((-6 * -5 + -7 * -6) < (12 * -2)) or (鬣蜥是鸟类。))) or ((-12 * -13) >= (4 ** 3))) and ((地球是距离太阳第4近的行星。) or ((((10 + 18) != (4 % 2)) and (99大于1。)) or (not not ((20 * 18) != (10 * -5 * -2 * 9)))))) and (not not (((not (二氧化碳在常温下是气体。)) or ((泰坦尼克号沉没发生在1910年。) and (十二月有31天。))) or ((-16 * 17) >= (-19 - -14)) or (((28 % 10) < (17 * 15) < (-3 - -7)) and (企鹅是鸟类。))))
B. not not (((氢的化学符号是H。) or ((19 - -8) == (-10 - -6)) or (新加坡的货币是克朗。)) and ((((1896年奥运会在伦敦举办。) or ((-7 + 14) < (42 % 4) < (2 * -2 + 6 * 1))) and ((-5 - -20) != (-8 * -9 + -8 * -9))) and (not not (not (1976年奥运会在赫尔辛基举办。)))))
C. not (((not (电流比光速更快。)) or (not (巴西的货币是英镑。))) and (((((-20 - 14) < (-11 * -12) < (-5 * -18)) or ((3 + -5) >= (3 % 6))) or (not not ((45 % 9) >= (4 * 2 - 8 * -7)))) and (法国大革命开始发生在1787年。)))
D. not (((((6 - -18) == (17 + 4)) and ((2078年是闰年。) and (木头在常温下是固体。))) and (泰坦尼克号沉没发生在1902年。)) or ((6 + 0) > (41 % 1)) or (not ((not not ((20 - -7) >= (13 * 13))) or (not (氦的化学符号是He。)))))
E. ((not not (中国长城是在一年内建成的。)) or ((铀的化学符号是U。) and ((-14 + 8) < (43 % 4)) and ((12 - -6) != (-6 * 10 + -9 * 2)))) or ((银在常温下是固体。) or (((1912年奥运会在巴黎举办。) or ((-4 * -5) > (12 % 4))) or ((韩国的货币是克朗。) and ((5 * -6 * 1 * 0) > (6 * -8))))) or ((not not ((((-13 + 20) != (3 * 8 - 3 * 10)) or (捷克的首都是布鲁塞尔。)) and (not ((26 % 9) != (4 + -11))))) and (not not ((((7 * 0 * 8 * -1) <= (1 * 10)) and ((10 * 8 * -2 * -1) <= (-8 * 3 + -1 * 7) <= (-1 - 20))) and ((肯尼亚的首都是内罗毕。) or (巴西的货币是雷亚尔。)))))
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,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 30281875,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. (((((11 + 19) < (7 + 13)) or (((-6 * -5 + -7 * -6) < (12 * -2)) or (鬣蜥是鸟类。))) or ((-12 * -13) >= (4 ** 3))) and ((地球是距离太阳第4近的行星。) or ((((10 + 18) != (4 % 2)) and (99大于1。)) or (not not ((20 * 18) != (10 * -5 * -2 * 9)))))) and (not not (((not (二氧化碳在常温下是气体。)) or ((泰坦尼克号沉没发生在1910年。) and (十二月有31天。))) or ((-16 * 17) >= (-19 - -14)) or (((28 % 10) < (17 * 15) < (-3 - -7)) and (企鹅是鸟类。))))\nB. not not (((氢的化学符号是H。) or ((19 - -8) == (-10 - -6)) or (新加坡的货币是克朗。)) and ((((1896年奥运会在伦敦举办。) or ((-7 + 14) < (42 % 4) < (2 * -2 + 6 * 1))) and ((-5 - -20) != (-8 * -9 + -8 * -9))) and (not not (not (1976年奥运会在赫尔辛基举办。)))))\nC. not (((not (电流比光速更快。)) or (not (巴西的货币是英镑。))) and (((((-20 - 14) < (-11 * -12) < (-5 * -18)) or ((3 + -5) >= (3 % 6))) or (not not ((45 % 9) >= (4 * 2 - 8 * -7)))) and (法国大革命开始发生在1787年。)))\nD. not (((((6 - -18) == (17 + 4)) and ((2078年是闰年。) and (木头在常温下是固体。))) and (泰坦尼克号沉没发生在1902年。)) or ((6 + 0) > (41 % 1)) or (not ((not not ((20 - -7) >= (13 * 13))) or (not (氦的化学符号是He。)))))\nE. ((not not (中国长城是在一年内建成的。)) or ((铀的化学符号是U。) and ((-14 + 8) < (43 % 4)) and ((12 - -6) != (-6 * 10 + -9 * 2)))) or ((银在常温下是固体。) or (((1912年奥运会在巴黎举办。) or ((-4 * -5) > (12 % 4))) or ((韩国的货币是克朗。) and ((5 * -6 * 1 * 0) > (6 * -8))))) or ((not not ((((-13 + 20) != (3 * 8 - 3 * 10)) or (捷克的首都是布鲁塞尔。)) and (not ((26 % 9) != (4 + -11))))) and (not not ((((7 * 0 * 8 * -1) <= (1 * 10)) and ((10 * 8 * -2 * -1) <= (-8 * 3 + -1 * 7) <= (-1 - 20))) and ((肯尼亚的首都是内罗毕。) or (巴西的货币是雷亚尔。)))))\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": 30281875,
"true_count": 2
},
"seed": 30281875,
"task_id": 630281875,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((((磷的化学符号是Co。) and (not not ((6 + -18) <= (-14 + 1)))) and (((四月有30天。) and ((-18 * 6) == (-6 * -8))) and (not not ((2 ** 3) == (2 ** 1))))) and (((18 - -15) != (16 - 10)) and ((-11 - 2) > (-8 * 11)))) and ((((4 * -8 - 8 * 4) > (-4 + -8)) and (not (((1 ** 2) < (-16 - -19)) or (中国长城是在一年内建成的。)))) or ((((38 % 6) >= (-8 * 8 - 6 * -4)) and (not not (锰的化学符号是Mn。))) or (not ((短吻鳄是爬行动物。) and ((1 * -6 + 1 * 10) < (1 + -3) < (4 ** 3))))))
B. (not (((智利位于南美洲。) and (((-10 + -14) == (-9 * -11)) and (2042年是闰年。))) or (((1992年奥运会在巴塞罗那举办。) or (二月有28天。)) or ((法国位于欧洲。) and ((-6 + 19) == (1 ** 3)))))) and (not not ((水星是距离太阳第1近的行星。) and ((15 % 5) != (2 ** 2))))
C. not not (((not not (not ((-18 - 0) != (3 % 10)))) or ((20 % 8) != (34 % 8))) and (not not ((龙虾有8条腿。) and (加拿大的首都是雅典。))) and (not (((鸟有2条腿。) and ((7 * -18) != (1 ** 2))) and (海王星是距离太阳第8近的行星。))))
D. ((((-4 * 9 - 9 * -4) == (8 + -7)) and (((100的平方根是9。) or (菲律宾的货币是克朗。)) or ((英国位于亚洲。) and (氯的化学符号是Cl。)))) and (not ((5 ** 1) > (3 * 5)))) or ((not (1900年是闰年。)) or ((((人类只使用了大脑的10%。) and (空气在常温下是气体。)) or ((瑞典的货币是克朗。) and ((-10 - 16) == (14 - -15)))) or (氖的化学符号是He。)))
E. ((not not (((18 - 6) >= (16 * -12)) and ((摩洛哥位于北美洲。) and ((4 ** 1) == (-9 - 4))))) and ((银在常温下是气体。) and ((9 * 12) != (7 * -2 + 5 * 2)))) and ((not (((金的化学符号是Au。) or ((19 % 5) < (5 * -7 - 9 * 9))) and ((12 % 10) <= (-15 - 20)))) or ((not not (((-18 + 1) <= (16 + -7)) or (79是质数。))) and (not (((2 + 16) > (-18 * 14)) or (汞在常温下是液体。)))))
F. (((not (not not (人体有206块骨头。))) and (not not (((1 + -13) != (-9 * 8)) and ((4 * -5 + -3 * -9) <= (7 * 9 - -5 * -2))))) and (((1900年奥运会在东京举办。) and ((氦气在常温下是液体。) or (美国的货币是美元。))) and (((智利的货币是里拉。) and ((6 - 6) == (-2 * -3 + 2 * 6))) and ((蚂蚁是昆虫。) and (波兰的首都是里斯本。))))) or ((not ((五月有31天。) or (马是昆虫。))) or (not (((2 ** 3) <= (35 % 3) <= (17 % 8)) and ((8 - -5) < (-2 + 19))))) or (not (not (not ((3 * 17) >= (2 ** 3)))))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 61426699,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. ((((磷的化学符号是Co。) and (not not ((6 + -18) <= (-14 + 1)))) and (((四月有30天。) and ((-18 * 6) == (-6 * -8))) and (not not ((2 ** 3) == (2 ** 1))))) and (((18 - -15) != (16 - 10)) and ((-11 - 2) > (-8 * 11)))) and ((((4 * -8 - 8 * 4) > (-4 + -8)) and (not (((1 ** 2) < (-16 - -19)) or (中国长城是在一年内建成的。)))) or ((((38 % 6) >= (-8 * 8 - 6 * -4)) and (not not (锰的化学符号是Mn。))) or (not ((短吻鳄是爬行动物。) and ((1 * -6 + 1 * 10) < (1 + -3) < (4 ** 3))))))\nB. (not (((智利位于南美洲。) and (((-10 + -14) == (-9 * -11)) and (2042年是闰年。))) or (((1992年奥运会在巴塞罗那举办。) or (二月有28天。)) or ((法国位于欧洲。) and ((-6 + 19) == (1 ** 3)))))) and (not not ((水星是距离太阳第1近的行星。) and ((15 % 5) != (2 ** 2))))\nC. not not (((not not (not ((-18 - 0) != (3 % 10)))) or ((20 % 8) != (34 % 8))) and (not not ((龙虾有8条腿。) and (加拿大的首都是雅典。))) and (not (((鸟有2条腿。) and ((7 * -18) != (1 ** 2))) and (海王星是距离太阳第8近的行星。))))\nD. ((((-4 * 9 - 9 * -4) == (8 + -7)) and (((100的平方根是9。) or (菲律宾的货币是克朗。)) or ((英国位于亚洲。) and (氯的化学符号是Cl。)))) and (not ((5 ** 1) > (3 * 5)))) or ((not (1900年是闰年。)) or ((((人类只使用了大脑的10%。) and (空气在常温下是气体。)) or ((瑞典的货币是克朗。) and ((-10 - 16) == (14 - -15)))) or (氖的化学符号是He。)))\nE. ((not not (((18 - 6) >= (16 * -12)) and ((摩洛哥位于北美洲。) and ((4 ** 1) == (-9 - 4))))) and ((银在常温下是气体。) and ((9 * 12) != (7 * -2 + 5 * 2)))) and ((not (((金的化学符号是Au。) or ((19 % 5) < (5 * -7 - 9 * 9))) and ((12 % 10) <= (-15 - 20)))) or ((not not (((-18 + 1) <= (16 + -7)) or (79是质数。))) and (not (((2 + 16) > (-18 * 14)) or (汞在常温下是液体。)))))\nF. (((not (not not (人体有206块骨头。))) and (not not (((1 + -13) != (-9 * 8)) and ((4 * -5 + -3 * -9) <= (7 * 9 - -5 * -2))))) and (((1900年奥运会在东京举办。) and ((氦气在常温下是液体。) or (美国的货币是美元。))) and (((智利的货币是里拉。) and ((6 - 6) == (-2 * -3 + 2 * 6))) and ((蚂蚁是昆虫。) and (波兰的首都是里斯本。))))) or ((not ((五月有31天。) or (马是昆虫。))) or (not (((2 ** 3) <= (35 % 3) <= (17 % 8)) and ((8 - -5) < (-2 + 19))))) or (not (not (not ((3 * 17) >= (2 ** 3)))))\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": 6,
"seed": 61426699,
"true_count": 2
},
"seed": 61426699,
"task_id": 661426699,
"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 ((5 * -1 + -3 * 5) < (8 * -6))) or ((0 - 1) < (-20 - -16)) or ((not ((-18 + -13) < (2 * -7 + 5 * 10) < (16 - 19))) and (人类有三个肺。)))
B. not ((not not ((光速比声速快。) and (2001年是闰年。))) or (新西兰的货币是新西兰元。) or (埃及位于南极洲。))
C. ((not (((-10 * 9 - -1 * -3) <= (10 + 9) <= (50 % 6)) or ((-16 - -19) != (-12 * -18)))) or (not ((17 - 8) < (-10 * -4 + 7 * -1) < (-3 + -17)))) and ((((木星是距离太阳第2近的行星。) and (酒精在常温下是液体。)) and ((-19 + -14) != (-11 * 0))) and (((-9 - 2) == (3 - 13)) or (1955年是闰年。)) and (((俄罗斯的货币是卢布。) or (1928年奥运会在伦敦举办。)) or ((-6 + -4) == (43 % 5))))
D. (((10 - 6) > (0 + -12)) and (not (((11 + -1) <= (-12 + -4) <= (5 ** 1)) and ((6 * 1 - 6 * 2) < (3 - -1) < (4 - 9))))) or (((印度尼西亚的货币是日元。) or ((13 - -16) != (49 % 4))) and (((14 * -16) == (37 % 2)) or (硅的化学符号是Co。))) or (not not ((12 * 16) < (-3 * 9 + -8 * 0) < (-9 - 17)))
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": 4,
"language": "cn",
"num_options": 4,
"seed": 95850881,
"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 ((not not ((5 * -1 + -3 * 5) < (8 * -6))) or ((0 - 1) < (-20 - -16)) or ((not ((-18 + -13) < (2 * -7 + 5 * 10) < (16 - 19))) and (人类有三个肺。)))\nB. not ((not not ((光速比声速快。) and (2001年是闰年。))) or (新西兰的货币是新西兰元。) or (埃及位于南极洲。))\nC. ((not (((-10 * 9 - -1 * -3) <= (10 + 9) <= (50 % 6)) or ((-16 - -19) != (-12 * -18)))) or (not ((17 - 8) < (-10 * -4 + 7 * -1) < (-3 + -17)))) and ((((木星是距离太阳第2近的行星。) and (酒精在常温下是液体。)) and ((-19 + -14) != (-11 * 0))) and (((-9 - 2) == (3 - 13)) or (1955年是闰年。)) and (((俄罗斯的货币是卢布。) or (1928年奥运会在伦敦举办。)) or ((-6 + -4) == (43 % 5))))\nD. (((10 - 6) > (0 + -12)) and (not (((11 + -1) <= (-12 + -4) <= (5 ** 1)) and ((6 * 1 - 6 * 2) < (3 - -1) < (4 - 9))))) or (((印度尼西亚的货币是日元。) or ((13 - -16) != (49 % 4))) and (((14 * -16) == (37 % 2)) or (硅的化学符号是Co。))) or (not not ((12 * 16) < (-3 * 9 + -8 * 0) < (-9 - 17)))\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": 4,
"language": "cn",
"num_options": 4,
"seed": 95850881,
"true_count": 2
},
"seed": 95850881,
"task_id": 695850881,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not (((not not ((Copper is a gas at room temperature.) and (Humans have five fingers on each hand.))) or (not not ((17 + 9) <= (3 * -8)))) or (The Great Fire of London occurred in 1666.) or ((not (not (Uranus is the 2nd planet from the Sun.))) or ((not ((5 ** 2) > (-15 - 4))) and (not not ((6 * 18) >= (1 * -9 * -4 * 0))))))
B. not not ((((((-6 * -11) == (0 - -9)) and (The capital of Russia is Athens.)) and ((46 % 7) <= (4 % 2))) and ((The chemical symbol for Calcium is Ca.) or ((The currency of Turkey is the Lira.) or (The 1952 Olympics were held in Helsinki.)))) and ((not not ((-4 - -4) <= (7 * -3 - 2 * -6))) or ((3 ** 1) != (4 ** 3))) and (not (not (((-8 * 1 - -2 * -6) <= (5 ** 1) <= (-5 * 2)) and (88 is an odd number.)))))
C. not not (((((The chemical symbol for Nitrogen is N.) and ((3 ** 1) <= (9 + -3) <= (5 ** 1))) and (A butterfly has 6 legs.)) and (((A crab has 10 legs.) and ((20 + 20) != (-4 + -11))) and (not (Oxygen is a gas at room temperature.)))) and ((((The capital of Malaysia is Cairo.) or ((13 - -10) > (-15 - -10))) and ((The currency of Egypt is the Pound.) or (The capital of Canada is Ottawa.))) and (not (not ((12 * 9) < (9 - -6))))))
D. not not ((((not not (The Earth revolves around the Sun.)) or ((4 * -6) <= (2 % 2))) or ((-11 + 12) < (6 * -9))) and (((not not ((1 - -16) != (5 - 2))) or ((1957 is a leap year.) or (A iguana is an insect.))) or ((67 is greater than 2.) and ((45 % 2) != (3 ** 2))) or ((The 2024 Olympics were held in Tokyo.) or (Spiders are insects.))))
E. not not (not (not ((((-10 + -4) != (-19 - -5)) or (The 1980 Olympics were held in Antwerp.)) and (The capital of Vietnam is Hanoi.))))
F. not (not not (not not ((Oxygen is a gas at room temperature.) and ((Nitrogen is a liquid at room temperature.) and (The currency of Japan is the Yen.)))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 88252890,
"true_count": 2
},
"question": "Consider the following logical expressions:\n\nA. not (((not not ((Copper is a gas at room temperature.) and (Humans have five fingers on each hand.))) or (not not ((17 + 9) <= (3 * -8)))) or (The Great Fire of London occurred in 1666.) or ((not (not (Uranus is the 2nd planet from the Sun.))) or ((not ((5 ** 2) > (-15 - 4))) and (not not ((6 * 18) >= (1 * -9 * -4 * 0))))))\nB. not not ((((((-6 * -11) == (0 - -9)) and (The capital of Russia is Athens.)) and ((46 % 7) <= (4 % 2))) and ((The chemical symbol for Calcium is Ca.) or ((The currency of Turkey is the Lira.) or (The 1952 Olympics were held in Helsinki.)))) and ((not not ((-4 - -4) <= (7 * -3 - 2 * -6))) or ((3 ** 1) != (4 ** 3))) and (not (not (((-8 * 1 - -2 * -6) <= (5 ** 1) <= (-5 * 2)) and (88 is an odd number.)))))\nC. not not (((((The chemical symbol for Nitrogen is N.) and ((3 ** 1) <= (9 + -3) <= (5 ** 1))) and (A butterfly has 6 legs.)) and (((A crab has 10 legs.) and ((20 + 20) != (-4 + -11))) and (not (Oxygen is a gas at room temperature.)))) and ((((The capital of Malaysia is Cairo.) or ((13 - -10) > (-15 - -10))) and ((The currency of Egypt is the Pound.) or (The capital of Canada is Ottawa.))) and (not (not ((12 * 9) < (9 - -6))))))\nD. not not ((((not not (The Earth revolves around the Sun.)) or ((4 * -6) <= (2 % 2))) or ((-11 + 12) < (6 * -9))) and (((not not ((1 - -16) != (5 - 2))) or ((1957 is a leap year.) or (A iguana is an insect.))) or ((67 is greater than 2.) and ((45 % 2) != (3 ** 2))) or ((The 2024 Olympics were held in Tokyo.) or (Spiders are insects.))))\nE. not not (not (not ((((-10 + -4) != (-19 - -5)) or (The 1980 Olympics were held in Antwerp.)) and (The capital of Vietnam is Hanoi.))))\nF. not (not not (not not ((Oxygen is a gas at room temperature.) and ((Nitrogen is a liquid at room temperature.) and (The currency of Japan is the Yen.)))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 88252890,
"true_count": 2
},
"seed": 88252890,
"task_id": 688252890,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (-20 + -17) != (9 - 16)
B. (Whales are fish.) or (not not ((-10 * 0 - 7 * -9) < (0 * 20)))
C. (-20 - -14) > (-9 + -1)
D. (There are 30 days in March.) and (((2 * -5 + 5 * -4) < (-7 * -2)) and (97 is divisible by 2.))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 40988634,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (-20 + -17) != (9 - 16)\nB. (Whales are fish.) or (not not ((-10 * 0 - 7 * -9) < (0 * 20)))\nC. (-20 - -14) > (-9 + -1)\nD. (There are 30 days in March.) and (((2 * -5 + 5 * -4) < (-7 * -2)) and (97 is divisible by 2.))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 40988634,
"true_count": 2
},
"seed": 40988634,
"task_id": 640988634,
"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) < (17 - 10)) or ((-14 - 14) != (3 * -10 * -7 * 4))))) and ((((The capital of Austria is Vienna.) or ((-6 * -1 * 4 * 9) != (4 * -3 * 7 * 7))) and (Steam is a gas at room temperature.)) or (Steam is a gas at room temperature.))
B. not not (not not (not (not not ((11 * -12) >= (1 * -7 - -9 * 6)))))
C. (not not ((8 + 2) <= (3 ** 1))) or (not (not ((9 * 8 + -8 * 3) != (-3 * -4 * 1 * 5)))) or (not (((16 * 19) == (-10 * 5 + -5 * 7)) or (105 is an even number.)))
D. ((There are 30 days in April.) or ((-9 * 9 * -7 * -4) < (-14 - 6) < (4 ** 1)) or ((41 % 1) >= (-1 * -10))) or (((6 + -16) > (0 * 3 * 9 * 1)) and (not not (A cat has 0 legs.))) or (not not (not not (A horse is a mammal.)))
E. (((not ((5 ** 1) != (3 ** 3))) and (Mercury is the 2nd planet from the Sun.)) and ((not (The 2000 Olympics were held in Los Angeles.)) or (not not (Vietnam is in Asia.)))) or (not ((-8 - 10) <= (6 % 2))) or ((not not ((-11 * -8) < (10 * 14) < (-18 + -2))) or ((not not (Water boils at 100 degrees Celsius at sea level.)) and (2039 is a leap year.)))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 37339744,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (not not (not not (((3 ** 2) < (17 - 10)) or ((-14 - 14) != (3 * -10 * -7 * 4))))) and ((((The capital of Austria is Vienna.) or ((-6 * -1 * 4 * 9) != (4 * -3 * 7 * 7))) and (Steam is a gas at room temperature.)) or (Steam is a gas at room temperature.))\nB. not not (not not (not (not not ((11 * -12) >= (1 * -7 - -9 * 6)))))\nC. (not not ((8 + 2) <= (3 ** 1))) or (not (not ((9 * 8 + -8 * 3) != (-3 * -4 * 1 * 5)))) or (not (((16 * 19) == (-10 * 5 + -5 * 7)) or (105 is an even number.)))\nD. ((There are 30 days in April.) or ((-9 * 9 * -7 * -4) < (-14 - 6) < (4 ** 1)) or ((41 % 1) >= (-1 * -10))) or (((6 + -16) > (0 * 3 * 9 * 1)) and (not not (A cat has 0 legs.))) or (not not (not not (A horse is a mammal.)))\nE. (((not ((5 ** 1) != (3 ** 3))) and (Mercury is the 2nd planet from the Sun.)) and ((not (The 2000 Olympics were held in Los Angeles.)) or (not not (Vietnam is in Asia.)))) or (not ((-8 - 10) <= (6 % 2))) or ((not not ((-11 * -8) < (10 * 14) < (-18 + -2))) or ((not not (Water boils at 100 degrees Celsius at sea level.)) and (2039 is a leap year.)))\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": 5,
"seed": 37339744,
"true_count": 4
},
"seed": 37339744,
"task_id": 637339744,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (not not (The currency of Hungary is the Forint.)) or (((Earth is the 2nd planet from the Sun.) or (The Moon orbits the Earth.)) or (Diamond is a liquid at room temperature.)) or (not not (not not ((Saudi Arabia is in Antarctica.) or (The capital of Finland is Cairo.))))
B. (not not ((((19 + -15) <= (6 * -20)) and (Uranus is the 4th planet from the Sun.)) or (((17 * -11) != (3 ** 1)) and ((-2 - 18) != (-4 * 3))))) or ((not not (((-14 - -7) != (5 ** 1)) and ((37 % 4) == (-5 + -15)))) and (not (Humans only use 10% of their brain.)) and (not ((97 is a prime number.) and (The chemical symbol for Sodium is Na.))))
C. (not not ((not not (The chemical symbol for Tin is Hg.)) or (((3 * -4 * 3 * -5) <= (-5 + 20)) or (The currency of Brazil is the Real.)))) or (((-19 * -4) != (20 - 6)) or (Alcohol is a liquid at room temperature.))
D. not (((((17 - 6) < (-12 - 5)) or (96 is greater than 82.)) or ((Sound travels faster in a vacuum.) and (Mars is the 4th planet from the Sun.))) and (not not (((15 + 5) == (-7 * -8 - 3 * -5)) or ((14 - 8) <= (18 % 10)))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 34836008,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. (not not (The currency of Hungary is the Forint.)) or (((Earth is the 2nd planet from the Sun.) or (The Moon orbits the Earth.)) or (Diamond is a liquid at room temperature.)) or (not not (not not ((Saudi Arabia is in Antarctica.) or (The capital of Finland is Cairo.))))\nB. (not not ((((19 + -15) <= (6 * -20)) and (Uranus is the 4th planet from the Sun.)) or (((17 * -11) != (3 ** 1)) and ((-2 - 18) != (-4 * 3))))) or ((not not (((-14 - -7) != (5 ** 1)) and ((37 % 4) == (-5 + -15)))) and (not (Humans only use 10% of their brain.)) and (not ((97 is a prime number.) and (The chemical symbol for Sodium is Na.))))\nC. (not not ((not not (The chemical symbol for Tin is Hg.)) or (((3 * -4 * 3 * -5) <= (-5 + 20)) or (The currency of Brazil is the Real.)))) or (((-19 * -4) != (20 - 6)) or (Alcohol is a liquid at room temperature.))\nD. not (((((17 - 6) < (-12 - 5)) or (96 is greater than 82.)) or ((Sound travels faster in a vacuum.) and (Mars is the 4th planet from the Sun.))) and (not not (((15 + 5) == (-7 * -8 - 3 * -5)) or ((14 - 8) <= (18 % 10)))))\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": 34836008,
"true_count": 3
},
"seed": 34836008,
"task_id": 634836008,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((-19 - 8) < (3 * -4 + 10 * -6)) and (2000年奥运会在悉尼举办。)
B. (((-8 * 3 * -1 * -4) == (5 % 2)) and ((-11 + 8) > (5 * -18))) or (not (not not (韩国的首都是首尔。)))
C. (((越南的货币是澳元。) and ((45 % 8) > (-3 - 0))) and (哥伦布到达美洲发生在1492年。)) and ((not ((9 * -2 - -9 * 8) == (-14 + 0))) and ((罗马尼亚的首都是伯尔尼。) and (土星是距离太阳第5近的行星。)))
D. ((-2 * -5 - -8 * 4) < (4 * -5 * 3 * 0) < (2 * -2)) or ((-1 + 17) != (-18 - -3)) or (天王星是距离太阳第6近的行星。)
E. (not not (1932年奥运会在赫尔辛基举办。)) and (not not (not (1904年奥运会在圣路易斯举办。)))
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": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 16089246,
"true_count": 1
},
"question": "分析以下逻辑表达式：\n\nA. ((-19 - 8) < (3 * -4 + 10 * -6)) and (2000年奥运会在悉尼举办。)\nB. (((-8 * 3 * -1 * -4) == (5 % 2)) and ((-11 + 8) > (5 * -18))) or (not (not not (韩国的首都是首尔。)))\nC. (((越南的货币是澳元。) and ((45 % 8) > (-3 - 0))) and (哥伦布到达美洲发生在1492年。)) and ((not ((9 * -2 - -9 * 8) == (-14 + 0))) and ((罗马尼亚的首都是伯尔尼。) and (土星是距离太阳第5近的行星。)))\nD. ((-2 * -5 - -8 * 4) < (4 * -5 * 3 * 0) < (2 * -2)) or ((-1 + 17) != (-18 - -3)) or (天王星是距离太阳第6近的行星。)\nE. (not not (1932年奥运会在赫尔辛基举办。)) and (not not (not (1904年奥运会在圣路易斯举办。)))\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": 5,
"seed": 16089246,
"true_count": 1
},
"seed": 16089246,
"task_id": 616089246,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (not not (not ((-14 - -15) == (0 * -10 - 6 * 10)))) and (((not (九月有30天。)) or (((5 ** 2) <= (6 + 9)) or ((-8 * 0 - -10 * -7) <= (-10 * 2 * -5 * 8) <= (3 * -10 * 1 * -6)))) and ((((-12 - 8) < (1 ** 3)) and ((-19 - -4) <= (-2 * 6 + 5 * 7) <= (-3 * 12))) and ((地球是距离太阳第3近的行星。) and ((-14 * 10) <= (2 * -6) <= (-18 * -2)))))
B. (((not (鸭子是鸟类。)) or (1918年是闰年。)) or ((声音无法在真空中传播。) or (月球绕地球运转。))) or (((not (第一次世界大战结束发生在1928年。)) and (金星是距离太阳第2近的行星。)) and ((-1 + -15) != (28 % 2)))
C. ((not ((氧气对人类生存是必需的。) and ((11 - 15) < (-10 * -10 * -10 * -1)))) and ((((12 + 4) == (14 % 7)) or ((5 - 0) <= (2 * 2 - -4 * 5))) or (第二次世界大战结束发生在1946年。))) or (2098年是闰年。) or (((8 + -5) != (13 - 4)) or ((9 - -15) > (36 % 5)) or ((铁在常温下是气体。) or (((9 * 2 + 0 * 8) < (8 - -10) < (-14 + -2)) and (1960年奥运会在莫斯科举办。))))
D. not not ((not (not (汞的化学符号是Hg。))) or (秘鲁位于亚洲。) or (((金星是距离太阳第6近的行星。) or (第二次世界大战结束发生在1945年。)) or (((-8 + 8) <= (13 - 13)) or (日本的首都是东京。))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 84849724,
"true_count": 3
},
"question": "评估以下每个表达式：\n\nA. (not not (not ((-14 - -15) == (0 * -10 - 6 * 10)))) and (((not (九月有30天。)) or (((5 ** 2) <= (6 + 9)) or ((-8 * 0 - -10 * -7) <= (-10 * 2 * -5 * 8) <= (3 * -10 * 1 * -6)))) and ((((-12 - 8) < (1 ** 3)) and ((-19 - -4) <= (-2 * 6 + 5 * 7) <= (-3 * 12))) and ((地球是距离太阳第3近的行星。) and ((-14 * 10) <= (2 * -6) <= (-18 * -2)))))\nB. (((not (鸭子是鸟类。)) or (1918年是闰年。)) or ((声音无法在真空中传播。) or (月球绕地球运转。))) or (((not (第一次世界大战结束发生在1928年。)) and (金星是距离太阳第2近的行星。)) and ((-1 + -15) != (28 % 2)))\nC. ((not ((氧气对人类生存是必需的。) and ((11 - 15) < (-10 * -10 * -10 * -1)))) and ((((12 + 4) == (14 % 7)) or ((5 - 0) <= (2 * 2 - -4 * 5))) or (第二次世界大战结束发生在1946年。))) or (2098年是闰年。) or (((8 + -5) != (13 - 4)) or ((9 - -15) > (36 % 5)) or ((铁在常温下是气体。) or (((9 * 2 + 0 * 8) < (8 - -10) < (-14 + -2)) and (1960年奥运会在莫斯科举办。))))\nD. not not ((not (not (汞的化学符号是Hg。))) or (秘鲁位于亚洲。) or (((金星是距离太阳第6近的行星。) or (第二次世界大战结束发生在1945年。)) or (((-8 + 8) <= (13 - 13)) or (日本的首都是东京。))))\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": 4,
"seed": 84849724,
"true_count": 3
},
"seed": 84849724,
"task_id": 684849724,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not (((狗有4条腿。) or (not ((-8 * 3 + 2 * 4) != (-7 * 4 + -4 * -5)))) and ((西班牙位于欧洲。) or (not (埃及位于非洲。))))
B. not not ((海王星是距离太阳第8近的行星。) or ((硫的化学符号是S。) and ((10 * 16) < (-16 * -2))) or (((水蒸气在常温下是气体。) and ((-7 + -9) <= (-11 - 5))) and (not not ((12 - -7) > (15 - 7)))))
C. not ((((11 * 8) != (6 * 3 * 6 * 2)) or (日本位于大洋洲。)) and ((镁的化学符号是Hg。) or (((-10 - -4) < (-15 - -1)) and (酒精在常温下是气体。))))
D. not not (not (not not (not ((0 * 7 * -6 * -7) > (2 ** 1)))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 62087511,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. not (((狗有4条腿。) or (not ((-8 * 3 + 2 * 4) != (-7 * 4 + -4 * -5)))) and ((西班牙位于欧洲。) or (not (埃及位于非洲。))))\nB. not not ((海王星是距离太阳第8近的行星。) or ((硫的化学符号是S。) and ((10 * 16) < (-16 * -2))) or (((水蒸气在常温下是气体。) and ((-7 + -9) <= (-11 - 5))) and (not not ((12 - -7) > (15 - 7)))))\nC. not ((((11 * 8) != (6 * 3 * 6 * 2)) or (日本位于大洋洲。)) and ((镁的化学符号是Hg。) or (((-10 - -4) < (-15 - -1)) and (酒精在常温下是气体。))))\nD. not not (not (not not (not ((0 * 7 * -6 * -7) > (2 ** 1)))))\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": 4,
"language": "cn",
"num_options": 4,
"seed": 62087511,
"true_count": 2
},
"seed": 62087511,
"task_id": 662087511,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not ((not ((not (加拿大的货币是加元。)) and ((-9 + 6) <= (25 % 7) <= (2 ** 2)))) or ((not (((二月有28天。) or (钴的化学符号是Pb。)) or (意大利位于亚洲。))) or (not not (not not (not not (柏林墙倒塌发生在1988年。))))))
B. not not ((((巴西的首都是巴西利亚。) and (not ((-2 * -13) <= (19 + -15))) and (螃蟹有8条腿。)) or ((((7 * 4 - 0 * -4) > (-3 * 20)) or (地球是距离太阳第3近的行星。)) or (硅的化学符号是Si。) or (((-16 + -6) >= (-13 - -7)) and (not (磷的化学符号是Au。))))) or (not not (not not ((2 ** 2) != (14 - 3)))))
C. not (not not ((((((-19 + 19) >= (24 % 9)) and (印度尼西亚的货币是印尼盾。)) and (not ((8 * 4 - -10 * 5) <= (2 ** 2)))) or (not not (((20 * -4) <= (7 * 6 - 8 * -2)) and (韩国位于亚洲。)))) and (not ((((4 ** 3) > (12 - 10)) or ((16 * -19) < (17 * 1) < (4 ** 3))) and (not not ((3 ** 3) <= (6 * 17)))))))
D. not not ((not not (((((-5 * 3 + -7 * 9) == (3 - 1)) or (摩洛哥的首都是阿姆斯特丹。)) or (((-4 * 0 - 4 * 4) >= (21 % 9)) or ((18 + -20) < (-15 * 11) < (19 + 15)))) or (((-7 * 0) <= (13 * 13)) or (鲤鱼是昆虫。)) or (not ((埃及的首都是维也纳。) or ((-6 * 10 - 1 * 1) < (19 - 16) < (-7 + -8)))))) or (not not (not ((铂的化学符号是Pt。) and ((2 ** 3) <= (-3 * -10 * -4 * 0) <= (21 % 4))))))
E. not not (((not not ((1 ** 2) < (4 ** 2))) or ((((水星是距离太阳第1近的行星。) and (五月有31天。)) or (not ((4 * 3 - -3 * 0) == (3 ** 3)))) and ((80能被9整除。) and ((2 + -13) < (-5 * 19))) and (天王星是距离太阳第7近的行星。))) or ((not (((铀的化学符号是U。) and ((8 * -9 * -6 * -2) < (-6 - 8))) and ((铁在常温下是气体。) or (1912年奥运会在亚特兰大举办。)))) and (not not ((((-17 * 11) < (-8 * -1 * -1 * -7)) or ((4 * -8 + -4 * -7) < (5 ** 3) < (8 * 4 * -10 * 3))) or ((1 - -20) == (-5 * -8 * -4 * 8))))))
F. (not ((((((26 % 3) == (7 + 6)) or ((1 ** 1) != (18 - 4))) or ((第二次世界大战开始发生在1939年。) and (罗马尼亚的首都是雅典。))) or (((西班牙位于欧洲。) or ((14 + -9) < (17 * 6) < (-20 + 12))) or (1928年奥运会在阿姆斯特丹举办。))) or (not not (挪威的货币是新西兰元。)))) and (not not ((41是质数。) or (((4 * 7 + 1 * -2) <= (-5 * 0 + 3 * -8)) and ((-9 - -17) <= (3 ** 1) <= (-7 * 6 + -1 * 1))) or ((日本的首都是东京。) or (not ((3 ** 3) == (3 ** 1)))))) and (not not (not (not ((0 * -16) != (14 * 16)))))
G. not not ((not not ((((肯尼亚位于非洲。) or ((8 * -4) >= (2 ** 2))) and ((9 - 4) == (-1 + 2))) and ((not (天王星是距离太阳第7近的行星。)) and ((495是斐波那契数。) and (英国的货币是埃及镑。))))) or (not (not not (460是斐波那契数。))))
H. ((not (not ((((13 * -19) == (3 ** 1)) or (氖的化学符号是Ne。)) or (not (古巴的首都是里斯本。))))) or ((not ((7 * -3) > (4 + 2))) or (not not ((水蒸气在常温下是气体。) or (((-13 - -10) != (5 + -8)) or (光速比声速快。)))))) and (not (not not (not not ((-1 * -10 - 1 * 8) >= (-16 + 9))))) and (not ((((((2 - 19) < (-19 + 2)) and (阿根廷位于北美洲。)) and (not ((-2 + -7) <= (17 - -11)))) or ((5 ** 2) >= (32 % 3))) or (not not (((哥伦比亚的首都是马德里。) or (泰坦尼克号沉没发生在1922年。)) and (土星是距离太阳第6近的行星。)))))
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": "B,C,D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 89489026,
"true_count": 5
},
"question": "给定以下布尔表达式：\n\nA. not ((not ((not (加拿大的货币是加元。)) and ((-9 + 6) <= (25 % 7) <= (2 ** 2)))) or ((not (((二月有28天。) or (钴的化学符号是Pb。)) or (意大利位于亚洲。))) or (not not (not not (not not (柏林墙倒塌发生在1988年。))))))\nB. not not ((((巴西的首都是巴西利亚。) and (not ((-2 * -13) <= (19 + -15))) and (螃蟹有8条腿。)) or ((((7 * 4 - 0 * -4) > (-3 * 20)) or (地球是距离太阳第3近的行星。)) or (硅的化学符号是Si。) or (((-16 + -6) >= (-13 - -7)) and (not (磷的化学符号是Au。))))) or (not not (not not ((2 ** 2) != (14 - 3)))))\nC. not (not not ((((((-19 + 19) >= (24 % 9)) and (印度尼西亚的货币是印尼盾。)) and (not ((8 * 4 - -10 * 5) <= (2 ** 2)))) or (not not (((20 * -4) <= (7 * 6 - 8 * -2)) and (韩国位于亚洲。)))) and (not ((((4 ** 3) > (12 - 10)) or ((16 * -19) < (17 * 1) < (4 ** 3))) and (not not ((3 ** 3) <= (6 * 17)))))))\nD. not not ((not not (((((-5 * 3 + -7 * 9) == (3 - 1)) or (摩洛哥的首都是阿姆斯特丹。)) or (((-4 * 0 - 4 * 4) >= (21 % 9)) or ((18 + -20) < (-15 * 11) < (19 + 15)))) or (((-7 * 0) <= (13 * 13)) or (鲤鱼是昆虫。)) or (not ((埃及的首都是维也纳。) or ((-6 * 10 - 1 * 1) < (19 - 16) < (-7 + -8)))))) or (not not (not ((铂的化学符号是Pt。) and ((2 ** 3) <= (-3 * -10 * -4 * 0) <= (21 % 4))))))\nE. not not (((not not ((1 ** 2) < (4 ** 2))) or ((((水星是距离太阳第1近的行星。) and (五月有31天。)) or (not ((4 * 3 - -3 * 0) == (3 ** 3)))) and ((80能被9整除。) and ((2 + -13) < (-5 * 19))) and (天王星是距离太阳第7近的行星。))) or ((not (((铀的化学符号是U。) and ((8 * -9 * -6 * -2) < (-6 - 8))) and ((铁在常温下是气体。) or (1912年奥运会在亚特兰大举办。)))) and (not not ((((-17 * 11) < (-8 * -1 * -1 * -7)) or ((4 * -8 + -4 * -7) < (5 ** 3) < (8 * 4 * -10 * 3))) or ((1 - -20) == (-5 * -8 * -4 * 8))))))\nF. (not ((((((26 % 3) == (7 + 6)) or ((1 ** 1) != (18 - 4))) or ((第二次世界大战开始发生在1939年。) and (罗马尼亚的首都是雅典。))) or (((西班牙位于欧洲。) or ((14 + -9) < (17 * 6) < (-20 + 12))) or (1928年奥运会在阿姆斯特丹举办。))) or (not not (挪威的货币是新西兰元。)))) and (not not ((41是质数。) or (((4 * 7 + 1 * -2) <= (-5 * 0 + 3 * -8)) and ((-9 - -17) <= (3 ** 1) <= (-7 * 6 + -1 * 1))) or ((日本的首都是东京。) or (not ((3 ** 3) == (3 ** 1)))))) and (not not (not (not ((0 * -16) != (14 * 16)))))\nG. not not ((not not ((((肯尼亚位于非洲。) or ((8 * -4) >= (2 ** 2))) and ((9 - 4) == (-1 + 2))) and ((not (天王星是距离太阳第7近的行星。)) and ((495是斐波那契数。) and (英国的货币是埃及镑。))))) or (not (not not (460是斐波那契数。))))\nH. ((not (not ((((13 * -19) == (3 ** 1)) or (氖的化学符号是Ne。)) or (not (古巴的首都是里斯本。))))) or ((not ((7 * -3) > (4 + 2))) or (not not ((水蒸气在常温下是气体。) or (((-13 - -10) != (5 + -8)) or (光速比声速快。)))))) and (not (not not (not not ((-1 * -10 - 1 * 8) >= (-16 + 9))))) and (not ((((((2 - 19) < (-19 + 2)) and (阿根廷位于北美洲。)) and (not ((-2 + -7) <= (17 - -11)))) or ((5 ** 2) >= (32 % 3))) or (not not (((哥伦比亚的首都是马德里。) or (泰坦尼克号沉没发生在1922年。)) and (土星是距离太阳第6近的行星。)))))\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": 8,
"seed": 89489026,
"true_count": 5
},
"seed": 89489026,
"task_id": 689489026,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not not (not not (The capital of Russia is Moscow.))
B. (((-5 * -6 + 9 * -1) > (10 * -3 + -2 * 8)) and ((3 ** 3) <= (-5 - 11) <= (3 ** 2))) or (A swan is a bird.)
C. (((14 - 20) == (-19 + 19)) and (A bird has 2 legs.)) and (not (Humans have five fingers on each hand.))
D. not ((The 1924 Olympics were held in Paris.) and (1997 is a leap year.))
E. (1954 is a leap year.) and (((-9 * 8 - -1 * 4) < (26 % 2) < (-2 + 19)) and (A day on Earth is 24 hours.))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 18223011,
"true_count": 3
},
"question": "Analyze these boolean expressions:\n\nA. not not (not not (The capital of Russia is Moscow.))\nB. (((-5 * -6 + 9 * -1) > (10 * -3 + -2 * 8)) and ((3 ** 3) <= (-5 - 11) <= (3 ** 2))) or (A swan is a bird.)\nC. (((14 - 20) == (-19 + 19)) and (A bird has 2 legs.)) and (not (Humans have five fingers on each hand.))\nD. not ((The 1924 Olympics were held in Paris.) and (1997 is a leap year.))\nE. (1954 is a leap year.) and (((-9 * 8 - -1 * 4) < (26 % 2) < (-2 + 19)) and (A day on Earth is 24 hours.))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 18223011,
"true_count": 3
},
"seed": 18223011,
"task_id": 618223011,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (not not ((1 - 6) == (3 ** 2)))
B. (((2062 is a leap year.) and (Venus is the 2nd planet from the Sun.)) or (Mexico is in Asia.)) and ((not not (The capital of Malaysia is Kuala Lumpur.)) or ((The chemical symbol for Lead is Pb.) and ((10 * -2) < (16 - 8))))
C. (A tuna is a fish.) or (The speed of light is approximately 300,000 km/s.)
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 86128937,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (not not ((1 - 6) == (3 ** 2)))\nB. (((2062 is a leap year.) and (Venus is the 2nd planet from the Sun.)) or (Mexico is in Asia.)) and ((not not (The capital of Malaysia is Kuala Lumpur.)) or ((The chemical symbol for Lead is Pb.) and ((10 * -2) < (16 - 8))))\nC. (A tuna is a fish.) or (The speed of light is approximately 300,000 km/s.)\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": 3,
"seed": 86128937,
"true_count": 1
},
"seed": 86128937,
"task_id": 686128937,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. 新加坡的货币是新加坡元。
B. ((283是斐波那契数。) and (肯尼亚的首都是内罗毕。)) and ((十二月有31天。) and ((-10 + 0) > (6 % 7)))
C. not (not ((2 * -4 - 4 * 9) != (7 + 0)))
D. not ((加拿大位于北美洲。) or (企鹅能飞翔。))
E. (1900年奥运会在巴黎举办。) or (((1 ** 2) > (-7 * -16)) or ((-8 * 8 * 6 * -6) <= (-6 - -9)))
F. (50 % 7) == (12 + -18)
G. (4 ** 2) <= (-5 * -5 - -6 * -9)
H. (((3 % 4) >= (20 - -17)) or (铁在常温下是固体。)) and (((27 % 5) > (-6 + -8)) or ((9 % 8) > (-10 + -8)))
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,C,E,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 69403958,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. 新加坡的货币是新加坡元。\nB. ((283是斐波那契数。) and (肯尼亚的首都是内罗毕。)) and ((十二月有31天。) and ((-10 + 0) > (6 % 7)))\nC. not (not ((2 * -4 - 4 * 9) != (7 + 0)))\nD. not ((加拿大位于北美洲。) or (企鹅能飞翔。))\nE. (1900年奥运会在巴黎举办。) or (((1 ** 2) > (-7 * -16)) or ((-8 * 8 * 6 * -6) <= (-6 - -9)))\nF. (50 % 7) == (12 + -18)\nG. (4 ** 2) <= (-5 * -5 - -6 * -9)\nH. (((3 % 4) >= (20 - -17)) or (铁在常温下是固体。)) and (((27 % 5) > (-6 + -8)) or ((9 % 8) > (-10 + -8)))\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": 8,
"seed": 69403958,
"true_count": 4
},
"seed": 69403958,
"task_id": 669403958,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. ((((-2 * 1) > (5 ** 1)) and ((1 * -8 + -9 * -5) > (15 + 14))) and (埃及位于非洲。)) and (((not not (2082年是闰年。)) and (((-11 + 12) < (-9 * 9 - 0 * 10)) and ((2 * -4 + 5 * -9) >= (4 ** 1)))) or (not not (冰在常温下是固体。)) or (((金鱼是鱼类。) and ((5 ** 3) >= (-2 * 1 + 5 * -3))) and ((哥伦布到达美洲发生在1492年。) and ((12 + -17) > (-16 - 11)))))
B. ((考拉是鱼类。) and (((-16 - -1) <= (0 * 10 + -7 * -9)) or (((-5 * 4 * -9 * 5) >= (-12 + -8)) and ((17 + -2) != (11 + -15))))) or (not not (((声音无法在真空中传播。) and (美国的货币是美元。)) or ((13是质数。) and ((-4 * 6 - -10 * -3) > (4 % 5)))))
C. not not (((菲律宾的货币是澳元。) or (((-10 + 9) <= (-12 * 10) <= (9 * -10 - -6 * 6)) and (1937年是闰年。))) and (not not ((1996年奥运会在首尔举办。) and ((-9 * 10 - -3 * 5) <= (-9 - 11)))))
D. ((((-1 * -2 * 4 * -2) <= (-2 * -2 - -2 * 0)) or (not ((5 ** 1) >= (-17 + 9)))) and (((-2 - -3) == (15 - -4)) or (猪有4条腿。))) and ((((0 * 4 + 1 * -5) != (1 ** 2)) or (法国大革命开始发生在1789年。)) or ((1952年奥运会在赫尔辛基举办。) or ((-4 * -1 * 1 * 7) == (5 - 18)))) and (((龙虾有10条腿。) and (((18 % 4) <= (-16 + 7) <= (5 ** 1)) and ((49 % 9) < (15 - 3)))) and (not not ((-6 * 2) <= (14 - 18) <= (-13 - 15))))
E. (not not ((-2 - -9) <= (-6 - -12))) or (not ((水蒸气在常温下是气体。) and (not (中国的首都是北京。))))
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": "B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 69823581,
"true_count": 2
},
"question": "给定以下布尔表达式：\n\nA. ((((-2 * 1) > (5 ** 1)) and ((1 * -8 + -9 * -5) > (15 + 14))) and (埃及位于非洲。)) and (((not not (2082年是闰年。)) and (((-11 + 12) < (-9 * 9 - 0 * 10)) and ((2 * -4 + 5 * -9) >= (4 ** 1)))) or (not not (冰在常温下是固体。)) or (((金鱼是鱼类。) and ((5 ** 3) >= (-2 * 1 + 5 * -3))) and ((哥伦布到达美洲发生在1492年。) and ((12 + -17) > (-16 - 11)))))\nB. ((考拉是鱼类。) and (((-16 - -1) <= (0 * 10 + -7 * -9)) or (((-5 * 4 * -9 * 5) >= (-12 + -8)) and ((17 + -2) != (11 + -15))))) or (not not (((声音无法在真空中传播。) and (美国的货币是美元。)) or ((13是质数。) and ((-4 * 6 - -10 * -3) > (4 % 5)))))\nC. not not (((菲律宾的货币是澳元。) or (((-10 + 9) <= (-12 * 10) <= (9 * -10 - -6 * 6)) and (1937年是闰年。))) and (not not ((1996年奥运会在首尔举办。) and ((-9 * 10 - -3 * 5) <= (-9 - 11)))))\nD. ((((-1 * -2 * 4 * -2) <= (-2 * -2 - -2 * 0)) or (not ((5 ** 1) >= (-17 + 9)))) and (((-2 - -3) == (15 - -4)) or (猪有4条腿。))) and ((((0 * 4 + 1 * -5) != (1 ** 2)) or (法国大革命开始发生在1789年。)) or ((1952年奥运会在赫尔辛基举办。) or ((-4 * -1 * 1 * 7) == (5 - 18)))) and (((龙虾有10条腿。) and (((18 % 4) <= (-16 + 7) <= (5 ** 1)) and ((49 % 9) < (15 - 3)))) and (not not ((-6 * 2) <= (14 - 18) <= (-13 - 15))))\nE. (not not ((-2 - -9) <= (-6 - -12))) or (not ((水蒸气在常温下是气体。) and (not (中国的首都是北京。))))\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": 4,
"language": "cn",
"num_options": 5,
"seed": 69823581,
"true_count": 2
},
"seed": 69823581,
"task_id": 669823581,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. not ((((((法国的首都是巴黎。) or ((-8 * -5) < (40 % 1))) or (not not (水蒸气在常温下是气体。))) or ((壁虎是爬行动物。) or (水蒸气在常温下是固体。))) and (((((8 * 10 * 3 * 4) > (9 - 16)) and ((9 * -18) == (-5 * -16))) and ((-5 - 7) < (0 * -3 - 2 * -8) < (-5 * -1))) and ((((1 ** 3) == (-6 * -15)) and (人类有三个肺。)) or ((8 + -4) <= (35 % 1))))) or ((not (not not (not not (意大利的首都是巴黎。)))) and ((not not (酒精在常温下是固体。)) and (46小于等于56。)) and (((36 % 1) != (30 % 4)) and (蜘蛛是昆虫。))))
B. (not not (not ((水蒸气在常温下是气体。) and ((16 * 4) < (7 * -10))))) and (not ((not not ((鸟有8条腿。) or ((1 ** 1) == (-13 + 2)))) and (not not (苏联解体发生在1991年。))))
C. (not not ((not not (((49 % 6) != (5 ** 2)) or (((-5 + -8) == (3 - 0)) and ((-1 * -19) != (16 * 15))))) and (not not (not (((7 - 6) < (-15 * -3)) or (意大利位于北美洲。)))))) and (((((not not (伦敦大火发生在1668年。)) or ((-3 + 15) < (19 - -16))) and ((新西兰位于大洋洲。) or (俄罗斯位于欧洲。)) and ((-11 + -9) < (1 + -7))) and ((泰坦尼克号沉没发生在1914年。) and (not ((11 - -3) == (5 ** 3))))) or ((((2 * 10 - -6 * -7) >= (5 ** 2)) or (not (莱特兄弟首次飞行发生在1905年。))) and (not not (not not (钙的化学符号是S。)))))
D. not ((((not not ((金星是距离太阳第6近的行星。) or ((-20 + 3) <= (42 % 9)))) and ((波兰的首都是北京。) and (((4 ** 3) < (-15 - 9) < (-17 * 12)) or (一月有31天。)))) or ((10 * -17) > (37 % 8)) or ((not (116是偶数。)) and ((not not ((-4 + 12) < (0 + 11))) and (not not (意大利位于欧洲。))))) or ((not (not (((26 % 1) < (-10 * -4 + 3 * 4)) or (巴西的首都是巴西利亚。)))) and ((0 - -8) <= (-8 - 5)) and ((1972年奥运会在慕尼黑举办。) or ((33大于27。) and ((14 - 19) <= (17 * -18) <= (20 % 5))))))
E. not ((not ((汞在常温下是液体。) or (四月有30天。))) and (not not (哥伦比亚的货币是日元。)) and (not (not not (1956年奥运会在墨尔本举办。))))
F. not (not (not ((not (not (智利位于南极洲。))) and (墨西哥位于北美洲。) and (俄罗斯的首都是北京。))))
G. not (((not ((鸭子是鸟类。) or (((-2 - -6) <= (-18 - -12)) and (地球是距离太阳第1近的行星。)))) or ((-7 * -9 - -8 * -1) != (3 ** 3)) or (((not ((21 % 2) <= (19 + -10))) or ((3 ** 3) >= (-16 * 4))) or ((1936年奥运会在柏林举办。) and (((5 ** 3) == (2 + -18)) or (铀的化学符号是Mg。))))) or ((not not ((-9 + 20) > (-2 * -13))) and (not ((not not (猫头鹰是爬行动物。)) or (巴西位于南极洲。)))))
H. (not not ((not not (1935年是闰年。)) or (((((-3 * -3 * -3 * -5) == (-20 + -1)) or (金在常温下是固体。)) and (冰在常温下是固体。)) or (not ((蚂蚁是昆虫。) or ((-6 + -7) == (1 * 5 * -7 * 7))))))) and ((((not ((-5 * 1 * -8 * 5) == (23 % 1))) or ((((1 ** 1) > (18 + 18)) and (金星是距离太阳第3近的行星。)) or (not (汞的化学符号是Hg。)))) or ((((加拿大的首都是巴黎。) and ((14 * -20) <= (-20 * 11) <= (9 * 9 - 8 * 8))) and (1952年奥运会在巴黎举办。)) and (not ((-4 * -8) == (1 ** 2))))) and (not ((not not (not (火星是距离太阳最近的行星。))) or (铂的化学符号是Pt。))))
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": "A,B,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 33730658,
"true_count": 5
},
"question": "分析以下逻辑表达式：\n\nA. not ((((((法国的首都是巴黎。) or ((-8 * -5) < (40 % 1))) or (not not (水蒸气在常温下是气体。))) or ((壁虎是爬行动物。) or (水蒸气在常温下是固体。))) and (((((8 * 10 * 3 * 4) > (9 - 16)) and ((9 * -18) == (-5 * -16))) and ((-5 - 7) < (0 * -3 - 2 * -8) < (-5 * -1))) and ((((1 ** 3) == (-6 * -15)) and (人类有三个肺。)) or ((8 + -4) <= (35 % 1))))) or ((not (not not (not not (意大利的首都是巴黎。)))) and ((not not (酒精在常温下是固体。)) and (46小于等于56。)) and (((36 % 1) != (30 % 4)) and (蜘蛛是昆虫。))))\nB. (not not (not ((水蒸气在常温下是气体。) and ((16 * 4) < (7 * -10))))) and (not ((not not ((鸟有8条腿。) or ((1 ** 1) == (-13 + 2)))) and (not not (苏联解体发生在1991年。))))\nC. (not not ((not not (((49 % 6) != (5 ** 2)) or (((-5 + -8) == (3 - 0)) and ((-1 * -19) != (16 * 15))))) and (not not (not (((7 - 6) < (-15 * -3)) or (意大利位于北美洲。)))))) and (((((not not (伦敦大火发生在1668年。)) or ((-3 + 15) < (19 - -16))) and ((新西兰位于大洋洲。) or (俄罗斯位于欧洲。)) and ((-11 + -9) < (1 + -7))) and ((泰坦尼克号沉没发生在1914年。) and (not ((11 - -3) == (5 ** 3))))) or ((((2 * 10 - -6 * -7) >= (5 ** 2)) or (not (莱特兄弟首次飞行发生在1905年。))) and (not not (not not (钙的化学符号是S。)))))\nD. not ((((not not ((金星是距离太阳第6近的行星。) or ((-20 + 3) <= (42 % 9)))) and ((波兰的首都是北京。) and (((4 ** 3) < (-15 - 9) < (-17 * 12)) or (一月有31天。)))) or ((10 * -17) > (37 % 8)) or ((not (116是偶数。)) and ((not not ((-4 + 12) < (0 + 11))) and (not not (意大利位于欧洲。))))) or ((not (not (((26 % 1) < (-10 * -4 + 3 * 4)) or (巴西的首都是巴西利亚。)))) and ((0 - -8) <= (-8 - 5)) and ((1972年奥运会在慕尼黑举办。) or ((33大于27。) and ((14 - 19) <= (17 * -18) <= (20 % 5))))))\nE. not ((not ((汞在常温下是液体。) or (四月有30天。))) and (not not (哥伦比亚的货币是日元。)) and (not (not not (1956年奥运会在墨尔本举办。))))\nF. not (not (not ((not (not (智利位于南极洲。))) and (墨西哥位于北美洲。) and (俄罗斯的首都是北京。))))\nG. not (((not ((鸭子是鸟类。) or (((-2 - -6) <= (-18 - -12)) and (地球是距离太阳第1近的行星。)))) or ((-7 * -9 - -8 * -1) != (3 ** 3)) or (((not ((21 % 2) <= (19 + -10))) or ((3 ** 3) >= (-16 * 4))) or ((1936年奥运会在柏林举办。) and (((5 ** 3) == (2 + -18)) or (铀的化学符号是Mg。))))) or ((not not ((-9 + 20) > (-2 * -13))) and (not ((not not (猫头鹰是爬行动物。)) or (巴西位于南极洲。)))))\nH. (not not ((not not (1935年是闰年。)) or (((((-3 * -3 * -3 * -5) == (-20 + -1)) or (金在常温下是固体。)) and (冰在常温下是固体。)) or (not ((蚂蚁是昆虫。) or ((-6 + -7) == (1 * 5 * -7 * 7))))))) and ((((not ((-5 * 1 * -8 * 5) == (23 % 1))) or ((((1 ** 1) > (18 + 18)) and (金星是距离太阳第3近的行星。)) or (not (汞的化学符号是Hg。)))) or ((((加拿大的首都是巴黎。) and ((14 * -20) <= (-20 * 11) <= (9 * 9 - 8 * 8))) and (1952年奥运会在巴黎举办。)) and (not ((-4 * -8) == (1 ** 2))))) and (not ((not not (not (火星是距离太阳最近的行星。))) or (铂的化学符号是Pt。))))\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": 6,
"language": "cn",
"num_options": 8,
"seed": 33730658,
"true_count": 5
},
"seed": 33730658,
"task_id": 633730658,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not ((5 % 1) >= (-1 * 8 * -10 * -10))
B. The capital of Vietnam is Hanoi.
C. (not not (Germany is in Europe.)) or ((The capital of Ukraine is Tokyo.) and (A flamingo is a bird.))
D. (16 + 12) < (-3 * -8 - -9 * 10)
E. 126 is a perfect square.
F. not (not ((2 ** 2) <= (-16 * 0)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 68541308,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. not ((5 % 1) >= (-1 * 8 * -10 * -10))\nB. The capital of Vietnam is Hanoi.\nC. (not not (Germany is in Europe.)) or ((The capital of Ukraine is Tokyo.) and (A flamingo is a bird.))\nD. (16 + 12) < (-3 * -8 - -9 * 10)\nE. 126 is a perfect square.\nF. not (not ((2 ** 2) <= (-16 * 0)))\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": 68541308,
"true_count": 3
},
"seed": 68541308,
"task_id": 668541308,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (-6 - 6) != (-9 + 19)
B. (not not ((2 ** 2) != (1 ** 1))) or ((15 * -11) < (16 - 6))
C. Diamonds are made of carbon.
D. (not not ((48 % 4) == (-9 * 5 + -5 * -6))) or (((1 * -6 + -3 * -1) > (3 ** 3)) and ((0 * 5) <= (-18 - 8)))
E. (The Berlin Wall fell occurred in 1989.) and ((The 1956 Olympics were held in Los Angeles.) and ((-3 * -7 + 10 * 1) < (2 ** 1)))
F. (-11 - -18) > (-2 * -18)
G. not not (not (The chemical symbol for Nickel is Pb.))
H. ((15 * 9) <= (-7 + 2) <= (39 % 1)) and (not ((2 ** 1) >= (-6 * -20)))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,B,C,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 57170625,
"true_count": 4
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (-6 - 6) != (-9 + 19)\nB. (not not ((2 ** 2) != (1 ** 1))) or ((15 * -11) < (16 - 6))\nC. Diamonds are made of carbon.\nD. (not not ((48 % 4) == (-9 * 5 + -5 * -6))) or (((1 * -6 + -3 * -1) > (3 ** 3)) and ((0 * 5) <= (-18 - 8)))\nE. (The Berlin Wall fell occurred in 1989.) and ((The 1956 Olympics were held in Los Angeles.) and ((-3 * -7 + 10 * 1) < (2 ** 1)))\nF. (-11 - -18) > (-2 * -18)\nG. not not (not (The chemical symbol for Nickel is Pb.))\nH. ((15 * 9) <= (-7 + 2) <= (39 % 1)) and (not ((2 ** 1) >= (-6 * -20)))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 57170625,
"true_count": 4
},
"seed": 57170625,
"task_id": 657170625,
"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 (((氖的化学符号是Ag。) or ((氯的化学符号是Cl。) and (1955年是闰年。))) or (196的平方根是14。) or (((-14 - 9) == (1 % 8)) and (not (铂的化学符号是Pt。))))) or (not (not not ((((-12 + -7) > (10 * 2)) and (39是质数。)) and (印度位于亚洲。))))) or (not not ((((not not (印度位于大洋洲。)) or ((3 * 8) <= (-19 - 13))) or ((木星是距离太阳第5近的行星。) or ((1 ** 2) != (-5 - -16))) or (章鱼有10条腿。)) and ((现代奥运会首届举办发生在1895年。) or (瑞典的首都是斯德哥尔摩。)) and ((not not ((-2 - -2) == (-4 + -10))) and (not not ((-11 - -6) < (1 ** 1))) and (not not (海王星是距离太阳第5近的行星。)))))
B. (not (not (not not ((not not (伦敦大火发生在1676年。)) and (蚂蚁是昆虫。))))) and (not ((((0 * 9 * 9 * 4) != (40 % 2)) and ((2 * -7 - -10 * -1) != (-10 * -9 * -10 * 4))) or (not ((5 % 4) < (-9 + -19)))))
C. (not not ((((not ((-14 + 6) == (16 + -11))) and ((韩国的货币是卢布。) and (袋鼠是哺乳动物。))) or ((not not ((20 - 14) <= (3 - -15))) or ((第一次世界大战结束发生在1918年。) and ((4 ** 2) < (28 % 3) < (1 ** 2))))) or ((法国大革命开始发生在1788年。) or ((47 % 7) >= (8 + -17))))) or (not ((not (闪电不会两次击中同一个地方。)) or ((((1968年奥运会在墨西哥城举办。) or (八月有31天。)) and ((2022年是闰年。) and (柏林墙倒塌发生在1988年。))) and (海王星是距离太阳第8近的行星。))))
D. (not ((not (not not (智利的货币是索尔。))) and (not not (not (光速约为每秒30万公里。))))) or (not not (((not not (章鱼有8条腿。)) and (not not (天王星是距离太阳第6近的行星。)) and ((2 * -8 + 5 * 7) != (-18 - 4))) and ((((埃及的首都是阿布贾。) or (第一次世界大战开始发生在1914年。)) and (not not ((-10 + -17) <= (11 + 12)))) and (((鹦鹉是鸟类。) or (蚂蚁有6条腿。)) or (not ((-1 + -11) < (0 + -9)))))))
E. not not ((((((阿根廷位于南美洲。) or (2003年是闰年。)) or ((地球是距离太阳第6近的行星。) or (镍的化学符号是Ni。))) and (法国的首都是哈瓦那。)) or ((((15 + -4) <= (7 % 4)) or (((19 + 17) <= (-9 * -1 - 4 * -9) <= (-4 + 16)) and ((-16 * 2) == (-4 * 7 * -9 * -3)))) or ((金星是距离太阳第3近的行星。) and ((7 + -17) >= (-14 - -12))) or (not not ((巴西位于南美洲。) or (蝴蝶有6条腿。))))) and ((not ((13 + -1) != (-9 - -7))) and (not (瑞典的货币是克朗。)) and (声音无法在真空中传播。)) and (not not (not (((地球上一天是24小时。) or (金星是距离太阳第2近的行星。)) and ((地球是距离太阳第3近的行星。) or ((-12 - 12) < (-2 + 1)))))))
F. (not not (not ((((水星是距离太阳第1近的行星。) or (埃及的首都是开罗。)) or ((鸭子有4条腿。) and (1963年是闰年。))) and (((-20 * -7) > (-16 - -7)) or (韩国的首都是内罗毕。)) and (not not (沙特阿拉伯位于欧洲。))))) or (not (not not ((2 * -4 * 0 * -4) <= (12 * 5)))) or ((not (((not not ((-9 + 4) != (28 % 7))) and ((18 + 2) >= (-3 + 11))) or ((not not (地球是距离太阳第3近的行星。)) or (((1 * 9 + -10 * 5) <= (2 ** 3)) or ((2 - 20) < (-7 - -1)))))) and (not not (not (意大利位于欧洲。))))
G. not (((not (挪威的货币是克朗。)) or ((((1984年奥运会在洛杉矶举办。) and ((16 % 5) <= (20 % 5))) or (((8 * -4 * 2 * -6) > (-11 + 14)) and (新西兰位于亚洲。))) and ((7 * 18) < (43 % 5) < (-16 + -14)) and (中国的首都是加拉加斯。))) and (not ((((1964年奥运会在巴黎举办。) and (氧气在常温下是气体。)) or (((-6 * -1 - 9 * -8) < (-8 - -8)) and (196的平方根是2。))) and (十二月有30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。 | {
"game_data": {
"answer": "A,C,D,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 7,
"seed": 552567,
"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. ((not not (((氖的化学符号是Ag。) or ((氯的化学符号是Cl。) and (1955年是闰年。))) or (196的平方根是14。) or (((-14 - 9) == (1 % 8)) and (not (铂的化学符号是Pt。))))) or (not (not not ((((-12 + -7) > (10 * 2)) and (39是质数。)) and (印度位于亚洲。))))) or (not not ((((not not (印度位于大洋洲。)) or ((3 * 8) <= (-19 - 13))) or ((木星是距离太阳第5近的行星。) or ((1 ** 2) != (-5 - -16))) or (章鱼有10条腿。)) and ((现代奥运会首届举办发生在1895年。) or (瑞典的首都是斯德哥尔摩。)) and ((not not ((-2 - -2) == (-4 + -10))) and (not not ((-11 - -6) < (1 ** 1))) and (not not (海王星是距离太阳第5近的行星。)))))\nB. (not (not (not not ((not not (伦敦大火发生在1676年。)) and (蚂蚁是昆虫。))))) and (not ((((0 * 9 * 9 * 4) != (40 % 2)) and ((2 * -7 - -10 * -1) != (-10 * -9 * -10 * 4))) or (not ((5 % 4) < (-9 + -19)))))\nC. (not not ((((not ((-14 + 6) == (16 + -11))) and ((韩国的货币是卢布。) and (袋鼠是哺乳动物。))) or ((not not ((20 - 14) <= (3 - -15))) or ((第一次世界大战结束发生在1918年。) and ((4 ** 2) < (28 % 3) < (1 ** 2))))) or ((法国大革命开始发生在1788年。) or ((47 % 7) >= (8 + -17))))) or (not ((not (闪电不会两次击中同一个地方。)) or ((((1968年奥运会在墨西哥城举办。) or (八月有31天。)) and ((2022年是闰年。) and (柏林墙倒塌发生在1988年。))) and (海王星是距离太阳第8近的行星。))))\nD. (not ((not (not not (智利的货币是索尔。))) and (not not (not (光速约为每秒30万公里。))))) or (not not (((not not (章鱼有8条腿。)) and (not not (天王星是距离太阳第6近的行星。)) and ((2 * -8 + 5 * 7) != (-18 - 4))) and ((((埃及的首都是阿布贾。) or (第一次世界大战开始发生在1914年。)) and (not not ((-10 + -17) <= (11 + 12)))) and (((鹦鹉是鸟类。) or (蚂蚁有6条腿。)) or (not ((-1 + -11) < (0 + -9)))))))\nE. not not ((((((阿根廷位于南美洲。) or (2003年是闰年。)) or ((地球是距离太阳第6近的行星。) or (镍的化学符号是Ni。))) and (法国的首都是哈瓦那。)) or ((((15 + -4) <= (7 % 4)) or (((19 + 17) <= (-9 * -1 - 4 * -9) <= (-4 + 16)) and ((-16 * 2) == (-4 * 7 * -9 * -3)))) or ((金星是距离太阳第3近的行星。) and ((7 + -17) >= (-14 - -12))) or (not not ((巴西位于南美洲。) or (蝴蝶有6条腿。))))) and ((not ((13 + -1) != (-9 - -7))) and (not (瑞典的货币是克朗。)) and (声音无法在真空中传播。)) and (not not (not (((地球上一天是24小时。) or (金星是距离太阳第2近的行星。)) and ((地球是距离太阳第3近的行星。) or ((-12 - 12) < (-2 + 1)))))))\nF. (not not (not ((((水星是距离太阳第1近的行星。) or (埃及的首都是开罗。)) or ((鸭子有4条腿。) and (1963年是闰年。))) and (((-20 * -7) > (-16 - -7)) or (韩国的首都是内罗毕。)) and (not not (沙特阿拉伯位于欧洲。))))) or (not (not not ((2 * -4 * 0 * -4) <= (12 * 5)))) or ((not (((not not ((-9 + 4) != (28 % 7))) and ((18 + 2) >= (-3 + 11))) or ((not not (地球是距离太阳第3近的行星。)) or (((1 * 9 + -10 * 5) <= (2 ** 3)) or ((2 - 20) < (-7 - -1)))))) and (not not (not (意大利位于欧洲。))))\nG. not (((not (挪威的货币是克朗。)) or ((((1984年奥运会在洛杉矶举办。) and ((16 % 5) <= (20 % 5))) or (((8 * -4 * 2 * -6) > (-11 + 14)) and (新西兰位于亚洲。))) and ((7 * 18) < (43 % 5) < (-16 + -14)) and (中国的首都是加拉加斯。))) and (not ((((1964年奥运会在巴黎举办。) and (氧气在常温下是气体。)) or (((-6 * -1 - 9 * -8) < (-8 - -8)) and (196的平方根是2。))) and (十二月有30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。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 7,
"seed": 552567,
"true_count": 5
},
"seed": 552567,
"task_id": 600552567,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (0 + 20) <= (3 + 20)
B. not not (((3 * -7 * -5 * 2) < (-12 * -6)) or ((8 - 8) == (-6 * -6 * -3 * 1)))
C. (7 * 4 + -9 * 2) <= (-7 + 6)
D. ((9 * 2 + 0 * 6) < (6 * 9 + -4 * -7) < (-19 * 19)) or ((地球是距离太阳第2近的行星。) or (木星是距离太阳第6近的行星。))
E. (哥伦比亚位于欧洲。) and (not ((3 * 5 * 10 * 10) <= (9 - -13)))
F. (0 * -3 * 3 * 1) != (23 % 5)
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 37538560,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. (0 + 20) <= (3 + 20)\nB. not not (((3 * -7 * -5 * 2) < (-12 * -6)) or ((8 - 8) == (-6 * -6 * -3 * 1)))\nC. (7 * 4 + -9 * 2) <= (-7 + 6)\nD. ((9 * 2 + 0 * 6) < (6 * 9 + -4 * -7) < (-19 * 19)) or ((地球是距离太阳第2近的行星。) or (木星是距离太阳第6近的行星。))\nE. (哥伦比亚位于欧洲。) and (not ((3 * 5 * 10 * 10) <= (9 - -13)))\nF. (0 * -3 * 3 * 1) != (23 % 5)\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": 6,
"seed": 37538560,
"true_count": 2
},
"seed": 37538560,
"task_id": 637538560,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not ((The chemical symbol for Cobalt is Al.) or (not (Uranus is the 7th planet from the Sun.)))
B. not (not not (not not (Air is a gas at room temperature.)))
C. not (((5 ** 3) == (-4 - -11)) and (78 is an odd number.))
D. ((-19 + 16) > (30 % 7)) and (2045 is a leap year.) and ((-1 - 19) < (12 * 8))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 15032749,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. not ((The chemical symbol for Cobalt is Al.) or (not (Uranus is the 7th planet from the Sun.)))\nB. not (not not (not not (Air is a gas at room temperature.)))\nC. not (((5 ** 3) == (-4 - -11)) and (78 is an odd number.))\nD. ((-19 + 16) > (30 % 7)) and (2045 is a leap year.) and ((-1 - 19) < (12 * 8))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 15032749,
"true_count": 2
},
"seed": 15032749,
"task_id": 615032749,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not (((The capital of Malaysia is Ankara.) or ((0 + 18) < (19 * -5))) and (((5 * 2 + 2 * -4) >= (37 % 9)) and (The currency of Japan is the Shekel.)))
B. ((-7 * -2 + 2 * -7) > (-16 - -18)) and ((The chemical symbol for Hydrogen is H.) or ((The capital of Kenya is Nairobi.) or (The currency of Israel is the Shekel.)))
C. not not (((The Pacific Ocean is the largest ocean.) or ((3 ** 3) < (7 * -2 + -9 * -3) < (-15 - 16))) or (((-9 * -17) < (8 * -10 - 6 * -10)) and (The capital of Ireland is Ankara.)))
D. not (not not (The chemical symbol for Copper is Fe.))
E. not not (not ((-6 + 0) != (10 * -12)))
F. (((The capital of Germany is New Delhi.) or (The 2012 Olympics were held in Montreal.)) and (The square root of 169 is 13.)) or (Mars is the 4th planet from the Sun.)
G. (not not ((13 - 3) <= (-5 * -8 - 2 * -8))) or ((not ((3 ** 1) > (20 - 10))) or (not ((1 ** 3) < (28 % 6))))
H. not (not (not ((2 * 9 - -10 * 6) <= (2 * -2 + 4 * 6))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,C,D,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 76999767,
"true_count": 6
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not (((The capital of Malaysia is Ankara.) or ((0 + 18) < (19 * -5))) and (((5 * 2 + 2 * -4) >= (37 % 9)) and (The currency of Japan is the Shekel.)))\nB. ((-7 * -2 + 2 * -7) > (-16 - -18)) and ((The chemical symbol for Hydrogen is H.) or ((The capital of Kenya is Nairobi.) or (The currency of Israel is the Shekel.)))\nC. not not (((The Pacific Ocean is the largest ocean.) or ((3 ** 3) < (7 * -2 + -9 * -3) < (-15 - 16))) or (((-9 * -17) < (8 * -10 - 6 * -10)) and (The capital of Ireland is Ankara.)))\nD. not (not not (The chemical symbol for Copper is Fe.))\nE. not not (not ((-6 + 0) != (10 * -12)))\nF. (((The capital of Germany is New Delhi.) or (The 2012 Olympics were held in Montreal.)) and (The square root of 169 is 13.)) or (Mars is the 4th planet from the Sun.)\nG. (not not ((13 - 3) <= (-5 * -8 - 2 * -8))) or ((not ((3 ** 1) > (20 - 10))) or (not ((1 ** 3) < (28 % 6))))\nH. not (not (not ((2 * 9 - -10 * 6) <= (2 * -2 + 4 * 6))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 76999767,
"true_count": 6
},
"seed": 76999767,
"task_id": 676999767,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (not ((((-9 * 6 * -4 * 8) < (9 - -19) < (10 % 3)) or ((-12 * 13) <= (7 - 1) <= (-14 + 12))) and ((1988年奥运会在首尔举办。) and ((-9 * 0 * 9 * -1) != (-18 - 7))))) or ((意大利的首都是新德里。) or (not not (1908年奥运会在伦敦举办。))) or ((not (not not ((1 * -5) < (8 * -9 - -8 * 1) < (-20 + -4)))) and ((((-13 + -8) >= (-6 * 7)) or (1999年是闰年。)) or (((1 ** 2) < (-6 * 3 + 3 * -7)) and (镁的化学符号是Mg。))))
B. not not ((七月有31天。) or ((((4 ** 1) >= (1 ** 1)) and (加拿大的首都是哥本哈根。)) or (not (钾的化学符号是K。))))
C. ((((蜘蛛是昆虫。) and (823是斐波那契数。)) or (铬的化学符号是Na。)) and (((1911年是闰年。) or ((-7 - 17) <= (5 + -14) <= (-18 * -16))) and ((2030年是闰年。) or ((33 % 4) > (8 + 9))))) and ((not (not not (天王星是距离太阳第1近的行星。))) or (not ((40大于8。) and ((11 - -16) == (0 * 0)))))
D. (not ((2 * -6 * 10 * -2) <= (7 - 9) <= (-2 * -6 * -6 * 10))) or (((((0 - 3) < (14 * 0)) or (墨西哥位于北美洲。)) and (((-14 * 2) >= (-18 * -2)) and (火星是距离太阳第4近的行星。))) or (not (第一部iPhone发布发生在2007年。)) or (((荷兰的首都是阿姆斯特丹。) or ((11 % 9) != (1 * 7 * 3 * -7))) and (((6 * -15) <= (-9 * -7 - -3 * -10)) and (汞在常温下是液体。))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 99936446,
"true_count": 3
},
"question": "审视以下逻辑表达式：\n\nA. (not ((((-9 * 6 * -4 * 8) < (9 - -19) < (10 % 3)) or ((-12 * 13) <= (7 - 1) <= (-14 + 12))) and ((1988年奥运会在首尔举办。) and ((-9 * 0 * 9 * -1) != (-18 - 7))))) or ((意大利的首都是新德里。) or (not not (1908年奥运会在伦敦举办。))) or ((not (not not ((1 * -5) < (8 * -9 - -8 * 1) < (-20 + -4)))) and ((((-13 + -8) >= (-6 * 7)) or (1999年是闰年。)) or (((1 ** 2) < (-6 * 3 + 3 * -7)) and (镁的化学符号是Mg。))))\nB. not not ((七月有31天。) or ((((4 ** 1) >= (1 ** 1)) and (加拿大的首都是哥本哈根。)) or (not (钾的化学符号是K。))))\nC. ((((蜘蛛是昆虫。) and (823是斐波那契数。)) or (铬的化学符号是Na。)) and (((1911年是闰年。) or ((-7 - 17) <= (5 + -14) <= (-18 * -16))) and ((2030年是闰年。) or ((33 % 4) > (8 + 9))))) and ((not (not not (天王星是距离太阳第1近的行星。))) or (not ((40大于8。) and ((11 - -16) == (0 * 0)))))\nD. (not ((2 * -6 * 10 * -2) <= (7 - 9) <= (-2 * -6 * -6 * 10))) or (((((0 - 3) < (14 * 0)) or (墨西哥位于北美洲。)) and (((-14 * 2) >= (-18 * -2)) and (火星是距离太阳第4近的行星。))) or (not (第一部iPhone发布发生在2007年。)) or (((荷兰的首都是阿姆斯特丹。) or ((11 % 9) != (1 * 7 * 3 * -7))) and (((6 * -15) <= (-9 * -7 - -3 * -10)) and (汞在常温下是液体。))))\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": 4,
"seed": 99936446,
"true_count": 3
},
"seed": 99936446,
"task_id": 699936446,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not ((9 + 17) <= (5 + 7) <= (-10 * 20))) or ((Jupiter is the 3rd planet from the Sun.) or (Water is a gas at room temperature.))
B. not (not (Oxygen is a gas at room temperature.))
C. (((8 * 10 - 2 * -10) != (4 + 20)) or ((50 % 7) == (49 % 9))) or (((3 ** 1) == (-2 * 3 + -9 * 7)) and (88 is less than or equal to 31.))
D. (((4 - -20) <= (15 + 13)) and (The 1960 Olympics were held in Rome.)) or (not not ((-2 * -19) != (-2 + 7)))
E. ((Venus is the 3rd planet from the Sun.) or (473 is a Fibonacci number.)) and ((7 + -4) < (26 % 4))
F. (Light travels faster than sound.) and (((32 % 4) < (-12 * -1)) and (The capital of Norway is Oslo.))
G. (not (Light travels faster than sound.)) or (((2 * -6 - 1 * -7) != (3 ** 1)) and ((33 % 10) != (-16 + -19)))
H. (((8 * 0 - -10 * 3) < (-8 * 6 - -7 * 7) < (2 * 4 - 4 * 7)) and ((1 - -15) > (-10 * -4))) or (((-3 * 11) == (-3 - 20)) or ((3 * -10 + -9 * 5) != (3 * -18)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C,D,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 34960874,
"true_count": 7
},
"question": "Study the following logical statements:\n\nA. (not ((9 + 17) <= (5 + 7) <= (-10 * 20))) or ((Jupiter is the 3rd planet from the Sun.) or (Water is a gas at room temperature.))\nB. not (not (Oxygen is a gas at room temperature.))\nC. (((8 * 10 - 2 * -10) != (4 + 20)) or ((50 % 7) == (49 % 9))) or (((3 ** 1) == (-2 * 3 + -9 * 7)) and (88 is less than or equal to 31.))\nD. (((4 - -20) <= (15 + 13)) and (The 1960 Olympics were held in Rome.)) or (not not ((-2 * -19) != (-2 + 7)))\nE. ((Venus is the 3rd planet from the Sun.) or (473 is a Fibonacci number.)) and ((7 + -4) < (26 % 4))\nF. (Light travels faster than sound.) and (((32 % 4) < (-12 * -1)) and (The capital of Norway is Oslo.))\nG. (not (Light travels faster than sound.)) or (((2 * -6 - 1 * -7) != (3 ** 1)) and ((33 % 10) != (-16 + -19)))\nH. (((8 * 0 - -10 * 3) < (-8 * 6 - -7 * 7) < (2 * 4 - 4 * 7)) and ((1 - -15) > (-10 * -4))) or (((-3 * 11) == (-3 - 20)) or ((3 * -10 + -9 * 5) != (3 * -18)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 34960874,
"true_count": 7
},
"seed": 34960874,
"task_id": 634960874,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not ((1948年奥运会在伦敦举办。) or (第一次世界大战结束发生在1928年。))
B. 氧气对人类生存是必需的。
C. 西班牙的首都是哥本哈根。
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 60268878,
"true_count": 1
},
"question": "检验这些表达式：\n\nA. not ((1948年奥运会在伦敦举办。) or (第一次世界大战结束发生在1928年。))\nB. 氧气对人类生存是必需的。\nC. 西班牙的首都是哥本哈根。\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": 3,
"seed": 60268878,
"true_count": 1
},
"seed": 60268878,
"task_id": 660268878,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. (not not ((10 * 3) != (-19 + 13))) or (((-13 * -1) > (17 * -9)) and (not ((-14 - 16) <= (-4 * -5 - 2 * 7) <= (10 * -8 + 3 * -4))))
B. ((((0 - 6) >= (1 ** 1)) or ((-17 - -5) <= (18 - -15))) and (((15 - -14) < (-14 - -10)) or (Brazil is in Europe.))) and ((11 - -15) <= (-13 - -15)) and (2010 is a leap year.)
C. ((18 * 20) <= (4 - -19)) and ((9 * 1 - -9 * -5) > (20 + 9))
D. not ((176 is a perfect square.) or (The chemical symbol for Hydrogen is Co.))
E. ((((-4 + -15) < (-2 - -19)) or ((30 % 1) > (-10 * -1 - 6 * -9))) and ((China is in Asia.) or ((10 * -7 - -10 * 6) != (5 ** 2)))) or (The currency of Saudi Arabia is the Real.)
F. (((Kenya is in Africa.) and ((49 % 7) < (13 + -11))) and (not (Jupiter is the 5th planet from the Sun.))) and (not (The chemical symbol for Calcium is U.))
G. ((((-5 - 20) < (-12 + -17)) and (64 is greater than 11.)) and (((-7 * -1 * -1 * 1) < (-9 + 13)) and (Uranus is the 3rd planet from the Sun.))) and ((-2 * -7) >= (-4 + -19))
H. (((Saudi Arabia is in Oceania.) and (The capital of Netherlands is Bucharest.)) or (The 2004 Olympics were held in Athens.)) and ((11 - 20) >= (3 ** 3))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 59621230,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. (not not ((10 * 3) != (-19 + 13))) or (((-13 * -1) > (17 * -9)) and (not ((-14 - 16) <= (-4 * -5 - 2 * 7) <= (10 * -8 + 3 * -4))))\nB. ((((0 - 6) >= (1 ** 1)) or ((-17 - -5) <= (18 - -15))) and (((15 - -14) < (-14 - -10)) or (Brazil is in Europe.))) and ((11 - -15) <= (-13 - -15)) and (2010 is a leap year.)\nC. ((18 * 20) <= (4 - -19)) and ((9 * 1 - -9 * -5) > (20 + 9))\nD. not ((176 is a perfect square.) or (The chemical symbol for Hydrogen is Co.))\nE. ((((-4 + -15) < (-2 - -19)) or ((30 % 1) > (-10 * -1 - 6 * -9))) and ((China is in Asia.) or ((10 * -7 - -10 * 6) != (5 ** 2)))) or (The currency of Saudi Arabia is the Real.)\nF. (((Kenya is in Africa.) and ((49 % 7) < (13 + -11))) and (not (Jupiter is the 5th planet from the Sun.))) and (not (The chemical symbol for Calcium is U.))\nG. ((((-5 - 20) < (-12 + -17)) and (64 is greater than 11.)) and (((-7 * -1 * -1 * 1) < (-9 + 13)) and (Uranus is the 3rd planet from the Sun.))) and ((-2 * -7) >= (-4 + -19))\nH. (((Saudi Arabia is in Oceania.) and (The capital of Netherlands is Bucharest.)) or (The 2004 Olympics were held in Athens.)) and ((11 - 20) >= (3 ** 3))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 59621230,
"true_count": 3
},
"seed": 59621230,
"task_id": 659621230,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (-8 * -9 - -9 * -5) >= (-2 * -6 * -3 * -6)
B. The capital of Philippines is Cairo.
C. (-14 + -5) <= (-18 * -7) <= (0 + 20)
D. (((-1 * 1 + -7 * 5) <= (4 ** 3)) or (Sound cannot travel through a vacuum.)) and ((17 * -15) <= (-5 * 4 + -7 * 8) <= (-7 + 2))
E. not ((The chemical symbol for Copper is Mg.) or ((-9 * 14) >= (7 - -5)))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 96500563,
"true_count": 2
},
"question": "Consider the following logical expressions:\n\nA. (-8 * -9 - -9 * -5) >= (-2 * -6 * -3 * -6)\nB. The capital of Philippines is Cairo.\nC. (-14 + -5) <= (-18 * -7) <= (0 + 20)\nD. (((-1 * 1 + -7 * 5) <= (4 ** 3)) or (Sound cannot travel through a vacuum.)) and ((17 * -15) <= (-5 * 4 + -7 * 8) <= (-7 + 2))\nE. not ((The chemical symbol for Copper is Mg.) or ((-9 * 14) >= (7 - -5)))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 96500563,
"true_count": 2
},
"seed": 96500563,
"task_id": 696500563,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (6 - -4) != (-12 - -20)
B. (1 * 14) <= (3 ** 3)
C. The Titanic sank occurred in 1912.
D. not not ((90 is less than or equal to 43.) and ((9 * -6 + 5 * 1) < (-3 - -11)))
E. (((5 ** 1) == (1 * 7 * 1 * 6)) or (80 is divisible by 12.)) and ((454 is a Fibonacci number.) and (Mars is the 2nd planet from the Sun.))
F. The 1932 Olympics were held in Los Angeles.
G. not ((Japan is in Oceania.) or (India is in Asia.))
H. (11 * 5) > (8 - -11)
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 19970545,
"true_count": 5
},
"question": "Consider the following logical expressions:\n\nA. (6 - -4) != (-12 - -20)\nB. (1 * 14) <= (3 ** 3)\nC. The Titanic sank occurred in 1912.\nD. not not ((90 is less than or equal to 43.) and ((9 * -6 + 5 * 1) < (-3 - -11)))\nE. (((5 ** 1) == (1 * 7 * 1 * 6)) or (80 is divisible by 12.)) and ((454 is a Fibonacci number.) and (Mars is the 2nd planet from the Sun.))\nF. The 1932 Olympics were held in Los Angeles.\nG. not ((Japan is in Oceania.) or (India is in Asia.))\nH. (11 * 5) > (8 - -11)\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 19970545,
"true_count": 5
},
"seed": 19970545,
"task_id": 619970545,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (The 1952 Olympics were held in Amsterdam.)
B. (not (not not ((-7 - 11) == (-9 * -2)))) and (not not (Saturn is the 7th planet from the Sun.))
C. ((4 ** 2) > (-12 + -2)) and (((Sound cannot travel through a vacuum.) and (The chemical symbol for Copper is Pt.)) and (((-4 * 4 + -3 * -8) >= (-13 + 11)) or ((-19 + -19) >= (19 * 4))))
D. not not (not not (Whales are fish.))
E. not not (The United States declared independence occurred in 1776.)
F. (not not (((0 * -6) != (-2 - -11)) and (223 is a perfect square.))) or (((-18 + -1) < (-18 + 4)) or ((6 % 3) < (-4 * 1 + -4 * 6))) or ((((12 + -20) == (8 - -5)) or ((-14 - 11) >= (17 % 1))) and ((Peru is in South America.) and ((-14 + -13) <= (2 ** 3))))
G. (((25 is less than or equal to 12.) or ((-11 * -17) <= (8 * -9 - 10 * 4))) and (The capital of Saudi Arabia is Jakarta.)) and (not not ((Brazil is in North America.) or ((3 * 0 + 9 * -2) != (10 * 3))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 47708653,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not (The 1952 Olympics were held in Amsterdam.)\nB. (not (not not ((-7 - 11) == (-9 * -2)))) and (not not (Saturn is the 7th planet from the Sun.))\nC. ((4 ** 2) > (-12 + -2)) and (((Sound cannot travel through a vacuum.) and (The chemical symbol for Copper is Pt.)) and (((-4 * 4 + -3 * -8) >= (-13 + 11)) or ((-19 + -19) >= (19 * 4))))\nD. not not (not not (Whales are fish.))\nE. not not (The United States declared independence occurred in 1776.)\nF. (not not (((0 * -6) != (-2 - -11)) and (223 is a perfect square.))) or (((-18 + -1) < (-18 + 4)) or ((6 % 3) < (-4 * 1 + -4 * 6))) or ((((12 + -20) == (8 - -5)) or ((-14 - 11) >= (17 % 1))) and ((Peru is in South America.) and ((-14 + -13) <= (2 ** 3))))\nG. (((25 is less than or equal to 12.) or ((-11 * -17) <= (8 * -9 - 10 * 4))) and (The capital of Saudi Arabia is Jakarta.)) and (not not ((Brazil is in North America.) or ((3 * 0 + 9 * -2) != (10 * 3))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 47708653,
"true_count": 3
},
"seed": 47708653,
"task_id": 647708653,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. (30 % 10) > (-10 * -6 * 1 * 9)
B. (19 - 8) >= (-6 + 9)
C. (0 + 14) != (38 % 1)
D. ((The 2020 Olympics were held in Tokyo.) and (There are 30 days in April.)) or (not not (There are 29 days in February.))
E. (((9 + 3) >= (-4 * 8 + 2 * 5)) or (275 is a Fibonacci number.)) or (not (India is in Asia.))
F. The 1984 Olympics were held in Athens.
G. not not (((12 + 1) >= (15 - 19)) or ((8 * 8 * 1 * -9) == (10 * -10)))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "B,C,D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 37731547,
"true_count": 5
},
"question": "Evaluate each expression below:\n\nA. (30 % 10) > (-10 * -6 * 1 * 9)\nB. (19 - 8) >= (-6 + 9)\nC. (0 + 14) != (38 % 1)\nD. ((The 2020 Olympics were held in Tokyo.) and (There are 30 days in April.)) or (not not (There are 29 days in February.))\nE. (((9 + 3) >= (-4 * 8 + 2 * 5)) or (275 is a Fibonacci number.)) or (not (India is in Asia.))\nF. The 1984 Olympics were held in Athens.\nG. not not (((12 + 1) >= (15 - 19)) or ((8 * 8 * 1 * -9) == (10 * -10)))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 37731547,
"true_count": 5
},
"seed": 37731547,
"task_id": 637731547,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not not (not ((((((-8 - -18) == (-10 * 18)) or (The currency of Hungary is the Forint.)) and (not (The chemical symbol for Titanium is Ti.))) or (A chicken is a reptile.) or ((The 2012 Olympics were held in London.) and (Carbon dioxide is a solid at room temperature.))) or (not ((-5 - -14) > (-3 - 10)))))
B. not (((not ((not not ((0 * -10 * -10 * 8) == (-5 * -3 - 6 * -3))) and ((816 is a Fibonacci number.) and ((-17 + -19) != (-17 + 11))))) or (not not (World War II ended occurred in 1945.))) and (((not not (((-1 + -19) >= (6 - 10)) and ((-16 + -10) > (2 ** 3)))) or ((not not ((6 * -4 * 5 * 10) >= (-4 * -2 * 5 * 2))) or (35 is greater than 65.))) or (not ((78 is divisible by 7.) and ((The chemical symbol for Manganese is N.) and ((41 % 10) > (18 - -10)))))))
C. not (not ((((4 ** 3) >= (-2 * -2 - 4 * -8)) or ((1972 is a leap year.) and ((1 ** 3) < (5 * 8 + 4 * -6)))) and (((((-11 + 19) <= (5 * -16) <= (4 ** 2)) and (The capital of India is New Delhi.)) or (not not ((31 % 4) <= (-11 + 3) <= (-10 - -14)))) or (The currency of Saudi Arabia is the Riyal.))))
D. not not (not not (not (not not (Jupiter is the 5th planet from the Sun.))))
E. (not (not (not (((A fly is an insect.) and (A turtle is a reptile.)) or ((3 * -4) <= (18 + -14)))))) and (((not (not ((The currency of Egypt is the Pound.) and (The currency of Brazil is the Real.)))) and ((2091 is a leap year.) and (The first iPhone was released occurred in 2007.))) and (not not ((Thailand is in Oceania.) and (not not (A cat has 4 legs.)))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 66805982,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. not not (not ((((((-8 - -18) == (-10 * 18)) or (The currency of Hungary is the Forint.)) and (not (The chemical symbol for Titanium is Ti.))) or (A chicken is a reptile.) or ((The 2012 Olympics were held in London.) and (Carbon dioxide is a solid at room temperature.))) or (not ((-5 - -14) > (-3 - 10)))))\nB. not (((not ((not not ((0 * -10 * -10 * 8) == (-5 * -3 - 6 * -3))) and ((816 is a Fibonacci number.) and ((-17 + -19) != (-17 + 11))))) or (not not (World War II ended occurred in 1945.))) and (((not not (((-1 + -19) >= (6 - 10)) and ((-16 + -10) > (2 ** 3)))) or ((not not ((6 * -4 * 5 * 10) >= (-4 * -2 * 5 * 2))) or (35 is greater than 65.))) or (not ((78 is divisible by 7.) and ((The chemical symbol for Manganese is N.) and ((41 % 10) > (18 - -10)))))))\nC. not (not ((((4 ** 3) >= (-2 * -2 - 4 * -8)) or ((1972 is a leap year.) and ((1 ** 3) < (5 * 8 + 4 * -6)))) and (((((-11 + 19) <= (5 * -16) <= (4 ** 2)) and (The capital of India is New Delhi.)) or (not not ((31 % 4) <= (-11 + 3) <= (-10 - -14)))) or (The currency of Saudi Arabia is the Riyal.))))\nD. not not (not not (not (not not (Jupiter is the 5th planet from the Sun.))))\nE. (not (not (not (((A fly is an insect.) and (A turtle is a reptile.)) or ((3 * -4) <= (18 + -14)))))) and (((not (not ((The currency of Egypt is the Pound.) and (The currency of Brazil is the Real.)))) and ((2091 is a leap year.) and (The first iPhone was released occurred in 2007.))) and (not not ((Thailand is in Oceania.) and (not not (A cat has 4 legs.)))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 66805982,
"true_count": 2
},
"seed": 66805982,
"task_id": 666805982,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. ((狗有4条腿。) or (not (161是完全平方数。))) or ((((-3 + -18) == (0 + 13)) and (铬的化学符号是Cr。)) or (((-1 * -10 - -7 * 2) <= (-7 * -18)) and (水星是距离太阳第1近的行星。)))
B. (not (((-17 * -17) == (-5 * -5)) and ((-16 - -10) >= (2 ** 1)))) or ((-3 * -13) != (-18 * -18)) or ((((-4 + 3) == (1 ** 2)) or (2025年是闰年。)) and (马来西亚的货币是林吉特。))
C. ((-5 - -1) != (-6 * 10 - 10 * -2)) and (((铁的化学符号是Zn。) and ((-9 * 12) >= (-13 - 1))) or ((1 ** 1) <= (-16 + -16)))
D. (蚊子是鱼类。) or (not (2000年奥运会在悉尼举办。))
E. ((not not (泰坦尼克号沉没发生在1912年。)) or ((第二次世界大战结束发生在1945年。) and ((4 ** 2) >= (-16 * 13)))) or (波兰的首都是首尔。)
F. ((-16 - 14) < (5 ** 2) < (-8 - 5)) or ((-6 * 2 + -6 * -4) != (18 + -11)) or ((((5 - 9) == (5 ** 2)) or ((-5 * 4 - 3 * 10) <= (5 ** 1))) and (((-8 + -20) > (-9 * 7 + -3 * -10)) or (二氧化碳在常温下是液体。)))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 77264304,
"true_count": 4
},
"question": "考虑以下布尔表达式：\n\nA. ((狗有4条腿。) or (not (161是完全平方数。))) or ((((-3 + -18) == (0 + 13)) and (铬的化学符号是Cr。)) or (((-1 * -10 - -7 * 2) <= (-7 * -18)) and (水星是距离太阳第1近的行星。)))\nB. (not (((-17 * -17) == (-5 * -5)) and ((-16 - -10) >= (2 ** 1)))) or ((-3 * -13) != (-18 * -18)) or ((((-4 + 3) == (1 ** 2)) or (2025年是闰年。)) and (马来西亚的货币是林吉特。))\nC. ((-5 - -1) != (-6 * 10 - 10 * -2)) and (((铁的化学符号是Zn。) and ((-9 * 12) >= (-13 - 1))) or ((1 ** 1) <= (-16 + -16)))\nD. (蚊子是鱼类。) or (not (2000年奥运会在悉尼举办。))\nE. ((not not (泰坦尼克号沉没发生在1912年。)) or ((第二次世界大战结束发生在1945年。) and ((4 ** 2) >= (-16 * 13)))) or (波兰的首都是首尔。)\nF. ((-16 - 14) < (5 ** 2) < (-8 - 5)) or ((-6 * 2 + -6 * -4) != (18 + -11)) or ((((5 - 9) == (5 ** 2)) or ((-5 * 4 - 3 * 10) <= (5 ** 1))) and (((-8 + -20) > (-9 * 7 + -3 * -10)) or (二氧化碳在常温下是液体。)))\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": 77264304,
"true_count": 4
},
"seed": 77264304,
"task_id": 677264304,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. ((not not (钻石由碳元素组成。)) and ((哥伦比亚位于大洋洲。) and (天王星是距离太阳第7近的行星。) and ((印度位于亚洲。) or (汞在常温下是液体。)))) and (not not (((1 * -10) < (-18 + -6)) or (((-18 + -3) <= (-6 - -18)) and (泰国的货币是泰铢。)) or ((11 - -8) >= (-2 + -17))))
B. (not not ((((月球绕地球运转。) or (十二月有29天。)) or (not ((16 + 6) <= (5 - -10)))) or (375是斐波那契数。) or ((5 ** 2) <= (10 - -3) <= (-10 + 6)))) or ((((((12 * 10) <= (4 ** 1)) and (氦气在常温下是固体。)) and (1920年奥运会在安特卫普举办。)) or ((not ((-11 * 2) >= (-13 - -18))) or (((-7 - 14) <= (7 * 4 * 1 * -5) <= (11 + 2)) and (蝴蝶有6条腿。)))) or ((1984年奥运会在洛杉矶举办。) and (水星是距离太阳第1近的行星。)))
C. (not not ((not (68是偶数。)) and ((not ((-20 - -11) == (19 - -6))) and (((12 + 14) == (13 - -7)) and ((31 % 5) <= (-15 * -10)))))) or ((not not (((-3 * -5) != (19 * -20)) and ((7 + 18) == (-6 * -3)))) and (((南非位于南极洲。) or ((34 % 10) < (10 + 10) < (-3 * -10))) or (2084年是闰年。)) and ((not not ((1964年奥运会在东京举办。) or (捷克的货币是克朗。))) or ((猪有4条腿。) and ((蜻蜓是爬行动物。) or ((13 % 2) < (10 * 7 + -9 * 8) < (6 % 5))))))
D. ((not (铬的化学符号是Pt。)) and (((not not (土星是距离太阳第6近的行星。)) or ((蚱蜢是鱼类。) and (地球是距离太阳第2近的行星。))) and (((35 % 2) < (-2 * -4) < (10 - 9)) or (((-7 * -1) == (-3 - -3)) and (地球是距离太阳第6近的行星。))))) or ((((not ((22 % 7) < (-12 - 20) < (-4 * 16))) or ((鲤鱼是鱼类。) or (蜘蛛是昆虫。))) and (not not (智利位于北美洲。))) or ((not not (((14 + -1) == (12 * -15)) or (人体有206块骨头。))) or (((1968年奥运会在亚特兰大举办。) or (越南位于亚洲。)) and (((3 + -15) < (2 * 4 + -6 * 9)) or (铜的化学符号是K。)))))
E. not ((((not not (金星是距离太阳第2近的行星。)) and (((-9 * 2 * 4 * -1) == (7 - -9)) or (2012年奥运会在东京举办。))) or (((5 * 3 + 1 * -7) <= (-1 - -17) <= (5 ** 2)) and (2035年是闰年。)) or (((新加坡的首都是新加坡。) or ((4 * -2 - 6 * -1) != (1 ** 3))) or (not not (现代奥运会首届举办发生在1896年。)))) and ((not not ((2020年奥运会在东京举办。) and ((-8 * 8 + 6 * -8) == (-7 * -3 * 6 * 8)))) or (((越南的货币是兹罗提。) and ((4 ** 1) <= (7 * -7 + 4 * -5))) or (((-7 + -14) > (20 - 8)) or (98是奇数。)))))
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": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 32121511,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. ((not not (钻石由碳元素组成。)) and ((哥伦比亚位于大洋洲。) and (天王星是距离太阳第7近的行星。) and ((印度位于亚洲。) or (汞在常温下是液体。)))) and (not not (((1 * -10) < (-18 + -6)) or (((-18 + -3) <= (-6 - -18)) and (泰国的货币是泰铢。)) or ((11 - -8) >= (-2 + -17))))\nB. (not not ((((月球绕地球运转。) or (十二月有29天。)) or (not ((16 + 6) <= (5 - -10)))) or (375是斐波那契数。) or ((5 ** 2) <= (10 - -3) <= (-10 + 6)))) or ((((((12 * 10) <= (4 ** 1)) and (氦气在常温下是固体。)) and (1920年奥运会在安特卫普举办。)) or ((not ((-11 * 2) >= (-13 - -18))) or (((-7 - 14) <= (7 * 4 * 1 * -5) <= (11 + 2)) and (蝴蝶有6条腿。)))) or ((1984年奥运会在洛杉矶举办。) and (水星是距离太阳第1近的行星。)))\nC. (not not ((not (68是偶数。)) and ((not ((-20 - -11) == (19 - -6))) and (((12 + 14) == (13 - -7)) and ((31 % 5) <= (-15 * -10)))))) or ((not not (((-3 * -5) != (19 * -20)) and ((7 + 18) == (-6 * -3)))) and (((南非位于南极洲。) or ((34 % 10) < (10 + 10) < (-3 * -10))) or (2084年是闰年。)) and ((not not ((1964年奥运会在东京举办。) or (捷克的货币是克朗。))) or ((猪有4条腿。) and ((蜻蜓是爬行动物。) or ((13 % 2) < (10 * 7 + -9 * 8) < (6 % 5))))))\nD. ((not (铬的化学符号是Pt。)) and (((not not (土星是距离太阳第6近的行星。)) or ((蚱蜢是鱼类。) and (地球是距离太阳第2近的行星。))) and (((35 % 2) < (-2 * -4) < (10 - 9)) or (((-7 * -1) == (-3 - -3)) and (地球是距离太阳第6近的行星。))))) or ((((not ((22 % 7) < (-12 - 20) < (-4 * 16))) or ((鲤鱼是鱼类。) or (蜘蛛是昆虫。))) and (not not (智利位于北美洲。))) or ((not not (((14 + -1) == (12 * -15)) or (人体有206块骨头。))) or (((1968年奥运会在亚特兰大举办。) or (越南位于亚洲。)) and (((3 + -15) < (2 * 4 + -6 * 9)) or (铜的化学符号是K。)))))\nE. not ((((not not (金星是距离太阳第2近的行星。)) and (((-9 * 2 * 4 * -1) == (7 - -9)) or (2012年奥运会在东京举办。))) or (((5 * 3 + 1 * -7) <= (-1 - -17) <= (5 ** 2)) and (2035年是闰年。)) or (((新加坡的首都是新加坡。) or ((4 * -2 - 6 * -1) != (1 ** 3))) or (not not (现代奥运会首届举办发生在1896年。)))) and ((not not ((2020年奥运会在东京举办。) and ((-8 * 8 + 6 * -8) == (-7 * -3 * 6 * 8)))) or (((越南的货币是兹罗提。) and ((4 ** 1) <= (7 * -7 + 4 * -5))) or (((-7 + -14) > (20 - 8)) or (98是奇数。)))))\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": 32121511,
"true_count": 3
},
"seed": 32121511,
"task_id": 632121511,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (((9 - -4) < (-6 * 10)) or (A kangaroo has 2 legs.) or ((The currency of China is the Sol.) or (((11 * 19) != (10 + 10)) or (The Moon produces its own light.)))) and (((((-18 + -5) == (-8 * -10 * 9 * 7)) and (Uranus is the 7th planet from the Sun.)) or (175 is an odd number.)) or ((The currency of Mexico is the Peso.) and ((The currency of Malaysia is the Pound.) or (The capital of Switzerland is Athens.))))
B. (((not not (The 1896 Olympics were held in Paris.)) or (The capital of Singapore is Singapore.)) and (((10 * -8 + -1 * -3) <= (-16 * -16)) or (The currency of Nigeria is the Peso.)) and ((The capital of Vietnam is Hanoi.) and ((Silver is a solid at room temperature.) and (The currency of Singapore is the Dollar.)))) and (((4 - 4) >= (2 * -7 + 4 * 7)) or (The 1936 Olympics were held in Athens.) or ((not (There are 28 days in February.)) or (not not (The capital of Argentina is Kuala Lumpur.))))
C. not (((not not (The Pacific Ocean is the largest ocean.)) and ((10 * 9) >= (-12 * 9))) or ((not ((-9 * 7 * 6 * -3) <= (10 * -20))) or (not (The capital of Italy is Helsinki.))))
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": 4,
"language": "en",
"num_options": 3,
"seed": 51767252,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. (((9 - -4) < (-6 * 10)) or (A kangaroo has 2 legs.) or ((The currency of China is the Sol.) or (((11 * 19) != (10 + 10)) or (The Moon produces its own light.)))) and (((((-18 + -5) == (-8 * -10 * 9 * 7)) and (Uranus is the 7th planet from the Sun.)) or (175 is an odd number.)) or ((The currency of Mexico is the Peso.) and ((The currency of Malaysia is the Pound.) or (The capital of Switzerland is Athens.))))\nB. (((not not (The 1896 Olympics were held in Paris.)) or (The capital of Singapore is Singapore.)) and (((10 * -8 + -1 * -3) <= (-16 * -16)) or (The currency of Nigeria is the Peso.)) and ((The capital of Vietnam is Hanoi.) and ((Silver is a solid at room temperature.) and (The currency of Singapore is the Dollar.)))) and (((4 - 4) >= (2 * -7 + 4 * 7)) or (The 1936 Olympics were held in Athens.) or ((not (There are 28 days in February.)) or (not not (The capital of Argentina is Kuala Lumpur.))))\nC. not (((not not (The Pacific Ocean is the largest ocean.)) and ((10 * 9) >= (-12 * 9))) or ((not ((-9 * 7 * 6 * -3) <= (10 * -20))) or (not (The capital of Italy is Helsinki.))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 51767252,
"true_count": 1
},
"seed": 51767252,
"task_id": 651767252,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. Sharks are mammals.
B. (Saudi Arabia is in Oceania.) or ((1 * -10) != (1 ** 2))
C. not (not ((18 % 5) < (-6 - 15) < (16 - -8)))
D. not not (not ((3 * -7 + -1 * 3) > (3 * 12)))
E. (Japan is in Asia.) or (not not ((18 + 3) > (-17 - -20)))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 70916419,
"true_count": 3
},
"question": "Consider the following logical expressions:\n\nA. Sharks are mammals.\nB. (Saudi Arabia is in Oceania.) or ((1 * -10) != (1 ** 2))\nC. not (not ((18 % 5) < (-6 - 15) < (16 - -8)))\nD. not not (not ((3 * -7 + -1 * 3) > (3 * 12)))\nE. (Japan is in Asia.) or (not not ((18 + 3) > (-17 - -20)))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 70916419,
"true_count": 3
},
"seed": 70916419,
"task_id": 670916419,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not ((6 * 2 * -1 * -6) <= (13 * 18) <= (13 % 10))
B. ((1975 is a leap year.) and (The Soviet Union dissolved occurred in 1991.)) or (not ((3 ** 2) <= (14 - -1)))
C. (Copper is a gas at room temperature.) and (not ((6 * 3) > (18 + -19)))
D. not ((1 * -5) < (1 ** 2) < (8 * -1 * 3 * -10))
E. The 1956 Olympics were held in Melbourne.
F. (-1 + -19) <= (4 ** 2)
G. (-20 * -9) <= (-5 - -10) <= (-6 - 18)
H. Diamonds are made of carbon.
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,E,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 93535160,
"true_count": 4
},
"question": "Evaluate each expression below:\n\nA. not ((6 * 2 * -1 * -6) <= (13 * 18) <= (13 % 10))\nB. ((1975 is a leap year.) and (The Soviet Union dissolved occurred in 1991.)) or (not ((3 ** 2) <= (14 - -1)))\nC. (Copper is a gas at room temperature.) and (not ((6 * 3) > (18 + -19)))\nD. not ((1 * -5) < (1 ** 2) < (8 * -1 * 3 * -10))\nE. The 1956 Olympics were held in Melbourne.\nF. (-1 + -19) <= (4 ** 2)\nG. (-20 * -9) <= (-5 - -10) <= (-6 - 18)\nH. Diamonds are made of carbon.\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 93535160,
"true_count": 4
},
"seed": 93535160,
"task_id": 693535160,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((((越南位于亚洲。) or (芬兰的首都是阿布贾。)) or ((第二次世界大战开始发生在1939年。) or (油在常温下是液体。))) and ((氧气对人类生存是必需的。) or ((-2 + -17) == (-1 * -9 * 5 * 0))) and (not ((丹麦的首都是布鲁塞尔。) and ((-14 + 4) >= (-5 * 0))))) or (((((2 + 11) < (-4 * -7 - -4 * 5)) or ((11 * 13) > (8 * -8))) and (((-7 * -4 + -1 * 7) >= (7 - 17)) or (意大利位于大洋洲。))) or (((三月有31天。) and ((-3 * 6) == (14 * 5))) or (蜘蛛是昆虫。)))
B. (not not ((((2 + 13) < (1 - 17)) and (木星是距离太阳第4近的行星。)) or ((人体有150块骨头。) and (哥伦布到达美洲发生在1497年。)))) and (((-3 - -16) == (2 * 3 + 10 * -9)) or ((17 * -9) > (4 ** 3)))
C. (not ((not not (二氧化碳在常温下是液体。)) and ((澳大利亚的货币是澳元。) and (巴西的首都是巴西利亚。)))) or (not (((-6 + -20) <= (-9 * 9)) or (((9 - -16) <= (-19 * -18)) or ((11 * -12) != (0 * 1 + 8 * -10)))))
D. not ((1968年奥运会在墨西哥城举办。) or ((71是奇数。) and (not ((-8 * 7 * 6 * -4) > (6 * 2)))))
E. (not not ((not (肯尼亚的首都是内罗毕。)) or (((10 * 10 + -4 * 0) == (7 * 10 + -5 * -2)) and ((0 * -11) != (17 + -4))))) and (天王星是距离太阳第7近的行星。) and (((-13 - 6) > (-14 - 19)) and ((not not ((3 * -7 + -5 * 6) < (-17 + 8))) and (((-13 * -2) <= (4 * 4 - -6 * 7)) and (俄罗斯位于欧洲。))))
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. ((((越南位于亚洲。) or (芬兰的首都是阿布贾。)) or ((第二次世界大战开始发生在1939年。) or (油在常温下是液体。))) and ((氧气对人类生存是必需的。) or ((-2 + -17) == (-1 * -9 * 5 * 0))) and (not ((丹麦的首都是布鲁塞尔。) and ((-14 + 4) >= (-5 * 0))))) or (((((2 + 11) < (-4 * -7 - -4 * 5)) or ((11 * 13) > (8 * -8))) and (((-7 * -4 + -1 * 7) >= (7 - 17)) or (意大利位于大洋洲。))) or (((三月有31天。) and ((-3 * 6) == (14 * 5))) or (蜘蛛是昆虫。)))\nB. (not not ((((2 + 13) < (1 - 17)) and (木星是距离太阳第4近的行星。)) or ((人体有150块骨头。) and (哥伦布到达美洲发生在1497年。)))) and (((-3 - -16) == (2 * 3 + 10 * -9)) or ((17 * -9) > (4 ** 3)))\nC. (not ((not not (二氧化碳在常温下是液体。)) and ((澳大利亚的货币是澳元。) and (巴西的首都是巴西利亚。)))) or (not (((-6 + -20) <= (-9 * 9)) or (((9 - -16) <= (-19 * -18)) or ((11 * -12) != (0 * 1 + 8 * -10)))))\nD. not ((1968年奥运会在墨西哥城举办。) or ((71是奇数。) and (not ((-8 * 7 * 6 * -4) > (6 * 2)))))\nE. (not not ((not (肯尼亚的首都是内罗毕。)) or (((10 * 10 + -4 * 0) == (7 * 10 + -5 * -2)) and ((0 * -11) != (17 + -4))))) and (天王星是距离太阳第7近的行星。) and (((-13 - 6) > (-14 - 19)) and ((not not ((3 * -7 + -5 * 6) < (-17 + 8))) and (((-13 * -2) <= (4 * 4 - -6 * 7)) and (俄罗斯位于欧洲。))))\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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"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (3 % 5) > (9 % 2)
B. not ((The French Revolution began occurred in 1789.) or (1967 is a leap year.))
C. not not (not (The 1952 Olympics were held in Helsinki.))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
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"question": "Consider the following logical expressions:\n\nA. (3 % 5) > (9 % 2)\nB. not ((The French Revolution began occurred in 1789.) or (1967 is a leap year.))\nC. not not (not (The 1952 Olympics were held in Helsinki.))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
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"seed": 58373729,
"true_count": 1
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"seed": 58373729,
"task_id": 658373729,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not not ((not (((Spain is in Antarctica.) or (not not (The 2016 Olympics were held in Rio de Janeiro.))) and (There are 30 days in April.))) or ((not (1962 is a leap year.)) or (((4 + -5) < (11 + 18)) and (((18 * 6) < (16 - 9)) or (The chemical symbol for Uranium is P.)) and (((There are 29 days in March.) or ((3 + 15) > (19 % 6))) and ((2050 is a leap year.) or (206 is a perfect square.))))))
B. not not ((not (not ((not not (There are 31 days in March.)) or (((2 ** 1) != (5 - 16)) and (A owl is a bird.))))) or (not ((not ((Mexico is in South America.) or (Thailand is in Asia.))) or (((-3 * 17) > (9 + -6)) or (Mars is the 8th planet from the Sun.)) or (not not ((-4 + 16) < (-4 * -9 - -4 * -10))))))
C. not (not not (not not (((not not (A duck has 0 legs.)) and (((11 - 19) <= (-11 + -8)) and ((-2 * -10 + 9 * 6) == (10 * 5 * 9 * 6)))) and ((-8 + -16) <= (-19 + -1)))))
D. not (((not (((-3 - -14) < (-11 - -17) < (-4 * 12)) and ((The currency of Hungary is the Koruna.) and ((-8 * 13) <= (9 + -4))))) or (not not (There are 30 days in November.))) or ((not not (The currency of Norway is the Real.)) and (not not ((not not ((-5 * 6 - -1 * 10) == (-10 * -7 * 3 * 10))) or (Mars is the 1st planet from the Sun.)))))
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 (((Spain is in Antarctica.) or (not not (The 2016 Olympics were held in Rio de Janeiro.))) and (There are 30 days in April.))) or ((not (1962 is a leap year.)) or (((4 + -5) < (11 + 18)) and (((18 * 6) < (16 - 9)) or (The chemical symbol for Uranium is P.)) and (((There are 29 days in March.) or ((3 + 15) > (19 % 6))) and ((2050 is a leap year.) or (206 is a perfect square.))))))\nB. not not ((not (not ((not not (There are 31 days in March.)) or (((2 ** 1) != (5 - 16)) and (A owl is a bird.))))) or (not ((not ((Mexico is in South America.) or (Thailand is in Asia.))) or (((-3 * 17) > (9 + -6)) or (Mars is the 8th planet from the Sun.)) or (not not ((-4 + 16) < (-4 * -9 - -4 * -10))))))\nC. not (not not (not not (((not not (A duck has 0 legs.)) and (((11 - 19) <= (-11 + -8)) and ((-2 * -10 + 9 * 6) == (10 * 5 * 9 * 6)))) and ((-8 + -16) <= (-19 + -1)))))\nD. not (((not (((-3 - -14) < (-11 - -17) < (-4 * 12)) and ((The currency of Hungary is the Koruna.) and ((-8 * 13) <= (9 + -4))))) or (not not (There are 30 days in November.))) or ((not not (The currency of Norway is the Real.)) and (not not ((not not ((-5 * 6 - -1 * 10) == (-10 * -7 * 3 * 10))) or (Mars is the 1st planet from the Sun.)))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
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"language": "en",
"num_options": 4,
"seed": 20305749,
"true_count": 3
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"seed": 20305749,
"task_id": 620305749,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (((not ((-2 + 16) <= (4 ** 2) <= (17 * -6))) and ((not (鳄鱼是爬行动物。)) or ((2000年奥运会在悉尼举办。) or ((2016年奥运会在里约热内卢举办。) or ((9 * -5 * -5 * 10) <= (-8 + -1)))))) or (not ((1976年奥运会在墨尔本举办。) and (not not (((19 % 8) < (5 ** 2) < (-6 * 15)) and ((3 + 0) <= (38 % 5))))))) or (not not (not not ((氖的化学符号是Zn。) or (not not ((6 * -9 + 1 * -8) == (3 ** 3))))))
B. (not not (((马来西亚的首都是新加坡。) or (泰坦尼克号沉没发生在1912年。)) and ((((-2 * -8 - -7 * -8) == (2 + -15)) or ((16 % 5) > (10 + -15))) and ((((14 - -15) < (0 - -7)) and (第一次世界大战结束发生在1918年。)) or (1960年奥运会在罗马举办。))))) and (((not ((-8 * 15) <= (-11 - -11) <= (-8 * -7 + -5 * -9))) or (not not (((104是完全平方数。) and (蝙蝠是瞎的。)) or ((瑞典的首都是赫尔辛基。) or (铝的化学符号是Au。))))) or (not (not not (((中国的首都是北京。) and (人类有三个肺。)) and (二氧化碳在常温下是固体。)))))
C. not (((not not ((((20 - 11) >= (-7 + -11)) and (1967年是闰年。)) and ((水蒸气在常温下是固体。) or (77是质数。)))) or ((钻石在常温下是固体。) and (not not (((-3 * -7) >= (8 * -10 - 10 * -7)) or ((10 + -4) <= (6 + -14)))))) and (((泰国的首都是曼谷。) and ((((-2 * 16) >= (-18 - -6)) or ((18 % 2) >= (3 * -19))) and ((土星是距离太阳第1近的行星。) or (银的化学符号是Si。)))) or (鲨鱼是哺乳动物。) or (((not ((13 + 6) < (20 * -19))) or ((意大利的首都是赫尔辛基。) and (人体有206块骨头。))) or (月球自己发光。))))
D. not (not (((((30是完全平方数。) and (印度尼西亚的货币是里拉。)) and ((-17 + 0) >= (6 * 5 + 2 * 9))) or (六月有30天。)) or (not not (not not (哥伦布到达美洲发生在1492年。)))))
E. not not (not (((not (not ((2 ** 3) == (5 ** 3)))) or ((太阳绕地球运转。) and (油在常温下是液体。)) or (水星是距离太阳第4近的行星。)) or (not not ((地球上一天是24小时。) and (44能被12整除。))) or ((4的平方根是9。) or ((((16 % 7) >= (-4 * -4)) or (泰坦尼克号沉没发生在1912年。)) and ((14 - 4) != (-14 + -12))))))
F. not not ((((鱼有8条腿。) and (((埃及的货币是加元。) or (115是完全平方数。)) or ((1908年奥运会在伦敦举办。) or ((-1 * -8 + 8 * 0) == (-1 + 0))))) and ((((-4 - 11) >= (-8 + 7)) or (人类首次登月发生在1971年。)) and (not not (1936年奥运会在亚特兰大举办。))) and ((苏联解体发生在1993年。) or (95大于97。))) or (not not ((((-1 * 1 * 4 * -7) < (-12 + 2)) or (1970年是闰年。)) or (1988年奥运会在首尔举办。))) or (not not (not ((丹麦的货币是奈拉。) or ((1的平方根是8。) or (荷兰的首都是阿姆斯特丹。))))))
G. (not (not (not not (摩洛哥的首都是首尔。)))) or (not (((((2 ** 3) != (5 * 5)) or ((十二月有31天。) and (瑞典的货币是克朗。))) and ((not not (泰国位于亚洲。)) and ((丹麦的货币是美元。) and ((12 - 3) <= (5 * -5 + 6 * -8) <= (3 - 10))))) or (((2008年奥运会在洛杉矶举办。) or ((3 + 15) == (2 ** 2))) and (not (木头在常温下是固体。))) or (((-4 * 2 * 10 * -4) == (2 ** 1)) and ((not ((-7 * 10 + -5 * -7) == (-16 + -2))) or (not not (摩洛哥位于非洲。))))))
H. ((not (not (((挪威的货币是澳元。) or (第一部iPhone发布发生在2007年。)) or ((鲨鱼是鸟类。) and ((14 * 0) <= (8 * 7 + 6 * -9)))))) and ((((3 ** 1) != (-4 - 17)) and ((水蒸气在常温下是气体。) or (((9 - 19) != (-3 * -10 + 6 * -9)) and (伦敦大火发生在1666年。)))) or (not not (尼日利亚的货币是克朗。)))) and (not not ((((((20 * -3) == (19 + 12)) or ((-2 * -19) <= (5 ** 3) <= (3 ** 3))) and (火星是距离太阳第6近的行星。)) or (((-13 * 1) == (3 + -20)) and (马来西亚的首都是吉隆坡。))) or ((not (((-19 - 0) < (-1 * 9 - -7 * 2)) and (声音在真空中传播更快。))) and (钛的化学符号是Pb。))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
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"difficulty": 1,
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"question": "评估以下每个表达式：\n\nA. (((not ((-2 + 16) <= (4 ** 2) <= (17 * -6))) and ((not (鳄鱼是爬行动物。)) or ((2000年奥运会在悉尼举办。) or ((2016年奥运会在里约热内卢举办。) or ((9 * -5 * -5 * 10) <= (-8 + -1)))))) or (not ((1976年奥运会在墨尔本举办。) and (not not (((19 % 8) < (5 ** 2) < (-6 * 15)) and ((3 + 0) <= (38 % 5))))))) or (not not (not not ((氖的化学符号是Zn。) or (not not ((6 * -9 + 1 * -8) == (3 ** 3))))))\nB. (not not (((马来西亚的首都是新加坡。) or (泰坦尼克号沉没发生在1912年。)) and ((((-2 * -8 - -7 * -8) == (2 + -15)) or ((16 % 5) > (10 + -15))) and ((((14 - -15) < (0 - -7)) and (第一次世界大战结束发生在1918年。)) or (1960年奥运会在罗马举办。))))) and (((not ((-8 * 15) <= (-11 - -11) <= (-8 * -7 + -5 * -9))) or (not not (((104是完全平方数。) and (蝙蝠是瞎的。)) or ((瑞典的首都是赫尔辛基。) or (铝的化学符号是Au。))))) or (not (not not (((中国的首都是北京。) and (人类有三个肺。)) and (二氧化碳在常温下是固体。)))))\nC. not (((not not ((((20 - 11) >= (-7 + -11)) and (1967年是闰年。)) and ((水蒸气在常温下是固体。) or (77是质数。)))) or ((钻石在常温下是固体。) and (not not (((-3 * -7) >= (8 * -10 - 10 * -7)) or ((10 + -4) <= (6 + -14)))))) and (((泰国的首都是曼谷。) and ((((-2 * 16) >= (-18 - -6)) or ((18 % 2) >= (3 * -19))) and ((土星是距离太阳第1近的行星。) or (银的化学符号是Si。)))) or (鲨鱼是哺乳动物。) or (((not ((13 + 6) < (20 * -19))) or ((意大利的首都是赫尔辛基。) and (人体有206块骨头。))) or (月球自己发光。))))\nD. not (not (((((30是完全平方数。) and (印度尼西亚的货币是里拉。)) and ((-17 + 0) >= (6 * 5 + 2 * 9))) or (六月有30天。)) or (not not (not not (哥伦布到达美洲发生在1492年。)))))\nE. not not (not (((not (not ((2 ** 3) == (5 ** 3)))) or ((太阳绕地球运转。) and (油在常温下是液体。)) or (水星是距离太阳第4近的行星。)) or (not not ((地球上一天是24小时。) and (44能被12整除。))) or ((4的平方根是9。) or ((((16 % 7) >= (-4 * -4)) or (泰坦尼克号沉没发生在1912年。)) and ((14 - 4) != (-14 + -12))))))\nF. not not ((((鱼有8条腿。) and (((埃及的货币是加元。) or (115是完全平方数。)) or ((1908年奥运会在伦敦举办。) or ((-1 * -8 + 8 * 0) == (-1 + 0))))) and ((((-4 - 11) >= (-8 + 7)) or (人类首次登月发生在1971年。)) and (not not (1936年奥运会在亚特兰大举办。))) and ((苏联解体发生在1993年。) or (95大于97。))) or (not not ((((-1 * 1 * 4 * -7) < (-12 + 2)) or (1970年是闰年。)) or (1988年奥运会在首尔举办。))) or (not not (not ((丹麦的货币是奈拉。) or ((1的平方根是8。) or (荷兰的首都是阿姆斯特丹。))))))\nG. (not (not (not not (摩洛哥的首都是首尔。)))) or (not (((((2 ** 3) != (5 * 5)) or ((十二月有31天。) and (瑞典的货币是克朗。))) and ((not not (泰国位于亚洲。)) and ((丹麦的货币是美元。) and ((12 - 3) <= (5 * -5 + 6 * -8) <= (3 - 10))))) or (((2008年奥运会在洛杉矶举办。) or ((3 + 15) == (2 ** 2))) and (not (木头在常温下是固体。))) or (((-4 * 2 * 10 * -4) == (2 ** 1)) and ((not ((-7 * 10 + -5 * -7) == (-16 + -2))) or (not not (摩洛哥位于非洲。))))))\nH. ((not (not (((挪威的货币是澳元。) or (第一部iPhone发布发生在2007年。)) or ((鲨鱼是鸟类。) and ((14 * 0) <= (8 * 7 + 6 * -9)))))) and ((((3 ** 1) != (-4 - 17)) and ((水蒸气在常温下是气体。) or (((9 - 19) != (-3 * -10 + 6 * -9)) and (伦敦大火发生在1666年。)))) or (not not (尼日利亚的货币是克朗。)))) and (not not ((((((20 * -3) == (19 + 12)) or ((-2 * -19) <= (5 ** 3) <= (3 ** 3))) and (火星是距离太阳第6近的行星。)) or (((-13 * 1) == (3 + -20)) and (马来西亚的首都是吉隆坡。))) or ((not (((-19 - 0) < (-1 * 9 - -7 * 2)) and (声音在真空中传播更快。))) and (钛的化学符号是Pb。))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
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"seed": 38354427,
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"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not (not not (((Ice is a solid at room temperature.) or (The Titanic sank occurred in 1912.)) or ((((1 % 5) >= (34 % 10)) or ((6 - 14) <= (8 + -5))) and (not (The 1932 Olympics were held in Antwerp.)))))
B. not (not (((9 - -13) <= (3 * -5 + -6 * -10)) and (not not (((4 * -8 * 0 * 10) <= (-3 * 12) <= (4 ** 2)) and (Ice is a solid at room temperature.)))))
C. (not not (((16 % 8) != (3 ** 1)) and ((not ((-9 * -7) != (3 - 1))) and (((-15 + -2) > (-3 + 16)) or (Plants produce oxygen through photosynthesis.))))) or ((not (((The currency of Mexico is the Koruna.) or (Egypt is in Africa.)) and ((2 - 4) == (10 * 7 * -1 * -9)))) and (not not ((-14 - 6) < (17 * -4) < (18 - -14))))
D. not ((not ((-9 + -8) == (8 - 12))) and (not ((Carbon dioxide is a gas at room temperature.) or ((3 * 4 - 3 * 6) < (-8 * 4 - 9 * -10)))) and (((((19 - -12) == (2 ** 3)) and (A owl is a bird.)) and (not not (2079 is a leap year.))) and (not ((The capital of Romania is Santiago.) or ((25 % 7) == (16 + 11))))))
E. not (not not (((-13 + -8) <= (0 + -12)) or (34 is divisible by 4.)))
F. not not ((((((-5 + 15) == (-4 * 10 + 8 * -4)) or ((15 + 3) != (-15 - -4))) and (not not (Uranus is the 7th planet from the Sun.))) or (((-6 * -16) <= (2 + 2)) or ((830 is a Fibonacci number.) or ((-2 - 1) >= (20 - 20))))) or (((((9 * 0) < (-13 + -1) < (2 * -2 - 8 * -6)) and (The capital of Denmark is Mexico City.)) and (not (The chemical symbol for Carbon is C.))) and (not (The 1980 Olympics were held in Paris.))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
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"true_count": 3
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"question": "Study the following logical statements:\n\nA. not not (not not (((Ice is a solid at room temperature.) or (The Titanic sank occurred in 1912.)) or ((((1 % 5) >= (34 % 10)) or ((6 - 14) <= (8 + -5))) and (not (The 1932 Olympics were held in Antwerp.)))))\nB. not (not (((9 - -13) <= (3 * -5 + -6 * -10)) and (not not (((4 * -8 * 0 * 10) <= (-3 * 12) <= (4 ** 2)) and (Ice is a solid at room temperature.)))))\nC. (not not (((16 % 8) != (3 ** 1)) and ((not ((-9 * -7) != (3 - 1))) and (((-15 + -2) > (-3 + 16)) or (Plants produce oxygen through photosynthesis.))))) or ((not (((The currency of Mexico is the Koruna.) or (Egypt is in Africa.)) and ((2 - 4) == (10 * 7 * -1 * -9)))) and (not not ((-14 - 6) < (17 * -4) < (18 - -14))))\nD. not ((not ((-9 + -8) == (8 - 12))) and (not ((Carbon dioxide is a gas at room temperature.) or ((3 * 4 - 3 * 6) < (-8 * 4 - 9 * -10)))) and (((((19 - -12) == (2 ** 3)) and (A owl is a bird.)) and (not not (2079 is a leap year.))) and (not ((The capital of Romania is Santiago.) or ((25 % 7) == (16 + 11))))))\nE. not (not not (((-13 + -8) <= (0 + -12)) or (34 is divisible by 4.)))\nF. not not ((((((-5 + 15) == (-4 * 10 + 8 * -4)) or ((15 + 3) != (-15 - -4))) and (not not (Uranus is the 7th planet from the Sun.))) or (((-6 * -16) <= (2 + 2)) or ((830 is a Fibonacci number.) or ((-2 - 1) >= (20 - 20))))) or (((((9 * 0) < (-13 + -1) < (2 * -2 - 8 * -6)) and (The capital of Denmark is Mexico City.)) and (not (The chemical symbol for Carbon is C.))) and (not (The 1980 Olympics were held in Paris.))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 10790238,
"true_count": 3
},
"seed": 10790238,
"task_id": 610790238,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (((((12 + -4) > (6 + -19)) and (not not (法国大革命开始发生在1789年。))) or ((-15 + 15) <= (16 % 1))) or (((4 ** 2) <= (4 % 8)) and ((钛的化学符号是Ti。) and ((19 + -3) >= (2 ** 3))) and (not (光速约为每秒30万公里。)))) and (not (not ((not (龙虾有100条腿。)) and (not (丹麦的货币是卢比。)))))
B. (not (not not (((-1 * -1 + 1 * 2) < (-18 + -11)) and ((-1 - -1) < (-19 * -4))))) and ((((not ((2 ** 1) > (4 ** 2))) and (木头在常温下是固体。)) or (((8 * -19) != (6 * -18)) and ((9的平方根是3。) and (英国的货币是英镑。)))) or (not not (not (声音无法在真空中传播。))))
C. (not not (not (not not (秘鲁位于南美洲。)))) or (not not ((丹麦的货币是美元。) and ((2036年是闰年。) and ((-15 - 3) <= (5 ** 2))) and ((-8 * 4 * -5 * -3) <= (16 * -18))))
D. not not (not (((俄罗斯的货币是卢布。) and (not not (天王星是距离太阳第5近的行星。))) or (not not (土耳其的货币是里拉。)) or ((蜘蛛有8条腿。) and (1996年奥运会在亚特兰大举办。))))
E. ((((((16 + -12) < (24 % 9)) or ((3 ** 3) != (-9 - -5))) and (((5 * -9 + 8 * 7) > (38 % 6)) or ((-20 * -19) != (-8 * 16)))) or (((-1 + -4) < (-7 - 15) < (16 - -9)) or ((9 * -9) < (27 % 8))) or (((38小于等于69。) or (印度尼西亚的货币是英镑。)) and (not not ((20 + -4) <= (-1 * 17))))) and ((哥伦布到达美洲发生在1493年。) and ((not ((-3 * -6 + -5 * -1) <= (-20 * -7))) or ((声音在真空中传播更快。) or ((7 * 7 * -10 * -8) > (18 + -12)))))) and ((not (not (not (越南的货币是越南盾。)))) or ((not (not not (中国位于亚洲。))) or (俄罗斯位于欧洲。)))
F. (not not (((((-1 + -13) < (10 + -12) < (-2 * 7 - 2 * 9)) and (2000年奥运会在北京举办。)) and ((人体有206块骨头。) or (2008年奥运会在北京举办。))) and ((七月有28天。) and (((15 + 8) < (-7 + -1) < (1 ** 1)) and (铝的化学符号是C。))))) and ((((((13 + -3) == (4 - 16)) and (锡的化学符号是Sn。)) and ((2 * 1) >= (20 + 6))) and (((摩洛哥位于南美洲。) or ((48 % 2) <= (1 + 19) <= (12 - 11))) or (木星是距离太阳第7近的行星。))) and (not not (荷兰的首都是波哥大。)))
G. ((not not ((2 ** 1) != (-9 + 10))) and ((not not ((2 ** 3) > (43 % 9))) and (((哥伦布到达美洲发生在1492年。) or ((4 + 12) <= (-17 + 2))) and (((-9 + 7) >= (5 ** 3)) and (日本位于亚洲。))))) and ((((not not ((-19 - -9) <= (-5 * 0 - 2 * 10) <= (-5 * 5 - 8 * -3))) or (十二月有30天。)) or (not ((1943年是闰年。) and ((-4 - 2) != (9 % 8))))) or ((((1960年奥运会在伦敦举办。) and (1977年是闰年。)) or ((第一次世界大战结束发生在1918年。) or ((-10 * -7 - -3 * -8) == (16 - 3)))) and ((天王星是距离太阳第4近的行星。) or (not not (空气在常温下是气体。)))))
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": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"question": "分析以下逻辑表达式：\n\nA. (((((12 + -4) > (6 + -19)) and (not not (法国大革命开始发生在1789年。))) or ((-15 + 15) <= (16 % 1))) or (((4 ** 2) <= (4 % 8)) and ((钛的化学符号是Ti。) and ((19 + -3) >= (2 ** 3))) and (not (光速约为每秒30万公里。)))) and (not (not ((not (龙虾有100条腿。)) and (not (丹麦的货币是卢比。)))))\nB. (not (not not (((-1 * -1 + 1 * 2) < (-18 + -11)) and ((-1 - -1) < (-19 * -4))))) and ((((not ((2 ** 1) > (4 ** 2))) and (木头在常温下是固体。)) or (((8 * -19) != (6 * -18)) and ((9的平方根是3。) and (英国的货币是英镑。)))) or (not not (not (声音无法在真空中传播。))))\nC. (not not (not (not not (秘鲁位于南美洲。)))) or (not not ((丹麦的货币是美元。) and ((2036年是闰年。) and ((-15 - 3) <= (5 ** 2))) and ((-8 * 4 * -5 * -3) <= (16 * -18))))\nD. not not (not (((俄罗斯的货币是卢布。) and (not not (天王星是距离太阳第5近的行星。))) or (not not (土耳其的货币是里拉。)) or ((蜘蛛有8条腿。) and (1996年奥运会在亚特兰大举办。))))\nE. ((((((16 + -12) < (24 % 9)) or ((3 ** 3) != (-9 - -5))) and (((5 * -9 + 8 * 7) > (38 % 6)) or ((-20 * -19) != (-8 * 16)))) or (((-1 + -4) < (-7 - 15) < (16 - -9)) or ((9 * -9) < (27 % 8))) or (((38小于等于69。) or (印度尼西亚的货币是英镑。)) and (not not ((20 + -4) <= (-1 * 17))))) and ((哥伦布到达美洲发生在1493年。) and ((not ((-3 * -6 + -5 * -1) <= (-20 * -7))) or ((声音在真空中传播更快。) or ((7 * 7 * -10 * -8) > (18 + -12)))))) and ((not (not (not (越南的货币是越南盾。)))) or ((not (not not (中国位于亚洲。))) or (俄罗斯位于欧洲。)))\nF. (not not (((((-1 + -13) < (10 + -12) < (-2 * 7 - 2 * 9)) and (2000年奥运会在北京举办。)) and ((人体有206块骨头。) or (2008年奥运会在北京举办。))) and ((七月有28天。) and (((15 + 8) < (-7 + -1) < (1 ** 1)) and (铝的化学符号是C。))))) and ((((((13 + -3) == (4 - 16)) and (锡的化学符号是Sn。)) and ((2 * 1) >= (20 + 6))) and (((摩洛哥位于南美洲。) or ((48 % 2) <= (1 + 19) <= (12 - 11))) or (木星是距离太阳第7近的行星。))) and (not not (荷兰的首都是波哥大。)))\nG. ((not not ((2 ** 1) != (-9 + 10))) and ((not not ((2 ** 3) > (43 % 9))) and (((哥伦布到达美洲发生在1492年。) or ((4 + 12) <= (-17 + 2))) and (((-9 + 7) >= (5 ** 3)) and (日本位于亚洲。))))) and ((((not not ((-19 - -9) <= (-5 * 0 - 2 * 10) <= (-5 * 5 - 8 * -3))) or (十二月有30天。)) or (not ((1943年是闰年。) and ((-4 - 2) != (9 % 8))))) or ((((1960年奥运会在伦敦举办。) and (1977年是闰年。)) or ((第一次世界大战结束发生在1918年。) or ((-10 * -7 - -3 * -8) == (16 - 3)))) and ((天王星是距离太阳第4近的行星。) or (not not (空气在常温下是气体。)))))\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": 7,
"seed": 34115081,
"true_count": 2
},
"seed": 34115081,
"task_id": 634115081,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (第二次世界大战结束发生在1955年。) or (not not ((9 - -9) <= (-12 * 19))) or (not (not (硫的化学符号是Na。)))
B. not not (新加坡的货币是日元。)
C. 氧气对人类生存是必需的。
D. not not ((((11 - 7) < (10 * -7 + 2 * -7)) and ((6 * 15) <= (17 + -16))) or ((秘鲁位于南美洲。) and ((8 * -7 + 4 * 5) >= (-2 * 17))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 85171664,
"true_count": 1
},
"question": "检验这些表达式：\n\nA. (第二次世界大战结束发生在1955年。) or (not not ((9 - -9) <= (-12 * 19))) or (not (not (硫的化学符号是Na。)))\nB. not not (新加坡的货币是日元。)\nC. 氧气对人类生存是必需的。\nD. not not ((((11 - 7) < (10 * -7 + 2 * -7)) and ((6 * 15) <= (17 + -16))) or ((秘鲁位于南美洲。) and ((8 * -7 + 4 * 5) >= (-2 * 17))))\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": 85171664,
"true_count": 1
},
"seed": 85171664,
"task_id": 685171664,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((not (十二月有30天。)) or ((20 + 12) <= (21 % 10))) and ((爱尔兰的首都是都柏林。) or (((-2 * -2 + 0 * -1) < (8 * -2 * -9 * 10)) or (583是斐波那契数。)))) or ((((3 * -7) != (-13 - -10)) or ((瑞士的首都是伯尔尼。) or (82能被12整除。))) or (not not ((鸵鸟是鸟类。) and (铀的化学符号是U。))))
B. ((not ((21 % 6) == (6 + -19))) and (not not (中国的货币是瑞士法郎。)) and ((-13 + 17) <= (-14 - -14))) or ((not not (((5 ** 3) <= (8 % 10)) or ((-10 - 2) != (-13 + 3)))) or ((not (三文鱼是鱼类。)) and ((-5 * 8 + -9 * 4) >= (18 + 7))))
C. not ((泰国的货币是奈拉。) or ((8 + 14) == (12 * -3)))
D. (((20 % 6) == (5 ** 1)) or (((-16 + 14) <= (3 ** 2)) and ((6 - -8) != (-16 * 12))) or (狗是哺乳动物。)) and (五月有31天。) and (not not ((13 + -7) < (-5 + -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,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 7072866,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. (((not (十二月有30天。)) or ((20 + 12) <= (21 % 10))) and ((爱尔兰的首都是都柏林。) or (((-2 * -2 + 0 * -1) < (8 * -2 * -9 * 10)) or (583是斐波那契数。)))) or ((((3 * -7) != (-13 - -10)) or ((瑞士的首都是伯尔尼。) or (82能被12整除。))) or (not not ((鸵鸟是鸟类。) and (铀的化学符号是U。))))\nB. ((not ((21 % 6) == (6 + -19))) and (not not (中国的货币是瑞士法郎。)) and ((-13 + 17) <= (-14 - -14))) or ((not not (((5 ** 3) <= (8 % 10)) or ((-10 - 2) != (-13 + 3)))) or ((not (三文鱼是鱼类。)) and ((-5 * 8 + -9 * 4) >= (18 + 7))))\nC. not ((泰国的货币是奈拉。) or ((8 + 14) == (12 * -3)))\nD. (((20 % 6) == (5 ** 1)) or (((-16 + 14) <= (3 ** 2)) and ((6 - -8) != (-16 * 12))) or (狗是哺乳动物。)) and (五月有31天。) and (not not ((13 + -7) < (-5 + -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": 4,
"language": "cn",
"num_options": 4,
"seed": 7072866,
"true_count": 3
},
"seed": 7072866,
"task_id": 607072866,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not not ((not (not not ((-17 - 7) >= (9 - -8)))) and ((6 * -7 + 1 * -1) == (-1 + 10)) and ((3 * -5) < (2 * 7 * 0 * -8)))) and (((not (((8 * 8) > (-3 - 5)) or (A kangaroo has 8 legs.))) or ((19 - 16) <= (-4 - 5)) or (not (Australia is in Oceania.))) or (not (not not (Iron is a solid at room temperature.))))
B. not not (not not (((not not (World War I ended occurred in 1918.)) and (Electricity flows faster than light.)) and (There are 31 days in January.) and ((((-7 * 6 + -8 * -8) != (-4 - -7)) or (The capital of Indonesia is Bangkok.)) and (((3 * 9) >= (22 % 6)) and ((48 % 5) < (18 - 2) < (13 * 2))))))
C. (not not (((5 - -10) <= (-20 * 6) <= (6 * 3 * 10 * -6)) and ((((15 * 19) == (-12 + 4)) or (The Earth revolves around the Sun.)) and ((The chemical symbol for Iron is Fe.) and ((5 ** 3) >= (12 % 6)))))) and (not not (not not ((-3 - -12) <= (3 ** 3) <= (-3 * 17))))
D. (not not ((The currency of Vietnam is the Euro.) or ((not not ((13 + 0) != (-4 - -9))) or (not ((-11 - -15) == (5 * 1 - -6 * -7)))))) or (not ((not not (not not ((4 * 10 + 0 * -3) <= (11 % 3) <= (5 * 12)))) or (((30 % 6) > (17 * -12)) or (The capital of Hungary is Budapest.)) or ((((8 * -13) < (15 % 2)) and ((19 * -6) == (-13 - -15))) or ((A snake has 0 legs.) or (Ice is less dense than liquid water.)))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
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"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "en",
"num_options": 4,
"seed": 46015464,
"true_count": 1
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"question": "Below are several boolean expressions:\n\nA. (not not ((not (not not ((-17 - 7) >= (9 - -8)))) and ((6 * -7 + 1 * -1) == (-1 + 10)) and ((3 * -5) < (2 * 7 * 0 * -8)))) and (((not (((8 * 8) > (-3 - 5)) or (A kangaroo has 8 legs.))) or ((19 - 16) <= (-4 - 5)) or (not (Australia is in Oceania.))) or (not (not not (Iron is a solid at room temperature.))))\nB. not not (not not (((not not (World War I ended occurred in 1918.)) and (Electricity flows faster than light.)) and (There are 31 days in January.) and ((((-7 * 6 + -8 * -8) != (-4 - -7)) or (The capital of Indonesia is Bangkok.)) and (((3 * 9) >= (22 % 6)) and ((48 % 5) < (18 - 2) < (13 * 2))))))\nC. (not not (((5 - -10) <= (-20 * 6) <= (6 * 3 * 10 * -6)) and ((((15 * 19) == (-12 + 4)) or (The Earth revolves around the Sun.)) and ((The chemical symbol for Iron is Fe.) and ((5 ** 3) >= (12 % 6)))))) and (not not (not not ((-3 - -12) <= (3 ** 3) <= (-3 * 17))))\nD. (not not ((The currency of Vietnam is the Euro.) or ((not not ((13 + 0) != (-4 - -9))) or (not ((-11 - -15) == (5 * 1 - -6 * -7)))))) or (not ((not not (not not ((4 * 10 + 0 * -3) <= (11 % 3) <= (5 * 12)))) or (((30 % 6) > (17 * -12)) or (The capital of Hungary is Budapest.)) or ((((8 * -13) < (15 % 2)) and ((19 * -6) == (-13 - -15))) or ((A snake has 0 legs.) or (Ice is less dense than liquid water.)))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 46015464,
"true_count": 1
},
"seed": 46015464,
"task_id": 646015464,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not (not (not not ((15 + 19) < (18 * 20)))))
B. ((((0 - 6) >= (4 * 2 * 9 * -3)) and ((not not (The chemical symbol for Nickel is Ni.)) or (((0 * 9 - 0 * 5) != (10 % 3)) or ((5 - 0) == (17 * 7))))) and ((not not ((3 * -15) != (-1 * -16))) and ((2 - 20) != (40 % 1)))) or ((((((5 * 6 * 5 * -3) == (13 - -9)) and (The Earth revolves around the Sun.)) and (not not (The 1972 Olympics were held in Munich.))) or ((8 + -6) < (2 - 17))) or (not ((not not (World War I began occurred in 1914.)) or (The currency of Norway is the Yen.))))
C. (not not ((((Diamonds are made of carbon.) and (The chemical symbol for Mercury is Hg.)) or (not not (Antarctica is the coldest continent.))) and ((7 - 17) == (8 * -19)))) and ((not ((not not ((20 % 3) < (9 * -4 + -1 * -7))) or (not not (Chile is in South America.)))) and (((The square root of 64 is 8.) or ((-8 * -9 * 4 * 3) > (5 ** 3))) and (((-18 + 8) < (-18 * 17) < (-16 - -20)) or (The chemical symbol for Nickel is Ni.))) and (not (India is in Africa.)))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
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"question": "Evaluate each expression below:\n\nA. not (not (not (not not ((15 + 19) < (18 * 20)))))\nB. ((((0 - 6) >= (4 * 2 * 9 * -3)) and ((not not (The chemical symbol for Nickel is Ni.)) or (((0 * 9 - 0 * 5) != (10 % 3)) or ((5 - 0) == (17 * 7))))) and ((not not ((3 * -15) != (-1 * -16))) and ((2 - 20) != (40 % 1)))) or ((((((5 * 6 * 5 * -3) == (13 - -9)) and (The Earth revolves around the Sun.)) and (not not (The 1972 Olympics were held in Munich.))) or ((8 + -6) < (2 - 17))) or (not ((not not (World War I began occurred in 1914.)) or (The currency of Norway is the Yen.))))\nC. (not not ((((Diamonds are made of carbon.) and (The chemical symbol for Mercury is Hg.)) or (not not (Antarctica is the coldest continent.))) and ((7 - 17) == (8 * -19)))) and ((not ((not not ((20 % 3) < (9 * -4 + -1 * -7))) or (not not (Chile is in South America.)))) and (((The square root of 64 is 8.) or ((-8 * -9 * 4 * 3) > (5 ** 3))) and (((-18 + 8) < (-18 * 17) < (-16 - -20)) or (The chemical symbol for Nickel is Ni.))) and (not (India is in Africa.)))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
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"language": "en",
"num_options": 3,
"seed": 80454077,
"true_count": 1
},
"seed": 80454077,
"task_id": 680454077,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not not (((not (Saturn is the 4th planet from the Sun.)) or (not not (The speed of light is approximately 300,000 km/s.))) or ((1905 is a leap year.) and ((16 * 3) <= (-7 * 4))) or (((The currency of European Union is the Euro.) and (A pig has 4 legs.)) or ((The speed of light is approximately 300,000 km/s.) or (2060 is a leap year.))))
B. (not (not not ((The 1952 Olympics were held in Helsinki.) and ((-9 - 0) < (-8 * 2 + 10 * -4) < (9 + -10))))) and ((Russia is in Asia.) and (not (((10 * -1 * 2 * -4) != (-11 - -11)) or ((-12 * -10) > (14 + -10)))))
C. not ((not not ((A gecko is a reptile.) and (The square root of 36 is 15.))) or (((3 ** 2) != (10 - -7)) and ((1 * 17) < (1 - 2))))
D. (not not (not ((New Zealand is in Oceania.) and (The 1908 Olympics were held in Sydney.)))) and ((((0 * -4) == (1 ** 2)) and (A elephant has 4 legs.)) and ((Russia is in Europe.) or (Humans only use 10% of their brain.))) and (((not not ((0 * -2 + -5 * 0) >= (4 * 13))) or (((7 - -10) <= (10 * 0 + -2 * -9) <= (5 ** 3)) and ((-11 - -3) <= (-2 * -1 + 9 * 6) <= (2 * 1 - 4 * 3)))) or ((76 is a perfect square.) or (((6 + -12) >= (-16 + -8)) or ((19 + 0) > (21 % 8)))))
E. not not ((Neptune is the 8th planet from the Sun.) and ((1 ** 1) > (1 ** 1)))
F. (not not (((6 - -6) < (-15 + 5) < (8 % 2)) or (((-18 - -11) >= (-5 * 10 * 3 * 3)) or (A crow is a mammal.)))) or ((((Vietnam is in North America.) and ((-2 * 14) != (-19 - 10))) or (not not ((-7 * 5 + -5 * -10) == (-10 - -2)))) or (((Sharks are mammals.) and (313 is a perfect square.)) or ((8 * -4) <= (7 + -15) <= (-19 + -4))))
G. not not ((Silver is a gas at room temperature.) and (((180 is an even number.) and ((16 * -9) == (-1 - 10))) and ((Canada is in South America.) or (Sharks are mammals.))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 7747163,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. not not (((not (Saturn is the 4th planet from the Sun.)) or (not not (The speed of light is approximately 300,000 km/s.))) or ((1905 is a leap year.) and ((16 * 3) <= (-7 * 4))) or (((The currency of European Union is the Euro.) and (A pig has 4 legs.)) or ((The speed of light is approximately 300,000 km/s.) or (2060 is a leap year.))))\nB. (not (not not ((The 1952 Olympics were held in Helsinki.) and ((-9 - 0) < (-8 * 2 + 10 * -4) < (9 + -10))))) and ((Russia is in Asia.) and (not (((10 * -1 * 2 * -4) != (-11 - -11)) or ((-12 * -10) > (14 + -10)))))\nC. not ((not not ((A gecko is a reptile.) and (The square root of 36 is 15.))) or (((3 ** 2) != (10 - -7)) and ((1 * 17) < (1 - 2))))\nD. (not not (not ((New Zealand is in Oceania.) and (The 1908 Olympics were held in Sydney.)))) and ((((0 * -4) == (1 ** 2)) and (A elephant has 4 legs.)) and ((Russia is in Europe.) or (Humans only use 10% of their brain.))) and (((not not ((0 * -2 + -5 * 0) >= (4 * 13))) or (((7 - -10) <= (10 * 0 + -2 * -9) <= (5 ** 3)) and ((-11 - -3) <= (-2 * -1 + 9 * 6) <= (2 * 1 - 4 * 3)))) or ((76 is a perfect square.) or (((6 + -12) >= (-16 + -8)) or ((19 + 0) > (21 % 8)))))\nE. not not ((Neptune is the 8th planet from the Sun.) and ((1 ** 1) > (1 ** 1)))\nF. (not not (((6 - -6) < (-15 + 5) < (8 % 2)) or (((-18 - -11) >= (-5 * 10 * 3 * 3)) or (A crow is a mammal.)))) or ((((Vietnam is in North America.) and ((-2 * 14) != (-19 - 10))) or (not not ((-7 * 5 + -5 * -10) == (-10 - -2)))) or (((Sharks are mammals.) and (313 is a perfect square.)) or ((8 * -4) <= (7 + -15) <= (-19 + -4))))\nG. not not ((Silver is a gas at room temperature.) and (((180 is an even number.) and ((16 * -9) == (-1 - 10))) and ((Canada is in South America.) or (Sharks are mammals.))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 7747163,
"true_count": 3
},
"seed": 7747163,
"task_id": 607747163,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (((not not (The 1912 Olympics were held in Stockholm.)) or (The currency of United States is the Dollar.)) and ((10 % 10) < (2 ** 2) < (18 - -6))) or (not not ((The chemical symbol for Cobalt is Fe.) and ((Gold is a solid at room temperature.) or (Uranus is the 7th planet from the Sun.))))
B. (not ((A crocodile is a reptile.) or (((4 * 3) < (11 + 14)) and ((-5 * -3) <= (-11 - -19))))) and (Humans have five fingers on each hand.) and (not ((not ((3 % 2) == (24 % 2))) or ((A cod is a fish.) and (The capital of Australia is Bucharest.))))
C. (not ((not ((18 - -15) >= (18 * 11))) and ((1919 is a leap year.) or (Oxygen is necessary for human survival.)))) or ((Light travels faster than sound.) and (not (not (The 2000 Olympics were held in Sydney.))))
D. not (((((-17 * -11) == (-20 - 2)) and ((0 + 4) < (18 * -12))) or (((10 % 6) > (2 * -9)) and ((17 * 0) >= (4 - 18)))) or (((Indonesia is in Asia.) or ((44 % 10) <= (-18 + 3))) and (not not (798 is a Fibonacci number.))))
E. (not not (((The currency of South Africa is the Rand.) and (137 is an odd number.)) and (not (A duck has 6 legs.)))) or ((not (There are 30 days in June.)) or ((((-1 + 7) != (2 ** 1)) or (Iron is a gas at room temperature.)) and ((The currency of Russia is the Ruble.) or (Steam is a gas at room temperature.))))
F. (not ((not not ((3 ** 1) < (2 + -15))) or (The currency of Malaysia is the Yen.))) or (((((19 * 16) > (5 ** 3)) or (A kangaroo has 2 legs.)) or ((The 2020 Olympics were held in London.) and (The chemical symbol for Aluminum is Al.))) or ((Saudi Arabia is in Asia.) and ((The Great Wall of China was built in one year.) or (The currency of Czech Republic is the Koruna.))))
G. (((((36 % 2) != (-9 + -13)) or ((-14 * -11) < (15 - 17))) and ((The capital of Chile is Seoul.) or (South Korea is in North America.))) and ((235 is a perfect square.) and (A dog has 6 legs.)) and (The chemical symbol for Chromium is Zn.)) or ((not (Air is a gas at room temperature.)) and (((63 is a prime number.) and (The capital of Greece is Riyadh.)) or ((The speed of light is approximately 300,000 km/s.) and ((-7 - 0) <= (-15 * -8) <= (0 * -20)))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 15575722,
"true_count": 4
},
"question": "Review these logical expressions:\n\nA. (((not not (The 1912 Olympics were held in Stockholm.)) or (The currency of United States is the Dollar.)) and ((10 % 10) < (2 ** 2) < (18 - -6))) or (not not ((The chemical symbol for Cobalt is Fe.) and ((Gold is a solid at room temperature.) or (Uranus is the 7th planet from the Sun.))))\nB. (not ((A crocodile is a reptile.) or (((4 * 3) < (11 + 14)) and ((-5 * -3) <= (-11 - -19))))) and (Humans have five fingers on each hand.) and (not ((not ((3 % 2) == (24 % 2))) or ((A cod is a fish.) and (The capital of Australia is Bucharest.))))\nC. (not ((not ((18 - -15) >= (18 * 11))) and ((1919 is a leap year.) or (Oxygen is necessary for human survival.)))) or ((Light travels faster than sound.) and (not (not (The 2000 Olympics were held in Sydney.))))\nD. not (((((-17 * -11) == (-20 - 2)) and ((0 + 4) < (18 * -12))) or (((10 % 6) > (2 * -9)) and ((17 * 0) >= (4 - 18)))) or (((Indonesia is in Asia.) or ((44 % 10) <= (-18 + 3))) and (not not (798 is a Fibonacci number.))))\nE. (not not (((The currency of South Africa is the Rand.) and (137 is an odd number.)) and (not (A duck has 6 legs.)))) or ((not (There are 30 days in June.)) or ((((-1 + 7) != (2 ** 1)) or (Iron is a gas at room temperature.)) and ((The currency of Russia is the Ruble.) or (Steam is a gas at room temperature.))))\nF. (not ((not not ((3 ** 1) < (2 + -15))) or (The currency of Malaysia is the Yen.))) or (((((19 * 16) > (5 ** 3)) or (A kangaroo has 2 legs.)) or ((The 2020 Olympics were held in London.) and (The chemical symbol for Aluminum is Al.))) or ((Saudi Arabia is in Asia.) and ((The Great Wall of China was built in one year.) or (The currency of Czech Republic is the Koruna.))))\nG. (((((36 % 2) != (-9 + -13)) or ((-14 * -11) < (15 - 17))) and ((The capital of Chile is Seoul.) or (South Korea is in North America.))) and ((235 is a perfect square.) and (A dog has 6 legs.)) and (The chemical symbol for Chromium is Zn.)) or ((not (Air is a gas at room temperature.)) and (((63 is a prime number.) and (The capital of Greece is Riyadh.)) or ((The speed of light is approximately 300,000 km/s.) and ((-7 - 0) <= (-15 * -8) <= (0 * -20)))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 15575722,
"true_count": 4
},
"seed": 15575722,
"task_id": 615575722,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not not (((5 ** 1) != (18 * 8)) or (not not ((38 % 7) <= (-3 - 20))))
B. not not (not ((A duck has 2 legs.) and (The chemical symbol for Zinc is Zn.)))
C. (((Wood is a gas at room temperature.) and (The chemical symbol for Gold is Au.)) or ((A octopus has 4 legs.) and (The 2008 Olympics were held in Stockholm.))) or (not not ((19 * 7) != (3 ** 1))) or (((Sound cannot travel through a vacuum.) and (The currency of Indonesia is the Rupiah.)) or (((16 * -4) <= (-4 + 17)) and ((-15 * -5) != (20 * 13))))
D. ((((9 * -9 - 6 * 1) <= (12 - -10)) or ((4 * -16) != (4 ** 2))) or ((The capital of New Zealand is Tokyo.) or ((-3 + 11) < (1 ** 1) < (2 % 6)))) or (((-1 * -6 - -3 * 1) <= (16 + -13)) or (The capital of Philippines is Tokyo.)) or (not (The 1988 Olympics were held in Rome.))
E. not ((19 + -11) == (0 * 0 * -2 * 9))
F. ((The square root of 100 is 4.) or ((The capital of Cuba is Hanoi.) or (The currency of Sweden is the Krona.))) or (not ((Australia is in Oceania.) or (Morocco is in Africa.)))
G. ((The currency of New Zealand is the Dollar.) and (Mercury is a liquid at room temperature.)) and ((not not ((-1 * 13) < (6 - 16) < (30 % 10))) and (((8 * 5 * 5 * -1) == (7 - -9)) or (The currency of South Africa is the Won.)))
H. ((((-10 + -12) < (-2 * 8 - 3 * 1) < (5 * 9 + 7 * -7)) and (The 1956 Olympics were held in Melbourne.)) and (((9 * 2) < (49 % 9)) or (2091 is a leap year.))) or (((A carp is a reptile.) or (The currency of Poland is the Forint.)) or ((24 % 5) < (-4 + -5)))
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": 9263474,
"true_count": 5
},
"question": "Consider the following logical expressions:\n\nA. not not (((5 ** 1) != (18 * 8)) or (not not ((38 % 7) <= (-3 - 20))))\nB. not not (not ((A duck has 2 legs.) and (The chemical symbol for Zinc is Zn.)))\nC. (((Wood is a gas at room temperature.) and (The chemical symbol for Gold is Au.)) or ((A octopus has 4 legs.) and (The 2008 Olympics were held in Stockholm.))) or (not not ((19 * 7) != (3 ** 1))) or (((Sound cannot travel through a vacuum.) and (The currency of Indonesia is the Rupiah.)) or (((16 * -4) <= (-4 + 17)) and ((-15 * -5) != (20 * 13))))\nD. ((((9 * -9 - 6 * 1) <= (12 - -10)) or ((4 * -16) != (4 ** 2))) or ((The capital of New Zealand is Tokyo.) or ((-3 + 11) < (1 ** 1) < (2 % 6)))) or (((-1 * -6 - -3 * 1) <= (16 + -13)) or (The capital of Philippines is Tokyo.)) or (not (The 1988 Olympics were held in Rome.))\nE. not ((19 + -11) == (0 * 0 * -2 * 9))\nF. ((The square root of 100 is 4.) or ((The capital of Cuba is Hanoi.) or (The currency of Sweden is the Krona.))) or (not ((Australia is in Oceania.) or (Morocco is in Africa.)))\nG. ((The currency of New Zealand is the Dollar.) and (Mercury is a liquid at room temperature.)) and ((not not ((-1 * 13) < (6 - 16) < (30 % 10))) and (((8 * 5 * 5 * -1) == (7 - -9)) or (The currency of South Africa is the Won.)))\nH. ((((-10 + -12) < (-2 * 8 - 3 * 1) < (5 * 9 + 7 * -7)) and (The 1956 Olympics were held in Melbourne.)) and (((9 * 2) < (49 % 9)) or (2091 is a leap year.))) or (((A carp is a reptile.) or (The currency of Poland is the Forint.)) or ((24 % 5) < (-4 + -5)))\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": 9263474,
"true_count": 5
},
"seed": 9263474,
"task_id": 609263474,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not (((-3 - 8) == (-4 + -13)) or ((15 * -19) == (-10 + 4)))
B. (not ((The capital of Venezuela is Caracas.) and (Sound cannot travel through a vacuum.))) and (not not (Chile is in Antarctica.)) and ((((8 * 8) == (-8 * 9 - 8 * 9)) and (The square root of 25 is 14.)) or (Light travels faster than sound.))
C. ((((4 ** 3) > (-6 - 2)) or (The capital of Singapore is Nairobi.)) or (((-8 * 8 * -9 * -6) <= (16 - 13)) and ((-2 * 2 * 5 * 5) != (-12 * -1)))) or (not ((18 * -17) <= (-9 * -9 + -5 * 8))) or ((4 ** 2) >= (10 * 6 * 4 * -2))
D. not not (The capital of Portugal is Lisbon.)
E. not ((Sound cannot travel through a vacuum.) or ((0 * -9 + -7 * 9) >= (3 - 5)))
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": 5,
"seed": 31428316,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. not not (((-3 - 8) == (-4 + -13)) or ((15 * -19) == (-10 + 4)))\nB. (not ((The capital of Venezuela is Caracas.) and (Sound cannot travel through a vacuum.))) and (not not (Chile is in Antarctica.)) and ((((8 * 8) == (-8 * 9 - 8 * 9)) and (The square root of 25 is 14.)) or (Light travels faster than sound.))\nC. ((((4 ** 3) > (-6 - 2)) or (The capital of Singapore is Nairobi.)) or (((-8 * 8 * -9 * -6) <= (16 - 13)) and ((-2 * 2 * 5 * 5) != (-12 * -1)))) or (not ((18 * -17) <= (-9 * -9 + -5 * 8))) or ((4 ** 2) >= (10 * 6 * 4 * -2))\nD. not not (The capital of Portugal is Lisbon.)\nE. not ((Sound cannot travel through a vacuum.) or ((0 * -9 + -7 * 9) >= (3 - 5)))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 31428316,
"true_count": 2
},
"seed": 31428316,
"task_id": 631428316,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not (not ((((The chemical symbol for Phosphorus is H.) and (129 is an odd number.)) or ((-9 * 5) == (2 + -7))) or (((Venus is the 8th planet from the Sun.) or ((5 % 1) < (-6 - 2) < (10 * -1))) and ((Oil is a liquid at room temperature.) or ((17 + 18) >= (1 + 19)))))))
B. not (not ((not not ((Argentina is in South America.) and ((A human has 2 legs.) and ((7 * 1 - -5 * 5) > (12 * 1))))) or ((The currency of India is the Rupee.) or (not not ((679 is a Fibonacci number.) and (The chemical symbol for Uranium is Zn.))))))
C. (not not ((not ((5 ** 2) != (10 + 20))) and ((not not (not (A horse has 4 legs.))) and (Mercury is the 6th planet from the Sun.)))) or ((not not (((1 ** 2) != (1 ** 2)) and ((((-10 * -6 - -4 * -8) < (-18 * 2) < (11 * -9)) and (The capital of Norway is Oslo.)) and ((The capital of Mexico is Ankara.) and (The currency of South Africa is the Forint.))))) and (not not (not (not ((The capital of Greece is Athens.) and (The currency of New Zealand is the Real.))))))
D. not not (not not ((((-6 * 20) < (-1 * 4) < (-2 + 12)) and (((25 % 1) < (-9 + -17)) or (((-7 - -18) > (-14 * -7)) or ((10 * -6 * -4 * -8) <= (2 ** 2))))) and (((The chemical symbol for Iron is Fe.) and (Helium is a gas at room temperature.)) and ((((3 ** 1) == (-9 + 10)) or ((10 * 6) == (-6 * 13))) or ((-9 * -9) < (-10 - 6) < (14 + -1))))))
E. not not (not ((not (not not (The Pacific Ocean is the largest ocean.))) and ((not not (The currency of New Zealand is the Ringgit.)) or (The currency of Thailand is the Lira.) or ((not not ((5 ** 2) > (2 * -15))) and ((5 ** 3) <= (20 * -14))))))
F. not (not ((not not ((19 - -18) != (17 * -4))) and (((not ((-1 * 6 - 6 * 6) <= (-6 * 4))) and (not (A fly is a reptile.))) or (((88 is divisible by 9.) and ((-4 * -4 - -8 * -7) <= (-18 - 5) <= (4 * 2 + -3 * 6))) and ((The Earth revolves around the Sun.) or (There are 31 days in August.))))))
G. not not ((not not ((not not ((The chemical symbol for Platinum is He.) and ((9 + -2) <= (-7 * -7 * -10 * 9)))) and ((((10 + 20) > (-3 - 5)) or ((-16 - 17) != (13 - 8))) or ((Neptune is the 8th planet from the Sun.) and ((9 * -3 - 3 * 10) < (-4 + 10) < (-5 + 20)))))) and (((Chile is in South America.) or ((5 ** 1) == (-17 * -11))) and (not (The currency of South Africa is the Rand.)) and (not (((13 * 2) <= (2 ** 3)) and (((16 - 13) >= (2 + 6)) and ((9 + 3) > (7 * -9 - 2 * 1)))))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 21307630,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not (not (not ((((The chemical symbol for Phosphorus is H.) and (129 is an odd number.)) or ((-9 * 5) == (2 + -7))) or (((Venus is the 8th planet from the Sun.) or ((5 % 1) < (-6 - 2) < (10 * -1))) and ((Oil is a liquid at room temperature.) or ((17 + 18) >= (1 + 19)))))))\nB. not (not ((not not ((Argentina is in South America.) and ((A human has 2 legs.) and ((7 * 1 - -5 * 5) > (12 * 1))))) or ((The currency of India is the Rupee.) or (not not ((679 is a Fibonacci number.) and (The chemical symbol for Uranium is Zn.))))))\nC. (not not ((not ((5 ** 2) != (10 + 20))) and ((not not (not (A horse has 4 legs.))) and (Mercury is the 6th planet from the Sun.)))) or ((not not (((1 ** 2) != (1 ** 2)) and ((((-10 * -6 - -4 * -8) < (-18 * 2) < (11 * -9)) and (The capital of Norway is Oslo.)) and ((The capital of Mexico is Ankara.) and (The currency of South Africa is the Forint.))))) and (not not (not (not ((The capital of Greece is Athens.) and (The currency of New Zealand is the Real.))))))\nD. not not (not not ((((-6 * 20) < (-1 * 4) < (-2 + 12)) and (((25 % 1) < (-9 + -17)) or (((-7 - -18) > (-14 * -7)) or ((10 * -6 * -4 * -8) <= (2 ** 2))))) and (((The chemical symbol for Iron is Fe.) and (Helium is a gas at room temperature.)) and ((((3 ** 1) == (-9 + 10)) or ((10 * 6) == (-6 * 13))) or ((-9 * -9) < (-10 - 6) < (14 + -1))))))\nE. not not (not ((not (not not (The Pacific Ocean is the largest ocean.))) and ((not not (The currency of New Zealand is the Ringgit.)) or (The currency of Thailand is the Lira.) or ((not not ((5 ** 2) > (2 * -15))) and ((5 ** 3) <= (20 * -14))))))\nF. not (not ((not not ((19 - -18) != (17 * -4))) and (((not ((-1 * 6 - 6 * 6) <= (-6 * 4))) and (not (A fly is a reptile.))) or (((88 is divisible by 9.) and ((-4 * -4 - -8 * -7) <= (-18 - 5) <= (4 * 2 + -3 * 6))) and ((The Earth revolves around the Sun.) or (There are 31 days in August.))))))\nG. not not ((not not ((not not ((The chemical symbol for Platinum is He.) and ((9 + -2) <= (-7 * -7 * -10 * 9)))) and ((((10 + 20) > (-3 - 5)) or ((-16 - 17) != (13 - 8))) or ((Neptune is the 8th planet from the Sun.) and ((9 * -3 - 3 * 10) < (-4 + 10) < (-5 + 20)))))) and (((Chile is in South America.) or ((5 ** 1) == (-17 * -11))) and (not (The currency of South Africa is the Rand.)) and (not (((13 * 2) <= (2 ** 3)) and (((16 - 13) >= (2 + 6)) and ((9 + 3) > (7 * -9 - 2 * 1)))))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 21307630,
"true_count": 3
},
"seed": 21307630,
"task_id": 621307630,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (-18 + 10) != (3 ** 3)
B. not (((-3 * 10) <= (0 * -13) <= (-5 * -7 * -1 * 9)) and ((17 * -6) < (-3 * 15)))
C. not not ((The 1972 Olympics were held in Munich.) or (The capital of Saudi Arabia is Riyadh.))
D. The capital of Morocco is Rabat.
E. not (2013 is a leap year.)
F. ((The chemical symbol for Calcium is Al.) or (A human has 2 legs.)) or (not (39 is divisible by 3.))
G. ((Kenya is in Antarctica.) or ((5 ** 3) >= (0 * 1 + -9 * -9))) and (((8 * 0) > (-5 - -15)) or (The currency of Israel is the Shekel.))
H. New Zealand is in South America.
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,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 19412294,
"true_count": 7
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (-18 + 10) != (3 ** 3)\nB. not (((-3 * 10) <= (0 * -13) <= (-5 * -7 * -1 * 9)) and ((17 * -6) < (-3 * 15)))\nC. not not ((The 1972 Olympics were held in Munich.) or (The capital of Saudi Arabia is Riyadh.))\nD. The capital of Morocco is Rabat.\nE. not (2013 is a leap year.)\nF. ((The chemical symbol for Calcium is Al.) or (A human has 2 legs.)) or (not (39 is divisible by 3.))\nG. ((Kenya is in Antarctica.) or ((5 ** 3) >= (0 * 1 + -9 * -9))) and (((8 * 0) > (-5 - -15)) or (The currency of Israel is the Shekel.))\nH. New Zealand is in South America.\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 19412294,
"true_count": 7
},
"seed": 19412294,
"task_id": 619412294,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not ((18 - -9) < (-3 + 8))
B. (8 * 4) == (-14 + -17)
C. (-8 * 7 + 9 * -7) >= (18 + 5)
D. ((The chemical symbol for Nickel is Ni.) or ((20 * 2) != (3 + 0))) and (((-1 - -3) == (3 * 10 - 0 * -2)) and (Mercury is the 1st planet from the Sun.))
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": 2,
"language": "en",
"num_options": 4,
"seed": 297266,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. not ((18 - -9) < (-3 + 8))\nB. (8 * 4) == (-14 + -17)\nC. (-8 * 7 + 9 * -7) >= (18 + 5)\nD. ((The chemical symbol for Nickel is Ni.) or ((20 * 2) != (3 + 0))) and (((-1 - -3) == (3 * 10 - 0 * -2)) and (Mercury is the 1st planet from the Sun.))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 297266,
"true_count": 1
},
"seed": 297266,
"task_id": 600297266,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (not ((not not ((((34 % 2) > (2 ** 2)) and (Steam is a solid at room temperature.)) or (not (The currency of Mexico is the Pound.)))) or ((not not ((The 1948 Olympics were held in Atlanta.) or (The currency of New Zealand is the Dollar.))) or (The currency of Russia is the Peso.))))
B. not (not not ((not (61 is a perfect square.)) or ((((1900 is a leap year.) and ((6 * -3) <= (-4 * -2 - 6 * 6) <= (9 * -13))) and ((The capital of Thailand is Wellington.) and ((-8 * 0 + 5 * 4) <= (1 + 13) <= (-2 * -16)))) or (Earth is the 5th planet from the Sun.))))
C. not (not not ((not not (The 1920 Olympics were held in Antwerp.)) or (The chemical symbol for Cobalt is Ni.) or (not not (not not (((-2 * -5 * 5 * 0) <= (11 % 7) <= (17 - -10)) or (The currency of Canada is the Dollar.))))))
D. not not ((not ((((There are 30 days in April.) and ((-8 * 0 + 1 * -9) < (-10 + 10))) or ((-17 * 10) == (-1 * 10 - 9 * 8))) and ((10 * -15) >= (20 + -2)))) or (not not ((((Colombia is in South America.) or (Water boils at 100 degrees Celsius at sea level.)) or ((Saturn is the 1st planet from the Sun.) or ((-7 * 7 - -8 * 4) != (-10 * -1)))) and ((not not ((15 % 7) < (15 + 8) < (-5 + 7))) and (not ((13 * 11) <= (-16 + -8)))))))
E. not (not not ((not not ((((-7 * -6 + -4 * -1) != (-5 - -10)) or (The capital of Italy is Rome.)) or ((Diamonds are made of carbon.) and ((-13 * 15) < (-7 * 8 + -8 * 9) < (38 % 5))))) or (not (((-10 * 4 - 7 * 5) < (8 * -5 * -1 * 10) < (-3 * -11)) and (The capital of Canada is Ottawa.))) or (not not ((((-20 - 14) <= (8 * 7 - -9 * 9) <= (-13 + 5)) and (Sound travels faster in a vacuum.)) or ((There are 30 days in November.) and (172 is an odd number.))))))
F. not not (not not ((((-18 + 9) != (11 - -10)) and ((2 - 1) <= (19 - -2))) or ((not not ((20 + -20) < (-8 * 10 * -3 * -8) < (3 ** 3))) or (Earth is the 3rd planet from the Sun.)) or (not (not (not not ((-9 - 13) < (12 + -3) < (-18 + -1)))))))
G. not not ((not ((Jupiter is the 5th planet from the Sun.) or ((((12 - -1) != (-1 + -1)) or (Mercury is the 1st planet from the Sun.)) and (The capital of Greece is Athens.)))) and ((((Light travels faster than sound.) or (((1 * 6 + -9 * -5) <= (-11 + -14)) and (The chemical symbol for Titanium is Ti.))) and (not not (The square root of 225 is 2.)) and (not ((140 is an even number.) and ((10 * -19) > (11 * -16))))) or (not (There are 30 days in January.))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 71217030,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not not (not ((not not ((((34 % 2) > (2 ** 2)) and (Steam is a solid at room temperature.)) or (not (The currency of Mexico is the Pound.)))) or ((not not ((The 1948 Olympics were held in Atlanta.) or (The currency of New Zealand is the Dollar.))) or (The currency of Russia is the Peso.))))\nB. not (not not ((not (61 is a perfect square.)) or ((((1900 is a leap year.) and ((6 * -3) <= (-4 * -2 - 6 * 6) <= (9 * -13))) and ((The capital of Thailand is Wellington.) and ((-8 * 0 + 5 * 4) <= (1 + 13) <= (-2 * -16)))) or (Earth is the 5th planet from the Sun.))))\nC. not (not not ((not not (The 1920 Olympics were held in Antwerp.)) or (The chemical symbol for Cobalt is Ni.) or (not not (not not (((-2 * -5 * 5 * 0) <= (11 % 7) <= (17 - -10)) or (The currency of Canada is the Dollar.))))))\nD. not not ((not ((((There are 30 days in April.) and ((-8 * 0 + 1 * -9) < (-10 + 10))) or ((-17 * 10) == (-1 * 10 - 9 * 8))) and ((10 * -15) >= (20 + -2)))) or (not not ((((Colombia is in South America.) or (Water boils at 100 degrees Celsius at sea level.)) or ((Saturn is the 1st planet from the Sun.) or ((-7 * 7 - -8 * 4) != (-10 * -1)))) and ((not not ((15 % 7) < (15 + 8) < (-5 + 7))) and (not ((13 * 11) <= (-16 + -8)))))))\nE. not (not not ((not not ((((-7 * -6 + -4 * -1) != (-5 - -10)) or (The capital of Italy is Rome.)) or ((Diamonds are made of carbon.) and ((-13 * 15) < (-7 * 8 + -8 * 9) < (38 % 5))))) or (not (((-10 * 4 - 7 * 5) < (8 * -5 * -1 * 10) < (-3 * -11)) and (The capital of Canada is Ottawa.))) or (not not ((((-20 - 14) <= (8 * 7 - -9 * 9) <= (-13 + 5)) and (Sound travels faster in a vacuum.)) or ((There are 30 days in November.) and (172 is an odd number.))))))\nF. not not (not not ((((-18 + 9) != (11 - -10)) and ((2 - 1) <= (19 - -2))) or ((not not ((20 + -20) < (-8 * 10 * -3 * -8) < (3 ** 3))) or (Earth is the 3rd planet from the Sun.)) or (not (not (not not ((-9 - 13) < (12 + -3) < (-18 + -1)))))))\nG. not not ((not ((Jupiter is the 5th planet from the Sun.) or ((((12 - -1) != (-1 + -1)) or (Mercury is the 1st planet from the Sun.)) and (The capital of Greece is Athens.)))) and ((((Light travels faster than sound.) or (((1 * 6 + -9 * -5) <= (-11 + -14)) and (The chemical symbol for Titanium is Ti.))) and (not not (The square root of 225 is 2.)) and (not ((140 is an even number.) and ((10 * -19) > (11 * -16))))) or (not (There are 30 days in January.))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 71217030,
"true_count": 2
},
"seed": 71217030,
"task_id": 671217030,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (((((7 + 13) < (-6 * 19)) and ((8 + -6) == (5 ** 1))) or ((埃及位于非洲。) or (瑞典的货币是里亚尔。))) and (not not (((-20 * 19) != (14 * 4)) and (氦气在常温下是液体。)))) and (not not ((2 ** 1) < (15 * 3)))
B. ((第一部iPhone发布发生在2007年。) or ((((2 * 20) == (-11 + -10)) and (78大于47。)) and ((俄罗斯的首都是莫斯科。) or (澳大利亚的货币是澳元。)))) and (not (土星是距离太阳第6近的行星。))
C. (((汞在常温下是液体。) or ((巴西位于大洋洲。) or (葡萄牙的首都是罗马。))) or (not (日本的货币是日元。)) or ((((17 - 5) < (-12 + 17)) or ((5 ** 2) < (30 % 5) < (0 * 3))) or (钛的化学符号是Zn。))) or ((10 + -9) <= (5 ** 3)) or ((2058年是闰年。) and (((-20 - -3) < (-7 * 8)) and ((49 % 5) < (9 - -18))) and (俄罗斯位于亚洲。))
D. (((not not (水蒸气在常温下是气体。)) and ((17 - -5) == (3 ** 3))) or (not (鬣蜥是鸟类。))) or ((((欧盟的货币是瑞士法郎。) or (菲律宾的首都是马尼拉。)) or ((葡萄牙的首都是安卡拉。) or ((-17 * -3) == (-2 - -3)))) or (not not ((地球是距离太阳第6近的行星。) or (2000年奥运会在圣路易斯举办。))))
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,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 42941050,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. (((((7 + 13) < (-6 * 19)) and ((8 + -6) == (5 ** 1))) or ((埃及位于非洲。) or (瑞典的货币是里亚尔。))) and (not not (((-20 * 19) != (14 * 4)) and (氦气在常温下是液体。)))) and (not not ((2 ** 1) < (15 * 3)))\nB. ((第一部iPhone发布发生在2007年。) or ((((2 * 20) == (-11 + -10)) and (78大于47。)) and ((俄罗斯的首都是莫斯科。) or (澳大利亚的货币是澳元。)))) and (not (土星是距离太阳第6近的行星。))\nC. (((汞在常温下是液体。) or ((巴西位于大洋洲。) or (葡萄牙的首都是罗马。))) or (not (日本的货币是日元。)) or ((((17 - 5) < (-12 + 17)) or ((5 ** 2) < (30 % 5) < (0 * 3))) or (钛的化学符号是Zn。))) or ((10 + -9) <= (5 ** 3)) or ((2058年是闰年。) and (((-20 - -3) < (-7 * 8)) and ((49 % 5) < (9 - -18))) and (俄罗斯位于亚洲。))\nD. (((not not (水蒸气在常温下是气体。)) and ((17 - -5) == (3 ** 3))) or (not (鬣蜥是鸟类。))) or ((((欧盟的货币是瑞士法郎。) or (菲律宾的首都是马尼拉。)) or ((葡萄牙的首都是安卡拉。) or ((-17 * -3) == (-2 - -3)))) or (not not ((地球是距离太阳第6近的行星。) or (2000年奥运会在圣路易斯举办。))))\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": 4,
"language": "cn",
"num_options": 4,
"seed": 42941050,
"true_count": 2
},
"seed": 42941050,
"task_id": 642941050,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (not not (not (Sharks are mammals.))) and (not ((not ((Ice is a solid at room temperature.) or ((2 - 18) < (6 - -12) < (-17 + 16)))) or (A dragonfly is an insect.)))
B. (not ((((35 % 3) >= (5 ** 3)) and ((3 ** 2) >= (4 * 12))) and (((The chemical symbol for Manganese is U.) or ((47 % 8) != (3 * 7 - -2 * 4))) or (Mars is the closest planet to the Sun.)))) or ((not ((The 1900 Olympics were held in Paris.) or ((2 ** 2) <= (10 * 6)))) or (not not ((25 % 2) < (3 + -11)))) or (not ((((4 * 10 * -8 * 7) < (8 - 13) < (-3 * 3 * -9 * -7)) and ((5 ** 2) >= (-12 - -11))) or ((not ((-10 * -11) < (-9 - -6))) and (The currency of Sweden is the Baht.))))
C. not not (not not ((((A trout is a fish.) or (The currency of Switzerland is the Franc.)) and (The 1956 Olympics were held in Los Angeles.)) or ((Brazil is in Asia.) and (The chemical symbol for Neon is Ne.)) or (((9 * 9 - -1 * -2) <= (6 * -7 + -5 * -5)) or (Saturn is the 5th planet from the Sun.))))
D. not (not not ((((2054 is a leap year.) or (Electricity flows faster than light.)) or (not ((9 - 18) <= (3 ** 3)))) or ((20 - 2) == (-12 - 13)) or (((The capital of France is Moscow.) or (39 is greater than 88.)) and ((There are 31 days in October.) and ((-1 * 8 + 6 * -3) >= (10 - -10))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 49879583,
"true_count": 2
},
"question": "Given the following boolean expressions:\n\nA. (not not (not (Sharks are mammals.))) and (not ((not ((Ice is a solid at room temperature.) or ((2 - 18) < (6 - -12) < (-17 + 16)))) or (A dragonfly is an insect.)))\nB. (not ((((35 % 3) >= (5 ** 3)) and ((3 ** 2) >= (4 * 12))) and (((The chemical symbol for Manganese is U.) or ((47 % 8) != (3 * 7 - -2 * 4))) or (Mars is the closest planet to the Sun.)))) or ((not ((The 1900 Olympics were held in Paris.) or ((2 ** 2) <= (10 * 6)))) or (not not ((25 % 2) < (3 + -11)))) or (not ((((4 * 10 * -8 * 7) < (8 - 13) < (-3 * 3 * -9 * -7)) and ((5 ** 2) >= (-12 - -11))) or ((not ((-10 * -11) < (-9 - -6))) and (The currency of Sweden is the Baht.))))\nC. not not (not not ((((A trout is a fish.) or (The currency of Switzerland is the Franc.)) and (The 1956 Olympics were held in Los Angeles.)) or ((Brazil is in Asia.) and (The chemical symbol for Neon is Ne.)) or (((9 * 9 - -1 * -2) <= (6 * -7 + -5 * -5)) or (Saturn is the 5th planet from the Sun.))))\nD. not (not not ((((2054 is a leap year.) or (Electricity flows faster than light.)) or (not ((9 - 18) <= (3 ** 3)))) or ((20 - 2) == (-12 - 13)) or (((The capital of France is Moscow.) or (39 is greater than 88.)) and ((There are 31 days in October.) and ((-1 * 8 + 6 * -3) >= (10 - -10))))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 49879583,
"true_count": 2
},
"seed": 49879583,
"task_id": 649879583,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not not (not not (not not ((9 * 0 * 1 * -8) == (2 * -12))))) or (((2081 is a leap year.) or (A day on Earth is 24 hours.)) and (not not ((-7 * 4 + 8 * -1) < (-7 * -6 + -9 * 9)))) or (((((-19 - 20) > (-7 * 4 - -1 * -1)) and (The Sun revolves around the Earth.)) or ((The capital of Chile is Santiago.) or ((-10 * 7 + 9 * 1) >= (0 * 9 - -7 * -1)))) and (The chemical symbol for Tin is Cl.))
B. not ((Morocco is in Africa.) or ((7 * 15) != (0 * 9 + -9 * -5)))
C. not ((not not (((-19 + -1) != (10 * 9 + -4 * 7)) or ((8 - -9) != (-14 * -2)))) and (The currency of China is the Pound.))
D. ((not not (((4 * -14) < (-3 + 19)) or ((7 * 9 - 4 * 9) <= (3 ** 2) <= (-4 - -7)))) and ((((-19 * 13) == (-3 + -13)) and ((-8 * -12) <= (2 ** 3))) and ((-19 + 4) < (-10 - -18) < (11 + 12)))) and (((14 * 3) <= (5 - 9)) and (not (not ((12 - 9) > (-10 * 3)))))
E. (((not not (The capital of Russia is Moscow.)) and (not not ((-2 * 9 - -6 * 1) <= (-14 - -2)))) or ((7 + -8) <= (35 % 7))) or ((((45 % 9) <= (-6 * -11)) or ((-4 - 7) > (-14 - 6))) or (not (1980 is a leap year.))) or (((The currency of Philippines is the Ringgit.) or (((-15 - -9) != (-8 - -11)) and (The capital of Singapore is Oslo.))) or (not ((The 1908 Olympics were held in Stockholm.) and (Iron is a liquid at room temperature.))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 73716856,
"true_count": 2
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (not not (not not (not not ((9 * 0 * 1 * -8) == (2 * -12))))) or (((2081 is a leap year.) or (A day on Earth is 24 hours.)) and (not not ((-7 * 4 + 8 * -1) < (-7 * -6 + -9 * 9)))) or (((((-19 - 20) > (-7 * 4 - -1 * -1)) and (The Sun revolves around the Earth.)) or ((The capital of Chile is Santiago.) or ((-10 * 7 + 9 * 1) >= (0 * 9 - -7 * -1)))) and (The chemical symbol for Tin is Cl.))\nB. not ((Morocco is in Africa.) or ((7 * 15) != (0 * 9 + -9 * -5)))\nC. not ((not not (((-19 + -1) != (10 * 9 + -4 * 7)) or ((8 - -9) != (-14 * -2)))) and (The currency of China is the Pound.))\nD. ((not not (((4 * -14) < (-3 + 19)) or ((7 * 9 - 4 * 9) <= (3 ** 2) <= (-4 - -7)))) and ((((-19 * 13) == (-3 + -13)) and ((-8 * -12) <= (2 ** 3))) and ((-19 + 4) < (-10 - -18) < (11 + 12)))) and (((14 * 3) <= (5 - 9)) and (not (not ((12 - 9) > (-10 * 3)))))\nE. (((not not (The capital of Russia is Moscow.)) and (not not ((-2 * 9 - -6 * 1) <= (-14 - -2)))) or ((7 + -8) <= (35 % 7))) or ((((45 % 9) <= (-6 * -11)) or ((-4 - 7) > (-14 - 6))) or (not (1980 is a leap year.))) or (((The currency of Philippines is the Ringgit.) or (((-15 - -9) != (-8 - -11)) and (The capital of Singapore is Oslo.))) or (not ((The 1908 Olympics were held in Stockholm.) and (Iron is a liquid at room temperature.))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 73716856,
"true_count": 2
},
"seed": 73716856,
"task_id": 673716856,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (not not (((Helium is a gas at room temperature.) or ((not (A octopus has 0 legs.)) and ((The capital of France is Paris.) and ((4 * -15) < (-9 * 9 + -3 * 4) < (3 ** 1))))) and ((The currency of United Kingdom is the Sol.) and ((Earth is the 3rd planet from the Sun.) and ((-10 * 12) <= (2 ** 3))) and (not (Diamonds are made of carbon.)))))
B. not (not (not ((The capital of Turkey is Athens.) or ((0 * 0 - -8 * 2) >= (40 % 6)))))
C. not (not (not not ((((Christopher Columbus reached America occurred in 1492.) or ((16 + 7) >= (3 ** 1))) or ((9 + 16) >= (9 + -18))) or (There are 30 days in November.))))
D. not not (not ((not not ((13 - 12) > (9 * -10 * 6 * -1))) and (((((-4 * 3 * 9 * 4) == (8 + 5)) and (The chemical symbol for Nitrogen is He.)) and ((The 1956 Olympics were held in Paris.) or (64 is a perfect square.))) or ((11 % 7) > (13 - -8)))))
E. not (not ((((-7 * 8 - -3 * 0) < (4 * -3 - -2 * -3) < (17 + -7)) and ((2 - 18) == (0 * 1 * -4 * -3)) and (not (not (The 2008 Olympics were held in Beijing.)))) and ((((5 ** 3) < (7 + -5)) or (not not ((17 - 12) > (-16 + 9)))) and ((-11 - -14) != (0 * 0 + 3 * -1)))))
F. not (not ((not not (Antarctica is the coldest continent.)) or (not not ((not not (19 is a prime number.)) or (The 1980 Olympics were held in Moscow.)))))
G. not (not not ((not ((((2 * 13) != (-4 * -8 + -2 * -2)) and ((-3 * -7 + -5 * 0) == (-15 - 20))) and (((-1 - 20) < (-6 - 8)) or (The capital of China is Kuala Lumpur.)))) or (((The capital of Canada is Ottawa.) or (The chemical symbol for Zinc is Pb.)) or ((-1 - -9) != (6 - 8))) or (((((18 - 8) <= (17 * -16)) or ((7 + 8) > (20 % 10))) or ((21 % 2) < (-9 - 1))) and (not not ((Saturn is the 6th planet from the Sun.) or (The currency of Brazil is the Peso.))))))
H. not not (not (((((A dragonfly is a fish.) and (The 1992 Olympics were held in Los Angeles.)) and (The currency of Czech Republic is the Baht.)) and ((-14 * -16) <= (15 + -15)) and (((-3 * 3 - 5 * 3) <= (5 + -12)) and ((The currency of South Korea is the Won.) and (A spider has 0 legs.)))) or ((not not ((Carbon dioxide is a gas at room temperature.) or (Japan is in Asia.))) and ((16 + -7) < (16 - 16)) and (not ((The square root of 1 is 4.) or ((14 * 1) <= (18 * -18) <= (-2 - 12)))))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,C,D,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 79680120,
"true_count": 5
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not not (((Helium is a gas at room temperature.) or ((not (A octopus has 0 legs.)) and ((The capital of France is Paris.) and ((4 * -15) < (-9 * 9 + -3 * 4) < (3 ** 1))))) and ((The currency of United Kingdom is the Sol.) and ((Earth is the 3rd planet from the Sun.) and ((-10 * 12) <= (2 ** 3))) and (not (Diamonds are made of carbon.)))))\nB. not (not (not ((The capital of Turkey is Athens.) or ((0 * 0 - -8 * 2) >= (40 % 6)))))\nC. not (not (not not ((((Christopher Columbus reached America occurred in 1492.) or ((16 + 7) >= (3 ** 1))) or ((9 + 16) >= (9 + -18))) or (There are 30 days in November.))))\nD. not not (not ((not not ((13 - 12) > (9 * -10 * 6 * -1))) and (((((-4 * 3 * 9 * 4) == (8 + 5)) and (The chemical symbol for Nitrogen is He.)) and ((The 1956 Olympics were held in Paris.) or (64 is a perfect square.))) or ((11 % 7) > (13 - -8)))))\nE. not (not ((((-7 * 8 - -3 * 0) < (4 * -3 - -2 * -3) < (17 + -7)) and ((2 - 18) == (0 * 1 * -4 * -3)) and (not (not (The 2008 Olympics were held in Beijing.)))) and ((((5 ** 3) < (7 + -5)) or (not not ((17 - 12) > (-16 + 9)))) and ((-11 - -14) != (0 * 0 + 3 * -1)))))\nF. not (not ((not not (Antarctica is the coldest continent.)) or (not not ((not not (19 is a prime number.)) or (The 1980 Olympics were held in Moscow.)))))\nG. not (not not ((not ((((2 * 13) != (-4 * -8 + -2 * -2)) and ((-3 * -7 + -5 * 0) == (-15 - 20))) and (((-1 - 20) < (-6 - 8)) or (The capital of China is Kuala Lumpur.)))) or (((The capital of Canada is Ottawa.) or (The chemical symbol for Zinc is Pb.)) or ((-1 - -9) != (6 - 8))) or (((((18 - 8) <= (17 * -16)) or ((7 + 8) > (20 % 10))) or ((21 % 2) < (-9 - 1))) and (not not ((Saturn is the 6th planet from the Sun.) or (The currency of Brazil is the Peso.))))))\nH. not not (not (((((A dragonfly is a fish.) and (The 1992 Olympics were held in Los Angeles.)) and (The currency of Czech Republic is the Baht.)) and ((-14 * -16) <= (15 + -15)) and (((-3 * 3 - 5 * 3) <= (5 + -12)) and ((The currency of South Korea is the Won.) and (A spider has 0 legs.)))) or ((not not ((Carbon dioxide is a gas at room temperature.) or (Japan is in Asia.))) and ((16 + -7) < (16 - 16)) and (not ((The square root of 1 is 4.) or ((14 * 1) <= (18 * -18) <= (-2 - 12)))))))\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": 8,
"seed": 79680120,
"true_count": 5
},
"seed": 79680120,
"task_id": 679680120,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not ((((25 % 2) <= (2 * -5 * -10 * -8)) and ((-16 - -5) < (5 ** 2))) and (not not (The Moon produces its own light.)))
B. (not not ((2026 is a leap year.) and ((3 * 3) < (3 * -15)))) or (not not (not ((-4 * -15) < (9 + -2))))
C. not (Electricity flows faster than light.)
D. (The currency of China is the Dollar.) or (The chemical symbol for Potassium is Pb.)
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 67384713,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. not ((((25 % 2) <= (2 * -5 * -10 * -8)) and ((-16 - -5) < (5 ** 2))) and (not not (The Moon produces its own light.)))\nB. (not not ((2026 is a leap year.) and ((3 * 3) < (3 * -15)))) or (not not (not ((-4 * -15) < (9 + -2))))\nC. not (Electricity flows faster than light.)\nD. (The currency of China is the Dollar.) or (The chemical symbol for Potassium is Pb.)\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 67384713,
"true_count": 3
},
"seed": 67384713,
"task_id": 667384713,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not not (((not not ((not not (The capital of Spain is Madrid.)) or (not not ((-13 + -13) != (-17 - -13))))) or (Nigeria is in Africa.) or (not not (not ((10 * -5) == (-6 - 0))))) and (((Mars is the 7th planet from the Sun.) or ((A dolphin is a fish.) and (((18 % 7) <= (8 * 20)) and ((-4 - -8) < (13 % 7) < (-10 * 10))))) and ((Colombia is in South America.) or ((The Earth revolves around the Sun.) or (The chemical symbol for Nitrogen is Na.)) or ((-16 - 1) < (17 - 11) < (2 * -15)))))
B. not (not not (((not not (((8 * 6 - -3 * -10) >= (-4 * -7 - -6 * 7)) or ((-7 * -3 + 7 * 2) == (2 % 2)))) and (((Ice is less dense than liquid water.) or (The French Revolution began occurred in 1789.)) and ((0 - -10) == (-7 * 17)))) and ((19 + -14) < (-6 + -18)) and (((-13 * -5) >= (14 + -7)) or (not not (((-7 * -10 * 2 * 2) >= (5 ** 2)) or ((2 * 0 - 1 * 2) != (-7 * -2 + -4 * -5)))))))
C. not not (not not (((not not ((Thailand is in Asia.) and ((18 + -6) <= (-9 * 2 + 10 * 5)))) and ((3 ** 1) != (11 * -19))) and (not ((not (The chemical symbol for Potassium is Si.)) or (((-7 * 7 - 6 * -7) < (16 + -10) < (1 + 13)) and (Brazil is in South America.))))))
D. not not (not (((The capital of Japan is Tokyo.) or ((-7 * 5 - -1 * 5) <= (-7 - 20)) or (There are 31 days in August.)) and (((((0 * -4) <= (4 ** 2)) and (323 is a perfect square.)) or (The human body has 150 bones.)) and (((A cow has 2 legs.) and ((-11 - 13) != (5 * -15))) or ((15 + 14) != (-12 * -10))))))
E. (not (not not (not not (The currency of China is the Yuan.)))) and (not not ((((10 - 4) < (-15 - 4) < (11 - 19)) or (((The square root of 49 is 7.) or (25 is less than or equal to 73.)) or ((The 1992 Olympics were held in Barcelona.) or (The capital of Mexico is Abuja.)))) or (not not ((-2 + 4) > (-6 + -14)))))
F. not not (not not ((((The 2016 Olympics were held in London.) or (1916 is a leap year.)) or ((There are 31 days in October.) and (The capital of India is Brussels.)) or (((1 - -16) == (22 % 4)) and (((8 - 1) <= (8 - 16) <= (5 ** 2)) or (The capital of Philippines is Canberra.)))) or (not (((32 is an even number.) and (The capital of Ukraine is Kyiv.)) and (not not ((-5 * -4) == (8 * -4 + 5 * -1)))))))
G. not (not not (not (not not ((not not ((-16 + -18) > (2 * -12))) and (((0 * 3 + 1 * -8) < (-11 - -4)) and (2081 is a leap year.))))))
H. not not (((not (Japan is in Asia.)) or (not not (Earth is the 3rd planet from the Sun.))) and ((not not ((((6 * -4 * -6 * 1) < (0 * 4 + 4 * -9) < (-6 * 15)) or (A horse has 8 legs.)) and ((1 ** 1) >= (6 * -1 - 6 * 0)))) and (((((7 * 8) <= (5 - -9)) or ((-16 * -10) >= (9 * -1 - -9 * 10))) or ((The currency of Norway is the Won.) or ((7 - 2) > (0 * 4 - 3 * -4)))) or (((36 is divisible by 8.) and (Helium is a gas at room temperature.)) and (not (The 1980 Olympics were held in Athens.))))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 88715327,
"true_count": 3
},
"question": "Consider the following logical expressions:\n\nA. not not (((not not ((not not (The capital of Spain is Madrid.)) or (not not ((-13 + -13) != (-17 - -13))))) or (Nigeria is in Africa.) or (not not (not ((10 * -5) == (-6 - 0))))) and (((Mars is the 7th planet from the Sun.) or ((A dolphin is a fish.) and (((18 % 7) <= (8 * 20)) and ((-4 - -8) < (13 % 7) < (-10 * 10))))) and ((Colombia is in South America.) or ((The Earth revolves around the Sun.) or (The chemical symbol for Nitrogen is Na.)) or ((-16 - 1) < (17 - 11) < (2 * -15)))))\nB. not (not not (((not not (((8 * 6 - -3 * -10) >= (-4 * -7 - -6 * 7)) or ((-7 * -3 + 7 * 2) == (2 % 2)))) and (((Ice is less dense than liquid water.) or (The French Revolution began occurred in 1789.)) and ((0 - -10) == (-7 * 17)))) and ((19 + -14) < (-6 + -18)) and (((-13 * -5) >= (14 + -7)) or (not not (((-7 * -10 * 2 * 2) >= (5 ** 2)) or ((2 * 0 - 1 * 2) != (-7 * -2 + -4 * -5)))))))\nC. not not (not not (((not not ((Thailand is in Asia.) and ((18 + -6) <= (-9 * 2 + 10 * 5)))) and ((3 ** 1) != (11 * -19))) and (not ((not (The chemical symbol for Potassium is Si.)) or (((-7 * 7 - 6 * -7) < (16 + -10) < (1 + 13)) and (Brazil is in South America.))))))\nD. not not (not (((The capital of Japan is Tokyo.) or ((-7 * 5 - -1 * 5) <= (-7 - 20)) or (There are 31 days in August.)) and (((((0 * -4) <= (4 ** 2)) and (323 is a perfect square.)) or (The human body has 150 bones.)) and (((A cow has 2 legs.) and ((-11 - 13) != (5 * -15))) or ((15 + 14) != (-12 * -10))))))\nE. (not (not not (not not (The currency of China is the Yuan.)))) and (not not ((((10 - 4) < (-15 - 4) < (11 - 19)) or (((The square root of 49 is 7.) or (25 is less than or equal to 73.)) or ((The 1992 Olympics were held in Barcelona.) or (The capital of Mexico is Abuja.)))) or (not not ((-2 + 4) > (-6 + -14)))))\nF. not not (not not ((((The 2016 Olympics were held in London.) or (1916 is a leap year.)) or ((There are 31 days in October.) and (The capital of India is Brussels.)) or (((1 - -16) == (22 % 4)) and (((8 - 1) <= (8 - 16) <= (5 ** 2)) or (The capital of Philippines is Canberra.)))) or (not (((32 is an even number.) and (The capital of Ukraine is Kyiv.)) and (not not ((-5 * -4) == (8 * -4 + 5 * -1)))))))\nG. not (not not (not (not not ((not not ((-16 + -18) > (2 * -12))) and (((0 * 3 + 1 * -8) < (-11 - -4)) and (2081 is a leap year.))))))\nH. not not (((not (Japan is in Asia.)) or (not not (Earth is the 3rd planet from the Sun.))) and ((not not ((((6 * -4 * -6 * 1) < (0 * 4 + 4 * -9) < (-6 * 15)) or (A horse has 8 legs.)) and ((1 ** 1) >= (6 * -1 - 6 * 0)))) and (((((7 * 8) <= (5 - -9)) or ((-16 * -10) >= (9 * -1 - -9 * 10))) or ((The currency of Norway is the Won.) or ((7 - 2) > (0 * 4 - 3 * -4)))) or (((36 is divisible by 8.) and (Helium is a gas at room temperature.)) and (not (The 1980 Olympics were held in Athens.))))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 88715327,
"true_count": 3
},
"seed": 88715327,
"task_id": 688715327,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not not ((not not ((not not ((The human body has 150 bones.) or ((8 * -6 - 6 * -9) >= (-8 * -7 - -2 * -6)))) or ((A swan is a bird.) and (26 is less than or equal to 47.)) or (not (not ((-20 * 17) < (7 + 1)))))) or ((((8 % 2) < (4 * 14)) or (not (Nigeria is in North America.))) and ((The first moon landing occurred in 1969.) and (not not (The capital of Egypt is Copenhagen.)))) or (not (not ((0 + -9) <= (5 ** 2)))))
B. (not (not not (not not (((4 ** 2) <= (11 - -17)) or (The chemical symbol for Chromium is Pt.))))) or (not not (not (not ((-20 * -1) > (-1 * 8 * 5 * 9)))))
C. not (not (((((The 2004 Olympics were held in Athens.) and ((2 + -3) < (-3 * -1 + 2 * -5) < (19 - -2))) and (((5 ** 2) == (2 - 15)) or ((3 - -17) > (18 + 19)))) or (((The chemical symbol for Phosphorus is C.) and ((48 % 3) != (-2 + 7))) and (Ice is less dense than liquid water.))) and (not not ((A salmon is a fish.) and ((-14 * -19) <= (11 * 18))))))
D. not not (not ((((not not (Alcohol is a liquid at room temperature.)) or ((-14 + -3) <= (49 % 7))) or (((26 % 3) != (8 - 5)) and ((Uranus is the 7th planet from the Sun.) or (New Zealand is in North America.)))) and (not not ((((-9 - -3) > (-1 * -10 * 0 * -4)) or (Australia is in Oceania.)) or ((-9 + 17) >= (4 * 16))))))
E. not (not not ((not not (1987 is a leap year.)) or (((11 - -19) < (17 + -3) < (-6 * -3 + -2 * 9)) or (((144 is a perfect square.) or ((14 * -15) != (-13 - -19))) or ((-14 * 18) >= (6 * -16))))))
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": 6,
"language": "en",
"num_options": 5,
"seed": 47828605,
"true_count": 2
},
"question": "Consider the following logical expressions:\n\nA. not not ((not not ((not not ((The human body has 150 bones.) or ((8 * -6 - 6 * -9) >= (-8 * -7 - -2 * -6)))) or ((A swan is a bird.) and (26 is less than or equal to 47.)) or (not (not ((-20 * 17) < (7 + 1)))))) or ((((8 % 2) < (4 * 14)) or (not (Nigeria is in North America.))) and ((The first moon landing occurred in 1969.) and (not not (The capital of Egypt is Copenhagen.)))) or (not (not ((0 + -9) <= (5 ** 2)))))\nB. (not (not not (not not (((4 ** 2) <= (11 - -17)) or (The chemical symbol for Chromium is Pt.))))) or (not not (not (not ((-20 * -1) > (-1 * 8 * 5 * 9)))))\nC. not (not (((((The 2004 Olympics were held in Athens.) and ((2 + -3) < (-3 * -1 + 2 * -5) < (19 - -2))) and (((5 ** 2) == (2 - 15)) or ((3 - -17) > (18 + 19)))) or (((The chemical symbol for Phosphorus is C.) and ((48 % 3) != (-2 + 7))) and (Ice is less dense than liquid water.))) and (not not ((A salmon is a fish.) and ((-14 * -19) <= (11 * 18))))))\nD. not not (not ((((not not (Alcohol is a liquid at room temperature.)) or ((-14 + -3) <= (49 % 7))) or (((26 % 3) != (8 - 5)) and ((Uranus is the 7th planet from the Sun.) or (New Zealand is in North America.)))) and (not not ((((-9 - -3) > (-1 * -10 * 0 * -4)) or (Australia is in Oceania.)) or ((-9 + 17) >= (4 * 16))))))\nE. not (not not ((not not (1987 is a leap year.)) or (((11 - -19) < (17 + -3) < (-6 * -3 + -2 * 9)) or (((144 is a perfect square.) or ((14 * -15) != (-13 - -19))) or ((-14 * 18) >= (6 * -16))))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 47828605,
"true_count": 2
},
"seed": 47828605,
"task_id": 647828605,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not ((not (Spiders are insects.)) or (not not ((6 % 10) < (0 - 7)))))
B. not ((not not (((2 - -17) == (2 - -9)) and (Saudi Arabia is in Oceania.) and (not not (The chemical symbol for Oxygen is Ca.)))) and (((((A bear is an insect.) or (World War I began occurred in 1914.)) or ((47 % 10) >= (-13 - -2))) and (((1 + 9) > (8 * -1 * 0 * -9)) and (((13 % 7) < (9 + 0)) or (802 is a Fibonacci number.)))) and (The currency of Chile is the Peso.) and (not (Neptune is the 8th planet from the Sun.))))
C. not not (((not ((17 + 8) <= (-20 * 12))) or (not not (not not (The chemical symbol for Nickel is Ni.)))) and (not (((4 ** 2) != (2 ** 2)) and (not not ((The capital of Ukraine is Lisbon.) or ((10 * -4 - -1 * 0) <= (18 + 17) <= (-4 * 0)))))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 49157246,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not (not ((not (Spiders are insects.)) or (not not ((6 % 10) < (0 - 7)))))\nB. not ((not not (((2 - -17) == (2 - -9)) and (Saudi Arabia is in Oceania.) and (not not (The chemical symbol for Oxygen is Ca.)))) and (((((A bear is an insect.) or (World War I began occurred in 1914.)) or ((47 % 10) >= (-13 - -2))) and (((1 + 9) > (8 * -1 * 0 * -9)) and (((13 % 7) < (9 + 0)) or (802 is a Fibonacci number.)))) and (The currency of Chile is the Peso.) and (not (Neptune is the 8th planet from the Sun.))))\nC. not not (((not ((17 + 8) <= (-20 * 12))) or (not not (not not (The chemical symbol for Nickel is Ni.)))) and (not (((4 ** 2) != (2 ** 2)) and (not not ((The capital of Ukraine is Lisbon.) or ((10 * -4 - -1 * 0) <= (18 + 17) <= (-4 * 0)))))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 49157246,
"true_count": 3
},
"seed": 49157246,
"task_id": 649157246,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. (12 - -13) != (-17 * -2)
B. Carbon dioxide is a gas at room temperature.
C. The speed of light is approximately 300,000 km/s.
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 61703012,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. (12 - -13) != (-17 * -2)\nB. Carbon dioxide is a gas at room temperature.\nC. The speed of light is approximately 300,000 km/s.\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 61703012,
"true_count": 3
},
"seed": 61703012,
"task_id": 661703012,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not not (not (((27 % 7) < (10 * 3 * 0 * 5)) or ((-1 + 18) > (12 + -15)) or (((The first iPhone was released occurred in 2007.) or ((-13 - -15) == (9 + -19))) or (Jupiter is the 5th planet from the Sun.))))) and (not (((((3 ** 2) >= (1 ** 2)) or (World War I began occurred in 1914.)) or (((There are 30 days in February.) or (The Earth revolves around the Sun.)) and (((6 * -19) <= (3 ** 3) <= (-16 - -15)) or ((4 ** 2) < (-18 + -17) < (-15 + -8))))) and (not ((19 + -20) != (-1 + 14)))))
B. (not (not (not ((not not (Nigeria is in Europe.)) and ((5 ** 2) <= (-7 - -15)))))) or (not not (not not (((not not ((20 * -16) <= (4 ** 1) <= (7 % 10))) and ((Earth is the 3rd planet from the Sun.) and (The capital of Saudi Arabia is Hanoi.))) and ((9 * 5 - 8 * -6) <= (27 % 10) <= (12 - -1)))))
C. not (not (((((26 % 6) >= (17 - -17)) and (not (Carbon dioxide is a gas at room temperature.))) or ((90 is a perfect square.) and (The chemical symbol for Aluminum is Al.))) and (((not not (1974 is a leap year.)) or (not not (Mars is the 4th planet from the Sun.))) or (not ((5 + -4) <= (-4 * -6 + 1 * 2) <= (-2 * -2 + 7 * 4))))))
D. not not (not ((not (not ((Russia is in Oceania.) and (The Moon orbits the Earth.)))) or (not (not not ((The Berlin Wall fell occurred in 1989.) and (The chemical symbol for Aluminum is Al.))))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 87608808,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. (not not (not (((27 % 7) < (10 * 3 * 0 * 5)) or ((-1 + 18) > (12 + -15)) or (((The first iPhone was released occurred in 2007.) or ((-13 - -15) == (9 + -19))) or (Jupiter is the 5th planet from the Sun.))))) and (not (((((3 ** 2) >= (1 ** 2)) or (World War I began occurred in 1914.)) or (((There are 30 days in February.) or (The Earth revolves around the Sun.)) and (((6 * -19) <= (3 ** 3) <= (-16 - -15)) or ((4 ** 2) < (-18 + -17) < (-15 + -8))))) and (not ((19 + -20) != (-1 + 14)))))\nB. (not (not (not ((not not (Nigeria is in Europe.)) and ((5 ** 2) <= (-7 - -15)))))) or (not not (not not (((not not ((20 * -16) <= (4 ** 1) <= (7 % 10))) and ((Earth is the 3rd planet from the Sun.) and (The capital of Saudi Arabia is Hanoi.))) and ((9 * 5 - 8 * -6) <= (27 % 10) <= (12 - -1)))))\nC. not (not (((((26 % 6) >= (17 - -17)) and (not (Carbon dioxide is a gas at room temperature.))) or ((90 is a perfect square.) and (The chemical symbol for Aluminum is Al.))) and (((not not (1974 is a leap year.)) or (not not (Mars is the 4th planet from the Sun.))) or (not ((5 + -4) <= (-4 * -6 + 1 * 2) <= (-2 * -2 + 7 * 4))))))\nD. not not (not ((not (not ((Russia is in Oceania.) and (The Moon orbits the Earth.)))) or (not (not not ((The Berlin Wall fell occurred in 1989.) and (The chemical symbol for Aluminum is Al.))))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 87608808,
"true_count": 2
},
"seed": 87608808,
"task_id": 687608808,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((not ((泰国位于亚洲。) or (1960年奥运会在罗马举办。))) and ((-18 + 4) < (-8 * 9 - 0 * -8))) and ((氦气在常温下是气体。) and (((-7 * -12) < (16 * -18)) or (古巴的首都是哈瓦那。)) and (((苏联解体发生在1989年。) and ((47 % 3) >= (-10 * 6 * -3 * 7))) or (((18 + 19) <= (-5 + 3)) or (第一次世界大战开始发生在1916年。))))
B. (not not (55小于等于7。)) or ((((硅的化学符号是Al。) or ((0 * -10) > (2 ** 1))) or (not not (第一次世界大战开始发生在1916年。))) or ((not ((-5 * -8 * -10 * 5) > (12 * 17))) or (1948年奥运会在安特卫普举办。)))
C. ((木星是距离太阳第6近的行星。) and ((not not (49的平方根是8。)) or ((第一部iPhone发布发生在2007年。) or ((8 % 2) < (-2 - -8))))) and (not (((木星是距离太阳第2近的行星。) and ((15 + 16) == (-7 - 15))) and ((泰国位于亚洲。) or ((37 % 7) == (-9 * 1 - 4 * 5)))))
D. (not (((3 * -4 * -7 * 4) > (5 ** 3)) or (not ((-14 - 9) <= (-5 * -4 - 8 * 2) <= (-7 * -7 + -10 * -10))))) or ((水星是距离太阳第1近的行星。) and (not (868是斐波那契数。))) or ((37能被6整除。) and ((金星是距离太阳第2近的行星。) and ((10 * 9 * 7 * -3) != (-9 + 18))) and (人类有6条腿。))
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": 4,
"language": "cn",
"num_options": 4,
"seed": 83011995,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. ((not ((泰国位于亚洲。) or (1960年奥运会在罗马举办。))) and ((-18 + 4) < (-8 * 9 - 0 * -8))) and ((氦气在常温下是气体。) and (((-7 * -12) < (16 * -18)) or (古巴的首都是哈瓦那。)) and (((苏联解体发生在1989年。) and ((47 % 3) >= (-10 * 6 * -3 * 7))) or (((18 + 19) <= (-5 + 3)) or (第一次世界大战开始发生在1916年。))))\nB. (not not (55小于等于7。)) or ((((硅的化学符号是Al。) or ((0 * -10) > (2 ** 1))) or (not not (第一次世界大战开始发生在1916年。))) or ((not ((-5 * -8 * -10 * 5) > (12 * 17))) or (1948年奥运会在安特卫普举办。)))\nC. ((木星是距离太阳第6近的行星。) and ((not not (49的平方根是8。)) or ((第一部iPhone发布发生在2007年。) or ((8 % 2) < (-2 - -8))))) and (not (((木星是距离太阳第2近的行星。) and ((15 + 16) == (-7 - 15))) and ((泰国位于亚洲。) or ((37 % 7) == (-9 * 1 - 4 * 5)))))\nD. (not (((3 * -4 * -7 * 4) > (5 ** 3)) or (not ((-14 - 9) <= (-5 * -4 - 8 * 2) <= (-7 * -7 + -10 * -10))))) or ((水星是距离太阳第1近的行星。) and (not (868是斐波那契数。))) or ((37能被6整除。) and ((金星是距离太阳第2近的行星。) and ((10 * 9 * 7 * -3) != (-9 + 18))) and (人类有6条腿。))\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": 4,
"language": "cn",
"num_options": 4,
"seed": 83011995,
"true_count": 2
},
"seed": 83011995,
"task_id": 683011995,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not ((not not (India is in South America.)) and (The capital of Netherlands is Amsterdam.))) and (not (Water is a liquid at room temperature.))
B. (((not (The chemical symbol for Calcium is Ca.)) and (South Korea is in Asia.)) and (((The 1948 Olympics were held in London.) or (The currency of Israel is the Shekel.)) and (Alcohol is a gas at room temperature.))) and (not ((not (The 1932 Olympics were held in Los Angeles.)) or ((The Titanic sank occurred in 1912.) or ((2 ** 1) == (5 ** 3)))))
C. not (not (not not (not ((-7 - 6) == (11 * 12)))))
D. ((((17 + 17) != (13 + 16)) or ((0 - -4) != (-3 - 1))) and (not not (((4 * -10 - -2 * 8) == (-14 + -15)) or ((-9 - 18) == (8 + 0))))) or (((((5 ** 2) >= (1 ** 3)) or (The capital of Indonesia is Mexico City.)) or ((-2 * 2 - -9 * -3) != (5 ** 3))) or ((4 * -7 - 5 * 4) > (19 + -2)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 65226814,
"true_count": 2
},
"question": "Below are several boolean expressions:\n\nA. (not ((not not (India is in South America.)) and (The capital of Netherlands is Amsterdam.))) and (not (Water is a liquid at room temperature.))\nB. (((not (The chemical symbol for Calcium is Ca.)) and (South Korea is in Asia.)) and (((The 1948 Olympics were held in London.) or (The currency of Israel is the Shekel.)) and (Alcohol is a gas at room temperature.))) and (not ((not (The 1932 Olympics were held in Los Angeles.)) or ((The Titanic sank occurred in 1912.) or ((2 ** 1) == (5 ** 3)))))\nC. not (not (not not (not ((-7 - 6) == (11 * 12)))))\nD. ((((17 + 17) != (13 + 16)) or ((0 - -4) != (-3 - 1))) and (not not (((4 * -10 - -2 * 8) == (-14 + -15)) or ((-9 - 18) == (8 + 0))))) or (((((5 ** 2) >= (1 ** 3)) or (The capital of Indonesia is Mexico City.)) or ((-2 * 2 - -9 * -3) != (5 ** 3))) or ((4 * -7 - 5 * 4) > (19 + -2)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 65226814,
"true_count": 2
},
"seed": 65226814,
"task_id": 665226814,
"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 (墨西哥位于北美洲。)) or ((not (((14 - -6) >= (14 + -7)) and (磷的化学符号是P。))) or (((-2 + 15) <= (-5 * 4 + 8 * -9) <= (-18 - -20)) or ((8 * 5 - 8 * -3) != (9 % 3))) or ((not (土耳其的首都是安卡拉。)) and ((加拿大的货币是日元。) and (泰坦尼克号沉没发生在1912年。))))) and (not (not not (企鹅能飞翔。))))
B. not (((((((-7 * 16) > (37 % 4)) and (螃蟹有4条腿。)) or ((6 - 17) > (9 * -11))) and (not not (327是完全平方数。)) and (((泰坦尼克号沉没发生在1912年。) and ((11 * 1) < (18 - 4) < (4 + -8))) and (水蒸气在常温下是固体。))) and (not not (not not (鲤鱼是鱼类。)))) or (((not (1939年是闰年。)) and ((((-7 * -3 * 2 * 1) >= (-2 + 12)) or ((15 + 10) == (13 * 11))) or (((10 + 2) <= (26 % 9) <= (-15 - 0)) and (钙的化学符号是Na。)))) and ((not ((93能被6整除。) and ((12 % 5) < (-10 * -3 * -3 * -9)))) and ((15 * -12) <= (37 % 1)))))
C. not ((not not ((铅的化学符号是Pt。) or (not not (铜的化学符号是Pb。)))) and ((((14 - -16) <= (50 % 10) <= (-1 * 17)) or (鸭子有0条腿。)) and (((2042年是闰年。) and (太平洋是最大的海洋。)) or (((-17 - 4) > (-10 * 8 - -8 * -8)) and ((-4 - -19) <= (19 * 17) <= (-17 + -17)))) and (((((-7 + 8) < (16 - -14) < (-2 + -2)) and (埃及位于南极洲。)) and (not (1936年奥运会在柏林举办。))) or (三月有29天。) or ((((14 + 2) == (-5 * -15)) or ((-2 * 7 - 10 * -6) <= (17 % 10) <= (-19 * 12))) or ((-10 + -6) != (-9 * 6 * 8 * -2))))))
D. (not not (not not (((古巴的首都是哈瓦那。) or (not ((0 + 16) <= (1 * -15)))) or (((钻石由碳元素组成。) and (汞在常温下是液体。)) and (not (氮气在常温下是气体。)))))) and ((((513是斐波那契数。) and (泰国位于亚洲。)) or ((1932年奥运会在巴黎举办。) or (秘鲁的货币是索尔。))) and ((美国宣布独立发生在1781年。) or (金星是距离太阳第2近的行星。))) and (not (not ((((钠的化学符号是Hg。) or (十二月有31天。)) and ((26 % 6) >= (8 * 5 - -9 * -1))) and ((((5 * 2 + 4 * 1) < (5 ** 2)) and ((-4 + 7) < (-18 - 5))) and (((-1 + 5) <= (-3 * -14)) and (1996年奥运会在赫尔辛基举办。))))))
E. not (not ((((-5 * -13) > (18 * 5)) and ((2 + 14) < (2 % 1)) and ((((46 % 8) <= (-8 * 7 + 6 * 8)) and (1909年是闰年。)) and ((铝的化学符号是Al。) or (哥伦比亚位于南美洲。)))) and (汞在常温下是液体。) and (((((1 * -7 - -5 * 6) < (7 * -3 - -2 * -8)) or ((-1 - -11) != (8 * 4 * 1 * 6))) and ((90能被2整除。) and ((-6 - 0) != (1 * -16)))) or (not (not ((-9 * -12) >= (-14 * 3)))))))
F. (not not ((((-13 - -1) == (-15 - 0)) or ((((-19 - -16) > (1 ** 3)) or (氮气在常温下是气体。)) and ((镁的化学符号是He。) or (现代奥运会首届举办发生在1901年。)))) or ((not (((6 + -5) <= (2 - -11)) or (831是斐波那契数。))) and ((3 * -13) > (20 % 8))))) or ((not (not not (not not ((瑞典的首都是阿布贾。) and ((20 - 7) == (17 - 7)))))) or (not (((澳大利亚的货币是人民币。) and ((水在常温下是液体。) or (德国位于欧洲。))) or (not ((5 ** 3) < (8 * -13))))))
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": "C,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 68307572,
"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 (((not not (墨西哥位于北美洲。)) or ((not (((14 - -6) >= (14 + -7)) and (磷的化学符号是P。))) or (((-2 + 15) <= (-5 * 4 + 8 * -9) <= (-18 - -20)) or ((8 * 5 - 8 * -3) != (9 % 3))) or ((not (土耳其的首都是安卡拉。)) and ((加拿大的货币是日元。) and (泰坦尼克号沉没发生在1912年。))))) and (not (not not (企鹅能飞翔。))))\nB. not (((((((-7 * 16) > (37 % 4)) and (螃蟹有4条腿。)) or ((6 - 17) > (9 * -11))) and (not not (327是完全平方数。)) and (((泰坦尼克号沉没发生在1912年。) and ((11 * 1) < (18 - 4) < (4 + -8))) and (水蒸气在常温下是固体。))) and (not not (not not (鲤鱼是鱼类。)))) or (((not (1939年是闰年。)) and ((((-7 * -3 * 2 * 1) >= (-2 + 12)) or ((15 + 10) == (13 * 11))) or (((10 + 2) <= (26 % 9) <= (-15 - 0)) and (钙的化学符号是Na。)))) and ((not ((93能被6整除。) and ((12 % 5) < (-10 * -3 * -3 * -9)))) and ((15 * -12) <= (37 % 1)))))\nC. not ((not not ((铅的化学符号是Pt。) or (not not (铜的化学符号是Pb。)))) and ((((14 - -16) <= (50 % 10) <= (-1 * 17)) or (鸭子有0条腿。)) and (((2042年是闰年。) and (太平洋是最大的海洋。)) or (((-17 - 4) > (-10 * 8 - -8 * -8)) and ((-4 - -19) <= (19 * 17) <= (-17 + -17)))) and (((((-7 + 8) < (16 - -14) < (-2 + -2)) and (埃及位于南极洲。)) and (not (1936年奥运会在柏林举办。))) or (三月有29天。) or ((((14 + 2) == (-5 * -15)) or ((-2 * 7 - 10 * -6) <= (17 % 10) <= (-19 * 12))) or ((-10 + -6) != (-9 * 6 * 8 * -2))))))\nD. (not not (not not (((古巴的首都是哈瓦那。) or (not ((0 + 16) <= (1 * -15)))) or (((钻石由碳元素组成。) and (汞在常温下是液体。)) and (not (氮气在常温下是气体。)))))) and ((((513是斐波那契数。) and (泰国位于亚洲。)) or ((1932年奥运会在巴黎举办。) or (秘鲁的货币是索尔。))) and ((美国宣布独立发生在1781年。) or (金星是距离太阳第2近的行星。))) and (not (not ((((钠的化学符号是Hg。) or (十二月有31天。)) and ((26 % 6) >= (8 * 5 - -9 * -1))) and ((((5 * 2 + 4 * 1) < (5 ** 2)) and ((-4 + 7) < (-18 - 5))) and (((-1 + 5) <= (-3 * -14)) and (1996年奥运会在赫尔辛基举办。))))))\nE. not (not ((((-5 * -13) > (18 * 5)) and ((2 + 14) < (2 % 1)) and ((((46 % 8) <= (-8 * 7 + 6 * 8)) and (1909年是闰年。)) and ((铝的化学符号是Al。) or (哥伦比亚位于南美洲。)))) and (汞在常温下是液体。) and (((((1 * -7 - -5 * 6) < (7 * -3 - -2 * -8)) or ((-1 - -11) != (8 * 4 * 1 * 6))) and ((90能被2整除。) and ((-6 - 0) != (1 * -16)))) or (not (not ((-9 * -12) >= (-14 * 3)))))))\nF. (not not ((((-13 - -1) == (-15 - 0)) or ((((-19 - -16) > (1 ** 3)) or (氮气在常温下是气体。)) and ((镁的化学符号是He。) or (现代奥运会首届举办发生在1901年。)))) or ((not (((6 + -5) <= (2 - -11)) or (831是斐波那契数。))) and ((3 * -13) > (20 % 8))))) or ((not (not not (not not ((瑞典的首都是阿布贾。) and ((20 - 7) == (17 - 7)))))) or (not (((澳大利亚的货币是人民币。) and ((水在常温下是液体。) or (德国位于欧洲。))) or (not ((5 ** 3) < (8 * -13))))))\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": 68307572,
"true_count": 2
},
"seed": 68307572,
"task_id": 668307572,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not not (((((-1 * -1 - 1 * 6) <= (-9 - -6)) and (2076 is a leap year.)) or (((31 % 1) < (5 ** 1) < (17 * 13)) or ((17 + 5) != (2 ** 3)))) and (not not ((not ((3 * 13) > (-18 - 10))) and ((Mercury is a liquid at room temperature.) or (109 is an even number.)))))) and (not ((((6 * -2 * 4 * 8) < (25 % 3)) or (not not ((9 % 8) == (-5 + -9)))) and ((-14 - -20) < (30 % 5)) and (not ((not not (There are 29 days in October.)) or (The currency of Hungary is the Krona.)))))
B. not (((((not not ((11 - -3) >= (6 * -3 * 4 * 9))) and (not not (World War I ended occurred in 1918.))) or ((1932 is a leap year.) or (Brazil is in South America.))) and (((not (1912 is a leap year.)) or ((1 * -1 + -2 * -3) > (14 - -18))) and (The 1928 Olympics were held in Berlin.))) and (not (not not (not not (((-9 * -6 * -9 * 2) >= (9 * 15)) or ((5 + -13) >= (2 * -20)))))))
C. not ((((not ((Uranus is the 8th planet from the Sun.) and (The 2020 Olympics were held in Tokyo.))) or ((-15 - -11) < (4 * 10))) or ((Saturn is the 8th planet from the Sun.) and (((2 * -9 * 6 * -2) >= (-8 * -8)) and (The 2024 Olympics were held in Paris.)))) or (not not ((World War II began occurred in 1939.) and ((The chemical symbol for Gold is Au.) or (not not (Egypt is in North America.))))))
D. not (not not (not not ((not (((5 % 5) < (-11 - 12) < (18 % 8)) or ((18 * 10) >= (18 * -7)))) or ((19 * -12) >= (8 - -9)))))
E. not not ((not (((5 * -3 * -1 * 3) != (-8 * 2 - 8 * 2)) and (not ((-18 * 19) != (9 + -6))) and (not not (not not (1935 is a leap year.))))) or ((not (The chemical symbol for Nitrogen is Mg.)) and (not (((1 ** 3) < (13 * -13) < (2 * 8)) or (The capital of Turkey is Ankara.))) and (not not (36 is divisible by 10.))))
F. not not (not not ((not (not (The capital of Brazil is Brasilia.))) or (((The chemical symbol for Uranium is U.) and (((16 + 11) <= (2 * 7 - 10 * 9) <= (17 + -6)) or ((-2 * 4) < (-17 * 11)))) and (((Uranus is the 8th planet from the Sun.) and ((1 - 12) == (17 - -13))) or ((The 1896 Olympics were held in Los Angeles.) or (Spain is in Europe.))))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 6,
"seed": 84268476,
"true_count": 4
},
"question": "Study the following logical statements:\n\nA. (not not (((((-1 * -1 - 1 * 6) <= (-9 - -6)) and (2076 is a leap year.)) or (((31 % 1) < (5 ** 1) < (17 * 13)) or ((17 + 5) != (2 ** 3)))) and (not not ((not ((3 * 13) > (-18 - 10))) and ((Mercury is a liquid at room temperature.) or (109 is an even number.)))))) and (not ((((6 * -2 * 4 * 8) < (25 % 3)) or (not not ((9 % 8) == (-5 + -9)))) and ((-14 - -20) < (30 % 5)) and (not ((not not (There are 29 days in October.)) or (The currency of Hungary is the Krona.)))))\nB. not (((((not not ((11 - -3) >= (6 * -3 * 4 * 9))) and (not not (World War I ended occurred in 1918.))) or ((1932 is a leap year.) or (Brazil is in South America.))) and (((not (1912 is a leap year.)) or ((1 * -1 + -2 * -3) > (14 - -18))) and (The 1928 Olympics were held in Berlin.))) and (not (not not (not not (((-9 * -6 * -9 * 2) >= (9 * 15)) or ((5 + -13) >= (2 * -20)))))))\nC. not ((((not ((Uranus is the 8th planet from the Sun.) and (The 2020 Olympics were held in Tokyo.))) or ((-15 - -11) < (4 * 10))) or ((Saturn is the 8th planet from the Sun.) and (((2 * -9 * 6 * -2) >= (-8 * -8)) and (The 2024 Olympics were held in Paris.)))) or (not not ((World War II began occurred in 1939.) and ((The chemical symbol for Gold is Au.) or (not not (Egypt is in North America.))))))\nD. not (not not (not not ((not (((5 % 5) < (-11 - 12) < (18 % 8)) or ((18 * 10) >= (18 * -7)))) or ((19 * -12) >= (8 - -9)))))\nE. not not ((not (((5 * -3 * -1 * 3) != (-8 * 2 - 8 * 2)) and (not ((-18 * 19) != (9 + -6))) and (not not (not not (1935 is a leap year.))))) or ((not (The chemical symbol for Nitrogen is Mg.)) and (not (((1 ** 3) < (13 * -13) < (2 * 8)) or (The capital of Turkey is Ankara.))) and (not not (36 is divisible by 10.))))\nF. not not (not not ((not (not (The capital of Brazil is Brasilia.))) or (((The chemical symbol for Uranium is U.) and (((16 + 11) <= (2 * 7 - 10 * 9) <= (17 + -6)) or ((-2 * 4) < (-17 * 11)))) and (((Uranus is the 8th planet from the Sun.) and ((1 - 12) == (17 - -13))) or ((The 1896 Olympics were held in Los Angeles.) or (Spain is in Europe.))))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 6,
"seed": 84268476,
"true_count": 4
},
"seed": 84268476,
"task_id": 684268476,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. There are 31 days in July.
B. (not (1982 is a leap year.)) or (((2 ** 3) < (11 + -3) < (31 % 3)) and (The currency of United Kingdom is the Peso.))
C. not not (The chemical symbol for Mercury is Hg.)
D. (32 % 7) < (-14 + -11)
E. (((10 - -13) < (-14 - 0)) and ((-14 - -18) != (4 * 0 - -1 * -6))) or ((7 % 5) == (14 * -5))
F. (not ((3 ** 2) <= (13 * 14))) and (((14 * -15) <= (16 - 1)) and (Diamond is a liquid at room temperature.))
G. The 1996 Olympics were held in Tokyo.
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 13295832,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. There are 31 days in July.\nB. (not (1982 is a leap year.)) or (((2 ** 3) < (11 + -3) < (31 % 3)) and (The currency of United Kingdom is the Peso.))\nC. not not (The chemical symbol for Mercury is Hg.)\nD. (32 % 7) < (-14 + -11)\nE. (((10 - -13) < (-14 - 0)) and ((-14 - -18) != (4 * 0 - -1 * -6))) or ((7 % 5) == (14 * -5))\nF. (not ((3 ** 2) <= (13 * 14))) and (((14 * -15) <= (16 - 1)) and (Diamond is a liquid at room temperature.))\nG. The 1996 Olympics were held in Tokyo.\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 13295832,
"true_count": 3
},
"seed": 13295832,
"task_id": 613295832,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not (not ((尼日利亚的首都是阿姆斯特丹。) and (2052年是闰年。)))
B. (not (((not (第一次世界大战开始发生在1914年。)) or ((牛有4条腿。) or (1908年奥运会在洛杉矶举办。))) and (银的化学符号是Ag。) and ((-6 * 0 * 0 * -8) < (18 * -11)))) or (((((智利的货币是兰特。) or (氮的化学符号是N。)) and ((丹麦的首都是雅典。) or ((11 + 14) >= (15 - 6)))) or (以色列的货币是克朗。)) or (((((-10 * 3) < (-1 + 7) < (20 - -9)) and ((-16 + 14) > (3 ** 2))) or (沙特阿拉伯位于亚洲。)) and ((汞在常温下是液体。) or (菲律宾的首都是柏林。)) and ((((6 - 20) == (-9 * -2)) or ((20 + -17) <= (5 * -10 + 10 * -5))) and (not (阿根廷位于南美洲。)))))
C. not not (not not (not (not not ((2020年奥运会在东京举办。) or (氖的化学符号是Ag。)))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 68515798,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. not (not ((尼日利亚的首都是阿姆斯特丹。) and (2052年是闰年。)))\nB. (not (((not (第一次世界大战开始发生在1914年。)) or ((牛有4条腿。) or (1908年奥运会在洛杉矶举办。))) and (银的化学符号是Ag。) and ((-6 * 0 * 0 * -8) < (18 * -11)))) or (((((智利的货币是兰特。) or (氮的化学符号是N。)) and ((丹麦的首都是雅典。) or ((11 + 14) >= (15 - 6)))) or (以色列的货币是克朗。)) or (((((-10 * 3) < (-1 + 7) < (20 - -9)) and ((-16 + 14) > (3 ** 2))) or (沙特阿拉伯位于亚洲。)) and ((汞在常温下是液体。) or (菲律宾的首都是柏林。)) and ((((6 - 20) == (-9 * -2)) or ((20 + -17) <= (5 * -10 + 10 * -5))) and (not (阿根廷位于南美洲。)))))\nC. not not (not not (not (not not ((2020年奥运会在东京举办。) or (氖的化学符号是Ag。)))))\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": 68515798,
"true_count": 1
},
"seed": 68515798,
"task_id": 668515798,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not (((1944 is a leap year.) and ((-12 - -2) >= (7 * 0 * -10 * 3))) and (((12 % 7) < (10 % 7) < (0 - 16)) and ((-17 * -8) == (-18 * 11))))
B. (((3 ** 3) < (-2 * 10 * -9 * -10)) or (((4 ** 2) < (18 % 8)) and ((6 - 16) < (9 - -19) < (2 * -2 + -5 * 3)))) and (not not (((-6 - -5) >= (1 ** 1)) or ((37 % 5) < (-10 + 5))))
C. ((18 + -1) != (-18 * 2)) and ((((-2 + -14) < (13 * -5) < (47 % 8)) or ((-19 - 19) >= (-9 + 19))) or (Chile is in South America.))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 69135174,
"true_count": 2
},
"question": "Review these logical expressions:\n\nA. not (((1944 is a leap year.) and ((-12 - -2) >= (7 * 0 * -10 * 3))) and (((12 % 7) < (10 % 7) < (0 - 16)) and ((-17 * -8) == (-18 * 11))))\nB. (((3 ** 3) < (-2 * 10 * -9 * -10)) or (((4 ** 2) < (18 % 8)) and ((6 - 16) < (9 - -19) < (2 * -2 + -5 * 3)))) and (not not (((-6 - -5) >= (1 ** 1)) or ((37 % 5) < (-10 + 5))))\nC. ((18 + -1) != (-18 * 2)) and ((((-2 + -14) < (13 * -5) < (47 % 8)) or ((-19 - 19) >= (-9 + 19))) or (Chile is in South America.))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 69135174,
"true_count": 2
},
"seed": 69135174,
"task_id": 669135174,
"task_type": "boolean_expressions"
} |
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