env stringclasses 1
value | prompt stringlengths 85 3.69k | extra dict |
|---|---|---|
logic-v2 | Study the following logical statements:
A. not not ((not not ((not (not (The currency of Hungary is the Shekel.))) and (The 1956 Olympics were held in Paris.))) or ((not ((((3 - 20) <= (-3 * 4 + -5 * -8)) or ((-10 - 19) >= (42 % 4))) or (((7 * -3 + -1 * -1) != (0 * 1)) and (Carbon dioxide is a gas at room temperature.)))) and (((not not (China is in Oceania.)) or ((88 is greater than 33.) and ((13 + 6) > (8 + -3)))) and ((((-9 * -4 + 2 * -3) < (8 * 15) < (-6 * -9 + -2 * 1)) or ((12 + 20) <= (7 - 19))) and (not ((4 ** 2) >= (3 ** 1)))))))
B. not not ((not not (not not (138 is a Fibonacci number.))) or ((not (A chicken has 2 legs.)) and ((not not ((-14 + 11) != (9 * -4))) and (not not (987 is a Fibonacci number.))) and ((((The currency of Malaysia is the Krone.) or ((3 - 18) > (16 - 3))) or (((-1 * 6 - -2 * -5) < (2 % 10)) or (The capital of Nigeria is Bangkok.))) and (not (The square root of 36 is 2.)) and ((A cod is a fish.) and (not (The 1964 Olympics were held in Moscow.))))))
C. Humans have five fingers on each hand.
D. not (not not (((not not (((6 * 19) > (9 * 19)) or ((8 * 10 * 7 * -2) == (7 + -1)))) or (((19 - 20) == (2 ** 3)) and (There are 31 days in October.)) or ((4 ** 3) < (12 + -6))) or (((((2 ** 3) >= (15 + -19)) or ((3 * 4 * -7 * 3) > (4 ** 1))) or ((5 + 0) > (-10 + 14))) or ((5 ** 3) < (8 - -6)))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 52650512,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. not not ((not not ((not (not (The currency of Hungary is the Shekel.))) and (The 1956 Olympics were held in Paris.))) or ((not ((((3 - 20) <= (-3 * 4 + -5 * -8)) or ((-10 - 19) >= (42 % 4))) or (((7 * -3 + -1 * -1) != (0 * 1)) and (Carbon dioxide is a gas at room temperature.)))) and (((not not (China is in Oceania.)) or ((88 is greater than 33.) and ((13 + 6) > (8 + -3)))) and ((((-9 * -4 + 2 * -3) < (8 * 15) < (-6 * -9 + -2 * 1)) or ((12 + 20) <= (7 - 19))) and (not ((4 ** 2) >= (3 ** 1)))))))\nB. not not ((not not (not not (138 is a Fibonacci number.))) or ((not (A chicken has 2 legs.)) and ((not not ((-14 + 11) != (9 * -4))) and (not not (987 is a Fibonacci number.))) and ((((The currency of Malaysia is the Krone.) or ((3 - 18) > (16 - 3))) or (((-1 * 6 - -2 * -5) < (2 % 10)) or (The capital of Nigeria is Bangkok.))) and (not (The square root of 36 is 2.)) and ((A cod is a fish.) and (not (The 1964 Olympics were held in Moscow.))))))\nC. Humans have five fingers on each hand.\nD. not (not not (((not not (((6 * 19) > (9 * 19)) or ((8 * 10 * 7 * -2) == (7 + -1)))) or (((19 - 20) == (2 ** 3)) and (There are 31 days in October.)) or ((4 ** 3) < (12 + -6))) or (((((2 ** 3) >= (15 + -19)) or ((3 * 4 * -7 * 3) > (4 ** 1))) or ((5 + 0) > (-10 + 14))) or ((5 ** 3) < (8 - -6)))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 52650512,
"true_count": 1
},
"seed": 52650512,
"task_id": 652650512,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. 冰的密度比液态水小。
B. not not ((((not not ((23小于等于29。) and (人体有150块骨头。))) and ((印度尼西亚的首都是雅加达。) or ((37是奇数。) or ((15 * -11) == (-19 + 7))))) or (not not (not not (not ((-3 - -18) >= (-10 * 4 - 8 * -1)))))) and ((((瑞典的首都是马尼拉。) or (锌的化学符号是Pt。)) or ((海王星是距离太阳第8近的行星。) or (土星是距离太阳第6近的行星。))) and (金星是距离太阳第2近的行星。) and ((not ((3 % 8) <= (8 % 1) <= (9 * 8 - 6 * -4))) or (第二次世界大战结束发生在1946年。))) and (not not (not not (not not (not ((15 * 15) != (-10 + 13)))))))
C. not not ((not (not not (((秘鲁位于非洲。) or ((3 ** 1) != (-3 - 10))) or (声音无法在真空中传播。)))) and ((((((-5 + -5) == (0 - -20)) and ((2 ** 3) >= (20 + -2))) or (硅的化学符号是C。)) and (not not (铁在常温下是固体。)) and (((莱特兄弟首次飞行发生在1903年。) or ((6 * 18) <= (6 + 14))) or ((2065年是闰年。) and (1900年奥运会在巴黎举办。)))) and ((((15 - 7) < (-6 * 5)) or (俄罗斯位于南极洲。)) or (1904年奥运会在圣路易斯举办。)) and (not not ((((4 - -17) > (19 * 17)) and (伦敦大火发生在1666年。)) or ((-3 * 12) <= (19 * 17))))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 477964,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. 冰的密度比液态水小。\nB. not not ((((not not ((23小于等于29。) and (人体有150块骨头。))) and ((印度尼西亚的首都是雅加达。) or ((37是奇数。) or ((15 * -11) == (-19 + 7))))) or (not not (not not (not ((-3 - -18) >= (-10 * 4 - 8 * -1)))))) and ((((瑞典的首都是马尼拉。) or (锌的化学符号是Pt。)) or ((海王星是距离太阳第8近的行星。) or (土星是距离太阳第6近的行星。))) and (金星是距离太阳第2近的行星。) and ((not ((3 % 8) <= (8 % 1) <= (9 * 8 - 6 * -4))) or (第二次世界大战结束发生在1946年。))) and (not not (not not (not not (not ((15 * 15) != (-10 + 13)))))))\nC. not not ((not (not not (((秘鲁位于非洲。) or ((3 ** 1) != (-3 - 10))) or (声音无法在真空中传播。)))) and ((((((-5 + -5) == (0 - -20)) and ((2 ** 3) >= (20 + -2))) or (硅的化学符号是C。)) and (not not (铁在常温下是固体。)) and (((莱特兄弟首次飞行发生在1903年。) or ((6 * 18) <= (6 + 14))) or ((2065年是闰年。) and (1900年奥运会在巴黎举办。)))) and ((((15 - 7) < (-6 * 5)) or (俄罗斯位于南极洲。)) or (1904年奥运会在圣路易斯举办。)) and (not not ((((4 - -17) > (19 * 17)) and (伦敦大火发生在1666年。)) or ((-3 * 12) <= (19 * 17))))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 477964,
"true_count": 1
},
"seed": 477964,
"task_id": 600477964,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not (not (((not not (((5 ** 2) <= (12 - -12)) or (金星是距离太阳第2近的行星。))) or (((瓢虫是哺乳动物。) or (哥伦比亚的首都是内罗毕。)) or (((4 ** 3) >= (18 * -20)) or (乌龟是昆虫。)))) and (not ((英国的货币是新西兰元。) or ((-13 - 14) != (-1 - -12)))) and ((二月有29天。) or ((2 ** 3) != (19 * -5)))))
B. not not (not not (((((-5 * -2 + 9 * -3) >= (1 * -8 + 0 * 10)) or (not not (法国的首都是赫尔辛基。))) and (not (51小于等于47。)) and ((not ((-10 * 14) < (-2 * 4))) or (((11 * 12) <= (2 * 19) <= (1 + -15)) and (鸡是鸟类。)))) or ((-3 * -14) > (9 * 8 * 9 * -6)) or ((not ((汞在常温下是液体。) and (狗有4条腿。))) and ((鸟有4条腿。) and (韩国的货币是韩元。)) and ((((29 % 7) >= (19 * -11)) or (印度尼西亚位于亚洲。)) or (((-10 * -3 - 6 * 9) <= (1 % 6)) or (哥伦比亚的货币是瑞士法郎。))))))
C. not (((not ((((-7 + 18) <= (12 - 20)) or ((19 - -7) < (16 - -20) < (2 * -10 - -7 * 9))) or (not (马来西亚的货币是林吉特。)))) or (not (not (铅的化学符号是Pb。)))) or (((荷兰的首都是华沙。) and (((阿根廷位于南美洲。) and ((-10 * -2) > (31 % 1))) and (((-5 - 5) <= (6 - 15)) or (伦敦大火发生在1666年。)))) or (((-13 - -4) <= (2 * 20) <= (-1 * 3 - 4 * -8)) or ((((-8 - -7) > (-6 * 8)) or (泰国位于亚洲。)) and (not not (秘鲁的货币是英镑。))))))
D. not not ((not not (not (not not ((2008年奥运会在伦敦举办。) and (瑞士的货币是克朗。))))) and (((哥伦布到达美洲发生在1492年。) and (((5 + -8) == (-10 + -3)) and (天王星是距离太阳第7近的行星。)) and (not (((3 * -8 - 2 * -5) >= (15 + 14)) and ((-9 * 7 - 6 * 5) != (3 * -13))))) or ((丹麦的货币是比索。) or ((肯尼亚的首都是内罗毕。) and (not ((0 + -18) <= (8 + 19) <= (2 ** 1)))))))
E. (not not ((not ((智利位于大洋洲。) and (((-13 * 5) > (3 * -11)) or ((6 * -1 * -7 * -10) != (7 * 9 - 2 * 9))))) or (not ((加拿大的首都是渥太华。) and (not not ((-2 * -6 + -3 * 3) < (3 ** 1))))))) and (not (not ((-16 + 11) < (-4 * 9 - -1 * 8)))) and (not (((((-2 + -16) != (10 * 7 + 2 * 1)) or (not (氮气在常温下是液体。))) or (not (智利的货币是克朗。))) or ((not not (not (匈牙利的首都是拉巴特。))) or (((埃及的货币是埃及镑。) and (1972年奥运会在圣路易斯举办。)) or (((48 % 2) != (8 * -9 - 10 * -8)) and (2020年奥运会在东京举办。))))))
F. not not ((((((-14 + -4) >= (-1 * -2 + 7 * 1)) and (墨西哥位于北美洲。)) and ((((-12 - 16) < (11 % 5)) or (第二次世界大战结束发生在1950年。)) and (((-15 * -11) >= (2 ** 3)) or ((5 ** 2) >= (5 ** 3))))) or ((尼日利亚的货币是奈拉。) or (not ((-4 * 7 - 5 * 9) >= (-7 + -6))))) and ((智利的货币是里拉。) and (not ((9 * 10 - -1 * -5) < (-8 - -11))) and (天王星是距离太阳第1近的行星。)) and (((四月有29天。) or (not not (人类有0条腿。))) or (95是质数。) or ((not not (((-12 - -1) < (5 + -11) < (6 * 0 - 0 * 8)) or (南极洲是最冷的大陆。))) and (not not (爱尔兰的首都是都柏林。)))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 7345919,
"true_count": 2
},
"question": "审视以下逻辑表达式：\n\nA. not (not (((not not (((5 ** 2) <= (12 - -12)) or (金星是距离太阳第2近的行星。))) or (((瓢虫是哺乳动物。) or (哥伦比亚的首都是内罗毕。)) or (((4 ** 3) >= (18 * -20)) or (乌龟是昆虫。)))) and (not ((英国的货币是新西兰元。) or ((-13 - 14) != (-1 - -12)))) and ((二月有29天。) or ((2 ** 3) != (19 * -5)))))\nB. not not (not not (((((-5 * -2 + 9 * -3) >= (1 * -8 + 0 * 10)) or (not not (法国的首都是赫尔辛基。))) and (not (51小于等于47。)) and ((not ((-10 * 14) < (-2 * 4))) or (((11 * 12) <= (2 * 19) <= (1 + -15)) and (鸡是鸟类。)))) or ((-3 * -14) > (9 * 8 * 9 * -6)) or ((not ((汞在常温下是液体。) and (狗有4条腿。))) and ((鸟有4条腿。) and (韩国的货币是韩元。)) and ((((29 % 7) >= (19 * -11)) or (印度尼西亚位于亚洲。)) or (((-10 * -3 - 6 * 9) <= (1 % 6)) or (哥伦比亚的货币是瑞士法郎。))))))\nC. not (((not ((((-7 + 18) <= (12 - 20)) or ((19 - -7) < (16 - -20) < (2 * -10 - -7 * 9))) or (not (马来西亚的货币是林吉特。)))) or (not (not (铅的化学符号是Pb。)))) or (((荷兰的首都是华沙。) and (((阿根廷位于南美洲。) and ((-10 * -2) > (31 % 1))) and (((-5 - 5) <= (6 - 15)) or (伦敦大火发生在1666年。)))) or (((-13 - -4) <= (2 * 20) <= (-1 * 3 - 4 * -8)) or ((((-8 - -7) > (-6 * 8)) or (泰国位于亚洲。)) and (not not (秘鲁的货币是英镑。))))))\nD. not not ((not not (not (not not ((2008年奥运会在伦敦举办。) and (瑞士的货币是克朗。))))) and (((哥伦布到达美洲发生在1492年。) and (((5 + -8) == (-10 + -3)) and (天王星是距离太阳第7近的行星。)) and (not (((3 * -8 - 2 * -5) >= (15 + 14)) and ((-9 * 7 - 6 * 5) != (3 * -13))))) or ((丹麦的货币是比索。) or ((肯尼亚的首都是内罗毕。) and (not ((0 + -18) <= (8 + 19) <= (2 ** 1)))))))\nE. (not not ((not ((智利位于大洋洲。) and (((-13 * 5) > (3 * -11)) or ((6 * -1 * -7 * -10) != (7 * 9 - 2 * 9))))) or (not ((加拿大的首都是渥太华。) and (not not ((-2 * -6 + -3 * 3) < (3 ** 1))))))) and (not (not ((-16 + 11) < (-4 * 9 - -1 * 8)))) and (not (((((-2 + -16) != (10 * 7 + 2 * 1)) or (not (氮气在常温下是液体。))) or (not (智利的货币是克朗。))) or ((not not (not (匈牙利的首都是拉巴特。))) or (((埃及的货币是埃及镑。) and (1972年奥运会在圣路易斯举办。)) or (((48 % 2) != (8 * -9 - 10 * -8)) and (2020年奥运会在东京举办。))))))\nF. not not ((((((-14 + -4) >= (-1 * -2 + 7 * 1)) and (墨西哥位于北美洲。)) and ((((-12 - 16) < (11 % 5)) or (第二次世界大战结束发生在1950年。)) and (((-15 * -11) >= (2 ** 3)) or ((5 ** 2) >= (5 ** 3))))) or ((尼日利亚的货币是奈拉。) or (not ((-4 * 7 - 5 * 9) >= (-7 + -6))))) and ((智利的货币是里拉。) and (not ((9 * 10 - -1 * -5) < (-8 - -11))) and (天王星是距离太阳第1近的行星。)) and (((四月有29天。) or (not not (人类有0条腿。))) or (95是质数。) or ((not not (((-12 - -1) < (5 + -11) < (6 * 0 - 0 * 8)) or (南极洲是最冷的大陆。))) and (not not (爱尔兰的首都是都柏林。)))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 7345919,
"true_count": 2
},
"seed": 7345919,
"task_id": 607345919,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (not not ((-18 - -17) == (5 ** 1))) or (not ((5 ** 1) == (1 ** 2)))
B. (((-8 * 9 + -5 * 9) == (4 + 13)) or ((-18 * 12) < (4 ** 1))) or (((0 * 6 + 4 * 0) == (19 * 15)) or ((7 + 2) < (-11 + -20)))
C. (((-10 * 3 * 5 * -1) != (4 ** 3)) and (土星是距离太阳第8近的行星。)) and (大象有4条腿。)
D. ((电流比光速更快。) or (兔子是爬行动物。)) and (埃及位于非洲。)
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 6281584,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (not not ((-18 - -17) == (5 ** 1))) or (not ((5 ** 1) == (1 ** 2)))\nB. (((-8 * 9 + -5 * 9) == (4 + 13)) or ((-18 * 12) < (4 ** 1))) or (((0 * 6 + 4 * 0) == (19 * 15)) or ((7 + 2) < (-11 + -20)))\nC. (((-10 * 3 * 5 * -1) != (4 ** 3)) and (土星是距离太阳第8近的行星。)) and (大象有4条腿。)\nD. ((电流比光速更快。) or (兔子是爬行动物。)) and (埃及位于非洲。)\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 6281584,
"true_count": 2
},
"seed": 6281584,
"task_id": 606281584,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (((((汞在常温下是液体。) and (声音无法在真空中传播。)) or ((12 + -9) != (-3 * 2 + 1 * -5))) and ((1 - -20) > (-5 * -3 * -2 * -4))) and (铁在常温下是固体。) and ((((氧的化学符号是Ag。) and ((5 * -8 + -9 * 10) <= (-5 * -11) <= (-20 - 9))) and (((-16 + -8) != (7 * -5 + -4 * 6)) and (人类首次登月发生在1971年。))) or ((((3 - 12) >= (9 + -15)) and (地球是距离太阳第6近的行星。)) and (章鱼有6条腿。)))) or (not (not (not not (not not (澳大利亚的货币是埃及镑。)))))
B. not not ((not ((-15 - 20) > (0 - 6))) and (not not (((18 * -13) == (4 * 10 + 5 * 3)) or (((3 ** 3) != (-9 - 9)) or (蜘蛛是昆虫。)))))
C. not not ((((((-20 * -16) > (6 * -4)) and ((3 ** 1) <= (-3 * 8 + 10 * 8))) or (((-6 * -1 * -7 * -3) != (19 - 16)) and ((-12 - -6) < (6 * 0 - -1 * 7) < (-15 + -13)))) and (not not (not ((-16 + -9) <= (1 ** 2) <= (-14 - 6))))) and (((((-2 - 20) <= (-2 * 2 - -6 * 3) <= (7 * -2 - 0 * -4)) and ((-20 - 1) <= (-9 + -11) <= (1 + 15))) and (印度尼西亚的货币是印尼盾。)) and (not not (意大利的首都是伯尔尼。)) and ((2 ** 3) >= (6 * 1))))
D. ((((6 * 1 - -6 * 7) != (16 - -13)) and (((乌龟是爬行动物。) and (木星是距离太阳第8近的行星。)) or ((水在常温下是液体。) and ((4 ** 2) >= (6 * 5 * -8 * 5))))) or (((鸟有4条腿。) and ((1900年奥运会在洛杉矶举办。) or ((4 * -10) < (8 - 20)))) or (not ((波兰的货币是卢布。) and ((-14 - 2) < (9 + 11) < (4 ** 1)))))) or ((not not (not (智利的货币是克朗。))) and (not not (四月有31天。)))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 56288529,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (((((汞在常温下是液体。) and (声音无法在真空中传播。)) or ((12 + -9) != (-3 * 2 + 1 * -5))) and ((1 - -20) > (-5 * -3 * -2 * -4))) and (铁在常温下是固体。) and ((((氧的化学符号是Ag。) and ((5 * -8 + -9 * 10) <= (-5 * -11) <= (-20 - 9))) and (((-16 + -8) != (7 * -5 + -4 * 6)) and (人类首次登月发生在1971年。))) or ((((3 - 12) >= (9 + -15)) and (地球是距离太阳第6近的行星。)) and (章鱼有6条腿。)))) or (not (not (not not (not not (澳大利亚的货币是埃及镑。)))))\nB. not not ((not ((-15 - 20) > (0 - 6))) and (not not (((18 * -13) == (4 * 10 + 5 * 3)) or (((3 ** 3) != (-9 - 9)) or (蜘蛛是昆虫。)))))\nC. not not ((((((-20 * -16) > (6 * -4)) and ((3 ** 1) <= (-3 * 8 + 10 * 8))) or (((-6 * -1 * -7 * -3) != (19 - 16)) and ((-12 - -6) < (6 * 0 - -1 * 7) < (-15 + -13)))) and (not not (not ((-16 + -9) <= (1 ** 2) <= (-14 - 6))))) and (((((-2 - 20) <= (-2 * 2 - -6 * 3) <= (7 * -2 - 0 * -4)) and ((-20 - 1) <= (-9 + -11) <= (1 + 15))) and (印度尼西亚的货币是印尼盾。)) and (not not (意大利的首都是伯尔尼。)) and ((2 ** 3) >= (6 * 1))))\nD. ((((6 * 1 - -6 * 7) != (16 - -13)) and (((乌龟是爬行动物。) and (木星是距离太阳第8近的行星。)) or ((水在常温下是液体。) and ((4 ** 2) >= (6 * 5 * -8 * 5))))) or (((鸟有4条腿。) and ((1900年奥运会在洛杉矶举办。) or ((4 * -10) < (8 - 20)))) or (not ((波兰的货币是卢布。) and ((-14 - 2) < (9 + 11) < (4 ** 1)))))) or ((not not (not (智利的货币是克朗。))) and (not not (四月有31天。)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
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} |
logic-v2 | 给定以下布尔表达式：
A. ((not (((1904年奥运会在墨尔本举办。) or ((-6 * 7 + 5 * -10) < (0 - -2))) or ((81的平方根是9。) and ((-16 - -15) < (-9 + -7))))) or (not not (((蚱蜢是鱼类。) or ((49 % 8) >= (-11 * 17))) or ((欧盟的货币是林吉特。) or (匈牙利的首都是布达佩斯。))))) and (((木头在常温下是气体。) and ((not not (水在海平面上的沸点是100摄氏度。)) and (((6 * 9 * 6 * 0) <= (0 + 14)) or ((9 + -20) == (-9 - 4))))) and (((16 * -1) == (-18 + -16)) and (not (欧盟的货币是欧元。))) and (((-10 - -19) != (46 % 9)) or ((9 % 4) > (3 - -20))))
B. ((not (52小于等于86。)) or (((冰在常温下是固体。) and (95能被4整除。)) and ((水在常温下是液体。) and (猪有4条腿。))) or (not ((((-12 - 12) <= (-5 * 3 + 7 * -5) <= (-9 - 7)) and ((-13 * 5) <= (-2 - -18))) or ((土星是距离太阳第7近的行星。) or ((20 * 16) == (19 * -11)))))) or (((锡的化学符号是S。) or (((-17 * 4) <= (12 * 1) <= (5 * 12)) and ((-12 * -13) == (-4 - -8))) or ((3 ** 2) <= (-2 * -14) <= (33 % 7))) or ((((新加坡的首都是波哥大。) or (1948年奥运会在伦敦举办。)) or (not ((-1 + -3) > (-14 * -9)))) and ((土星是距离太阳第2近的行星。) and (not not (1908年奥运会在墨尔本举办。)))))
C. not not (not (not not ((not not ((10 * -8 - 8 * 4) == (3 * 0 * -10 * -4))) and (not not (六月有30天。)))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"answer": "B,C",
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"question": "给定以下布尔表达式：\n\nA. ((not (((1904年奥运会在墨尔本举办。) or ((-6 * 7 + 5 * -10) < (0 - -2))) or ((81的平方根是9。) and ((-16 - -15) < (-9 + -7))))) or (not not (((蚱蜢是鱼类。) or ((49 % 8) >= (-11 * 17))) or ((欧盟的货币是林吉特。) or (匈牙利的首都是布达佩斯。))))) and (((木头在常温下是气体。) and ((not not (水在海平面上的沸点是100摄氏度。)) and (((6 * 9 * 6 * 0) <= (0 + 14)) or ((9 + -20) == (-9 - 4))))) and (((16 * -1) == (-18 + -16)) and (not (欧盟的货币是欧元。))) and (((-10 - -19) != (46 % 9)) or ((9 % 4) > (3 - -20))))\nB. ((not (52小于等于86。)) or (((冰在常温下是固体。) and (95能被4整除。)) and ((水在常温下是液体。) and (猪有4条腿。))) or (not ((((-12 - 12) <= (-5 * 3 + 7 * -5) <= (-9 - 7)) and ((-13 * 5) <= (-2 - -18))) or ((土星是距离太阳第7近的行星。) or ((20 * 16) == (19 * -11)))))) or (((锡的化学符号是S。) or (((-17 * 4) <= (12 * 1) <= (5 * 12)) and ((-12 * -13) == (-4 - -8))) or ((3 ** 2) <= (-2 * -14) <= (33 % 7))) or ((((新加坡的首都是波哥大。) or (1948年奥运会在伦敦举办。)) or (not ((-1 + -3) > (-14 * -9)))) and ((土星是距离太阳第2近的行星。) and (not not (1908年奥运会在墨尔本举办。)))))\nC. not not (not (not not ((not not ((10 * -8 - 8 * 4) == (3 * 0 * -10 * -4))) and (not not (六月有30天。)))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
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logic-v2 | Consider the following logical expressions:
A. ((not not (Jupiter is the 5th planet from the Sun.)) or (not ((4 * -10 + 8 * 4) <= (2 - 5)))) and ((9 is less than or equal to 38.) and (not ((Saturn is the 7th planet from the Sun.) or (World War I began occurred in 1914.)))) and ((not not ((not (20 is a prime number.)) and (((1 * 1) != (2 ** 3)) or (78 is less than or equal to 29.)))) and ((Japan is in Asia.) or ((-17 - -9) == (-15 * 7))))
B. (not (not (1933 is a leap year.))) and (not (not not (The 1956 Olympics were held in Melbourne.))) and (((((A horse has 4 legs.) and ((12 * -14) <= (3 + 7))) and (Spain is in Antarctica.)) and ((9 - 4) <= (0 - 20) <= (-7 + -7))) and ((not not (((-11 * 13) == (20 * -13)) or (The chemical symbol for Nickel is Ni.))) or ((not not (The chemical symbol for Uranium is Mg.)) or (((10 * -3 * 3 * -5) > (9 * -6)) or (Sound travels faster in a vacuum.)))))
C. ((not ((((4 ** 1) == (36 % 4)) and ((-17 + 14) != (-18 + -13))) or (not not (The Titanic sank occurred in 1912.)))) and ((not not (400 is a perfect square.)) or (Wood is a solid at room temperature.) or ((not ((5 * -5) > (8 % 7))) and (88 is less than or equal to 90.)))) or ((((New Zealand is in Oceania.) and ((A goldfish is a fish.) or ((0 * 5 - 3 * 3) >= (3 * -4 + 8 * 4)))) and (((5 ** 2) > (-6 + 2)) or (not (India is in Asia.)))) or (not not (The currency of South Africa is the Pound.)))
D. not not ((((11 - 2) <= (9 - -17) <= (-7 - -12)) and (not ((-10 - 11) < (14 + -20)))) and (Jupiter is the 5th planet from the Sun.) and ((((3 - -18) > (19 - -4)) and ((Humans have five fingers on each hand.) and (The 1904 Olympics were held in St. Louis.))) and (((The United States declared independence occurred in 1776.) or ((27 % 7) >= (-8 * 8 * 7 * -6))) and (not not ((-19 + 10) < (-4 * -14) < (-9 * 10 - -4 * -5))))))
E. ((((not (The currency of Vietnam is the Dong.)) or (not (8 is greater than 37.))) or (((The first Olympic Games of modern era occurred in 1896.) and ((-3 * 10 + 9 * 2) == (-6 - -13))) and (not ((50 % 1) < (-18 * -15))))) and ((((The chemical symbol for Magnesium is P.) or ((30 % 4) != (-3 * 1))) and (((5 ** 3) > (4 * -8 * 7 * 4)) or (The capital of Canada is Ottawa.))) or ((7 * -3 + -5 * -3) > (-12 - 0)))) and (not not ((39 is greater than 65.) or (The capital of Singapore is Singapore.)))
F. ((not not ((-1 * 1 + -2 * 8) <= (3 + 14))) or ((((The chemical symbol for Calcium is Na.) or ((-14 - -17) < (18 * -18))) or ((Colombia is in Asia.) and (India is in Asia.))) or (The first moon landing occurred in 1969.))) and (not not (((((20 + 18) < (8 + -20)) and ((3 * 1 - -2 * -6) >= (5 ** 2))) or (((-3 * 6 - -6 * 10) != (9 * -7)) and (There are 31 days in December.))) and (The chemical symbol for Tin is Sn.)))
G. (not (((20 + -8) != (2 * 2 - -10 * -9)) or (not not ((The currency of Saudi Arabia is the Riyal.) and (Saturn is the 7th planet from the Sun.))))) and (((not not ((1999 is a leap year.) or ((-8 * -18) == (2 * 4 + -10 * -2)))) or (The chemical symbol for Gold is Au.)) or ((15 + -16) == (-16 * -20)) or (not (((8 * 4 * 5 * -8) >= (4 * -12)) or ((The chemical symbol for Tin is Sn.) or ((-17 - -2) == (-13 * 15))))))
H. ((((-13 + -18) < (-14 * 0)) and (((33 is an even number.) and ((-6 - -10) == (2 ** 1))) or (not not (A crab has 0 legs.)))) or ((((A chicken is a bird.) or (The chemical symbol for Hydrogen is H.)) or ((13 * 14) != (17 + -6))) and ((1 ** 3) >= (4 * -9 + 7 * -5)))) or (not (not not (((The capital of New Zealand is Copenhagen.) and ((37 % 2) >= (1 ** 1))) or (((1 ** 2) >= (-8 * -7 * 2 * -2)) or ((15 * -14) < (-16 - 8))))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "C,E,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"question": "Consider the following logical expressions:\n\nA. ((not not (Jupiter is the 5th planet from the Sun.)) or (not ((4 * -10 + 8 * 4) <= (2 - 5)))) and ((9 is less than or equal to 38.) and (not ((Saturn is the 7th planet from the Sun.) or (World War I began occurred in 1914.)))) and ((not not ((not (20 is a prime number.)) and (((1 * 1) != (2 ** 3)) or (78 is less than or equal to 29.)))) and ((Japan is in Asia.) or ((-17 - -9) == (-15 * 7))))\nB. (not (not (1933 is a leap year.))) and (not (not not (The 1956 Olympics were held in Melbourne.))) and (((((A horse has 4 legs.) and ((12 * -14) <= (3 + 7))) and (Spain is in Antarctica.)) and ((9 - 4) <= (0 - 20) <= (-7 + -7))) and ((not not (((-11 * 13) == (20 * -13)) or (The chemical symbol for Nickel is Ni.))) or ((not not (The chemical symbol for Uranium is Mg.)) or (((10 * -3 * 3 * -5) > (9 * -6)) or (Sound travels faster in a vacuum.)))))\nC. ((not ((((4 ** 1) == (36 % 4)) and ((-17 + 14) != (-18 + -13))) or (not not (The Titanic sank occurred in 1912.)))) and ((not not (400 is a perfect square.)) or (Wood is a solid at room temperature.) or ((not ((5 * -5) > (8 % 7))) and (88 is less than or equal to 90.)))) or ((((New Zealand is in Oceania.) and ((A goldfish is a fish.) or ((0 * 5 - 3 * 3) >= (3 * -4 + 8 * 4)))) and (((5 ** 2) > (-6 + 2)) or (not (India is in Asia.)))) or (not not (The currency of South Africa is the Pound.)))\nD. not not ((((11 - 2) <= (9 - -17) <= (-7 - -12)) and (not ((-10 - 11) < (14 + -20)))) and (Jupiter is the 5th planet from the Sun.) and ((((3 - -18) > (19 - -4)) and ((Humans have five fingers on each hand.) and (The 1904 Olympics were held in St. Louis.))) and (((The United States declared independence occurred in 1776.) or ((27 % 7) >= (-8 * 8 * 7 * -6))) and (not not ((-19 + 10) < (-4 * -14) < (-9 * 10 - -4 * -5))))))\nE. ((((not (The currency of Vietnam is the Dong.)) or (not (8 is greater than 37.))) or (((The first Olympic Games of modern era occurred in 1896.) and ((-3 * 10 + 9 * 2) == (-6 - -13))) and (not ((50 % 1) < (-18 * -15))))) and ((((The chemical symbol for Magnesium is P.) or ((30 % 4) != (-3 * 1))) and (((5 ** 3) > (4 * -8 * 7 * 4)) or (The capital of Canada is Ottawa.))) or ((7 * -3 + -5 * -3) > (-12 - 0)))) and (not not ((39 is greater than 65.) or (The capital of Singapore is Singapore.)))\nF. ((not not ((-1 * 1 + -2 * 8) <= (3 + 14))) or ((((The chemical symbol for Calcium is Na.) or ((-14 - -17) < (18 * -18))) or ((Colombia is in Asia.) and (India is in Asia.))) or (The first moon landing occurred in 1969.))) and (not not (((((20 + 18) < (8 + -20)) and ((3 * 1 - -2 * -6) >= (5 ** 2))) or (((-3 * 6 - -6 * 10) != (9 * -7)) and (There are 31 days in December.))) and (The chemical symbol for Tin is Sn.)))\nG. (not (((20 + -8) != (2 * 2 - -10 * -9)) or (not not ((The currency of Saudi Arabia is the Riyal.) and (Saturn is the 7th planet from the Sun.))))) and (((not not ((1999 is a leap year.) or ((-8 * -18) == (2 * 4 + -10 * -2)))) or (The chemical symbol for Gold is Au.)) or ((15 + -16) == (-16 * -20)) or (not (((8 * 4 * 5 * -8) >= (4 * -12)) or ((The chemical symbol for Tin is Sn.) or ((-17 - -2) == (-13 * 15))))))\nH. ((((-13 + -18) < (-14 * 0)) and (((33 is an even number.) and ((-6 - -10) == (2 ** 1))) or (not not (A crab has 0 legs.)))) or ((((A chicken is a bird.) or (The chemical symbol for Hydrogen is H.)) or ((13 * 14) != (17 + -6))) and ((1 ** 3) >= (4 * -9 + 7 * -5)))) or (not (not not (((The capital of New Zealand is Copenhagen.) and ((37 % 2) >= (1 ** 1))) or (((1 ** 2) >= (-8 * -7 * 2 * -2)) or ((15 * -14) < (-16 - 8))))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
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"seed": 54760746,
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"seed": 54760746,
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"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (not ((20 % 1) <= (8 - 3) <= (5 ** 2)))
B. (((8 * -4) > (12 - -1)) or (((The first airplane flight by the Wright Brothers occurred in 1903.) and ((8 + -15) < (9 - -11))) or (The chemical symbol for Chromium is N.))) and ((Neptune is the 6th planet from the Sun.) or (((-1 * 2 * 4 * 2) != (-4 - 20)) and (not ((-16 - -5) <= (-19 + 15)))))
C. not not (((not not (Spain is in Europe.)) and ((Sharks are mammals.) or (35 is a prime number.))) or ((-1 * 4 - 7 * -9) < (19 % 4)))
D. not (not not ((The currency of Philippines is the Dollar.) or (not not ((0 + -17) <= (14 - -5)))))
E. ((((3 ** 1) == (-12 - -11)) and ((A crab has 10 legs.) or ((5 + 10) >= (5 - 16)))) or ((not (276 is a perfect square.)) or ((-16 + -9) <= (-6 * 8 - 3 * 9) <= (-1 * -4 * -5 * 10)))) and (((11 - -15) <= (3 ** 3)) and (((The 1976 Olympics were held in Montreal.) and (A pig has 4 legs.)) or (not not ((-9 * -1 * -1 * -10) < (-10 + 2)))))
F. (not not ((((-6 - 11) != (4 ** 2)) or ((-6 * -10 + 2 * 7) >= (13 + 19))) or ((-6 + -3) == (7 * 8 + 2 * -7)))) or ((World War II began occurred in 1939.) and (((The chemical symbol for Phosphorus is P.) and (The capital of Vietnam is Hanoi.)) or ((19 + 12) != (-13 - 6))))
G. (not not (not not (((3 * -2 - 10 * -10) <= (-12 * 5) <= (15 + 12)) and (The Great Fire of London occurred in 1666.)))) or ((not (not not (India is in Antarctica.))) or (((-7 * 0) > (1 + -6)) or ((45 % 10) >= (-2 * -1 + 1 * 2))))
H. ((((-7 * 6 * 5 * -4) >= (-2 * -3 * 10 * -6)) and (not not ((10 * -18) <= (6 % 7)))) or (((A owl is a bird.) and (A goldfish is a fish.)) and (The 1964 Olympics were held in Tokyo.))) or (not (((18 * -1) == (-14 + 13)) and ((16 * -12) == (-13 - -9)))) or (not (((Japan is in Oceania.) or (The capital of Colombia is Bogota.)) and ((9 + 13) >= (-1 - -9))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
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"answer": "A,E,F,G,H",
"difficulty": 1,
"gpt_response": "",
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"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not ((20 % 1) <= (8 - 3) <= (5 ** 2)))\nB. (((8 * -4) > (12 - -1)) or (((The first airplane flight by the Wright Brothers occurred in 1903.) and ((8 + -15) < (9 - -11))) or (The chemical symbol for Chromium is N.))) and ((Neptune is the 6th planet from the Sun.) or (((-1 * 2 * 4 * 2) != (-4 - 20)) and (not ((-16 - -5) <= (-19 + 15)))))\nC. not not (((not not (Spain is in Europe.)) and ((Sharks are mammals.) or (35 is a prime number.))) or ((-1 * 4 - 7 * -9) < (19 % 4)))\nD. not (not not ((The currency of Philippines is the Dollar.) or (not not ((0 + -17) <= (14 - -5)))))\nE. ((((3 ** 1) == (-12 - -11)) and ((A crab has 10 legs.) or ((5 + 10) >= (5 - 16)))) or ((not (276 is a perfect square.)) or ((-16 + -9) <= (-6 * 8 - 3 * 9) <= (-1 * -4 * -5 * 10)))) and (((11 - -15) <= (3 ** 3)) and (((The 1976 Olympics were held in Montreal.) and (A pig has 4 legs.)) or (not not ((-9 * -1 * -1 * -10) < (-10 + 2)))))\nF. (not not ((((-6 - 11) != (4 ** 2)) or ((-6 * -10 + 2 * 7) >= (13 + 19))) or ((-6 + -3) == (7 * 8 + 2 * -7)))) or ((World War II began occurred in 1939.) and (((The chemical symbol for Phosphorus is P.) and (The capital of Vietnam is Hanoi.)) or ((19 + 12) != (-13 - 6))))\nG. (not not (not not (((3 * -2 - 10 * -10) <= (-12 * 5) <= (15 + 12)) and (The Great Fire of London occurred in 1666.)))) or ((not (not not (India is in Antarctica.))) or (((-7 * 0) > (1 + -6)) or ((45 % 10) >= (-2 * -1 + 1 * 2))))\nH. ((((-7 * 6 * 5 * -4) >= (-2 * -3 * 10 * -6)) and (not not ((10 * -18) <= (6 % 7)))) or (((A owl is a bird.) and (A goldfish is a fish.)) and (The 1964 Olympics were held in Tokyo.))) or (not (((18 * -1) == (-14 + 13)) and ((16 * -12) == (-13 - -9)))) or (not (((Japan is in Oceania.) or (The capital of Colombia is Bogota.)) and ((9 + 13) >= (-1 - -9))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
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"seed": 60999499,
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"seed": 60999499,
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"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not not (((The currency of Denmark is the Euro.) or (The 1988 Olympics were held in Seoul.)) and (Russia is in Europe.))
B. not (not not (((7 * 11) < (33 % 1) < (6 * 0)) and ((1 + -8) == (1 - -10))))
C. (not (not (Earth is the 3rd planet from the Sun.))) or (((The 2020 Olympics were held in Tokyo.) and (27 is a perfect square.)) and ((1929 is a leap year.) and ((18 - 15) > (-1 * -3 + 8 * -4))))
D. not ((Jupiter is the 5th planet from the Sun.) or (((-1 * 4) == (-14 - 0)) and ((1 ** 1) > (49 % 3))))
E. (not (The chemical symbol for Iron is Fe.)) or ((7 * 14) <= (-18 - 14))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
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"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 49299897,
"true_count": 3
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"question": "Here are some boolean expressions to evaluate:\n\nA. not not (((The currency of Denmark is the Euro.) or (The 1988 Olympics were held in Seoul.)) and (Russia is in Europe.))\nB. not (not not (((7 * 11) < (33 % 1) < (6 * 0)) and ((1 + -8) == (1 - -10))))\nC. (not (not (Earth is the 3rd planet from the Sun.))) or (((The 2020 Olympics were held in Tokyo.) and (27 is a perfect square.)) and ((1929 is a leap year.) and ((18 - 15) > (-1 * -3 + 8 * -4))))\nD. not ((Jupiter is the 5th planet from the Sun.) or (((-1 * 4) == (-14 - 0)) and ((1 ** 1) > (49 % 3))))\nE. (not (The chemical symbol for Iron is Fe.)) or ((7 * 14) <= (-18 - 14))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 49299897,
"true_count": 3
},
"seed": 49299897,
"task_id": 649299897,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (not not (not (铜的化学符号是Ne。))) or (氖的化学符号是S。)
B. (丹麦的首都是奥斯陆。) or ((not not ((0 * 19) > (8 + -16))) and (not not (埃及的货币是比索。)))
C. (not (加拿大的首都是渥太华。)) and (((法国大革命开始发生在1794年。) and (地球是距离太阳第5近的行星。)) or (((-4 - -9) < (-8 * 16) < (4 * -7 - -10 * 6)) or (氦的化学符号是Ne。)))
D. ((not not ((-14 + -14) != (-13 - -14))) or (((0 * -2 * -10 * 10) < (10 + 19)) or (银的化学符号是Pb。))) and ((第一部iPhone发布发生在2007年。) and ((20 % 3) == (9 * 14))) and (not (((7 + -4) <= (29 % 1) <= (2 - -17)) or (尼日利亚位于南美洲。)))
E. ((not (人类只使用了大脑的10%。)) or ((英国位于欧洲。) and (哥伦比亚的首都是波哥大。))) and ((-7 + -19) <= (2 * 0 - 4 * -3)) and ((not (蜘蛛是昆虫。)) or ((-7 * 7) <= (11 + 4)))
F. (not ((1 ** 3) != (1 - 15))) or (葡萄牙的首都是赫尔辛基。)
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
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"answer": "A,E",
"difficulty": 1,
"gpt_response": "",
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"language": "cn",
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"seed": 26246089,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. (not not (not (铜的化学符号是Ne。))) or (氖的化学符号是S。)\nB. (丹麦的首都是奥斯陆。) or ((not not ((0 * 19) > (8 + -16))) and (not not (埃及的货币是比索。)))\nC. (not (加拿大的首都是渥太华。)) and (((法国大革命开始发生在1794年。) and (地球是距离太阳第5近的行星。)) or (((-4 - -9) < (-8 * 16) < (4 * -7 - -10 * 6)) or (氦的化学符号是Ne。)))\nD. ((not not ((-14 + -14) != (-13 - -14))) or (((0 * -2 * -10 * 10) < (10 + 19)) or (银的化学符号是Pb。))) and ((第一部iPhone发布发生在2007年。) and ((20 % 3) == (9 * 14))) and (not (((7 + -4) <= (29 % 1) <= (2 - -17)) or (尼日利亚位于南美洲。)))\nE. ((not (人类只使用了大脑的10%。)) or ((英国位于欧洲。) and (哥伦比亚的首都是波哥大。))) and ((-7 + -19) <= (2 * 0 - 4 * -3)) and ((not (蜘蛛是昆虫。)) or ((-7 * 7) <= (11 + 4)))\nF. (not ((1 ** 3) != (1 - 15))) or (葡萄牙的首都是赫尔辛基。)\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 26246089,
"true_count": 2
},
"seed": 26246089,
"task_id": 626246089,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not (The chemical symbol for Zinc is P.)
B. ((9 + 12) >= (3 ** 2)) and ((not (The capital of Australia is Bern.)) or (not (Saturn is the 7th planet from the Sun.)))
C. (not ((The chemical symbol for Mercury is Hg.) or (The capital of Belgium is Brussels.))) or (((Antarctica is the coldest continent.) or ((6 % 7) <= (3 ** 2))) or ((12 + -5) > (15 * -1)))
D. not (((4 * 5) != (-9 - -8)) and ((Russia is in Europe.) or (Canada is in North America.)))
E. not not ((5 + 20) == (-2 * 17))
F. ((((15 - -20) != (39 % 5)) or (The chemical symbol for Copper is Hg.)) or (The capital of Argentina is Paris.)) and (not not ((-6 * 3 + 6 * 6) <= (-8 * 3 + 1 * 7) <= (-6 * -3 * -1 * -1))) and (not not (not (Earth is the 8th planet from the Sun.)))
G. ((-3 - 4) < (2 ** 1)) or (((-13 - -4) >= (-3 - 20)) and (Electricity flows faster than light.)) or ((((4 - 4) <= (-16 - -4)) and (Whales are fish.)) and (((0 * 4 - -4 * 7) == (-14 - 5)) and ((-3 * -3 - -4 * 2) >= (16 - -9))))
H. not not (The capital of Norway is Buenos Aires.)
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,B,C,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 55522677,
"true_count": 4
},
"question": "Review these logical expressions:\n\nA. not (The chemical symbol for Zinc is P.)\nB. ((9 + 12) >= (3 ** 2)) and ((not (The capital of Australia is Bern.)) or (not (Saturn is the 7th planet from the Sun.)))\nC. (not ((The chemical symbol for Mercury is Hg.) or (The capital of Belgium is Brussels.))) or (((Antarctica is the coldest continent.) or ((6 % 7) <= (3 ** 2))) or ((12 + -5) > (15 * -1)))\nD. not (((4 * 5) != (-9 - -8)) and ((Russia is in Europe.) or (Canada is in North America.)))\nE. not not ((5 + 20) == (-2 * 17))\nF. ((((15 - -20) != (39 % 5)) or (The chemical symbol for Copper is Hg.)) or (The capital of Argentina is Paris.)) and (not not ((-6 * 3 + 6 * 6) <= (-8 * 3 + 1 * 7) <= (-6 * -3 * -1 * -1))) and (not not (not (Earth is the 8th planet from the Sun.)))\nG. ((-3 - 4) < (2 ** 1)) or (((-13 - -4) >= (-3 - 20)) and (Electricity flows faster than light.)) or ((((4 - 4) <= (-16 - -4)) and (Whales are fish.)) and (((0 * 4 - -4 * 7) == (-14 - 5)) and ((-3 * -3 - -4 * 2) >= (16 - -9))))\nH. not not (The capital of Norway is Buenos Aires.)\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 55522677,
"true_count": 4
},
"seed": 55522677,
"task_id": 655522677,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (((((8 * -15) != (-19 - 18)) and ((7 * -2 - 1 * 5) < (-2 * -7 + 9 * -8) < (-5 + 16))) and ((铅的化学符号是Pb。) or (天王星是距离太阳第4近的行星。))) or (1988年奥运会在洛杉矶举办。) or ((not not (中国的首都是河内。)) or ((-14 + 6) <= (-10 - 17)))) and ((((5 ** 2) == (-9 * -7)) or ((-12 - 6) >= (-2 * 15))) and (not not (1996年奥运会在亚特兰大举办。))) and (not (铁在常温下是固体。))
B. not (not (((2024年奥运会在巴黎举办。) or (1968年是闰年。)) or (1996年奥运会在伦敦举办。)))
C. (((not (154是偶数。)) or (not (人体有206块骨头。))) and ((-8 * -13) != (8 * 3 - 7 * 4)) and ((-10 * 10 - 7 * 10) < (4 * 10 + -3 * 10))) or (not not ((-10 * 18) < (12 % 10)))
D. not not ((not not (((-5 - 8) < (22 % 9)) or (罗马尼亚的首都是新加坡。))) or ((((12 - -7) >= (-11 - -17)) or (二月有28天。)) and ((菲律宾的货币是比索。) or (铅的化学符号是Na。))))
E. ((意大利位于南美洲。) and (not (法国大革命开始发生在1794年。)) and (鸟有4条腿。)) and (not not ((-8 + -19) > (3 ** 1))) and (((((-13 + 9) <= (12 + 9) <= (0 * -12)) or ((5 ** 2) < (23 % 1))) and ((企鹅能飞翔。) or ((-15 + 1) == (2 * -10 + 10 * 5)))) and (not (钴的化学符号是Sn。)) and ((-9 * 3 + -10 * -10) == (1 + 1)))
F. (not not ((-18 - 9) <= (4 * -2 + 3 * 1))) and (not (((-5 * 7 - 4 * 0) > (43 % 2)) or (蜘蛛是昆虫。))) and (((not (氧的化学符号是S。)) or ((19 % 7) < (9 % 6) < (-20 - -13))) or ((((-6 + 19) < (2 * -17)) or (泰坦尼克号沉没发生在1914年。)) and (((0 * 6 - 4 * -3) != (-3 - 6)) or ((10 * -10 + 9 * 1) < (-8 + 2) < (8 - 8)))))
G. (((not not ((14 * 0) < (5 ** 1) < (15 * 3))) or (((3 * -2 + 6 * 3) == (-6 * -10 + 4 * 10)) and (西班牙位于欧洲。))) or ((-3 * -8) < (3 ** 1)) or (((现代奥运会首届举办发生在1894年。) or (肯尼亚的首都是内罗毕。)) or (新加坡的首都是布达佩斯。))) and (((1928年奥运会在安特卫普举办。) and ((-5 * 18) <= (-2 * 4 + -5 * 5))) or (not (银的化学符号是Ag。))) and (((((16 * 10) == (37 % 2)) and (1964年奥运会在东京举办。)) or ((澳大利亚位于大洋洲。) and ((-18 + 6) < (49 % 2)))) and (((人类首次登月发生在1969年。) and (闪电不会两次击中同一个地方。)) or ((1942年是闰年。) and ((-19 * 16) == (6 + -18)))))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 75112462,
"true_count": 4
},
"question": "给定以下布尔表达式：\n\nA. (((((8 * -15) != (-19 - 18)) and ((7 * -2 - 1 * 5) < (-2 * -7 + 9 * -8) < (-5 + 16))) and ((铅的化学符号是Pb。) or (天王星是距离太阳第4近的行星。))) or (1988年奥运会在洛杉矶举办。) or ((not not (中国的首都是河内。)) or ((-14 + 6) <= (-10 - 17)))) and ((((5 ** 2) == (-9 * -7)) or ((-12 - 6) >= (-2 * 15))) and (not not (1996年奥运会在亚特兰大举办。))) and (not (铁在常温下是固体。))\nB. not (not (((2024年奥运会在巴黎举办。) or (1968年是闰年。)) or (1996年奥运会在伦敦举办。)))\nC. (((not (154是偶数。)) or (not (人体有206块骨头。))) and ((-8 * -13) != (8 * 3 - 7 * 4)) and ((-10 * 10 - 7 * 10) < (4 * 10 + -3 * 10))) or (not not ((-10 * 18) < (12 % 10)))\nD. not not ((not not (((-5 - 8) < (22 % 9)) or (罗马尼亚的首都是新加坡。))) or ((((12 - -7) >= (-11 - -17)) or (二月有28天。)) and ((菲律宾的货币是比索。) or (铅的化学符号是Na。))))\nE. ((意大利位于南美洲。) and (not (法国大革命开始发生在1794年。)) and (鸟有4条腿。)) and (not not ((-8 + -19) > (3 ** 1))) and (((((-13 + 9) <= (12 + 9) <= (0 * -12)) or ((5 ** 2) < (23 % 1))) and ((企鹅能飞翔。) or ((-15 + 1) == (2 * -10 + 10 * 5)))) and (not (钴的化学符号是Sn。)) and ((-9 * 3 + -10 * -10) == (1 + 1)))\nF. (not not ((-18 - 9) <= (4 * -2 + 3 * 1))) and (not (((-5 * 7 - 4 * 0) > (43 % 2)) or (蜘蛛是昆虫。))) and (((not (氧的化学符号是S。)) or ((19 % 7) < (9 % 6) < (-20 - -13))) or ((((-6 + 19) < (2 * -17)) or (泰坦尼克号沉没发生在1914年。)) and (((0 * 6 - 4 * -3) != (-3 - 6)) or ((10 * -10 + 9 * 1) < (-8 + 2) < (8 - 8)))))\nG. (((not not ((14 * 0) < (5 ** 1) < (15 * 3))) or (((3 * -2 + 6 * 3) == (-6 * -10 + 4 * 10)) and (西班牙位于欧洲。))) or ((-3 * -8) < (3 ** 1)) or (((现代奥运会首届举办发生在1894年。) or (肯尼亚的首都是内罗毕。)) or (新加坡的首都是布达佩斯。))) and (((1928年奥运会在安特卫普举办。) and ((-5 * 18) <= (-2 * 4 + -5 * 5))) or (not (银的化学符号是Ag。))) and (((((16 * 10) == (37 % 2)) and (1964年奥运会在东京举办。)) or ((澳大利亚位于大洋洲。) and ((-18 + 6) < (49 % 2)))) and (((人类首次登月发生在1969年。) and (闪电不会两次击中同一个地方。)) or ((1942年是闰年。) and ((-19 * 16) == (6 + -18)))))\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": 7,
"seed": 75112462,
"true_count": 4
},
"seed": 75112462,
"task_id": 675112462,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not ((not not ((4 * 0) < (4 ** 2))) and ((((The first airplane flight by the Wright Brothers occurred in 1903.) or ((-11 * 19) >= (-9 * 20))) and (((-6 - 16) != (1 ** 3)) or ((5 ** 2) == (1 ** 2)))) or ((The currency of Denmark is the Krone.) or ((-6 * -9) == (17 + 8))) or ((not not ((3 * -15) == (-4 * -3 * 3 * 3))) or (((3 % 10) != (-9 * 3 * 7 * -1)) or (The 1960 Olympics were held in Rome.)))))
B. (not (not not ((not ((-3 * -9) <= (1 ** 3))) or (not not (A ant has 8 legs.))))) and (not ((-4 * 6 * 0 * -6) <= (7 * 10))) and (not (((not not (A cow has 2 legs.)) and ((The human body has 150 bones.) or ((-6 - 15) == (14 * -3)))) or (not (Morocco is in Europe.))))
C. not not (not not (not ((((2 * 6 + -7 * 6) < (6 * 7 + -2 * 3)) and (The human body has 150 bones.)) and (not ((16 * 16) < (4 ** 1) < (13 * 12))))))
D. (not (not not (There are 29 days in June.))) or (not not ((1 ** 3) > (-19 * 0))) or (not not (not not (not ((A kangaroo has 10 legs.) and (A owl is a bird.)))))
E. (not not ((((Sound cannot travel through a vacuum.) or (The currency of Nigeria is the Ruble.)) and (((2 * -3) > (-10 * -5 * -3 * -6)) and ((-11 * -1) >= (9 - -15)))) or (The 1968 Olympics were held in Helsinki.))) and (((((1 - -13) != (-9 + 20)) or ((24 % 8) != (-20 - 10))) and ((A horse is a bird.) and ((Oxygen is necessary for human survival.) or (The 1932 Olympics were held in Los Angeles.)))) and (not not ((not (The capital of Thailand is Bangkok.)) or (613 is a Fibonacci number.))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 87946906,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not ((not not ((4 * 0) < (4 ** 2))) and ((((The first airplane flight by the Wright Brothers occurred in 1903.) or ((-11 * 19) >= (-9 * 20))) and (((-6 - 16) != (1 ** 3)) or ((5 ** 2) == (1 ** 2)))) or ((The currency of Denmark is the Krone.) or ((-6 * -9) == (17 + 8))) or ((not not ((3 * -15) == (-4 * -3 * 3 * 3))) or (((3 % 10) != (-9 * 3 * 7 * -1)) or (The 1960 Olympics were held in Rome.)))))\nB. (not (not not ((not ((-3 * -9) <= (1 ** 3))) or (not not (A ant has 8 legs.))))) and (not ((-4 * 6 * 0 * -6) <= (7 * 10))) and (not (((not not (A cow has 2 legs.)) and ((The human body has 150 bones.) or ((-6 - 15) == (14 * -3)))) or (not (Morocco is in Europe.))))\nC. not not (not not (not ((((2 * 6 + -7 * 6) < (6 * 7 + -2 * 3)) and (The human body has 150 bones.)) and (not ((16 * 16) < (4 ** 1) < (13 * 12))))))\nD. (not (not not (There are 29 days in June.))) or (not not ((1 ** 3) > (-19 * 0))) or (not not (not not (not ((A kangaroo has 10 legs.) and (A owl is a bird.)))))\nE. (not not ((((Sound cannot travel through a vacuum.) or (The currency of Nigeria is the Ruble.)) and (((2 * -3) > (-10 * -5 * -3 * -6)) and ((-11 * -1) >= (9 - -15)))) or (The 1968 Olympics were held in Helsinki.))) and (((((1 - -13) != (-9 + 20)) or ((24 % 8) != (-20 - 10))) and ((A horse is a bird.) and ((Oxygen is necessary for human survival.) or (The 1932 Olympics were held in Los Angeles.)))) and (not not ((not (The capital of Thailand is Bangkok.)) or (613 is a Fibonacci number.))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 87946906,
"true_count": 2
},
"seed": 87946906,
"task_id": 687946906,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (not not (((-14 - -7) > (-19 * -10)) and ((-10 * -9 * -1 * -4) <= (-3 - 8)))) or (not (((-16 - 12) == (14 * -12)) and ((-10 - -17) < (2 ** 1))))
B. ((not ((-12 - -4) != (3 ** 1))) or ((-9 * -16) < (-10 * 1 - 3 * -5))) or (尼日利亚位于南美洲。)
C. (((394是斐波那契数。) or (铂的化学符号是S。)) and (((-5 * -5 * -3 * 1) < (2 + 10)) or (氧气在常温下是气体。))) and (((32 % 9) <= (-17 + 3)) or (((2 + 0) != (13 * 10)) and (三月有31天。)))
D. (not not ((柏林墙倒塌发生在1989年。) or (加拿大的货币是加元。))) or (((1 + -4) < (6 * -4 * 9 * -3) < (3 * -2 * -2 * 7)) and ((19 - 16) > (2 ** 1))) or (not not ((硫的化学符号是S。) and ((-5 * 11) >= (0 * -5 + -5 * -1))))
E. ((狗有6条腿。) or (((-19 + 13) < (4 + -12)) and (水星是距离太阳第5近的行星。))) or (第一次世界大战结束发生在1908年。)
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,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 8372440,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. (not not (((-14 - -7) > (-19 * -10)) and ((-10 * -9 * -1 * -4) <= (-3 - 8)))) or (not (((-16 - 12) == (14 * -12)) and ((-10 - -17) < (2 ** 1))))\nB. ((not ((-12 - -4) != (3 ** 1))) or ((-9 * -16) < (-10 * 1 - 3 * -5))) or (尼日利亚位于南美洲。)\nC. (((394是斐波那契数。) or (铂的化学符号是S。)) and (((-5 * -5 * -3 * 1) < (2 + 10)) or (氧气在常温下是气体。))) and (((32 % 9) <= (-17 + 3)) or (((2 + 0) != (13 * 10)) and (三月有31天。)))\nD. (not not ((柏林墙倒塌发生在1989年。) or (加拿大的货币是加元。))) or (((1 + -4) < (6 * -4 * 9 * -3) < (3 * -2 * -2 * 7)) and ((19 - 16) > (2 ** 1))) or (not not ((硫的化学符号是S。) and ((-5 * 11) >= (0 * -5 + -5 * -1))))\nE. ((狗有6条腿。) or (((-19 + 13) < (4 + -12)) and (水星是距离太阳第5近的行星。))) or (第一次世界大战结束发生在1908年。)\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": 5,
"seed": 8372440,
"true_count": 2
},
"seed": 8372440,
"task_id": 608372440,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((((not not (罗马尼亚的首都是奥斯陆。)) and (not (第一部iPhone发布发生在2012年。))) and (not not ((瑞典的货币是新加坡元。) or ((-14 + 13) < (15 + 3))))) and (((not ((1 % 7) <= (21 % 6) <= (-3 * 5 * -7 * 4))) or (火星是距离太阳第5近的行星。)) and ((20 - 19) > (12 * 18)))) or ((((not (鲤鱼是鱼类。)) or (not (章鱼有2条腿。))) or ((2075年是闰年。) and ((-8 * 18) < (-6 - 17))) or ((-8 - 6) <= (10 * 0 * -8 * 2))) or ((((墨西哥位于欧洲。) or ((-9 * 1 - 10 * -9) > (24 % 10))) or ((秘鲁的货币是索尔。) or ((15 + -19) <= (-7 * 12)))) or (马有4条腿。)))
B. ((not (((15 * 16) == (-6 * -5 - -5 * 5)) or (not not (硫的化学符号是S。)))) and ((((7 % 6) >= (18 + -10)) and ((2094年是闰年。) and ((16 + 20) <= (-19 * 17)))) and (2021年是闰年。))) or ((((-1 * 10 * -6 * 4) >= (14 + -20)) and (空气在常温下是气体。)) and (((13 - -9) <= (1 - -10)) and (((钻石在常温下是液体。) or (瑞士的货币是谢克尔。)) or (((-1 * -9) < (0 * 0 + 1 * 2)) or (沙特阿拉伯位于亚洲。)))))
C. ((not ((金星是距离太阳第8近的行星。) or (蝴蝶是昆虫。))) or ((-2 * 2 * 1 * 9) > (14 - 10)) or (((18小于等于66。) and (not ((8 - -1) != (1 + 12)))) or (巴西位于亚洲。) or ((36 % 8) >= (8 * 9 * -1 * -7)))) or ((冰的密度比液态水小。) and ((((13 * 11) == (34 % 9)) and ((2 * 9) != (-15 - -10))) and (((-16 - -10) <= (14 + 18)) or (哥伦比亚位于南美洲。)))) or (((天王星是距离太阳第7近的行星。) and (((10 - 1) <= (17 % 4)) and ((9 - -5) == (3 ** 3)))) or ((((秘鲁位于南美洲。) or (金星是距离太阳第4近的行星。)) and ((-2 * 13) != (10 * 0 - 10 * 6))) or ((1909年是闰年。) and (太平洋是最大的海洋。))))
D. (((莱特兄弟首次飞行发生在1893年。) and ((挪威的货币是克朗。) or (not (地球上一天是24小时。)))) or (not not ((1900年奥运会在伦敦举办。) or (尼日利亚位于非洲。))) or (not (not not ((-18 * 2) < (-10 - -11))))) and (not (not not ((((1 * 0 - -8 * -2) != (4 ** 1)) or ((39 % 8) > (1 * -11))) and (((4 ** 1) == (-13 * 16)) or (2004年奥运会在斯德哥尔摩举办。)))))
E. not ((((not not ((22 % 2) <= (0 * -6 + -8 * -10))) or (585是斐波那契数。)) and (((泰国位于大洋洲。) and ((-8 * -9 + 3 * 4) > (-9 - 9))) or ((1956年奥运会在墨尔本举办。) or (美国宣布独立发生在1776年。)))) or (((not ((-19 * 8) <= (-12 + 15))) and ((-1 * -9 + 1 * 5) > (7 * 7 + -6 * -1))) and ((not not (冰在常温下是气体。)) and ((地球是距离太阳第8近的行星。) or ((5 % 3) < (-12 * -8))))))
F. ((not ((-9 - 17) > (9 * 2 + -6 * 2))) or ((((水星是距离太阳第1近的行星。) and (中国的货币是兰特。)) and (伦敦大火发生在1656年。)) and (not (not (钻石由碳元素组成。))))) and ((not not (金的化学符号是Ni。)) and (((加拿大的货币是越南盾。) and (西班牙位于北美洲。)) or (not (1的平方根是1。))) and (((not not ((3 ** 3) <= (6 - 12) <= (11 + -17))) or (人类首次登月发生在1969年。)) and ((((9 * -9 - -3 * 10) >= (5 ** 1)) or ((1 + -6) < (-18 + 13))) and (秘鲁位于亚洲。))))
G. (((((银在常温下是气体。) and (1900年是闰年。)) or ((马来西亚的货币是林吉特。) and (1964年奥运会在东京举办。))) or ((not ((-2 - -12) > (7 * 0 - 9 * -10))) or (not not (西班牙位于南美洲。)))) and ((((金的化学符号是Au。) and ((11 + -8) <= (-10 * -5 - -6 * 3))) and ((2024年奥运会在巴黎举办。) and (大象有4条腿。))) or (秘鲁的货币是比索。))) and (not not (not not (not not ((苏联解体发生在1991年。) and ((7 * -6 * 0 * -9) == (16 - -11))))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 96476636,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. ((((not not (罗马尼亚的首都是奥斯陆。)) and (not (第一部iPhone发布发生在2012年。))) and (not not ((瑞典的货币是新加坡元。) or ((-14 + 13) < (15 + 3))))) and (((not ((1 % 7) <= (21 % 6) <= (-3 * 5 * -7 * 4))) or (火星是距离太阳第5近的行星。)) and ((20 - 19) > (12 * 18)))) or ((((not (鲤鱼是鱼类。)) or (not (章鱼有2条腿。))) or ((2075年是闰年。) and ((-8 * 18) < (-6 - 17))) or ((-8 - 6) <= (10 * 0 * -8 * 2))) or ((((墨西哥位于欧洲。) or ((-9 * 1 - 10 * -9) > (24 % 10))) or ((秘鲁的货币是索尔。) or ((15 + -19) <= (-7 * 12)))) or (马有4条腿。)))\nB. ((not (((15 * 16) == (-6 * -5 - -5 * 5)) or (not not (硫的化学符号是S。)))) and ((((7 % 6) >= (18 + -10)) and ((2094年是闰年。) and ((16 + 20) <= (-19 * 17)))) and (2021年是闰年。))) or ((((-1 * 10 * -6 * 4) >= (14 + -20)) and (空气在常温下是气体。)) and (((13 - -9) <= (1 - -10)) and (((钻石在常温下是液体。) or (瑞士的货币是谢克尔。)) or (((-1 * -9) < (0 * 0 + 1 * 2)) or (沙特阿拉伯位于亚洲。)))))\nC. ((not ((金星是距离太阳第8近的行星。) or (蝴蝶是昆虫。))) or ((-2 * 2 * 1 * 9) > (14 - 10)) or (((18小于等于66。) and (not ((8 - -1) != (1 + 12)))) or (巴西位于亚洲。) or ((36 % 8) >= (8 * 9 * -1 * -7)))) or ((冰的密度比液态水小。) and ((((13 * 11) == (34 % 9)) and ((2 * 9) != (-15 - -10))) and (((-16 - -10) <= (14 + 18)) or (哥伦比亚位于南美洲。)))) or (((天王星是距离太阳第7近的行星。) and (((10 - 1) <= (17 % 4)) and ((9 - -5) == (3 ** 3)))) or ((((秘鲁位于南美洲。) or (金星是距离太阳第4近的行星。)) and ((-2 * 13) != (10 * 0 - 10 * 6))) or ((1909年是闰年。) and (太平洋是最大的海洋。))))\nD. (((莱特兄弟首次飞行发生在1893年。) and ((挪威的货币是克朗。) or (not (地球上一天是24小时。)))) or (not not ((1900年奥运会在伦敦举办。) or (尼日利亚位于非洲。))) or (not (not not ((-18 * 2) < (-10 - -11))))) and (not (not not ((((1 * 0 - -8 * -2) != (4 ** 1)) or ((39 % 8) > (1 * -11))) and (((4 ** 1) == (-13 * 16)) or (2004年奥运会在斯德哥尔摩举办。)))))\nE. not ((((not not ((22 % 2) <= (0 * -6 + -8 * -10))) or (585是斐波那契数。)) and (((泰国位于大洋洲。) and ((-8 * -9 + 3 * 4) > (-9 - 9))) or ((1956年奥运会在墨尔本举办。) or (美国宣布独立发生在1776年。)))) or (((not ((-19 * 8) <= (-12 + 15))) and ((-1 * -9 + 1 * 5) > (7 * 7 + -6 * -1))) and ((not not (冰在常温下是气体。)) and ((地球是距离太阳第8近的行星。) or ((5 % 3) < (-12 * -8))))))\nF. ((not ((-9 - 17) > (9 * 2 + -6 * 2))) or ((((水星是距离太阳第1近的行星。) and (中国的货币是兰特。)) and (伦敦大火发生在1656年。)) and (not (not (钻石由碳元素组成。))))) and ((not not (金的化学符号是Ni。)) and (((加拿大的货币是越南盾。) and (西班牙位于北美洲。)) or (not (1的平方根是1。))) and (((not not ((3 ** 3) <= (6 - 12) <= (11 + -17))) or (人类首次登月发生在1969年。)) and ((((9 * -9 - -3 * 10) >= (5 ** 1)) or ((1 + -6) < (-18 + 13))) and (秘鲁位于亚洲。))))\nG. (((((银在常温下是气体。) and (1900年是闰年。)) or ((马来西亚的货币是林吉特。) and (1964年奥运会在东京举办。))) or ((not ((-2 - -12) > (7 * 0 - 9 * -10))) or (not not (西班牙位于南美洲。)))) and ((((金的化学符号是Au。) and ((11 + -8) <= (-10 * -5 - -6 * 3))) and ((2024年奥运会在巴黎举办。) and (大象有4条腿。))) or (秘鲁的货币是比索。))) and (not not (not not (not not ((苏联解体发生在1991年。) and ((7 * -6 * 0 * -9) == (16 - -11))))))\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": 7,
"seed": 96476636,
"true_count": 3
},
"seed": 96476636,
"task_id": 696476636,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (((The currency of Norway is the Krone.) or ((-9 * 10 * -4 * -5) < (4 + 2))) and (((9 + -12) != (20 - -11)) or ((-1 + -11) < (-20 + -18))))
B. not (The chemical symbol for Chromium is Cr.)
C. ((-8 * -8) < (4 * 16)) or ((-7 * 7 + 7 * -5) == (-15 + 6))
D. (not (Earth is the 3rd planet from the Sun.)) or ((((-2 + 0) <= (14 - -14)) and ((-6 * 7 + 2 * 4) >= (20 - -12))) and (((-17 * 9) < (10 % 1) < (9 - 5)) and (The chemical symbol for Magnesium is Mg.)))
E. ((((10 - -1) <= (-12 - -13)) or (The capital of New Zealand is Wellington.)) and ((The Moon produces its own light.) or (The French Revolution began occurred in 1789.))) or ((Christopher Columbus reached America occurred in 1492.) and (The chemical symbol for Chlorine is Ca.)) or (Saturn is the 2nd planet from the Sun.)
F. ((not (2078 is a leap year.)) and (((-16 * -14) != (1 ** 3)) or (The currency of Thailand is the Zloty.))) or ((-9 * 9) > (9 * 15))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 1731856,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. not not (((The currency of Norway is the Krone.) or ((-9 * 10 * -4 * -5) < (4 + 2))) and (((9 + -12) != (20 - -11)) or ((-1 + -11) < (-20 + -18))))\nB. not (The chemical symbol for Chromium is Cr.)\nC. ((-8 * -8) < (4 * 16)) or ((-7 * 7 + 7 * -5) == (-15 + 6))\nD. (not (Earth is the 3rd planet from the Sun.)) or ((((-2 + 0) <= (14 - -14)) and ((-6 * 7 + 2 * 4) >= (20 - -12))) and (((-17 * 9) < (10 % 1) < (9 - 5)) and (The chemical symbol for Magnesium is Mg.)))\nE. ((((10 - -1) <= (-12 - -13)) or (The capital of New Zealand is Wellington.)) and ((The Moon produces its own light.) or (The French Revolution began occurred in 1789.))) or ((Christopher Columbus reached America occurred in 1492.) and (The chemical symbol for Chlorine is Ca.)) or (Saturn is the 2nd planet from the Sun.)\nF. ((not (2078 is a leap year.)) and (((-16 * -14) != (1 ** 3)) or (The currency of Thailand is the Zloty.))) or ((-9 * 9) > (9 * 15))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 1731856,
"true_count": 3
},
"seed": 1731856,
"task_id": 601731856,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. not ((2086年是闰年。) or ((2 * -19) > (-1 + -11)))
B. (not not ((6 * -4 + -9 * 3) >= (-5 + -6))) and ((电流比光速更快。) or (柏林墙倒塌发生在1989年。))
C. (((45 % 1) > (-18 * 1)) and (德国的首都是柏林。)) and (火星是距离太阳最近的行星。)
D. (((2 ** 2) == (6 + 12)) or ((0 * 12) > (2 * -9))) and (not not (水星是距离太阳第7近的行星。))
E. not ((新西兰的货币是欧元。) and ((6 * -5 - 8 * 2) == (0 * 9 * -10 * -4)))
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,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 70710310,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. not ((2086年是闰年。) or ((2 * -19) > (-1 + -11)))\nB. (not not ((6 * -4 + -9 * 3) >= (-5 + -6))) and ((电流比光速更快。) or (柏林墙倒塌发生在1989年。))\nC. (((45 % 1) > (-18 * 1)) and (德国的首都是柏林。)) and (火星是距离太阳最近的行星。)\nD. (((2 ** 2) == (6 + 12)) or ((0 * 12) > (2 * -9))) and (not not (水星是距离太阳第7近的行星。))\nE. not ((新西兰的货币是欧元。) and ((6 * -5 - 8 * 2) == (0 * 9 * -10 * -4)))\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": 2,
"language": "cn",
"num_options": 5,
"seed": 70710310,
"true_count": 2
},
"seed": 70710310,
"task_id": 670710310,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. not not ((not not (((-6 * 3 * 8 * -10) != (-8 * -3 - 4 * 1)) or (((-10 + 7) >= (-18 - 17)) and (((18 - 10) <= (-7 + 10)) or ((3 ** 1) >= (-1 - 0)))))) and ((not not (鸡有2条腿。)) or ((247是完全平方数。) or (第二次世界大战结束发生在1945年。)) or (((1 % 6) == (3 ** 3)) and ((9 - 3) < (-13 * 3)))) and (((苏联解体发生在1986年。) or (not not (柏林墙倒塌发生在1989年。))) or (((-11 + -17) < (-3 * 10 + -2 * 7) < (9 * 9)) and ((480是斐波那契数。) or (1956年奥运会在巴黎举办。))) or (not (((人类有三个肺。) and (铁在常温下是固体。)) and ((13 * 7) <= (1 ** 1))))))
B. not (not not (((((第一次世界大战开始发生在1915年。) and ((11 * -5) == (16 - -16))) and (((33 % 2) < (18 - 13)) or ((-1 * 15) < (-8 * 7 - 10 * -10)))) and (铬的化学符号是K。)) or ((摩洛哥位于非洲。) and ((闪电不会两次击中同一个地方。) or (氖的化学符号是Ne。))) or ((not (鸟有100条腿。)) or ((not ((-5 + 9) >= (45 % 7))) or ((沙特阿拉伯位于大洋洲。) or (酒精在常温下是液体。))))))
C. not (not not ((((not (81的平方根是9。)) or (人类有三个肺。)) or (((-16 + 1) >= (0 * 7 * 6 * -10)) or (鲨鱼是哺乳动物。))) or ((((钠的化学符号是Na。) and (加拿大的首都是北京。)) and (哥伦比亚的首都是波哥大。)) and ((5 ** 2) >= (-20 - -18)))))
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,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 74738216,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. not not ((not not (((-6 * 3 * 8 * -10) != (-8 * -3 - 4 * 1)) or (((-10 + 7) >= (-18 - 17)) and (((18 - 10) <= (-7 + 10)) or ((3 ** 1) >= (-1 - 0)))))) and ((not not (鸡有2条腿。)) or ((247是完全平方数。) or (第二次世界大战结束发生在1945年。)) or (((1 % 6) == (3 ** 3)) and ((9 - 3) < (-13 * 3)))) and (((苏联解体发生在1986年。) or (not not (柏林墙倒塌发生在1989年。))) or (((-11 + -17) < (-3 * 10 + -2 * 7) < (9 * 9)) and ((480是斐波那契数。) or (1956年奥运会在巴黎举办。))) or (not (((人类有三个肺。) and (铁在常温下是固体。)) and ((13 * 7) <= (1 ** 1))))))\nB. not (not not (((((第一次世界大战开始发生在1915年。) and ((11 * -5) == (16 - -16))) and (((33 % 2) < (18 - 13)) or ((-1 * 15) < (-8 * 7 - 10 * -10)))) and (铬的化学符号是K。)) or ((摩洛哥位于非洲。) and ((闪电不会两次击中同一个地方。) or (氖的化学符号是Ne。))) or ((not (鸟有100条腿。)) or ((not ((-5 + 9) >= (45 % 7))) or ((沙特阿拉伯位于大洋洲。) or (酒精在常温下是液体。))))))\nC. not (not not ((((not (81的平方根是9。)) or (人类有三个肺。)) or (((-16 + 1) >= (0 * 7 * 6 * -10)) or (鲨鱼是哺乳动物。))) or ((((钠的化学符号是Na。) and (加拿大的首都是北京。)) and (哥伦比亚的首都是波哥大。)) and ((5 ** 2) >= (-20 - -18)))))\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": 3,
"seed": 74738216,
"true_count": 2
},
"seed": 74738216,
"task_id": 674738216,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((((5 * -7 * -8 * 6) <= (9 * 12) <= (-16 * -19)) or ((哥伦布到达美洲发生在1491年。) and (木星是距离太阳第5近的行星。))) and (((-9 * 10 * 3 * 1) >= (13 + 15)) and ((0 - -3) < (4 ** 1) < (-9 * 1 - -1 * -1)))) and (not not ((现代奥运会首届举办发生在1896年。) or ((沙特阿拉伯的货币是里亚尔。) and ((18 + 15) < (3 ** 3)))))) and ((((埃及的货币是里亚尔。) or (not ((-4 * -9) >= (-7 - -7)))) or ((5 ** 1) <= (-9 - -10))) or (not not ((((-7 * 19) < (1 + -11)) or ((-6 * -4 + 6 * -3) >= (-1 * -10 * 5 * 10))) or (鲱鱼是昆虫。))))
B. (((not not (((-5 * 4 * -4 * -3) <= (4 * -15)) and (马来西亚的货币是新西兰元。))) and (((印度的货币是卢比。) and (1928年奥运会在赫尔辛基举办。)) or (not not ((3 ** 3) > (4 ** 1))))) and ((海王星是距离太阳第8近的行星。) and ((15 - 2) <= (-11 + -7) <= (-12 - 9)) and ((2016年奥运会在里约热内卢举办。) or ((10 * -1 + -4 * -7) <= (7 * 10) <= (4 ** 2))))) and (not (((9 * -2) < (-1 * 9 - -10 * 2)) and (((挪威的首都是奥斯陆。) and (火星是距离太阳第4近的行星。)) and (((8 * 5 - 6 * 9) > (-3 * 1 * -10 * 9)) and ((-12 - 3) < (-4 - 15) < (-5 + -14))))))
C. (((((12 * -20) >= (0 + -19)) or (金星是距离太阳第5近的行星。)) or ((-14 + 5) >= (-11 * 17)) or ((((18 * 11) <= (8 * 10 * -3 * -8)) and ((-10 * -6 - -4 * -3) == (-14 * -8))) and (第二次世界大战开始发生在1939年。))) or (not not (((11 + 15) != (4 * -2)) or (鱼有0条腿。)))) or (not not (((((-3 * 3 - -8 * -5) < (-16 - 9) < (4 * 0 + 3 * 0)) or (西班牙的首都是马德里。)) or ((八月有31天。) and (欧盟的货币是瑞士法郎。))) and ((孔雀是鸟类。) or (1988年奥运会在巴黎举办。))))
D. (not not (not not ((((-20 * 19) <= (0 + 0)) and (金星是距离太阳第2近的行星。)) or ((65是奇数。) or (电流比光速更快。))))) or ((not (巴西位于南美洲。)) and (((-3 * -6 - 2 * -7) <= (14 + 11) <= (1 * 9)) or ((2016年奥运会在里约热内卢举办。) and (not not (钾的化学符号是Ti。)))))
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": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 19949173,
"true_count": 2
},
"question": "考虑以下布尔表达式：\n\nA. (((((5 * -7 * -8 * 6) <= (9 * 12) <= (-16 * -19)) or ((哥伦布到达美洲发生在1491年。) and (木星是距离太阳第5近的行星。))) and (((-9 * 10 * 3 * 1) >= (13 + 15)) and ((0 - -3) < (4 ** 1) < (-9 * 1 - -1 * -1)))) and (not not ((现代奥运会首届举办发生在1896年。) or ((沙特阿拉伯的货币是里亚尔。) and ((18 + 15) < (3 ** 3)))))) and ((((埃及的货币是里亚尔。) or (not ((-4 * -9) >= (-7 - -7)))) or ((5 ** 1) <= (-9 - -10))) or (not not ((((-7 * 19) < (1 + -11)) or ((-6 * -4 + 6 * -3) >= (-1 * -10 * 5 * 10))) or (鲱鱼是昆虫。))))\nB. (((not not (((-5 * 4 * -4 * -3) <= (4 * -15)) and (马来西亚的货币是新西兰元。))) and (((印度的货币是卢比。) and (1928年奥运会在赫尔辛基举办。)) or (not not ((3 ** 3) > (4 ** 1))))) and ((海王星是距离太阳第8近的行星。) and ((15 - 2) <= (-11 + -7) <= (-12 - 9)) and ((2016年奥运会在里约热内卢举办。) or ((10 * -1 + -4 * -7) <= (7 * 10) <= (4 ** 2))))) and (not (((9 * -2) < (-1 * 9 - -10 * 2)) and (((挪威的首都是奥斯陆。) and (火星是距离太阳第4近的行星。)) and (((8 * 5 - 6 * 9) > (-3 * 1 * -10 * 9)) and ((-12 - 3) < (-4 - 15) < (-5 + -14))))))\nC. (((((12 * -20) >= (0 + -19)) or (金星是距离太阳第5近的行星。)) or ((-14 + 5) >= (-11 * 17)) or ((((18 * 11) <= (8 * 10 * -3 * -8)) and ((-10 * -6 - -4 * -3) == (-14 * -8))) and (第二次世界大战开始发生在1939年。))) or (not not (((11 + 15) != (4 * -2)) or (鱼有0条腿。)))) or (not not (((((-3 * 3 - -8 * -5) < (-16 - 9) < (4 * 0 + 3 * 0)) or (西班牙的首都是马德里。)) or ((八月有31天。) and (欧盟的货币是瑞士法郎。))) and ((孔雀是鸟类。) or (1988年奥运会在巴黎举办。))))\nD. (not not (not not ((((-20 * 19) <= (0 + 0)) and (金星是距离太阳第2近的行星。)) or ((65是奇数。) or (电流比光速更快。))))) or ((not (巴西位于南美洲。)) and (((-3 * -6 - 2 * -7) <= (14 + 11) <= (1 * 9)) or ((2016年奥运会在里约热内卢举办。) and (not not (钾的化学符号是Ti。)))))\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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"seed": 19949173,
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"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not ((not not ((not not (氮气在常温下是气体。)) and (月球自己发光。))) or ((((十二月有31天。) or ((-4 * 10) < (7 + -15))) or (((-6 + -14) > (4 * 2 + 0 * 8)) or ((20 - 9) != (7 * -3 * -4 * 8)))) or (((-8 + 11) >= (-1 - -4)) and (越南的货币是越南盾。)) or (2090年是闰年。)) or ((((1988年奥运会在圣路易斯举办。) and (not ((-10 * 11) == (5 * -8 + 3 * 4)))) and (not (not (植物通过光合作用产生氧气。)))) and (not ((((6 - 13) < (5 ** 2) < (5 ** 2)) or (1967年是闰年。)) and (((14 - -1) > (-15 * -9)) or (泰国的首都是北京。))))))
B. (not ((not not ((not (水星是距离太阳第1近的行星。)) or ((海王星是距离太阳第4近的行星。) and ((6 - -11) >= (5 * -9 * -9 * -1))))) and (not (((木头在常温下是气体。) and (摩洛哥的首都是拉巴特。)) or ((苏联解体发生在1991年。) and (天王星是距离太阳第7近的行星。)))))) and ((not not ((not (not (羊是昆虫。))) and ((-3 * 2 - -9 * -3) == (6 + 20)))) or ((not (64的平方根是8。)) and (not not (not ((73大于76。) or (南极洲是最冷的大陆。))))))
C. not ((not (((4 ** 1) <= (-3 - 9)) or (not not ((哥伦比亚位于南美洲。) or ((10 - -8) <= (-6 * 5 + -1 * 4) <= (8 * -13)))))) or ((((中国位于亚洲。) and (天王星是距离太阳第7近的行星。)) and (not not ((-2 * -1 - 4 * 2) != (18 % 7)))) and (冰的密度比液态水小。) and (((not not ((-5 * -6 - 2 * -9) == (24 % 3))) and (鳄鱼是爬行动物。)) and ((not not (1936年奥运会在斯德哥尔摩举办。)) or ((4 + -10) < (-4 + 16))))))
D. not not (((not not (((肯尼亚的首都是内罗毕。) or ((4 * -14) > (15 - 19))) or (((-6 + 14) == (12 - -9)) and (老鼠是哺乳动物。)))) and (not not (not ((金星是距离太阳第2近的行星。) or (澳大利亚的首都是华沙。))))) or (not not (((not (鸭子有2条腿。)) or (((-19 - 18) <= (-19 - 20)) or (苏联解体发生在1991年。))) or (not not (not (1964年是闰年。))))))
E. not (not not (((not ((大象有4条腿。) and ((-14 * 18) < (-13 * 12)))) and (not ((-10 - -1) != (12 - 17))) and (not not (not not (莱特兄弟首次飞行发生在1901年。)))) or ((not not (火星是距离太阳第4近的行星。)) and ((1904年奥运会在圣路易斯举办。) and (埃及的首都是开罗。))) or (((钠的化学符号是O。) and (not (乌龟是爬行动物。))) and ((16 * 12) < (20 * -5)) and (not not (23小于等于70。)))))
F. not (((not ((-9 + -19) == (13 + -13))) or (((((-2 * -8 * 8 * -4) != (17 + 5)) and (1952年奥运会在赫尔辛基举办。)) and (not (蝙蝠是哺乳动物。))) and (((氖的化学符号是Ne。) and ((1 ** 2) <= (-14 * 20) <= (-14 + 3))) and (not ((12 * 12) == (31 % 1)))))) or (((not (not ((13 % 6) <= (19 * 11)))) or ((((8 - 5) < (-10 * 10 * 9 * -5)) or (氯的化学符号是Cl。)) or (钻石由碳元素组成。))) and (not (not not (((16 % 9) == (43 % 2)) or (苍蝇是爬行动物。))))))
G. not ((not (((((-19 - -4) <= (1 - -11) <= (-15 - -5)) or (氯的化学符号是Cl。)) or ((2081年是闰年。) and ((-6 * 20) < (-12 + 17) < (-10 * -1 + 7 * -1)))) or (not not (((4 ** 1) < (1 + 12)) and (238是斐波那契数。))))) or (((((-11 + -11) != (26 % 8)) and (not not (短吻鳄是爬行动物。))) and ((3 % 5) != (-13 + 5)) and (not not ((41 % 10) != (2 * 2)))) and ((not ((11 * -2) != (2 % 8))) or ((印度尼西亚的货币是印尼盾。) and (二氧化碳在常温下是气体。)) or ((not (月球绕地球运转。)) or ((18 % 9) < (-2 * -10 + 9 * -3) < (-2 + -5))))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
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"answer": "A,C,D",
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"gpt_response": "",
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"question": "审视以下逻辑表达式：\n\nA. not not ((not not ((not not (氮气在常温下是气体。)) and (月球自己发光。))) or ((((十二月有31天。) or ((-4 * 10) < (7 + -15))) or (((-6 + -14) > (4 * 2 + 0 * 8)) or ((20 - 9) != (7 * -3 * -4 * 8)))) or (((-8 + 11) >= (-1 - -4)) and (越南的货币是越南盾。)) or (2090年是闰年。)) or ((((1988年奥运会在圣路易斯举办。) and (not ((-10 * 11) == (5 * -8 + 3 * 4)))) and (not (not (植物通过光合作用产生氧气。)))) and (not ((((6 - 13) < (5 ** 2) < (5 ** 2)) or (1967年是闰年。)) and (((14 - -1) > (-15 * -9)) or (泰国的首都是北京。))))))\nB. (not ((not not ((not (水星是距离太阳第1近的行星。)) or ((海王星是距离太阳第4近的行星。) and ((6 - -11) >= (5 * -9 * -9 * -1))))) and (not (((木头在常温下是气体。) and (摩洛哥的首都是拉巴特。)) or ((苏联解体发生在1991年。) and (天王星是距离太阳第7近的行星。)))))) and ((not not ((not (not (羊是昆虫。))) and ((-3 * 2 - -9 * -3) == (6 + 20)))) or ((not (64的平方根是8。)) and (not not (not ((73大于76。) or (南极洲是最冷的大陆。))))))\nC. not ((not (((4 ** 1) <= (-3 - 9)) or (not not ((哥伦比亚位于南美洲。) or ((10 - -8) <= (-6 * 5 + -1 * 4) <= (8 * -13)))))) or ((((中国位于亚洲。) and (天王星是距离太阳第7近的行星。)) and (not not ((-2 * -1 - 4 * 2) != (18 % 7)))) and (冰的密度比液态水小。) and (((not not ((-5 * -6 - 2 * -9) == (24 % 3))) and (鳄鱼是爬行动物。)) and ((not not (1936年奥运会在斯德哥尔摩举办。)) or ((4 + -10) < (-4 + 16))))))\nD. not not (((not not (((肯尼亚的首都是内罗毕。) or ((4 * -14) > (15 - 19))) or (((-6 + 14) == (12 - -9)) and (老鼠是哺乳动物。)))) and (not not (not ((金星是距离太阳第2近的行星。) or (澳大利亚的首都是华沙。))))) or (not not (((not (鸭子有2条腿。)) or (((-19 - 18) <= (-19 - 20)) or (苏联解体发生在1991年。))) or (not not (not (1964年是闰年。))))))\nE. not (not not (((not ((大象有4条腿。) and ((-14 * 18) < (-13 * 12)))) and (not ((-10 - -1) != (12 - 17))) and (not not (not not (莱特兄弟首次飞行发生在1901年。)))) or ((not not (火星是距离太阳第4近的行星。)) and ((1904年奥运会在圣路易斯举办。) and (埃及的首都是开罗。))) or (((钠的化学符号是O。) and (not (乌龟是爬行动物。))) and ((16 * 12) < (20 * -5)) and (not not (23小于等于70。)))))\nF. not (((not ((-9 + -19) == (13 + -13))) or (((((-2 * -8 * 8 * -4) != (17 + 5)) and (1952年奥运会在赫尔辛基举办。)) and (not (蝙蝠是哺乳动物。))) and (((氖的化学符号是Ne。) and ((1 ** 2) <= (-14 * 20) <= (-14 + 3))) and (not ((12 * 12) == (31 % 1)))))) or (((not (not ((13 % 6) <= (19 * 11)))) or ((((8 - 5) < (-10 * 10 * 9 * -5)) or (氯的化学符号是Cl。)) or (钻石由碳元素组成。))) and (not (not not (((16 % 9) == (43 % 2)) or (苍蝇是爬行动物。))))))\nG. not ((not (((((-19 - -4) <= (1 - -11) <= (-15 - -5)) or (氯的化学符号是Cl。)) or ((2081年是闰年。) and ((-6 * 20) < (-12 + 17) < (-10 * -1 + 7 * -1)))) or (not not (((4 ** 1) < (1 + 12)) and (238是斐波那契数。))))) or (((((-11 + -11) != (26 % 8)) and (not not (短吻鳄是爬行动物。))) and ((3 % 5) != (-13 + 5)) and (not not ((41 % 10) != (2 * 2)))) and ((not ((11 * -2) != (2 % 8))) or ((印度尼西亚的货币是印尼盾。) and (二氧化碳在常温下是气体。)) or ((not (月球绕地球运转。)) or ((18 % 9) < (-2 * -10 + 9 * -3) < (-2 + -5))))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
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"language": "cn",
"num_options": 7,
"seed": 39375025,
"true_count": 3
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"seed": 39375025,
"task_id": 639375025,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not (((Saturn is the 2nd planet from the Sun.) or ((37 % 1) <= (12 * -10))) and (not not ((-14 * 17) > (-14 - -6))))
B. (((20 - -16) <= (4 * -10)) or (not (Thailand is in Europe.))) and (not not ((1 * -20) >= (11 * 12)))
C. (not not ((-12 - 8) >= (-7 * 8 - -9 * -7))) and ((not not ((5 * -6 - -9 * -8) > (18 * 13))) and (((6 * -5 * 9 * 4) >= (37 % 10)) and ((2 * -2 * 5 * -10) > (-2 * 0 - 1 * -9))))
D. ((-5 * -18) > (7 + -3)) or (Saturn is the 8th planet from the Sun.)
E. ((((0 * -3 - -1 * 0) < (-10 * 7 + -9 * -5) < (14 + 7)) or ((-19 - 1) > (19 % 5))) or ((The square root of 144 is 4.) or ((3 ** 1) <= (13 + 4) <= (-1 * -11)))) or ((((5 * -3 + 7 * 7) > (14 + 15)) and ((1 ** 3) >= (3 ** 3))) and (not ((32 % 8) <= (-13 * -6))))
F. (Alcohol is a liquid at room temperature.) and (Humans have five fingers on each hand.)
G. (((The 1972 Olympics were held in Munich.) or (There are 30 days in August.)) and (not not ((-8 * 6) > (16 + -12)))) or ((3 * 3 + 3 * 10) <= (6 * 10))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "D,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 38264651,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. not not (((Saturn is the 2nd planet from the Sun.) or ((37 % 1) <= (12 * -10))) and (not not ((-14 * 17) > (-14 - -6))))\nB. (((20 - -16) <= (4 * -10)) or (not (Thailand is in Europe.))) and (not not ((1 * -20) >= (11 * 12)))\nC. (not not ((-12 - 8) >= (-7 * 8 - -9 * -7))) and ((not not ((5 * -6 - -9 * -8) > (18 * 13))) and (((6 * -5 * 9 * 4) >= (37 % 10)) and ((2 * -2 * 5 * -10) > (-2 * 0 - 1 * -9))))\nD. ((-5 * -18) > (7 + -3)) or (Saturn is the 8th planet from the Sun.)\nE. ((((0 * -3 - -1 * 0) < (-10 * 7 + -9 * -5) < (14 + 7)) or ((-19 - 1) > (19 % 5))) or ((The square root of 144 is 4.) or ((3 ** 1) <= (13 + 4) <= (-1 * -11)))) or ((((5 * -3 + 7 * 7) > (14 + 15)) and ((1 ** 3) >= (3 ** 3))) and (not ((32 % 8) <= (-13 * -6))))\nF. (Alcohol is a liquid at room temperature.) and (Humans have five fingers on each hand.)\nG. (((The 1972 Olympics were held in Munich.) or (There are 30 days in August.)) and (not not ((-8 * 6) > (16 + -12)))) or ((3 * 3 + 3 * 10) <= (6 * 10))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 38264651,
"true_count": 3
},
"seed": 38264651,
"task_id": 638264651,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (3 ** 3) <= (-13 - 0)
B. (((-9 * 14) == (17 + 17)) or ((13 * -10) >= (5 ** 2))) or (((-5 + 6) >= (-8 - 12)) or (Bats are blind.))
C. (-10 - -1) == (4 * 3 - 10 * 10)
D. Mercury is a liquid at room temperature.
E. The 1996 Olympics were held in Berlin.
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
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"seed": 69902585,
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"question": "Below are several boolean expressions:\n\nA. (3 ** 3) <= (-13 - 0)\nB. (((-9 * 14) == (17 + 17)) or ((13 * -10) >= (5 ** 2))) or (((-5 + 6) >= (-8 - 12)) or (Bats are blind.))\nC. (-10 - -1) == (4 * 3 - 10 * 10)\nD. Mercury is a liquid at room temperature.\nE. The 1996 Olympics were held in Berlin.\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 69902585,
"true_count": 2
},
"seed": 69902585,
"task_id": 669902585,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (21 % 3) >= (-19 + -4)
B. 1980年奥运会在莫斯科举办。
C. 294是完全平方数。
D. (not not (沙特阿拉伯的货币是里亚尔。)) or ((鲸鱼是鱼类。) and (8是质数。))
E. (43 % 1) <= (3 % 1)
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
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"seed": 19066366,
"true_count": 4
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"question": "评估以下每个表达式：\n\nA. (21 % 3) >= (-19 + -4)\nB. 1980年奥运会在莫斯科举办。\nC. 294是完全平方数。\nD. (not not (沙特阿拉伯的货币是里亚尔。)) or ((鲸鱼是鱼类。) and (8是质数。))\nE. (43 % 1) <= (3 % 1)\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 19066366,
"true_count": 4
},
"seed": 19066366,
"task_id": 619066366,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not (((Jupiter is the 4th planet from the Sun.) or ((Mars is the 8th planet from the Sun.) and (Saturn is the 6th planet from the Sun.))) or (((The currency of Thailand is the Koruna.) and (The 1988 Olympics were held in Paris.)) and ((15 * 16) < (-13 - -13))))
B. not (not (The chemical symbol for Oxygen is Pt.))
C. not not (not not (not not ((The chemical symbol for Lead is U.) and ((-12 - 6) != (-20 + 11)))))
D. not (((1 ** 3) >= (40 % 7)) and (((-8 * -1) != (5 * -10 * 3 * -8)) and ((-10 * 10 + -3 * 10) >= (12 - 4))) and ((not (The chemical symbol for Iron is Fe.)) and ((The 1920 Olympics were held in Antwerp.) or ((-1 * -9) <= (0 * -3 + 4 * -3)))))
E. not (not not (The capital of Indonesia is Jakarta.))
F. (((not (There are 30 days in November.)) or ((80 is divisible by 9.) or ((0 - 1) > (6 + 2)))) and ((((-4 * -6 - -1 * 6) <= (1 ** 2) <= (9 * 10 - -1 * 5)) and (1951 is a leap year.)) or ((9 - -18) >= (-7 * 14)))) and (not not (There are 29 days in August.))
G. ((((A tiger is a mammal.) and ((-7 + -7) > (-8 * 5 - -1 * 5))) and (Electricity flows faster than light.)) and ((not not (The currency of Vietnam is the Rand.)) and ((The currency of New Zealand is the Dollar.) or ((-4 * -18) > (-13 * -18))))) or ((not ((The currency of Israel is the Peso.) or (A pig has 4 legs.))) or ((((5 * 9 + -4 * 3) > (-9 + 8)) and ((7 - 10) <= (2 % 8))) or (not not ((0 - -13) > (1 * -6 + -7 * 10)))))
H. (((Neptune is the 8th planet from the Sun.) and (Humans have five fingers on each hand.)) or (There are 30 days in June.)) or (The 1924 Olympics were held in Moscow.) or (((not (World War II ended occurred in 1945.)) or (not not ((2 ** 3) == (1 * 13)))) and ((There are 31 days in October.) or ((-6 * 8) < (-4 + -3))) and ((3 ** 3) < (14 - 6)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,D,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 72590772,
"true_count": 4
},
"question": "Examine these expressions:\n\nA. not (((Jupiter is the 4th planet from the Sun.) or ((Mars is the 8th planet from the Sun.) and (Saturn is the 6th planet from the Sun.))) or (((The currency of Thailand is the Koruna.) and (The 1988 Olympics were held in Paris.)) and ((15 * 16) < (-13 - -13))))\nB. not (not (The chemical symbol for Oxygen is Pt.))\nC. not not (not not (not not ((The chemical symbol for Lead is U.) and ((-12 - 6) != (-20 + 11)))))\nD. not (((1 ** 3) >= (40 % 7)) and (((-8 * -1) != (5 * -10 * 3 * -8)) and ((-10 * 10 + -3 * 10) >= (12 - 4))) and ((not (The chemical symbol for Iron is Fe.)) and ((The 1920 Olympics were held in Antwerp.) or ((-1 * -9) <= (0 * -3 + 4 * -3)))))\nE. not (not not (The capital of Indonesia is Jakarta.))\nF. (((not (There are 30 days in November.)) or ((80 is divisible by 9.) or ((0 - 1) > (6 + 2)))) and ((((-4 * -6 - -1 * 6) <= (1 ** 2) <= (9 * 10 - -1 * 5)) and (1951 is a leap year.)) or ((9 - -18) >= (-7 * 14)))) and (not not (There are 29 days in August.))\nG. ((((A tiger is a mammal.) and ((-7 + -7) > (-8 * 5 - -1 * 5))) and (Electricity flows faster than light.)) and ((not not (The currency of Vietnam is the Rand.)) and ((The currency of New Zealand is the Dollar.) or ((-4 * -18) > (-13 * -18))))) or ((not ((The currency of Israel is the Peso.) or (A pig has 4 legs.))) or ((((5 * 9 + -4 * 3) > (-9 + 8)) and ((7 - 10) <= (2 % 8))) or (not not ((0 - -13) > (1 * -6 + -7 * 10)))))\nH. (((Neptune is the 8th planet from the Sun.) and (Humans have five fingers on each hand.)) or (There are 30 days in June.)) or (The 1924 Olympics were held in Moscow.) or (((not (World War II ended occurred in 1945.)) or (not not ((2 ** 3) == (1 * 13)))) and ((There are 31 days in October.) or ((-6 * 8) < (-4 + -3))) and ((3 ** 3) < (14 - 6)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 72590772,
"true_count": 4
},
"seed": 72590772,
"task_id": 672590772,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (11 - 20) <= (-18 - -4) <= (-19 + -14)
B. (9 * 9 + -7 * 7) > (-19 - -14)
C. (-1 * -3 * 3 * -5) <= (-16 + -19)
D. not ((人体有150块骨头。) or ((-16 - 9) == (-15 - 6)))
E. ((十二月有31天。) or (匈牙利的货币是新加坡元。)) and ((2 * -5 * 7 * -7) >= (-7 * 7 + -10 * -6))
F. ((金在常温下是固体。) and (秘鲁位于欧洲。)) and ((秘鲁位于北美洲。) and (2096年是闰年。))
G. (-8 + 12) <= (44 % 1) <= (15 * -8)
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 89496411,
"true_count": 4
},
"question": "检验这些表达式：\n\nA. (11 - 20) <= (-18 - -4) <= (-19 + -14)\nB. (9 * 9 + -7 * 7) > (-19 - -14)\nC. (-1 * -3 * 3 * -5) <= (-16 + -19)\nD. not ((人体有150块骨头。) or ((-16 - 9) == (-15 - 6)))\nE. ((十二月有31天。) or (匈牙利的货币是新加坡元。)) and ((2 * -5 * 7 * -7) >= (-7 * 7 + -10 * -6))\nF. ((金在常温下是固体。) and (秘鲁位于欧洲。)) and ((秘鲁位于北美洲。) and (2096年是闰年。))\nG. (-8 + 12) <= (44 % 1) <= (15 * -8)\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 89496411,
"true_count": 4
},
"seed": 89496411,
"task_id": 689496411,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not not (not not ((not (not ((氢的化学符号是Ca。) and (新加坡的首都是赫尔辛基。)))) or (((12 % 1) < (44 % 6) < (2 ** 1)) or ((泰坦尼克号沉没发生在1917年。) or (铜的化学符号是N。))) or ((not not (((3 ** 1) != (-10 * -2 + -6 * -7)) and ((8 - -10) >= (5 * -3 - -5 * -10)))) and (11小于等于60。))))
B. not (not not (not (((((4 ** 3) <= (8 - 17)) and ((12 - 11) == (0 + -1))) and ((7 * 9 + 8 * -9) < (-4 + 17))) or (1956年奥运会在墨尔本举办。))))
C. not ((((((镁的化学符号是He。) and (1908年奥运会在伦敦举办。)) or (not ((2 - -15) == (-10 * -7 + 7 * -3)))) or (not ((-11 - 5) > (1 + 11)))) or ((not (((5 * -10 - 5 * 2) < (18 % 4)) or ((-6 + 8) == (-15 + -6)))) and ((8 * -4 + 0 * -2) <= (-19 - 1)))) or (not (not not ((not not (2014年是闰年。)) and (not not ((46 % 6) != (8 * 4)))))))
D. (not not ((not ((not ((5 * 4 + -2 * 0) <= (14 - -12))) and (((-15 * -17) > (-14 + 15)) or ((3 * 4 + 4 * 3) == (13 - 2))))) and (not not ((15 % 2) >= (3 + -15))))) and (not (((not not ((油在常温下是液体。) or (氦气在常温下是固体。))) and (((-6 * 13) <= (-10 + -13)) or ((-3 * -10) <= (-3 * -7 * -10 * -9)))) and ((not ((10 * -9) >= (-17 * -4))) or (((13 - 0) >= (0 - -3)) and (氧气在常温下是气体。))) and (not not ((-10 - 6) == (-10 + 4)))))
E. (not not (((((意大利位于欧洲。) or ((11 + -4) < (34 % 6))) or ((埃及的首都是开罗。) or (1992年奥运会在罗马举办。))) and ((not (柏林墙倒塌发生在1989年。)) and ((1948年奥运会在伦敦举办。) and ((12 - -15) >= (10 + -12))))) or ((1986年是闰年。) and (((40 % 4) >= (4 ** 2)) and (荷兰的首都是利雅得。)) and ((not (加拿大的货币是加元。)) or ((3 * 10 - -4 * -5) != (-9 * 1 * -8 * 2)))))) and (not ((not (芬兰的首都是赫尔辛基。)) or (not not (铁在常温下是气体。)) or (((2 * 14) > (20 + 2)) and (not (not ((1 ** 1) != (-5 - 6)))))))
F. (((not (not not ((1996年奥运会在亚特兰大举办。) and (第一部iPhone发布发生在2007年。)))) or ((-10 * 6) > (2 ** 3)) or (not not ((-4 * 4 - 8 * -1) != (-3 * -11)))) or ((not ((17 * -3) < (5 ** 3) < (10 * 1 - -6 * 4))) and ((澳大利亚的货币是澳元。) and (not (加拿大的首都是布达佩斯。)) and (((32 % 5) >= (8 * -1 + -9 * 1)) or ((1956年奥运会在雅典举办。) or ((10 % 10) == (-6 * 4))))))) and (not not (not ((哥伦比亚的首都是巴西利亚。) and (not ((1 + 17) > (-1 - 10))) and ((not (铝的化学符号是Na。)) or ((南极洲是最冷的大陆。) and (十月有30天。))))))
G. (not (not (not ((((-8 - 2) == (5 * 3 * 5 * 8)) or (南非的货币是新西兰元。)) and ((金枪鱼是鱼类。) and (墨西哥位于非洲。)))))) and ((not ((印度尼西亚位于亚洲。) and ((((9 * 17) == (2 ** 3)) or ((9 * 3 - -10 * 1) < (-9 * -17))) or (not ((4 + 20) == (-6 - 0)))))) and (((银的化学符号是Ag。) or (太阳绕地球运转。)) and (((not ((47 % 1) < (1 + 1))) or (not not (摩洛哥位于非洲。))) and ((((-8 * -5) < (14 * -15)) and (98能被12整除。)) or (氯的化学符号是Cl。)))))
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,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 7,
"seed": 92038701,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. not not (not not ((not (not ((氢的化学符号是Ca。) and (新加坡的首都是赫尔辛基。)))) or (((12 % 1) < (44 % 6) < (2 ** 1)) or ((泰坦尼克号沉没发生在1917年。) or (铜的化学符号是N。))) or ((not not (((3 ** 1) != (-10 * -2 + -6 * -7)) and ((8 - -10) >= (5 * -3 - -5 * -10)))) and (11小于等于60。))))\nB. not (not not (not (((((4 ** 3) <= (8 - 17)) and ((12 - 11) == (0 + -1))) and ((7 * 9 + 8 * -9) < (-4 + 17))) or (1956年奥运会在墨尔本举办。))))\nC. not ((((((镁的化学符号是He。) and (1908年奥运会在伦敦举办。)) or (not ((2 - -15) == (-10 * -7 + 7 * -3)))) or (not ((-11 - 5) > (1 + 11)))) or ((not (((5 * -10 - 5 * 2) < (18 % 4)) or ((-6 + 8) == (-15 + -6)))) and ((8 * -4 + 0 * -2) <= (-19 - 1)))) or (not (not not ((not not (2014年是闰年。)) and (not not ((46 % 6) != (8 * 4)))))))\nD. (not not ((not ((not ((5 * 4 + -2 * 0) <= (14 - -12))) and (((-15 * -17) > (-14 + 15)) or ((3 * 4 + 4 * 3) == (13 - 2))))) and (not not ((15 % 2) >= (3 + -15))))) and (not (((not not ((油在常温下是液体。) or (氦气在常温下是固体。))) and (((-6 * 13) <= (-10 + -13)) or ((-3 * -10) <= (-3 * -7 * -10 * -9)))) and ((not ((10 * -9) >= (-17 * -4))) or (((13 - 0) >= (0 - -3)) and (氧气在常温下是气体。))) and (not not ((-10 - 6) == (-10 + 4)))))\nE. (not not (((((意大利位于欧洲。) or ((11 + -4) < (34 % 6))) or ((埃及的首都是开罗。) or (1992年奥运会在罗马举办。))) and ((not (柏林墙倒塌发生在1989年。)) and ((1948年奥运会在伦敦举办。) and ((12 - -15) >= (10 + -12))))) or ((1986年是闰年。) and (((40 % 4) >= (4 ** 2)) and (荷兰的首都是利雅得。)) and ((not (加拿大的货币是加元。)) or ((3 * 10 - -4 * -5) != (-9 * 1 * -8 * 2)))))) and (not ((not (芬兰的首都是赫尔辛基。)) or (not not (铁在常温下是气体。)) or (((2 * 14) > (20 + 2)) and (not (not ((1 ** 1) != (-5 - 6)))))))\nF. (((not (not not ((1996年奥运会在亚特兰大举办。) and (第一部iPhone发布发生在2007年。)))) or ((-10 * 6) > (2 ** 3)) or (not not ((-4 * 4 - 8 * -1) != (-3 * -11)))) or ((not ((17 * -3) < (5 ** 3) < (10 * 1 - -6 * 4))) and ((澳大利亚的货币是澳元。) and (not (加拿大的首都是布达佩斯。)) and (((32 % 5) >= (8 * -1 + -9 * 1)) or ((1956年奥运会在雅典举办。) or ((10 % 10) == (-6 * 4))))))) and (not not (not ((哥伦比亚的首都是巴西利亚。) and (not ((1 + 17) > (-1 - 10))) and ((not (铝的化学符号是Na。)) or ((南极洲是最冷的大陆。) and (十月有30天。))))))\nG. (not (not (not ((((-8 - 2) == (5 * 3 * 5 * 8)) or (南非的货币是新西兰元。)) and ((金枪鱼是鱼类。) and (墨西哥位于非洲。)))))) and ((not ((印度尼西亚位于亚洲。) and ((((9 * 17) == (2 ** 3)) or ((9 * 3 - -10 * 1) < (-9 * -17))) or (not ((4 + 20) == (-6 - 0)))))) and (((银的化学符号是Ag。) or (太阳绕地球运转。)) and (((not ((47 % 1) < (1 + 1))) or (not not (摩洛哥位于非洲。))) and ((((-8 * -5) < (14 * -15)) and (98能被12整除。)) or (氯的化学符号是Cl。)))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 7,
"seed": 92038701,
"true_count": 4
},
"seed": 92038701,
"task_id": 692038701,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. ((2067 is a leap year.) and (((The currency of India is the Forint.) or ((-1 * -3 + 1 * 0) == (16 * -17))) and ((Ice is a liquid at room temperature.) or (The chemical symbol for Gold is Au.)))) or ((not ((United Kingdom is in Europe.) or ((4 ** 2) <= (-12 - 12)))) and (((Mercury is a solid at room temperature.) and (The 1936 Olympics were held in Berlin.)) and ((The 1912 Olympics were held in Montreal.) and ((41 % 1) == (-18 + -10)))))
B. ((((2 ** 1) < (-5 + -13)) and ((6 + -9) > (8 + -16))) and (not (The capital of Spain is Madrid.))) or (((17 * -18) != (13 + -11)) and ((0 * -10) != (4 ** 2)))
C. not not ((Alcohol is a liquid at room temperature.) and (((The currency of Brazil is the Riyal.) or (The first airplane flight by the Wright Brothers occurred in 1903.)) and ((2 ** 3) != (-9 + 11))))
D. ((Mexico is in Antarctica.) and (The square root of 121 is 11.) and ((not not ((1 * 4 + 3 * 9) > (-3 * -18))) and (((-3 * -3 + 7 * 5) <= (-9 * 4 * -1 * 3)) or ((-17 * -15) == (17 - -1))))) or ((not ((-13 + -13) > (-7 * -5))) or (not (not not ((9 * -15) == (2 * 18)))))
E. (not not ((4 ** 3) < (-7 - 13) < (-3 - 0))) or (((Oil is a solid at room temperature.) and ((-1 + -3) <= (-19 * -13))) or (not not ((-10 * 5 - 8 * -2) == (-5 + -18)))) or ((not ((7 is an odd number.) or (The chemical symbol for Silver is S.))) or ((((-1 * -7) != (-16 + -6)) or (Uranus is the 7th planet from the Sun.)) or ((2037 is a leap year.) and ((0 * -10 + -5 * -8) < (11 * 11)))))
F. not (not not ((-17 - -5) < (5 ** 3) < (-5 * -3 - 3 * -9)))
G. (not ((((0 * 4) == (10 - -6)) or ((8 * 6 * 10 * -6) <= (-7 * -6 + -2 * -6) <= (4 ** 1))) and ((2071 is a leap year.) and (A snake is a reptile.)))) and ((The chemical symbol for Potassium is Si.) or (((Nitrogen is a gas at room temperature.) or ((-3 * 8 + 3 * -5) >= (43 % 10))) or ((Uranus is the 7th planet from the Sun.) and (The capital of Thailand is Bangkok.))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,D,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 22273712,
"true_count": 6
},
"question": "Below are several boolean expressions:\n\nA. ((2067 is a leap year.) and (((The currency of India is the Forint.) or ((-1 * -3 + 1 * 0) == (16 * -17))) and ((Ice is a liquid at room temperature.) or (The chemical symbol for Gold is Au.)))) or ((not ((United Kingdom is in Europe.) or ((4 ** 2) <= (-12 - 12)))) and (((Mercury is a solid at room temperature.) and (The 1936 Olympics were held in Berlin.)) and ((The 1912 Olympics were held in Montreal.) and ((41 % 1) == (-18 + -10)))))\nB. ((((2 ** 1) < (-5 + -13)) and ((6 + -9) > (8 + -16))) and (not (The capital of Spain is Madrid.))) or (((17 * -18) != (13 + -11)) and ((0 * -10) != (4 ** 2)))\nC. not not ((Alcohol is a liquid at room temperature.) and (((The currency of Brazil is the Riyal.) or (The first airplane flight by the Wright Brothers occurred in 1903.)) and ((2 ** 3) != (-9 + 11))))\nD. ((Mexico is in Antarctica.) and (The square root of 121 is 11.) and ((not not ((1 * 4 + 3 * 9) > (-3 * -18))) and (((-3 * -3 + 7 * 5) <= (-9 * 4 * -1 * 3)) or ((-17 * -15) == (17 - -1))))) or ((not ((-13 + -13) > (-7 * -5))) or (not (not not ((9 * -15) == (2 * 18)))))\nE. (not not ((4 ** 3) < (-7 - 13) < (-3 - 0))) or (((Oil is a solid at room temperature.) and ((-1 + -3) <= (-19 * -13))) or (not not ((-10 * 5 - 8 * -2) == (-5 + -18)))) or ((not ((7 is an odd number.) or (The chemical symbol for Silver is S.))) or ((((-1 * -7) != (-16 + -6)) or (Uranus is the 7th planet from the Sun.)) or ((2037 is a leap year.) and ((0 * -10 + -5 * -8) < (11 * 11)))))\nF. not (not not ((-17 - -5) < (5 ** 3) < (-5 * -3 - 3 * -9)))\nG. (not ((((0 * 4) == (10 - -6)) or ((8 * 6 * 10 * -6) <= (-7 * -6 + -2 * -6) <= (4 ** 1))) and ((2071 is a leap year.) and (A snake is a reptile.)))) and ((The chemical symbol for Potassium is Si.) or (((Nitrogen is a gas at room temperature.) or ((-3 * 8 + 3 * -5) >= (43 % 10))) or ((Uranus is the 7th planet from the Sun.) and (The capital of Thailand is Bangkok.))))\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": 22273712,
"true_count": 6
},
"seed": 22273712,
"task_id": 622273712,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (((15 % 10) >= (14 + -15)) and (not not ((6 * 2 * -3 * -1) > (15 % 1))))
B. ((-2 + 18) >= (15 + -17)) or ((-19 - 0) <= (-12 * -12))
C. ((-8 * 8) <= (1 ** 2)) or (not (not (A mosquito is a bird.)))
D. ((((-9 * 4) <= (-19 + -1)) or (A chameleon is a reptile.)) or (((-3 * -6 * -7 * 4) <= (-3 * 5)) and (The capital of Venezuela is Wellington.))) or (not (The 1972 Olympics were held in Amsterdam.)) or (((The 1904 Olympics were held in St. Louis.) or ((9 * -6 - 1 * -8) > (11 * 16))) or (((9 + 20) != (8 * -12)) and (The capital of Nigeria is Copenhagen.)))
E. (not ((Mercury is the 1st planet from the Sun.) or (There are 30 days in March.))) or (((New Zealand is in Oceania.) or (A kangaroo has 4 legs.)) or (not ((2 + 13) >= (-20 * 1))))
F. (not ((1 ** 1) <= (20 % 3))) or ((-4 * -5 - 2 * 10) < (9 + 15))
G. ((5 ** 3) <= (-5 * 0 * 3 * 1)) or ((Diamonds are made of carbon.) and (Russia is in Europe.)) or (not (not not (109 is an odd number.)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C,D,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 31426465,
"true_count": 7
},
"question": "Examine these expressions:\n\nA. not not (((15 % 10) >= (14 + -15)) and (not not ((6 * 2 * -3 * -1) > (15 % 1))))\nB. ((-2 + 18) >= (15 + -17)) or ((-19 - 0) <= (-12 * -12))\nC. ((-8 * 8) <= (1 ** 2)) or (not (not (A mosquito is a bird.)))\nD. ((((-9 * 4) <= (-19 + -1)) or (A chameleon is a reptile.)) or (((-3 * -6 * -7 * 4) <= (-3 * 5)) and (The capital of Venezuela is Wellington.))) or (not (The 1972 Olympics were held in Amsterdam.)) or (((The 1904 Olympics were held in St. Louis.) or ((9 * -6 - 1 * -8) > (11 * 16))) or (((9 + 20) != (8 * -12)) and (The capital of Nigeria is Copenhagen.)))\nE. (not ((Mercury is the 1st planet from the Sun.) or (There are 30 days in March.))) or (((New Zealand is in Oceania.) or (A kangaroo has 4 legs.)) or (not ((2 + 13) >= (-20 * 1))))\nF. (not ((1 ** 1) <= (20 % 3))) or ((-4 * -5 - 2 * 10) < (9 + 15))\nG. ((5 ** 3) <= (-5 * 0 * 3 * 1)) or ((Diamonds are made of carbon.) and (Russia is in Europe.)) or (not (not not (109 is an odd number.)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 31426465,
"true_count": 7
},
"seed": 31426465,
"task_id": 631426465,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((not not ((18 - 17) >= (4 * -7 + -10 * -4))) or ((14 + -18) <= (2 + 9) <= (-6 * -3 - 10 * 5)) or (((((-9 * 1 * -6 * 3) != (0 * -16)) or ((7 % 10) <= (48 % 5))) and (not not ((17 + 18) < (-5 * -2)))) or (not (not not ((1 - -15) > (-10 * 9 * 4 * -5)))))) or (not not ((((水星是距离太阳第1近的行星。) or ((5 * 11) < (7 * -13) < (1 * 10 - 10 * -6))) and (36的平方根是2。)) or (((10 * -6 + -1 * 4) > (17 + 5)) or (火星是距离太阳第4近的行星。)) or (新西兰位于大洋洲。)))) and (not not (not not ((莱特兄弟首次飞行发生在1903年。) and (莱特兄弟首次飞行发生在1901年。))))
B. not not (not not (((not not (泰国位于亚洲。)) and (硫的化学符号是S。)) or ((not (人类每只手有五个手指。)) and (((41 % 7) <= (-20 + 1) <= (20 + -9)) or (1932年奥运会在洛杉矶举办。))) or (not ((not (1952年奥运会在赫尔辛基举办。)) or ((太平洋是最大的海洋。) or ((3 ** 3) <= (14 * 17) <= (-6 * -1 + 8 * -9)))))))
C. (not not ((not ((((-4 - -20) == (8 + -4)) and (2004年奥运会在雅典举办。)) or (氮的化学符号是N。))) and (((-14 + 10) <= (-8 - -15)) or ((菲律宾的货币是新西兰元。) and ((美国的货币是越南盾。) and ((-4 - -4) == (-16 + -3))))))) and (not ((((1 - 17) <= (4 * -11)) or (2055年是闰年。)) or (((-16 * 16) != (-1 * 19)) or (not not (((20 - -12) == (6 + -12)) or (氯的化学符号是Si。))))))
D. not not (not not (((not not (((8 - 18) <= (-17 + -20)) and (钠的化学符号是Cr。))) or (not not ((12 - -15) < (3 + 13))) or ((金的化学符号是Cr。) and (((-2 - 10) <= (-9 + -2) <= (7 * 7 * -1 * -10)) or ((18 - 1) > (-14 + -1))))) or ((not (not not ((5 * -9 + 2 * -10) < (44 % 5)))) or (not not ((7 + -15) <= (1 + -20) <= (6 % 10))) or ((-7 - 6) == (11 * 5)))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 34124975,
"true_count": 1
},
"question": "考虑以下布尔表达式：\n\nA. (((not not ((18 - 17) >= (4 * -7 + -10 * -4))) or ((14 + -18) <= (2 + 9) <= (-6 * -3 - 10 * 5)) or (((((-9 * 1 * -6 * 3) != (0 * -16)) or ((7 % 10) <= (48 % 5))) and (not not ((17 + 18) < (-5 * -2)))) or (not (not not ((1 - -15) > (-10 * 9 * 4 * -5)))))) or (not not ((((水星是距离太阳第1近的行星。) or ((5 * 11) < (7 * -13) < (1 * 10 - 10 * -6))) and (36的平方根是2。)) or (((10 * -6 + -1 * 4) > (17 + 5)) or (火星是距离太阳第4近的行星。)) or (新西兰位于大洋洲。)))) and (not not (not not ((莱特兄弟首次飞行发生在1903年。) and (莱特兄弟首次飞行发生在1901年。))))\nB. not not (not not (((not not (泰国位于亚洲。)) and (硫的化学符号是S。)) or ((not (人类每只手有五个手指。)) and (((41 % 7) <= (-20 + 1) <= (20 + -9)) or (1932年奥运会在洛杉矶举办。))) or (not ((not (1952年奥运会在赫尔辛基举办。)) or ((太平洋是最大的海洋。) or ((3 ** 3) <= (14 * 17) <= (-6 * -1 + 8 * -9)))))))\nC. (not not ((not ((((-4 - -20) == (8 + -4)) and (2004年奥运会在雅典举办。)) or (氮的化学符号是N。))) and (((-14 + 10) <= (-8 - -15)) or ((菲律宾的货币是新西兰元。) and ((美国的货币是越南盾。) and ((-4 - -4) == (-16 + -3))))))) and (not ((((1 - 17) <= (4 * -11)) or (2055年是闰年。)) or (((-16 * 16) != (-1 * 19)) or (not not (((20 - -12) == (6 + -12)) or (氯的化学符号是Si。))))))\nD. not not (not not (((not not (((8 - 18) <= (-17 + -20)) and (钠的化学符号是Cr。))) or (not not ((12 - -15) < (3 + 13))) or ((金的化学符号是Cr。) and (((-2 - 10) <= (-9 + -2) <= (7 * 7 * -1 * -10)) or ((18 - 1) > (-14 + -1))))) or ((not (not not ((5 * -9 + 2 * -10) < (44 % 5)))) or (not not ((7 + -15) <= (1 + -20) <= (6 % 10))) or ((-7 - 6) == (11 * 5)))))\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": 6,
"language": "cn",
"num_options": 4,
"seed": 34124975,
"true_count": 1
},
"seed": 34124975,
"task_id": 634124975,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not (((((Egypt is in Africa.) or (The capital of Hungary is Cairo.)) and (The capital of Indonesia is Jakarta.)) and (not (((-7 * -1) <= (5 ** 2)) or (Venus is the 2nd planet from the Sun.)))) or ((((The chemical symbol for Cobalt is Co.) and (Mercury is the 1st planet from the Sun.)) or ((-9 - -20) < (-4 - -14))) or (((A octopus has 2 legs.) and (A octopus has 6 legs.)) or (not not (Nigeria is in Africa.)))))
B. not not ((((-6 - -4) != (-11 * -11)) or (The chemical symbol for Neon is Fe.)) and (((-6 * 5 + 1 * 0) != (19 * 1)) or (((-1 - 12) <= (10 % 6)) or (((1 ** 2) <= (-6 * 2 + 0 * 0)) or ((0 * 19) <= (2 + -11) <= (5 - -6))))))
C. not not (not (not not ((Water is a solid at room temperature.) or ((7 - -6) <= (-4 + 12) <= (6 * -6 - 0 * 0)))))
D. not ((((Indonesia is in Oceania.) or (not not ((-16 + -12) <= (-6 * 10)))) and (((13 - -2) <= (8 * -17) <= (8 - 6)) or (The currency of Russia is the Ruble.))) and ((The capital of Japan is Tokyo.) and (((-2 * 5 - -8 * -4) <= (9 * 3)) or (Water is a liquid at room temperature.))) and (((9 * -16) >= (15 + 6)) and ((11 + 16) <= (14 - -20))))
E. (not (not not (not (((17 + -1) <= (9 * -9 + -1 * 10)) and (Venus is the 2nd planet from the Sun.))))) and ((not (((Saturn is the 6th planet from the Sun.) and ((7 % 1) < (-8 * 9 * -8 * -1))) and (A spider has 2 legs.))) and (not ((not not (1921 is a leap year.)) and (((-1 + -13) >= (8 * 0 + -4 * -6)) or (The capital of Japan is Tokyo.)))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 18920617,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. not (((((Egypt is in Africa.) or (The capital of Hungary is Cairo.)) and (The capital of Indonesia is Jakarta.)) and (not (((-7 * -1) <= (5 ** 2)) or (Venus is the 2nd planet from the Sun.)))) or ((((The chemical symbol for Cobalt is Co.) and (Mercury is the 1st planet from the Sun.)) or ((-9 - -20) < (-4 - -14))) or (((A octopus has 2 legs.) and (A octopus has 6 legs.)) or (not not (Nigeria is in Africa.)))))\nB. not not ((((-6 - -4) != (-11 * -11)) or (The chemical symbol for Neon is Fe.)) and (((-6 * 5 + 1 * 0) != (19 * 1)) or (((-1 - 12) <= (10 % 6)) or (((1 ** 2) <= (-6 * 2 + 0 * 0)) or ((0 * 19) <= (2 + -11) <= (5 - -6))))))\nC. not not (not (not not ((Water is a solid at room temperature.) or ((7 - -6) <= (-4 + 12) <= (6 * -6 - 0 * 0)))))\nD. not ((((Indonesia is in Oceania.) or (not not ((-16 + -12) <= (-6 * 10)))) and (((13 - -2) <= (8 * -17) <= (8 - 6)) or (The currency of Russia is the Ruble.))) and ((The capital of Japan is Tokyo.) and (((-2 * 5 - -8 * -4) <= (9 * 3)) or (Water is a liquid at room temperature.))) and (((9 * -16) >= (15 + 6)) and ((11 + 16) <= (14 - -20))))\nE. (not (not not (not (((17 + -1) <= (9 * -9 + -1 * 10)) and (Venus is the 2nd planet from the Sun.))))) and ((not (((Saturn is the 6th planet from the Sun.) and ((7 % 1) < (-8 * 9 * -8 * -1))) and (A spider has 2 legs.))) and (not ((not not (1921 is a leap year.)) and (((-1 + -13) >= (8 * 0 + -4 * -6)) or (The capital of Japan is Tokyo.)))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 18920617,
"true_count": 3
},
"seed": 18920617,
"task_id": 618920617,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not not ((not ((((20 + 13) >= (0 - -19)) or (The chemical symbol for Zinc is Zn.)) or ((The currency of Norway is the Rand.) or (A day on Earth is 24 hours.)))) and (not not ((Venus is the 2nd planet from the Sun.) or ((2 ** 1) >= (7 + 2)))) and (((Japan is in Asia.) and ((Water is a gas at room temperature.) or (United Kingdom is in Europe.))) or (((10 - 14) <= (-10 - -16)) and ((5 * -5 - -8 * -5) < (46 % 3))) or (not not (not (There are 29 days in April.)))))
B. not not (not not (((The 1932 Olympics were held in Melbourne.) or (The currency of Brazil is the Forint.)) or ((((3 + 15) <= (2 + -17) <= (-6 * 3 + 9 * -6)) or (A duck is a bird.)) and (((-1 * -9 - 0 * -8) == (-2 * 9 + -2 * -2)) and ((-4 * -6 - 5 * 5) >= (25 % 10))))))
C. (not ((((Ice is a solid at room temperature.) and (United Kingdom is in Europe.)) and (not (The 1968 Olympics were held in Mexico City.))) and (not ((The chemical symbol for Chlorine is Co.) or (A day on Earth is 24 hours.))))) or (not (not (((A lobster has 10 legs.) or (The capital of Morocco is Rabat.)) and ((The chemical symbol for Lead is Pb.) and (Ice is a solid at room temperature.)))))
D. not (((Morocco is in Africa.) or ((not (The chemical symbol for Chromium is Cr.)) or (Neptune is the 6th planet from the Sun.))) or ((-3 + -18) > (13 - 10)) or (not (not (not not (Nitrogen is a gas at room temperature.)))))
E. not ((not ((9 * 14) <= (9 * 3 + -8 * 1))) and (((-3 * 6 - -10 * 10) <= (3 ** 2) <= (-18 * -2)) and ((not (The chemical symbol for Calcium is Ca.)) or (not ((-19 + 12) >= (9 - 12))))))
F. ((((not (A alligator is an insect.)) and ((10 * -7 + -7 * -9) != (5 + 7))) and ((((-9 - 6) <= (33 % 2)) or ((-1 * -9 + -4 * 0) >= (-1 * 9 + 0 * 8))) and (not not (There are 30 days in April.)))) and ((not not ((10 - 14) >= (5 * -8))) and ((5 ** 3) < (9 * -9 + -8 * -5)))) or ((not not (A frog has 4 legs.)) or ((The currency of European Union is the Dollar.) or ((The 1996 Olympics were held in Stockholm.) or ((1 + 14) < (-13 - 16))))) or (not not (not (The currency of South Korea is the Won.)))
G. not ((((-1 * 0 - 4 * 8) < (12 * -15)) or (not not ((-3 * -15) == (12 - 1))) or (not not ((Penguins can fly.) and (A duck has 4 legs.)))) or ((not (((0 * -5 - 5 * 5) <= (-18 * -3)) or ((5 % 4) >= (7 * 5)))) and (((13 - -2) >= (3 * 10 + 9 * 9)) and ((-5 * -12) == (-9 * 3 * -4 * 7)))))
H. (not not ((((The capital of China is Berlin.) or (China is in Asia.)) and (not not ((-2 + 4) <= (-14 + -18)))) and (((6 * 8 + 8 * -5) < (13 - 12)) and (not (The first Olympic Games of modern era occurred in 1896.))))) and (not not ((not (1908 is a leap year.)) and (((19 * -11) <= (37 % 8)) or ((2 - -5) == (-1 * 10 * 10 * -3))) and (405 is a Fibonacci number.)))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 61488296,
"true_count": 4
},
"question": "Analyze these boolean expressions:\n\nA. not not ((not ((((20 + 13) >= (0 - -19)) or (The chemical symbol for Zinc is Zn.)) or ((The currency of Norway is the Rand.) or (A day on Earth is 24 hours.)))) and (not not ((Venus is the 2nd planet from the Sun.) or ((2 ** 1) >= (7 + 2)))) and (((Japan is in Asia.) and ((Water is a gas at room temperature.) or (United Kingdom is in Europe.))) or (((10 - 14) <= (-10 - -16)) and ((5 * -5 - -8 * -5) < (46 % 3))) or (not not (not (There are 29 days in April.)))))\nB. not not (not not (((The 1932 Olympics were held in Melbourne.) or (The currency of Brazil is the Forint.)) or ((((3 + 15) <= (2 + -17) <= (-6 * 3 + 9 * -6)) or (A duck is a bird.)) and (((-1 * -9 - 0 * -8) == (-2 * 9 + -2 * -2)) and ((-4 * -6 - 5 * 5) >= (25 % 10))))))\nC. (not ((((Ice is a solid at room temperature.) and (United Kingdom is in Europe.)) and (not (The 1968 Olympics were held in Mexico City.))) and (not ((The chemical symbol for Chlorine is Co.) or (A day on Earth is 24 hours.))))) or (not (not (((A lobster has 10 legs.) or (The capital of Morocco is Rabat.)) and ((The chemical symbol for Lead is Pb.) and (Ice is a solid at room temperature.)))))\nD. not (((Morocco is in Africa.) or ((not (The chemical symbol for Chromium is Cr.)) or (Neptune is the 6th planet from the Sun.))) or ((-3 + -18) > (13 - 10)) or (not (not (not not (Nitrogen is a gas at room temperature.)))))\nE. not ((not ((9 * 14) <= (9 * 3 + -8 * 1))) and (((-3 * 6 - -10 * 10) <= (3 ** 2) <= (-18 * -2)) and ((not (The chemical symbol for Calcium is Ca.)) or (not ((-19 + 12) >= (9 - 12))))))\nF. ((((not (A alligator is an insect.)) and ((10 * -7 + -7 * -9) != (5 + 7))) and ((((-9 - 6) <= (33 % 2)) or ((-1 * -9 + -4 * 0) >= (-1 * 9 + 0 * 8))) and (not not (There are 30 days in April.)))) and ((not not ((10 - 14) >= (5 * -8))) and ((5 ** 3) < (9 * -9 + -8 * -5)))) or ((not not (A frog has 4 legs.)) or ((The currency of European Union is the Dollar.) or ((The 1996 Olympics were held in Stockholm.) or ((1 + 14) < (-13 - 16))))) or (not not (not (The currency of South Korea is the Won.)))\nG. not ((((-1 * 0 - 4 * 8) < (12 * -15)) or (not not ((-3 * -15) == (12 - 1))) or (not not ((Penguins can fly.) and (A duck has 4 legs.)))) or ((not (((0 * -5 - 5 * 5) <= (-18 * -3)) or ((5 % 4) >= (7 * 5)))) and (((13 - -2) >= (3 * 10 + 9 * 9)) and ((-5 * -12) == (-9 * 3 * -4 * 7)))))\nH. (not not ((((The capital of China is Berlin.) or (China is in Asia.)) and (not not ((-2 + 4) <= (-14 + -18)))) and (((6 * 8 + 8 * -5) < (13 - 12)) and (not (The first Olympic Games of modern era occurred in 1896.))))) and (not not ((not (1908 is a leap year.)) and (((19 * -11) <= (37 % 8)) or ((2 - -5) == (-1 * 10 * 10 * -3))) and (405 is a Fibonacci number.)))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 61488296,
"true_count": 4
},
"seed": 61488296,
"task_id": 661488296,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. The currency of United Kingdom is the Pound.
B. The currency of Thailand is the Rupee.
C. There are 31 days in July.
D. Mercury is a liquid at room temperature.
E. Iron is a liquid at room temperature.
F. (11 + -11) > (-7 * 17)
G. World War II began occurred in 1940.
H. not ((The 2016 Olympics were held in Rio de Janeiro.) and ((2 ** 3) != (10 * -15)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 6501395,
"true_count": 4
},
"question": "Examine these expressions:\n\nA. The currency of United Kingdom is the Pound.\nB. The currency of Thailand is the Rupee.\nC. There are 31 days in July.\nD. Mercury is a liquid at room temperature.\nE. Iron is a liquid at room temperature.\nF. (11 + -11) > (-7 * 17)\nG. World War II began occurred in 1940.\nH. not ((The 2016 Olympics were held in Rio de Janeiro.) and ((2 ** 3) != (10 * -15)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 6501395,
"true_count": 4
},
"seed": 6501395,
"task_id": 606501395,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not ((3 * -3 * -7 * -1) == (-5 * 10 * 3 * 7))
B. (not not ((7 * -3) < (-12 - 14))) and (The currency of Denmark is the Krone.)
C. not ((((15 + -1) > (3 * -3 * 0 * -6)) or ((10 * 12) < (39 % 5))) or ((4 * -9 * -9 * -4) == (5 ** 2)))
D. ((26 % 4) == (-17 * 2)) or (The 1996 Olympics were held in Rome.)
E. (((Jupiter is the 2nd planet from the Sun.) and ((4 ** 2) <= (14 + 11) <= (-5 - -12))) and ((Silver is a gas at room temperature.) or (There are 30 days in June.))) and (not not ((-10 * 10 - -8 * 10) <= (37 % 3))) and ((((14 % 10) >= (8 * 8 + 0 * -3)) or (The human body has 206 bones.)) and ((-13 + -13) <= (19 - -13)))
F. ((Mars is the 4th planet from the Sun.) and (The first moon landing occurred in 1969.)) and (not not ((15 - -14) != (2 - -17))) and ((((6 % 5) != (9 + 0)) or (The capital of Thailand is Caracas.)) and (not not ((7 % 2) == (18 * 1))))
G. ((((-3 * 2) > (-15 * 3)) and (Vietnam is in Asia.)) or (Saudi Arabia is in Asia.)) and (not (Indonesia is in Europe.)) and ((not (Ice is a solid at room temperature.)) and (not (The chemical symbol for Chlorine is Cl.)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 54239870,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. not ((3 * -3 * -7 * -1) == (-5 * 10 * 3 * 7))\nB. (not not ((7 * -3) < (-12 - 14))) and (The currency of Denmark is the Krone.)\nC. not ((((15 + -1) > (3 * -3 * 0 * -6)) or ((10 * 12) < (39 % 5))) or ((4 * -9 * -9 * -4) == (5 ** 2)))\nD. ((26 % 4) == (-17 * 2)) or (The 1996 Olympics were held in Rome.)\nE. (((Jupiter is the 2nd planet from the Sun.) and ((4 ** 2) <= (14 + 11) <= (-5 - -12))) and ((Silver is a gas at room temperature.) or (There are 30 days in June.))) and (not not ((-10 * 10 - -8 * 10) <= (37 % 3))) and ((((14 % 10) >= (8 * 8 + 0 * -3)) or (The human body has 206 bones.)) and ((-13 + -13) <= (19 - -13)))\nF. ((Mars is the 4th planet from the Sun.) and (The first moon landing occurred in 1969.)) and (not not ((15 - -14) != (2 - -17))) and ((((6 % 5) != (9 + 0)) or (The capital of Thailand is Caracas.)) and (not not ((7 % 2) == (18 * 1))))\nG. ((((-3 * 2) > (-15 * 3)) and (Vietnam is in Asia.)) or (Saudi Arabia is in Asia.)) and (not (Indonesia is in Europe.)) and ((not (Ice is a solid at room temperature.)) and (not (The chemical symbol for Chlorine is Cl.)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 54239870,
"true_count": 1
},
"seed": 54239870,
"task_id": 654239870,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((美国位于北美洲。) or ((阿根廷位于南美洲。) and (木星是距离太阳第1近的行星。)) or ((19 + -3) != (4 + -20))) or (not ((not not ((10 + -19) < (7 - 13) < (14 * 12))) and ((水蒸气在常温下是气体。) and (69是质数。))))) or (not not (not not (85是质数。)))
B. not not ((((-3 + -19) != (4 ** 3)) and (((11 % 1) > (2 + 6)) or (鲸鱼是鱼类。)) and ((哥伦比亚的货币是比索。) and (not (氢的化学符号是H。)))) or (not ((18 % 7) == (10 * -6 - 1 * -9))) or ((硅的化学符号是Si。) and ((2 + -14) < (16 - -12) < (13 * 20))))
C. ((not not (not not ((9 * -4 - 10 * 9) <= (-17 + -5)))) and ((((越南位于亚洲。) or (土星是距离太阳第5近的行星。)) or ((氦气在常温下是气体。) and ((-3 * -10 + -5 * 5) <= (1 ** 2) <= (49 % 2)))) or (金星是距离太阳第2近的行星。) or ((4 * 0 - 10 * -6) == (-14 + 10)))) or ((not not ((((7 * 1 * 6 * 3) <= (-10 - -12) <= (5 ** 1)) and (土星是距离太阳第8近的行星。)) and (((2 * -19) < (-3 * 16)) and (1972年奥运会在伦敦举办。)))) or (((现代奥运会首届举办发生在1896年。) or ((鲨鱼是哺乳动物。) and (水在常温下是液体。))) or (((-2 * 11) >= (11 - -18)) or ((-3 * 4 + 9 * 2) < (6 * -5)))))
D. (not not ((not (菲律宾的首都是圣地亚哥。)) and (土星是距离太阳第6近的行星。))) and (not not (not ((not ((8 * -2 - 4 * -8) > (-9 + 2))) and (人体有206块骨头。))))
E. not (((鱼有2条腿。) or ((((27 % 10) <= (33 % 6)) and (植物通过光合作用产生氧气。)) or ((3 ** 2) < (-8 + -2)))) and (not ((((-7 * 6 + -1 * -1) < (2 ** 2) < (8 * -18)) and (牛是哺乳动物。)) and (not (现代奥运会首届举办发生在1891年。)))))
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,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 46753684,
"true_count": 5
},
"question": "考虑以下布尔表达式：\n\nA. (((美国位于北美洲。) or ((阿根廷位于南美洲。) and (木星是距离太阳第1近的行星。)) or ((19 + -3) != (4 + -20))) or (not ((not not ((10 + -19) < (7 - 13) < (14 * 12))) and ((水蒸气在常温下是气体。) and (69是质数。))))) or (not not (not not (85是质数。)))\nB. not not ((((-3 + -19) != (4 ** 3)) and (((11 % 1) > (2 + 6)) or (鲸鱼是鱼类。)) and ((哥伦比亚的货币是比索。) and (not (氢的化学符号是H。)))) or (not ((18 % 7) == (10 * -6 - 1 * -9))) or ((硅的化学符号是Si。) and ((2 + -14) < (16 - -12) < (13 * 20))))\nC. ((not not (not not ((9 * -4 - 10 * 9) <= (-17 + -5)))) and ((((越南位于亚洲。) or (土星是距离太阳第5近的行星。)) or ((氦气在常温下是气体。) and ((-3 * -10 + -5 * 5) <= (1 ** 2) <= (49 % 2)))) or (金星是距离太阳第2近的行星。) or ((4 * 0 - 10 * -6) == (-14 + 10)))) or ((not not ((((7 * 1 * 6 * 3) <= (-10 - -12) <= (5 ** 1)) and (土星是距离太阳第8近的行星。)) and (((2 * -19) < (-3 * 16)) and (1972年奥运会在伦敦举办。)))) or (((现代奥运会首届举办发生在1896年。) or ((鲨鱼是哺乳动物。) and (水在常温下是液体。))) or (((-2 * 11) >= (11 - -18)) or ((-3 * 4 + 9 * 2) < (6 * -5)))))\nD. (not not ((not (菲律宾的首都是圣地亚哥。)) and (土星是距离太阳第6近的行星。))) and (not not (not ((not ((8 * -2 - 4 * -8) > (-9 + 2))) and (人体有206块骨头。))))\nE. not (((鱼有2条腿。) or ((((27 % 10) <= (33 % 6)) and (植物通过光合作用产生氧气。)) or ((3 ** 2) < (-8 + -2)))) and (not ((((-7 * 6 + -1 * -1) < (2 ** 2) < (8 * -18)) and (牛是哺乳动物。)) and (not (现代奥运会首届举办发生在1891年。)))))\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": 46753684,
"true_count": 5
},
"seed": 46753684,
"task_id": 646753684,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. World War I ended occurred in 1918.
B. (The capital of Egypt is Ankara.) or (not not (Peru is in South America.))
C. (The human body has 150 bones.) or (((5 ** 3) > (-1 - -4)) and (Air is a gas at room temperature.))
D. ((A butterfly has 2 legs.) and ((15 - 20) > (-4 - 4))) or (((2 * -14) > (-11 - -20)) and (The 1912 Olympics were held in Paris.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 22960261,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. World War I ended occurred in 1918.\nB. (The capital of Egypt is Ankara.) or (not not (Peru is in South America.))\nC. (The human body has 150 bones.) or (((5 ** 3) > (-1 - -4)) and (Air is a gas at room temperature.))\nD. ((A butterfly has 2 legs.) and ((15 - 20) > (-4 - 4))) or (((2 * -14) > (-11 - -20)) and (The 1912 Olympics were held in Paris.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 22960261,
"true_count": 3
},
"seed": 22960261,
"task_id": 622960261,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (((not (地球是距离太阳第3近的行星。)) or ((not not ((-1 * 10) <= (10 * 0 - 3 * -4))) and (柏林墙倒塌发生在1991年。))) or (not (((尼日利亚的货币是奈拉。) or ((17 * -8) != (4 - 1))) and ((水在常温下是液体。) and ((-3 + -16) <= (-9 - -8) <= (6 - 17))))) or ((((13能被6整除。) and (1936年是闰年。)) or ((19 + -18) >= (5 * 12))) or (not not (英国的货币是林吉特。)) or (not not (not (not (韩国的货币是印尼盾。)))))) and (not ((not not (阿根廷位于南美洲。)) or ((not not (((32 % 7) <= (7 + -15)) and (水星是距离太阳第7近的行星。))) or (not (((-13 * 8) != (-4 * -8)) or ((17 - 10) == (13 + 15)))))))
B. (not (((钻石由碳元素组成。) and ((柏林墙倒塌发生在1984年。) or ((钠的化学符号是K。) or (第一次世界大战开始发生在1914年。)))) and (((not ((-2 * 12) > (11 + 7))) and (第一次世界大战开始发生在1913年。)) and ((20 - 13) != (2 * -7 * -4 * -9)) and (金星是距离太阳第4近的行星。)))) or (not ((not not ((not (菲律宾的首都是马尼拉。)) or ((尼日利亚的首都是阿布贾。) or ((3 ** 1) <= (15 - -8))))) or ((not not (not not (氖的化学符号是Cr。))) and (((9 * 15) < (47 % 2)) and (25能被2整除。)) and (not (not not ((-5 * -8) == (10 * -1)))))))
C. (not ((not not ((49 % 3) == (2 * -10 * 7 * 6))) or ((钾的化学符号是K。) or (银在常温下是气体。)))) and (((((印度尼西亚的货币是印尼盾。) or (墨西哥的首都是墨西哥城。)) and (((11 - -16) < (-5 - -2)) or (1919年是闰年。)) and (not (not not ((16 + -14) <= (6 * -15) <= (-12 - 1))))) or (((-9 * 10) < (15 - -8) < (13 + 12)) or (not (not not ((-12 + 16) != (-5 - -3)))))) and ((not (not (奥地利的首都是哈瓦那。))) and (((((-6 * 19) <= (20 % 6)) or (46是质数。)) and (not not (捷克的货币是克朗。))) and (((2 ** 3) > (5 - -19)) or (((2 * 20) >= (-5 + 5)) or (土星是距离太阳第8近的行星。))))))
D. (not not (not not (not not ((not not ((20 * -2) != (-7 + -15))) or (not (地球绕太阳运转。)))))) or ((((not not (not not ((-14 - 2) == (5 ** 1)))) or (((苏联解体发生在1981年。) and ((-7 + -6) <= (-7 - -11))) or (鸭子有2条腿。))) or (((-15 - 7) > (-17 * -20)) and ((11 - -12) > (2 * -8 * -9 * 10)))) and (not ((((1912年奥运会在斯德哥尔摩举办。) or ((-8 + -9) < (20 * -11))) and (((37 % 10) != (15 - -2)) or (1907年是闰年。))) and (((6 + 18) <= (12 + 11)) and (1980年奥运会在莫斯科举办。)) and (氯的化学符号是Cl。))))
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,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
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"seed": 32090,
"true_count": 2
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"question": "给定以下布尔表达式：\n\nA. (((not (地球是距离太阳第3近的行星。)) or ((not not ((-1 * 10) <= (10 * 0 - 3 * -4))) and (柏林墙倒塌发生在1991年。))) or (not (((尼日利亚的货币是奈拉。) or ((17 * -8) != (4 - 1))) and ((水在常温下是液体。) and ((-3 + -16) <= (-9 - -8) <= (6 - 17))))) or ((((13能被6整除。) and (1936年是闰年。)) or ((19 + -18) >= (5 * 12))) or (not not (英国的货币是林吉特。)) or (not not (not (not (韩国的货币是印尼盾。)))))) and (not ((not not (阿根廷位于南美洲。)) or ((not not (((32 % 7) <= (7 + -15)) and (水星是距离太阳第7近的行星。))) or (not (((-13 * 8) != (-4 * -8)) or ((17 - 10) == (13 + 15)))))))\nB. (not (((钻石由碳元素组成。) and ((柏林墙倒塌发生在1984年。) or ((钠的化学符号是K。) or (第一次世界大战开始发生在1914年。)))) and (((not ((-2 * 12) > (11 + 7))) and (第一次世界大战开始发生在1913年。)) and ((20 - 13) != (2 * -7 * -4 * -9)) and (金星是距离太阳第4近的行星。)))) or (not ((not not ((not (菲律宾的首都是马尼拉。)) or ((尼日利亚的首都是阿布贾。) or ((3 ** 1) <= (15 - -8))))) or ((not not (not not (氖的化学符号是Cr。))) and (((9 * 15) < (47 % 2)) and (25能被2整除。)) and (not (not not ((-5 * -8) == (10 * -1)))))))\nC. (not ((not not ((49 % 3) == (2 * -10 * 7 * 6))) or ((钾的化学符号是K。) or (银在常温下是气体。)))) and (((((印度尼西亚的货币是印尼盾。) or (墨西哥的首都是墨西哥城。)) and (((11 - -16) < (-5 - -2)) or (1919年是闰年。)) and (not (not not ((16 + -14) <= (6 * -15) <= (-12 - 1))))) or (((-9 * 10) < (15 - -8) < (13 + 12)) or (not (not not ((-12 + 16) != (-5 - -3)))))) and ((not (not (奥地利的首都是哈瓦那。))) and (((((-6 * 19) <= (20 % 6)) or (46是质数。)) and (not not (捷克的货币是克朗。))) and (((2 ** 3) > (5 - -19)) or (((2 * 20) >= (-5 + 5)) or (土星是距离太阳第8近的行星。))))))\nD. (not not (not not (not not ((not not ((20 * -2) != (-7 + -15))) or (not (地球绕太阳运转。)))))) or ((((not not (not not ((-14 - 2) == (5 ** 1)))) or (((苏联解体发生在1981年。) and ((-7 + -6) <= (-7 - -11))) or (鸭子有2条腿。))) or (((-15 - 7) > (-17 * -20)) and ((11 - -12) > (2 * -8 * -9 * 10)))) and (not ((((1912年奥运会在斯德哥尔摩举办。) or ((-8 + -9) < (20 * -11))) and (((37 % 10) != (15 - -2)) or (1907年是闰年。))) and (((6 + 18) <= (12 + 11)) and (1980年奥运会在莫斯科举办。)) and (氯的化学符号是Cl。))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 32090,
"true_count": 2
},
"seed": 32090,
"task_id": 600032090,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (not (not not ((伦敦大火发生在1664年。) and (((11 - 12) >= (6 + -8)) and (肯尼亚位于南极洲。))))) and (not (not not (((6 * -1 + 0 * -8) == (5 * 7 * 9 * 2)) or (not not ((3 * 7 - 8 * -5) < (-9 * 20))))))
B. (((((鸟有8条腿。) and (钻石在常温下是固体。)) and ((中国长城是在一年内建成的。) and ((-10 + -4) != (3 * -6 * -3 * 4)))) or (((水蒸气在常温下是气体。) or (第二次世界大战结束发生在1945年。)) and ((-7 * -1 * 1 * 3) > (-5 * 2)))) and (((19 * 4) > (-8 - -5)) and (9的平方根是9。))) and (not ((沙特阿拉伯的首都是利雅得。) and (1904年奥运会在巴黎举办。)))
C. (not (not not ((-2 - 12) != (10 * -4 - -9 * -8)))) or ((not (((氢的化学符号是H。) or (牛有100条腿。)) or (not not ((4 * -5 * -7 * 1) <= (-13 - 4) <= (47 % 9))))) and ((not (not not ((-17 + 13) <= (3 ** 1)))) or (not ((美国的货币是雷亚尔。) and ((14 - -9) == (-7 - -16))))))
D. (not not (((not not ((34 % 9) == (2 ** 3))) and (光速约为每秒30万公里。)) and (((-16 + 7) < (-8 * -3)) and (波兰的货币是克朗。)) and ((33 % 1) < (6 * -3)))) and ((not (((1 - -7) <= (30 % 2)) and (((8 * 5) >= (0 + -16)) or ((18 * 17) <= (4 ** 2))))) and (not ((4 - 9) < (-8 * -10 + -10 * -3) < (14 * -8))))
E. (not (((((17 + -11) <= (1 ** 2) <= (5 % 4)) or (埃及的首都是开罗。)) or (41小于等于54。)) or ((2 * -6 + 3 * -2) == (12 + -19)))) and (not (not not ((((5 ** 2) < (18 * -8)) or (铬的化学符号是Cu。)) and (柏林墙倒塌发生在1988年。))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 45047035,
"true_count": 1
},
"question": "考虑以下布尔表达式：\n\nA. (not (not not ((伦敦大火发生在1664年。) and (((11 - 12) >= (6 + -8)) and (肯尼亚位于南极洲。))))) and (not (not not (((6 * -1 + 0 * -8) == (5 * 7 * 9 * 2)) or (not not ((3 * 7 - 8 * -5) < (-9 * 20))))))\nB. (((((鸟有8条腿。) and (钻石在常温下是固体。)) and ((中国长城是在一年内建成的。) and ((-10 + -4) != (3 * -6 * -3 * 4)))) or (((水蒸气在常温下是气体。) or (第二次世界大战结束发生在1945年。)) and ((-7 * -1 * 1 * 3) > (-5 * 2)))) and (((19 * 4) > (-8 - -5)) and (9的平方根是9。))) and (not ((沙特阿拉伯的首都是利雅得。) and (1904年奥运会在巴黎举办。)))\nC. (not (not not ((-2 - 12) != (10 * -4 - -9 * -8)))) or ((not (((氢的化学符号是H。) or (牛有100条腿。)) or (not not ((4 * -5 * -7 * 1) <= (-13 - 4) <= (47 % 9))))) and ((not (not not ((-17 + 13) <= (3 ** 1)))) or (not ((美国的货币是雷亚尔。) and ((14 - -9) == (-7 - -16))))))\nD. (not not (((not not ((34 % 9) == (2 ** 3))) and (光速约为每秒30万公里。)) and (((-16 + 7) < (-8 * -3)) and (波兰的货币是克朗。)) and ((33 % 1) < (6 * -3)))) and ((not (((1 - -7) <= (30 % 2)) and (((8 * 5) >= (0 + -16)) or ((18 * 17) <= (4 ** 2))))) and (not ((4 - 9) < (-8 * -10 + -10 * -3) < (14 * -8))))\nE. (not (((((17 + -11) <= (1 ** 2) <= (5 % 4)) or (埃及的首都是开罗。)) or (41小于等于54。)) or ((2 * -6 + 3 * -2) == (12 + -19)))) and (not (not not ((((5 ** 2) < (18 * -8)) or (铬的化学符号是Cu。)) and (柏林墙倒塌发生在1988年。))))\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": 45047035,
"true_count": 1
},
"seed": 45047035,
"task_id": 645047035,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not not ((((中国长城是在一年内建成的。) or ((51能被5整除。) or (泰坦尼克号沉没发生在1912年。))) and ((3 % 6) > (15 - 14)) and ((5 * 15) < (21 % 7))) and (((瑞士的货币是加元。) and (汞在常温下是液体。)) or (not ((10 + -8) <= (13 - 7)))) and ((((2003年是闰年。) or ((10 - -14) < (42 % 8) < (20 * 14))) and (1904年奥运会在洛杉矶举办。)) or (七月有31天。)))
B. ((((-3 - 7) > (17 % 6)) or ((13能被10整除。) or ((-17 - 0) >= (-7 - -4))) or ((not not (水在常温下是气体。)) or ((2 * -3 - 2 * -3) != (14 - 17)))) or ((((瓢虫是昆虫。) or ((17 + 8) > (18 - -17))) and ((1920年奥运会在墨尔本举办。) and (越南的货币是雷亚尔。))) or (地球上一天是24小时。) or (((20 + -3) == (-4 * -9 * -2 * 5)) or (((5 ** 3) > (5 ** 1)) or ((13 - -14) <= (7 * 0 * -1 * -5)))))) or (((智利的货币是加元。) or (not not ((龙虾有10条腿。) or (火星是距离太阳第4近的行星。)))) and ((铜在常温下是固体。) or (not ((50 % 10) == (-2 * -2 - -8 * 0)))))
C. not ((((((-2 * -7 * 9 * -3) >= (-2 - 15)) or (中国的货币是人民币。)) or (((-5 + 5) != (3 ** 1)) or ((13 * -4) <= (16 + -15) <= (25 % 8)))) or (((16 * -11) >= (14 + -1)) and (牛有4条腿。)) or ((南极洲是最冷的大陆。) and (((14 - -16) <= (19 - -17) <= (-7 * -4 * 4 * 9)) or (秘鲁位于南美洲。)))) or ((not not (not not ((14 - 13) > (10 * -5 + -5 * -5)))) and (((0 - 18) <= (-12 * -2)) and ((海王星是距离太阳第3近的行星。) or (水蒸气在常温下是气体。)))))
D. (not not ((1976年奥运会在墨尔本举办。) and ((not not (1973年是闰年。)) or (伦敦大火发生在1664年。)))) and ((not ((4 ** 3) < (6 * -16) < (-7 * 6))) and ((六月有29天。) or ((第一次世界大战结束发生在1916年。) and (六月有31天。))) and ((澳大利亚的货币是索尔。) and (苏联解体发生在1996年。)))
E. (not not ((闪电不会两次击中同一个地方。) or ((14 - 1) <= (1 ** 2) <= (8 - 6)))) or ((((((20 - 1) > (4 ** 1)) or (36是完全平方数。)) and (not not ((20 % 9) < (9 * 6 - -6 * 9)))) or ((not ((-1 - 10) <= (-5 + -19))) and (水星是距离太阳第8近的行星。))) or (not (((人体有206块骨头。) or (钻石在常温下是液体。)) and (not not ((3 + -17) > (2 + 3))))))
F. not not ((not not (((-5 + -20) <= (-17 + 6)) or (((15 * 5) > (-2 * 8 - -2 * 7)) and (酒精在常温下是气体。)))) or ((((二氧化碳在常温下是气体。) and (25的平方根是12。)) and ((埃及位于欧洲。) and (蜻蜓是昆虫。))) and (not not ((2 - -3) != (-7 * 3 - 0 * -5))) and (((-8 - -9) < (6 - -3)) or ((81是质数。) or (铁的化学符号是Pb。)))))
G. ((not not (碳的化学符号是C。)) and ((not not (沙特阿拉伯位于亚洲。)) and ((90能被5整除。) and (((8 - 2) < (2 - -15) < (7 % 3)) and ((-9 * -10) > (5 + -6)))))) or (not ((丹麦的货币是人民币。) and (((44 % 1) > (-15 + -6)) or (not (日本位于亚洲。)))))
H. (not not ((not ((电流比光速更快。) and (加拿大的首都是渥太华。))) and ((秘鲁的货币是索尔。) and (84是奇数。)) and ((氯的化学符号是Cl。) and (鲱鱼是鱼类。)))) or (((not not (莱特兄弟首次飞行发生在1898年。)) and ((((40 % 5) == (4 ** 3)) or (木星是距离太阳第7近的行星。)) and (光速约为每秒30万公里。))) and (((冰的密度比液态水小。) and ((美国宣布独立发生在1776年。) and ((9 + -1) != (-12 + 8)))) or (not not (第一次世界大战结束发生在1919年。)) or (哥伦比亚位于南美洲。)))
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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"answer": "B,E,F,G",
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"true_count": 4
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not not ((((中国长城是在一年内建成的。) or ((51能被5整除。) or (泰坦尼克号沉没发生在1912年。))) and ((3 % 6) > (15 - 14)) and ((5 * 15) < (21 % 7))) and (((瑞士的货币是加元。) and (汞在常温下是液体。)) or (not ((10 + -8) <= (13 - 7)))) and ((((2003年是闰年。) or ((10 - -14) < (42 % 8) < (20 * 14))) and (1904年奥运会在洛杉矶举办。)) or (七月有31天。)))\nB. ((((-3 - 7) > (17 % 6)) or ((13能被10整除。) or ((-17 - 0) >= (-7 - -4))) or ((not not (水在常温下是气体。)) or ((2 * -3 - 2 * -3) != (14 - 17)))) or ((((瓢虫是昆虫。) or ((17 + 8) > (18 - -17))) and ((1920年奥运会在墨尔本举办。) and (越南的货币是雷亚尔。))) or (地球上一天是24小时。) or (((20 + -3) == (-4 * -9 * -2 * 5)) or (((5 ** 3) > (5 ** 1)) or ((13 - -14) <= (7 * 0 * -1 * -5)))))) or (((智利的货币是加元。) or (not not ((龙虾有10条腿。) or (火星是距离太阳第4近的行星。)))) and ((铜在常温下是固体。) or (not ((50 % 10) == (-2 * -2 - -8 * 0)))))\nC. not ((((((-2 * -7 * 9 * -3) >= (-2 - 15)) or (中国的货币是人民币。)) or (((-5 + 5) != (3 ** 1)) or ((13 * -4) <= (16 + -15) <= (25 % 8)))) or (((16 * -11) >= (14 + -1)) and (牛有4条腿。)) or ((南极洲是最冷的大陆。) and (((14 - -16) <= (19 - -17) <= (-7 * -4 * 4 * 9)) or (秘鲁位于南美洲。)))) or ((not not (not not ((14 - 13) > (10 * -5 + -5 * -5)))) and (((0 - 18) <= (-12 * -2)) and ((海王星是距离太阳第3近的行星。) or (水蒸气在常温下是气体。)))))\nD. (not not ((1976年奥运会在墨尔本举办。) and ((not not (1973年是闰年。)) or (伦敦大火发生在1664年。)))) and ((not ((4 ** 3) < (6 * -16) < (-7 * 6))) and ((六月有29天。) or ((第一次世界大战结束发生在1916年。) and (六月有31天。))) and ((澳大利亚的货币是索尔。) and (苏联解体发生在1996年。)))\nE. (not not ((闪电不会两次击中同一个地方。) or ((14 - 1) <= (1 ** 2) <= (8 - 6)))) or ((((((20 - 1) > (4 ** 1)) or (36是完全平方数。)) and (not not ((20 % 9) < (9 * 6 - -6 * 9)))) or ((not ((-1 - 10) <= (-5 + -19))) and (水星是距离太阳第8近的行星。))) or (not (((人体有206块骨头。) or (钻石在常温下是液体。)) and (not not ((3 + -17) > (2 + 3))))))\nF. not not ((not not (((-5 + -20) <= (-17 + 6)) or (((15 * 5) > (-2 * 8 - -2 * 7)) and (酒精在常温下是气体。)))) or ((((二氧化碳在常温下是气体。) and (25的平方根是12。)) and ((埃及位于欧洲。) and (蜻蜓是昆虫。))) and (not not ((2 - -3) != (-7 * 3 - 0 * -5))) and (((-8 - -9) < (6 - -3)) or ((81是质数。) or (铁的化学符号是Pb。)))))\nG. ((not not (碳的化学符号是C。)) and ((not not (沙特阿拉伯位于亚洲。)) and ((90能被5整除。) and (((8 - 2) < (2 - -15) < (7 % 3)) and ((-9 * -10) > (5 + -6)))))) or (not ((丹麦的货币是人民币。) and (((44 % 1) > (-15 + -6)) or (not (日本位于亚洲。)))))\nH. (not not ((not ((电流比光速更快。) and (加拿大的首都是渥太华。))) and ((秘鲁的货币是索尔。) and (84是奇数。)) and ((氯的化学符号是Cl。) and (鲱鱼是鱼类。)))) or (((not not (莱特兄弟首次飞行发生在1898年。)) and ((((40 % 5) == (4 ** 3)) or (木星是距离太阳第7近的行星。)) and (光速约为每秒30万公里。))) and (((冰的密度比液态水小。) and ((美国宣布独立发生在1776年。) and ((9 + -1) != (-12 + 8)))) or (not not (第一次世界大战结束发生在1919年。)) or (哥伦比亚位于南美洲。)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 8,
"seed": 48631145,
"true_count": 4
},
"seed": 48631145,
"task_id": 648631145,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not ((((4 ** 1) != (-2 * 9 * 10 * 8)) or ((-9 * -6 * -4 * -10) == (-20 + 4))) or ((声音无法在真空中传播。) or (第一次世界大战开始发生在1914年。)))
B. ((十二月有31天。) and (not not ((12 + 4) >= (9 * 2 * 8 * -4)))) or ((17 + -11) == (7 * 4 * 7 * 2)) or ((-5 - 17) >= (4 * -6 + 8 * 4))
C. ((((-15 + 5) < (2 ** 3)) and ((-7 * 10 + 10 * 7) != (-19 * 17))) or (((6 - 2) >= (3 + -11)) and ((20 % 8) >= (0 * 1 + 0 * 4)))) or ((not not (金星是距离太阳第2近的行星。)) or ((-2 * -1 - 10 * -4) == (-5 * -7 + 4 * 9)))
D. not not (加拿大位于北美洲。)
E. not not ((not not (肯尼亚位于非洲。)) or (7是奇数。))
F. not not (not (not (油在常温下是液体。)))
G. ((((40 % 6) <= (9 - -17)) and (76是质数。)) or (not not (木头在常温下是液体。))) or ((((-5 - -16) != (-1 + -11)) and ((14 + -9) > (7 + 5))) and ((油在常温下是液体。) or ((3 * -3) == (2 ** 3))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,B,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 44912914,
"true_count": 6
},
"question": "审视以下逻辑表达式：\n\nA. not not ((((4 ** 1) != (-2 * 9 * 10 * 8)) or ((-9 * -6 * -4 * -10) == (-20 + 4))) or ((声音无法在真空中传播。) or (第一次世界大战开始发生在1914年。)))\nB. ((十二月有31天。) and (not not ((12 + 4) >= (9 * 2 * 8 * -4)))) or ((17 + -11) == (7 * 4 * 7 * 2)) or ((-5 - 17) >= (4 * -6 + 8 * 4))\nC. ((((-15 + 5) < (2 ** 3)) and ((-7 * 10 + 10 * 7) != (-19 * 17))) or (((6 - 2) >= (3 + -11)) and ((20 % 8) >= (0 * 1 + 0 * 4)))) or ((not not (金星是距离太阳第2近的行星。)) or ((-2 * -1 - 10 * -4) == (-5 * -7 + 4 * 9)))\nD. not not (加拿大位于北美洲。)\nE. not not ((not not (肯尼亚位于非洲。)) or (7是奇数。))\nF. not not (not (not (油在常温下是液体。)))\nG. ((((40 % 6) <= (9 - -17)) and (76是质数。)) or (not not (木头在常温下是液体。))) or ((((-5 - -16) != (-1 + -11)) and ((14 + -9) > (7 + 5))) and ((油在常温下是液体。) or ((3 * -3) == (2 ** 3))))\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": 7,
"seed": 44912914,
"true_count": 6
},
"seed": 44912914,
"task_id": 644912914,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (((1 - -1) == (14 * -19)) or ((7 * 9) >= (-8 * 9))) or (not not (not ((The currency of Nigeria is the Yuan.) or (Colombia is in South America.))))
B. not not (not not (2035 is a leap year.))
C. not ((There are 29 days in June.) or ((-14 + -14) < (-7 - -13)))
D. ((((Water is a gas at room temperature.) or (Humans only use 10% of their brain.)) or (not ((10 + -11) != (12 + -16)))) and ((-17 - -20) < (15 * -15) < (15 % 8))) and ((46 % 7) <= (1 ** 1)) and ((The chemical symbol for Magnesium is Hg.) or ((not not ((-4 - -1) == (-20 + 5))) and ((The 1920 Olympics were held in Antwerp.) or ((5 ** 2) < (15 - 16) < (4 ** 2)))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 700313,
"true_count": 1
},
"question": "Analyze these boolean expressions:\n\nA. (((1 - -1) == (14 * -19)) or ((7 * 9) >= (-8 * 9))) or (not not (not ((The currency of Nigeria is the Yuan.) or (Colombia is in South America.))))\nB. not not (not not (2035 is a leap year.))\nC. not ((There are 29 days in June.) or ((-14 + -14) < (-7 - -13)))\nD. ((((Water is a gas at room temperature.) or (Humans only use 10% of their brain.)) or (not ((10 + -11) != (12 + -16)))) and ((-17 - -20) < (15 * -15) < (15 % 8))) and ((46 % 7) <= (1 ** 1)) and ((The chemical symbol for Magnesium is Hg.) or ((not not ((-4 - -1) == (-20 + 5))) and ((The 1920 Olympics were held in Antwerp.) or ((5 ** 2) < (15 - 16) < (4 ** 2)))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 700313,
"true_count": 1
},
"seed": 700313,
"task_id": 600700313,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (not ((火星是距离太阳第4近的行星。) and (土星是距离太阳第6近的行星。))) or ((新加坡的货币是印尼盾。) and (((12 * -17) < (-3 * -3 * -9 * -7)) or (第一次世界大战开始发生在1914年。))) or (not not ((not ((18 + -15) > (2 ** 2))) and (not not (电流比光速更快。))))
B. ((((印度的货币是比索。) or ((22 % 7) >= (-4 * -5 * 5 * -5))) and (火星是距离太阳第2近的行星。)) or (755是斐波那契数。)) or (水星是距离太阳第1近的行星。) or (((3 * -5 * 7 * 2) == (-9 * 2)) and ((俄罗斯的货币是卢布。) or (光速约为每秒30万公里。)) and ((((5 ** 3) <= (17 - 16) <= (-2 * -9 * -10 * -9)) or (84是完全平方数。)) and (152是奇数。)))
C. (not ((-3 - 13) >= (10 + -6))) and (((((8 * 3) < (9 * -3 + 7 * -8) < (4 * 8)) or ((-8 * 0 - 3 * -6) < (9 + -3))) and ((-17 + -13) <= (-14 * -4))) and (((氧的化学符号是Cl。) and ((1 * 1 * -9 * 4) == (47 % 3))) or ((比利时的首都是布鲁塞尔。) and (尼日利亚位于南极洲。))))
D. not not ((not (((10 % 2) > (-19 - -4)) and (铜的化学符号是Si。))) and ((3 ** 2) < (0 * -11)))
E. ((印度位于亚洲。) and ((加拿大的货币是加元。) and ((土星是距离太阳第1近的行星。) or ((4 ** 2) != (-9 - 1))))) or ((((地球是距离太阳第4近的行星。) and ((-1 - -17) <= (13 * -14) <= (-7 * -7 - -2 * -2))) and (not (罗马尼亚的首都是布加勒斯特。))) and ((not (摩洛哥位于大洋洲。)) or (((18 % 10) <= (20 * -5)) and (法国位于欧洲。))))
F. not not ((((1972年奥运会在慕尼黑举办。) and ((-6 - -7) >= (28 % 5))) or ((金的化学符号是Au。) or (摩洛哥位于非洲。))) or ((9 * 1 + -3 * 3) <= (4 - 2) <= (1 * -5 - 8 * 5)))
G. not not (not not ((-20 + -4) < (-12 * -7) < (37 % 2)))
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": "B,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 7301300,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. (not ((火星是距离太阳第4近的行星。) and (土星是距离太阳第6近的行星。))) or ((新加坡的货币是印尼盾。) and (((12 * -17) < (-3 * -3 * -9 * -7)) or (第一次世界大战开始发生在1914年。))) or (not not ((not ((18 + -15) > (2 ** 2))) and (not not (电流比光速更快。))))\nB. ((((印度的货币是比索。) or ((22 % 7) >= (-4 * -5 * 5 * -5))) and (火星是距离太阳第2近的行星。)) or (755是斐波那契数。)) or (水星是距离太阳第1近的行星。) or (((3 * -5 * 7 * 2) == (-9 * 2)) and ((俄罗斯的货币是卢布。) or (光速约为每秒30万公里。)) and ((((5 ** 3) <= (17 - 16) <= (-2 * -9 * -10 * -9)) or (84是完全平方数。)) and (152是奇数。)))\nC. (not ((-3 - 13) >= (10 + -6))) and (((((8 * 3) < (9 * -3 + 7 * -8) < (4 * 8)) or ((-8 * 0 - 3 * -6) < (9 + -3))) and ((-17 + -13) <= (-14 * -4))) and (((氧的化学符号是Cl。) and ((1 * 1 * -9 * 4) == (47 % 3))) or ((比利时的首都是布鲁塞尔。) and (尼日利亚位于南极洲。))))\nD. not not ((not (((10 % 2) > (-19 - -4)) and (铜的化学符号是Si。))) and ((3 ** 2) < (0 * -11)))\nE. ((印度位于亚洲。) and ((加拿大的货币是加元。) and ((土星是距离太阳第1近的行星。) or ((4 ** 2) != (-9 - 1))))) or ((((地球是距离太阳第4近的行星。) and ((-1 - -17) <= (13 * -14) <= (-7 * -7 - -2 * -2))) and (not (罗马尼亚的首都是布加勒斯特。))) and ((not (摩洛哥位于大洋洲。)) or (((18 % 10) <= (20 * -5)) and (法国位于欧洲。))))\nF. not not ((((1972年奥运会在慕尼黑举办。) and ((-6 - -7) >= (28 % 5))) or ((金的化学符号是Au。) or (摩洛哥位于非洲。))) or ((9 * 1 + -3 * 3) <= (4 - 2) <= (1 * -5 - 8 * 5)))\nG. not not (not not ((-20 + -4) < (-12 * -7) < (37 % 2)))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 7301300,
"true_count": 3
},
"seed": 7301300,
"task_id": 607301300,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not (((1 * -8 * 4 * 10) > (17 * -19)) and (The chemical symbol for Silicon is S.))) and (not not (There are 28 days in November.))
B. ((((Japan is in South America.) or ((10 * 3 + 6 * -6) < (2 + -18) < (2 ** 1))) and ((10 is less than or equal to 85.) and (The chemical symbol for Iron is Fe.))) or (not not (Copper is a solid at room temperature.))) and (((A bird has 2 legs.) and (The currency of Turkey is the Lira.)) or ((19 % 6) == (5 + 7)))
C. (((19 * -6) == (1 - 18)) and ((The capital of Norway is Lisbon.) or ((-10 * -7) <= (19 - -16) <= (2 % 8))) and (((14 * -12) == (8 * -2 * 8 * -5)) and (((17 * -8) <= (-20 - 8)) and (Peru is in South America.)))) and (not not (not not (((3 * 6 - 3 * 10) < (-1 - 15) < (4 * 0 + 4 * -2)) and ((10 * -12) == (-18 + -8)))))
D. (((not not ((-10 - -1) > (-19 * -11))) and ((-9 * 10 * 8 * 5) != (14 - -5))) and ((((-16 + 6) == (-17 - -14)) and (The currency of Colombia is the Peso.)) and ((15 * 0) != (13 % 4)))) or ((42 is divisible by 5.) and (The capital of Vietnam is Bogota.))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 24231177,
"true_count": 1
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (not (((1 * -8 * 4 * 10) > (17 * -19)) and (The chemical symbol for Silicon is S.))) and (not not (There are 28 days in November.))\nB. ((((Japan is in South America.) or ((10 * 3 + 6 * -6) < (2 + -18) < (2 ** 1))) and ((10 is less than or equal to 85.) and (The chemical symbol for Iron is Fe.))) or (not not (Copper is a solid at room temperature.))) and (((A bird has 2 legs.) and (The currency of Turkey is the Lira.)) or ((19 % 6) == (5 + 7)))\nC. (((19 * -6) == (1 - 18)) and ((The capital of Norway is Lisbon.) or ((-10 * -7) <= (19 - -16) <= (2 % 8))) and (((14 * -12) == (8 * -2 * 8 * -5)) and (((17 * -8) <= (-20 - 8)) and (Peru is in South America.)))) and (not not (not not (((3 * 6 - 3 * 10) < (-1 - 15) < (4 * 0 + 4 * -2)) and ((10 * -12) == (-18 + -8)))))\nD. (((not not ((-10 - -1) > (-19 * -11))) and ((-9 * 10 * 8 * 5) != (14 - -5))) and ((((-16 + 6) == (-17 - -14)) and (The currency of Colombia is the Peso.)) and ((15 * 0) != (13 % 4)))) or ((42 is divisible by 5.) and (The capital of Vietnam is Bogota.))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 24231177,
"true_count": 1
},
"seed": 24231177,
"task_id": 624231177,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((((not (2086年是闰年。)) or (not (美国宣布独立发生在1776年。))) or (((-12 * -7) <= (-17 - -20)) and ((4 ** 1) != (1 - -3))) or (72大于90。)) or ((7 + -8) >= (-5 * -9)) or (((not ((16 + 4) == (3 * -15))) and ((4 ** 2) <= (3 ** 2))) and (1920年奥运会在巴塞罗那举办。) and ((-4 * 19) < (19 + 14)))) or (((not not ((7 + -19) > (-9 - 7))) and (水星是距离太阳第1近的行星。)) and ((not (海王星是距离太阳第5近的行星。)) or ((225的平方根是15。) and (((3 * -13) >= (2 ** 1)) or ((5 ** 3) < (9 * -5 * -3 * 9))))))
B. (not (((((20 * 1) < (-4 * -5)) or (哥伦比亚的首都是基辅。)) and (427是斐波那契数。)) or (钻石由碳元素组成。))) and ((not not (木星是距离太阳第5近的行星。)) or ((not not ((-2 * 3 * -2 * 7) == (-1 * 7))) or (not ((2000年奥运会在悉尼举办。) and (510是斐波那契数。)))))
C. (not (((((-16 - 12) <= (-16 * 2)) and ((-1 * -1 + 10 * -1) < (-7 + -16))) or (((-19 + 14) == (-9 + 3)) and ((0 * -2 + 2 * -10) >= (3 + -3)))) and ((-4 * -2 + 0 * -4) < (1 ** 3) < (-16 - 11)) and ((-10 * 8) >= (-13 + -11)))) or (((not not (((-14 + 16) < (-16 - 10) < (14 * 9)) or (天王星是距离太阳第5近的行星。))) or (not not ((-10 * 8 - 10 * 9) < (-5 * 1 - 4 * -5)))) or ((希腊的首都是雅典。) or (八月有31天。)))
D. not not ((((((4 * 16) > (-13 * 15)) and ((-12 * 1) > (12 - -18))) and ((-11 * 0) <= (11 * -11) <= (9 * -8 - -10 * -2))) or (1992年奥运会在柏林举办。)) or (not not ((木星是距离太阳第4近的行星。) and (天王星是距离太阳第5近的行星。))) or (((-20 * -13) >= (-17 - -5)) or ((((5 ** 3) != (10 * -1 + -7 * -8)) or (木星是距离太阳第5近的行星。)) and (((-7 * -8 - 4 * 3) >= (14 + -10)) or (2069年是闰年。)))))
E. ((((2 - -13) < (-1 * 6 + -2 * 5)) and ((木头在常温下是固体。) and (not not (196的平方根是8。)))) or ((((智利的首都是圣地亚哥。) or ((3 + 12) != (-8 * 6 - -1 * 5))) and (加拿大的货币是比索。)) and ((16 % 9) == (-13 * 14)))) or (((((4 ** 1) <= (11 + 10)) and (not not ((50 % 5) >= (-19 + -4)))) or ((not (美国位于北美洲。)) and (not not (印度尼西亚的首都是奥斯陆。)))) or (not not (((-1 * -6 + -9 * -1) < (4 - 16)) and (((1 * 14) > (19 + -2)) and (9大于97。)))))
F. not not ((not ((not (壁虎是爬行动物。)) or (((1 ** 1) == (11 + -19)) and (91是质数。)))) or (泰国的首都是曼谷。) or (not ((((5 - -7) >= (4 * 4 - -8 * 8)) and (土耳其的首都是加拉加斯。)) or (not not ((-10 * 1) >= (-10 - -6))))))
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,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"true_count": 5
},
"question": "分析以下逻辑表达式：\n\nA. ((((not (2086年是闰年。)) or (not (美国宣布独立发生在1776年。))) or (((-12 * -7) <= (-17 - -20)) and ((4 ** 1) != (1 - -3))) or (72大于90。)) or ((7 + -8) >= (-5 * -9)) or (((not ((16 + 4) == (3 * -15))) and ((4 ** 2) <= (3 ** 2))) and (1920年奥运会在巴塞罗那举办。) and ((-4 * 19) < (19 + 14)))) or (((not not ((7 + -19) > (-9 - 7))) and (水星是距离太阳第1近的行星。)) and ((not (海王星是距离太阳第5近的行星。)) or ((225的平方根是15。) and (((3 * -13) >= (2 ** 1)) or ((5 ** 3) < (9 * -5 * -3 * 9))))))\nB. (not (((((20 * 1) < (-4 * -5)) or (哥伦比亚的首都是基辅。)) and (427是斐波那契数。)) or (钻石由碳元素组成。))) and ((not not (木星是距离太阳第5近的行星。)) or ((not not ((-2 * 3 * -2 * 7) == (-1 * 7))) or (not ((2000年奥运会在悉尼举办。) and (510是斐波那契数。)))))\nC. (not (((((-16 - 12) <= (-16 * 2)) and ((-1 * -1 + 10 * -1) < (-7 + -16))) or (((-19 + 14) == (-9 + 3)) and ((0 * -2 + 2 * -10) >= (3 + -3)))) and ((-4 * -2 + 0 * -4) < (1 ** 3) < (-16 - 11)) and ((-10 * 8) >= (-13 + -11)))) or (((not not (((-14 + 16) < (-16 - 10) < (14 * 9)) or (天王星是距离太阳第5近的行星。))) or (not not ((-10 * 8 - 10 * 9) < (-5 * 1 - 4 * -5)))) or ((希腊的首都是雅典。) or (八月有31天。)))\nD. not not ((((((4 * 16) > (-13 * 15)) and ((-12 * 1) > (12 - -18))) and ((-11 * 0) <= (11 * -11) <= (9 * -8 - -10 * -2))) or (1992年奥运会在柏林举办。)) or (not not ((木星是距离太阳第4近的行星。) and (天王星是距离太阳第5近的行星。))) or (((-20 * -13) >= (-17 - -5)) or ((((5 ** 3) != (10 * -1 + -7 * -8)) or (木星是距离太阳第5近的行星。)) and (((-7 * -8 - 4 * 3) >= (14 + -10)) or (2069年是闰年。)))))\nE. ((((2 - -13) < (-1 * 6 + -2 * 5)) and ((木头在常温下是固体。) and (not not (196的平方根是8。)))) or ((((智利的首都是圣地亚哥。) or ((3 + 12) != (-8 * 6 - -1 * 5))) and (加拿大的货币是比索。)) and ((16 % 9) == (-13 * 14)))) or (((((4 ** 1) <= (11 + 10)) and (not not ((50 % 5) >= (-19 + -4)))) or ((not (美国位于北美洲。)) and (not not (印度尼西亚的首都是奥斯陆。)))) or (not not (((-1 * -6 + -9 * -1) < (4 - 16)) and (((1 * 14) > (19 + -2)) and (9大于97。)))))\nF. not not ((not ((not (壁虎是爬行动物。)) or (((1 ** 1) == (11 + -19)) and (91是质数。)))) or (泰国的首都是曼谷。) or (not ((((5 - -7) >= (4 * 4 - -8 * 8)) and (土耳其的首都是加拉加斯。)) or (not not ((-10 * 1) >= (-10 - -6))))))\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": 71737090,
"true_count": 5
},
"seed": 71737090,
"task_id": 671737090,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (12 + 7) < (-15 + -15)
B. ((-19 + 13) == (10 * -1 + 9 * 5)) or (((4 ** 3) != (5 * 1 * 7 * -6)) and ((-15 * 3) < (1 - -19) < (3 ** 3)))
C. not not (not (六月有30天。))
D. (铁在常温下是固体。) and ((氦气在常温下是气体。) or (人类只使用了大脑的10%。))
E. not (袋鼠是鸟类。)
F. (((-17 * 12) <= (10 * 19)) and ((-4 - -10) > (-18 - 7))) and ((埃及的首都是奥斯陆。) and (14是斐波那契数。))
G. not not (((-1 * -5 - 0 * -2) != (7 * 6 - 6 * 5)) and (西班牙位于欧洲。))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "B,D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 16241473,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. (12 + 7) < (-15 + -15)\nB. ((-19 + 13) == (10 * -1 + 9 * 5)) or (((4 ** 3) != (5 * 1 * 7 * -6)) and ((-15 * 3) < (1 - -19) < (3 ** 3)))\nC. not not (not (六月有30天。))\nD. (铁在常温下是固体。) and ((氦气在常温下是气体。) or (人类只使用了大脑的10%。))\nE. not (袋鼠是鸟类。)\nF. (((-17 * 12) <= (10 * 19)) and ((-4 - -10) > (-18 - 7))) and ((埃及的首都是奥斯陆。) and (14是斐波那契数。))\nG. not not (((-1 * -5 - 0 * -2) != (7 * 6 - 6 * 5)) and (西班牙位于欧洲。))\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": 16241473,
"true_count": 4
},
"seed": 16241473,
"task_id": 616241473,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (not not (Saturn is the 6th planet from the Sun.))
B. ((-7 * -9 + 8 * -7) == (2 - -19)) or ((9 + -14) == (-16 + -15))
C. (not not (not ((1 * -6 * -9 * -2) != (20 % 2)))) or ((Uranus is the 7th planet from the Sun.) or (not not (Oxygen is a liquid at room temperature.)))
D. not not (The square root of 36 is 11.)
E. not (The 1960 Olympics were held in Rome.)
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": 5,
"seed": 1514983,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not not (Saturn is the 6th planet from the Sun.))\nB. ((-7 * -9 + 8 * -7) == (2 - -19)) or ((9 + -14) == (-16 + -15))\nC. (not not (not ((1 * -6 * -9 * -2) != (20 % 2)))) or ((Uranus is the 7th planet from the Sun.) or (not not (Oxygen is a liquid at room temperature.)))\nD. not not (The square root of 36 is 11.)\nE. not (The 1960 Olympics were held in Rome.)\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": 5,
"seed": 1514983,
"true_count": 1
},
"seed": 1514983,
"task_id": 601514983,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (((((-17 - -5) <= (-3 * 5)) or ((3 ** 3) == (20 - 4))) and ((-6 * 20) < (12 * 13))) or (((Mars is the 8th planet from the Sun.) and (A cow is a mammal.)) and ((The first iPhone was released occurred in 2007.) and ((11 * -19) <= (7 * 10 * 0 * 0) <= (3 * 10 * 0 * 1)))))
B. (not not (((676 is a Fibonacci number.) or (196 is a Fibonacci number.)) or (not not ((16 - 15) < (-18 - -7) < (-10 - -15))))) or ((not not (((5 ** 1) < (1 ** 1) < (-9 * -6 - 6 * -9)) and ((3 - -6) == (0 - -18)))) or ((The square root of 4 is 2.) and (The capital of Thailand is Bangkok.)) or ((The chemical symbol for Phosphorus is Ca.) or (not not ((8 * 7 - -7 * 5) < (-3 * -1 * -5 * -1) < (18 * 12)))))
C. (not not (The 2024 Olympics were held in Paris.)) and (There are 30 days in August.) and ((not (not not (Christopher Columbus reached America occurred in 1492.))) and (((Helium is a gas at room temperature.) and ((-4 - -1) <= (21 % 10))) or ((Earth is the 4th planet from the Sun.) and ((-18 - -9) != (5 * 2 + 4 * 2)))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 86740127,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. not (((((-17 - -5) <= (-3 * 5)) or ((3 ** 3) == (20 - 4))) and ((-6 * 20) < (12 * 13))) or (((Mars is the 8th planet from the Sun.) and (A cow is a mammal.)) and ((The first iPhone was released occurred in 2007.) and ((11 * -19) <= (7 * 10 * 0 * 0) <= (3 * 10 * 0 * 1)))))\nB. (not not (((676 is a Fibonacci number.) or (196 is a Fibonacci number.)) or (not not ((16 - 15) < (-18 - -7) < (-10 - -15))))) or ((not not (((5 ** 1) < (1 ** 1) < (-9 * -6 - 6 * -9)) and ((3 - -6) == (0 - -18)))) or ((The square root of 4 is 2.) and (The capital of Thailand is Bangkok.)) or ((The chemical symbol for Phosphorus is Ca.) or (not not ((8 * 7 - -7 * 5) < (-3 * -1 * -5 * -1) < (18 * 12)))))\nC. (not not (The 2024 Olympics were held in Paris.)) and (There are 30 days in August.) and ((not (not not (Christopher Columbus reached America occurred in 1492.))) and (((Helium is a gas at room temperature.) and ((-4 - -1) <= (21 % 10))) or ((Earth is the 4th planet from the Sun.) and ((-18 - -9) != (5 * 2 + 4 * 2)))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 86740127,
"true_count": 2
},
"seed": 86740127,
"task_id": 686740127,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. ((not (((-10 * 8 * -4 * -4) < (7 * -15)) or (not ((2 ** 2) < (2 ** 3))))) or ((1915 is a leap year.) or (The Titanic sank occurred in 1912.) or ((((17 + 19) >= (-2 * 10 * -1 * -4)) or ((-11 - 20) < (5 % 1))) or ((49 % 4) >= (-2 + 18))))) or ((((((19 + 11) < (4 ** 3)) or (A cat has 4 legs.)) or (The capital of Hungary is Budapest.)) and ((not not (Whales are fish.)) or (not not ((8 + 17) < (2 * 19))))) or (not (World War I began occurred in 1914.)))
B. (not not ((The 1932 Olympics were held in Paris.) and (not ((28 % 1) == (1 ** 2))))) and ((A butterfly has 6 legs.) and ((2 * 1) < (-8 + -19) < (20 - 1)) and (The 1956 Olympics were held in Rio de Janeiro.)) and ((((-5 * 6) == (-18 * 14)) or (((-9 * -3 - 4 * 1) != (2 + -14)) or (The square root of 144 is 12.)) or (((11 - -5) >= (3 ** 3)) and ((Copper is a solid at room temperature.) or (The chemical symbol for Zinc is Zn.)))) or (not ((4 * -1 - 8 * -6) >= (2 + 3))))
C. ((((not ((-10 - 4) <= (-17 + 18))) or (not (Peru is in South America.))) and (not (not (A bird has 0 legs.)))) or ((Gold is a solid at room temperature.) or (The capital of Sweden is Stockholm.) or (not not (((1 ** 1) > (8 - -15)) and ((-2 * -9 - 7 * 10) < (-15 + -15)))))) and (not not (not not ((not (The currency of Poland is the Peso.)) or ((-13 * -18) == (5 * -2 - -2 * 8)))))
D. not (((Alcohol is a liquid at room temperature.) or ((The chemical symbol for Calcium is Ca.) or ((34 % 10) != (3 ** 1))) or (not (The Earth revolves around the Sun.))) or (Jupiter is the 5th planet from the Sun.) or (not ((-15 * -9) < (-15 + -2))))
E. not ((((((-11 * 10) == (43 % 7)) or ((-8 + -1) >= (11 + -2))) or (The chemical symbol for Manganese is Al.)) and (((The currency of Indonesia is the Dollar.) or (Japan is in North America.)) or (22 is a perfect square.))) and (not (((3 ** 2) < (13 + -4)) and ((3 - -15) < (34 % 7)))) and ((A ostrich is a bird.) or (not not (not not ((6 * -18) >= (-15 * 2))))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 66811161,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. ((not (((-10 * 8 * -4 * -4) < (7 * -15)) or (not ((2 ** 2) < (2 ** 3))))) or ((1915 is a leap year.) or (The Titanic sank occurred in 1912.) or ((((17 + 19) >= (-2 * 10 * -1 * -4)) or ((-11 - 20) < (5 % 1))) or ((49 % 4) >= (-2 + 18))))) or ((((((19 + 11) < (4 ** 3)) or (A cat has 4 legs.)) or (The capital of Hungary is Budapest.)) and ((not not (Whales are fish.)) or (not not ((8 + 17) < (2 * 19))))) or (not (World War I began occurred in 1914.)))\nB. (not not ((The 1932 Olympics were held in Paris.) and (not ((28 % 1) == (1 ** 2))))) and ((A butterfly has 6 legs.) and ((2 * 1) < (-8 + -19) < (20 - 1)) and (The 1956 Olympics were held in Rio de Janeiro.)) and ((((-5 * 6) == (-18 * 14)) or (((-9 * -3 - 4 * 1) != (2 + -14)) or (The square root of 144 is 12.)) or (((11 - -5) >= (3 ** 3)) and ((Copper is a solid at room temperature.) or (The chemical symbol for Zinc is Zn.)))) or (not ((4 * -1 - 8 * -6) >= (2 + 3))))\nC. ((((not ((-10 - 4) <= (-17 + 18))) or (not (Peru is in South America.))) and (not (not (A bird has 0 legs.)))) or ((Gold is a solid at room temperature.) or (The capital of Sweden is Stockholm.) or (not not (((1 ** 1) > (8 - -15)) and ((-2 * -9 - 7 * 10) < (-15 + -15)))))) and (not not (not not ((not (The currency of Poland is the Peso.)) or ((-13 * -18) == (5 * -2 - -2 * 8)))))\nD. not (((Alcohol is a liquid at room temperature.) or ((The chemical symbol for Calcium is Ca.) or ((34 % 10) != (3 ** 1))) or (not (The Earth revolves around the Sun.))) or (Jupiter is the 5th planet from the Sun.) or (not ((-15 * -9) < (-15 + -2))))\nE. not ((((((-11 * 10) == (43 % 7)) or ((-8 + -1) >= (11 + -2))) or (The chemical symbol for Manganese is Al.)) and (((The currency of Indonesia is the Dollar.) or (Japan is in North America.)) or (22 is a perfect square.))) and (not (((3 ** 2) < (13 + -4)) and ((3 - -15) < (34 % 7)))) and ((A ostrich is a bird.) or (not not (not not ((6 * -18) >= (-15 * 2))))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 66811161,
"true_count": 3
},
"seed": 66811161,
"task_id": 666811161,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (not not (((not (汞的化学符号是C。)) and (not not (哥伦比亚的货币是比索。))) and (not ((火星是距离太阳第3近的行星。) and ((7 * 5 + 8 * -3) <= (8 - -7) <= (11 - 12)))))) or ((not (not ((哥伦布到达美洲发生在1491年。) or (1964年奥运会在东京举办。)))) and ((225的平方根是15。) and ((1 ** 1) >= (2 + 8)) and (not (((-1 * -10 * 10 * 3) < (5 ** 1)) or (2020年奥运会在东京举办。)))))
B. (((木星是距离太阳第2近的行星。) and ((3 ** 2) <= (-4 * 7 - -8 * 0))) or (not ((-13 * -6) == (0 + 0)))) or (((((人类首次登月发生在1969年。) and (锡的化学符号是Sn。)) and (2007年是闰年。)) and ((南非位于非洲。) or (1965年是闰年。)) and ((中国长城是在一年内建成的。) and ((油在常温下是气体。) or (氧气在常温下是液体。)))) and (((美国位于南美洲。) and (not not (1905年是闰年。))) or (not (水星是距离太阳第1近的行星。)) or ((1904年奥运会在圣路易斯举办。) and (印度的货币是卢比。))))
C. not (not (not (not not ((17 + 20) == (-6 * 4 + 9 * -7)))))
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,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 98858097,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. (not not (((not (汞的化学符号是C。)) and (not not (哥伦比亚的货币是比索。))) and (not ((火星是距离太阳第3近的行星。) and ((7 * 5 + 8 * -3) <= (8 - -7) <= (11 - 12)))))) or ((not (not ((哥伦布到达美洲发生在1491年。) or (1964年奥运会在东京举办。)))) and ((225的平方根是15。) and ((1 ** 1) >= (2 + 8)) and (not (((-1 * -10 * 10 * 3) < (5 ** 1)) or (2020年奥运会在东京举办。)))))\nB. (((木星是距离太阳第2近的行星。) and ((3 ** 2) <= (-4 * 7 - -8 * 0))) or (not ((-13 * -6) == (0 + 0)))) or (((((人类首次登月发生在1969年。) and (锡的化学符号是Sn。)) and (2007年是闰年。)) and ((南非位于非洲。) or (1965年是闰年。)) and ((中国长城是在一年内建成的。) and ((油在常温下是气体。) or (氧气在常温下是液体。)))) and (((美国位于南美洲。) and (not not (1905年是闰年。))) or (not (水星是距离太阳第1近的行星。)) or ((1904年奥运会在圣路易斯举办。) and (印度的货币是卢比。))))\nC. not (not (not (not not ((17 + 20) == (-6 * 4 + 9 * -7)))))\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": 3,
"seed": 98858097,
"true_count": 3
},
"seed": 98858097,
"task_id": 698858097,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (((30 % 5) >= (20 + -15)) or (not not (The capital of South Korea is Dublin.)) or ((not not (The chemical symbol for Magnesium is Mg.)) or (The first iPhone was released occurred in 2007.))) and (((A beetle is an insect.) and (There are 29 days in August.)) or (not not (The currency of Singapore is the Dollar.))) and ((Neptune is the 8th planet from the Sun.) or (((-17 * 5) >= (17 + -4)) or ((-9 * 8 * -8 * -5) >= (4 + -17))))
B. not not ((((2041 is a leap year.) and (59 is an even number.)) or ((-8 * 3 * 7 * 7) >= (0 * 19))) or (Japan is in South America.) or ((-15 + -4) <= (5 ** 1)))
C. not ((The capital of Denmark is Rome.) and (not not ((11 * -6) < (38 % 10))) and ((A kangaroo has 2 legs.) and ((Mexico is in North America.) or (The capital of Sweden is Ottawa.))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 5023659,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. (((30 % 5) >= (20 + -15)) or (not not (The capital of South Korea is Dublin.)) or ((not not (The chemical symbol for Magnesium is Mg.)) or (The first iPhone was released occurred in 2007.))) and (((A beetle is an insect.) and (There are 29 days in August.)) or (not not (The currency of Singapore is the Dollar.))) and ((Neptune is the 8th planet from the Sun.) or (((-17 * 5) >= (17 + -4)) or ((-9 * 8 * -8 * -5) >= (4 + -17))))\nB. not not ((((2041 is a leap year.) and (59 is an even number.)) or ((-8 * 3 * 7 * 7) >= (0 * 19))) or (Japan is in South America.) or ((-15 + -4) <= (5 ** 1)))\nC. not ((The capital of Denmark is Rome.) and (not not ((11 * -6) < (38 % 10))) and ((A kangaroo has 2 legs.) and ((Mexico is in North America.) or (The capital of Sweden is Ottawa.))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 5023659,
"true_count": 3
},
"seed": 5023659,
"task_id": 605023659,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (not not ((((((-15 * -4) <= (9 * 6 - 7 * 7)) or (2008年奥运会在北京举办。)) or (((-8 + -17) != (-10 * -4 - 9 * 9)) and (2076年是闰年。))) and ((水星是距离太阳第1近的行星。) or ((5 * -10) <= (3 * 8 * 10 * 1))) and ((((7 - -17) <= (-1 + -9)) or (阿根廷的首都是布宜诺斯艾利斯。)) or (not (氮的化学符号是Ca。)))) and (not not (英国的货币是英镑。)))) and (not ((((中国位于亚洲。) and ((埃及的首都是哈瓦那。) or (铁在常温下是固体。))) or ((汞在常温下是液体。) and ((新西兰位于大洋洲。) and ((6 * 6 * -6 * 2) == (12 * -2))))) and (not (not ((3 ** 1) > (-10 * 3))))))
B. not not (not not (not not ((((俄罗斯位于欧洲。) or (蜻蜓是爬行动物。)) and ((磷的化学符号是Fe。) and ((5 * -9 * 2 * 2) >= (-14 - 20)))) and ((((15 + 19) > (13 - 17)) or (匈牙利的货币是福林。)) or (((-14 + 2) < (15 % 7) < (-9 * 4 - 3 * -2)) or ((-12 + -17) <= (-20 * -3)))))))
C. not not ((((钻石在常温下是固体。) and (((第二次世界大战开始发生在1938年。) and (1993年是闰年。)) and ((镁的化学符号是Ne。) or (1924年奥运会在墨尔本举办。)))) and ((not (not not (地球是距离太阳第3近的行星。))) or ((9 * 18) != (-5 - -14)))) and (((not not (not not ((18 + 15) <= (15 * 14)))) or (((火星是距离太阳最近的行星。) or (企鹅是哺乳动物。)) and (not (澳大利亚的货币是澳元。)))) and (not (not (((-13 * 11) > (-11 - 5)) and ((2 * 7) < (2 * 13)))))))
D. not (not ((not not (((海王星是距离太阳第8近的行星。) and (人类只使用了大脑的10%。)) or ((-10 * -6 * 1 * -8) <= (-19 + 2)))) or (not not ((6 + -18) == (4 % 10)))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 16105463,
"true_count": 1
},
"question": "检验这些表达式：\n\nA. (not not ((((((-15 * -4) <= (9 * 6 - 7 * 7)) or (2008年奥运会在北京举办。)) or (((-8 + -17) != (-10 * -4 - 9 * 9)) and (2076年是闰年。))) and ((水星是距离太阳第1近的行星。) or ((5 * -10) <= (3 * 8 * 10 * 1))) and ((((7 - -17) <= (-1 + -9)) or (阿根廷的首都是布宜诺斯艾利斯。)) or (not (氮的化学符号是Ca。)))) and (not not (英国的货币是英镑。)))) and (not ((((中国位于亚洲。) and ((埃及的首都是哈瓦那。) or (铁在常温下是固体。))) or ((汞在常温下是液体。) and ((新西兰位于大洋洲。) and ((6 * 6 * -6 * 2) == (12 * -2))))) and (not (not ((3 ** 1) > (-10 * 3))))))\nB. not not (not not (not not ((((俄罗斯位于欧洲。) or (蜻蜓是爬行动物。)) and ((磷的化学符号是Fe。) and ((5 * -9 * 2 * 2) >= (-14 - 20)))) and ((((15 + 19) > (13 - 17)) or (匈牙利的货币是福林。)) or (((-14 + 2) < (15 % 7) < (-9 * 4 - 3 * -2)) or ((-12 + -17) <= (-20 * -3)))))))\nC. not not ((((钻石在常温下是固体。) and (((第二次世界大战开始发生在1938年。) and (1993年是闰年。)) and ((镁的化学符号是Ne。) or (1924年奥运会在墨尔本举办。)))) and ((not (not not (地球是距离太阳第3近的行星。))) or ((9 * 18) != (-5 - -14)))) and (((not not (not not ((18 + 15) <= (15 * 14)))) or (((火星是距离太阳最近的行星。) or (企鹅是哺乳动物。)) and (not (澳大利亚的货币是澳元。)))) and (not (not (((-13 * 11) > (-11 - 5)) and ((2 * 7) < (2 * 13)))))))\nD. not (not ((not not (((海王星是距离太阳第8近的行星。) and (人类只使用了大脑的10%。)) or ((-10 * -6 * 1 * -8) <= (-19 + 2)))) or (not not ((6 + -18) == (4 % 10)))))\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": 6,
"language": "cn",
"num_options": 4,
"seed": 16105463,
"true_count": 1
},
"seed": 16105463,
"task_id": 616105463,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not ((-15 - -9) > (-10 + -1))
B. (not (((46 % 1) != (16 + 6)) and (Uranus is the 7th planet from the Sun.))) or ((The Moon produces its own light.) and (The currency of Singapore is the Lira.)) or (((9 + 5) < (-14 + 9)) and (not (A shark is an insect.)))
C. (1978 is a leap year.) or ((not not ((4 ** 2) <= (10 * 17) <= (25 % 4))) or ((-12 - 20) != (-11 + 1)))
D. not not (((A bee is a fish.) or ((48 % 10) < (29 % 5) < (3 ** 3))) and ((The chemical symbol for Silver is Ag.) and (The Moon orbits the Earth.)))
E. not not (((-17 - -3) < (2 ** 1) < (5 ** 2)) and (not not (The currency of Nigeria is the Naira.)))
F. (not not (((20 - -7) >= (-3 - 5)) or ((19 - -2) >= (-12 - -1)))) and ((5 - -18) >= (-19 * -9)) and (Uranus is the 7th planet from the Sun.)
G. (The currency of Russia is the Yuan.) and (not not (((-17 - 11) < (-13 * -3)) and ((2 * -2 * -10 * 7) != (25 % 9))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 87408360,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not not ((-15 - -9) > (-10 + -1))\nB. (not (((46 % 1) != (16 + 6)) and (Uranus is the 7th planet from the Sun.))) or ((The Moon produces its own light.) and (The currency of Singapore is the Lira.)) or (((9 + 5) < (-14 + 9)) and (not (A shark is an insect.)))\nC. (1978 is a leap year.) or ((not not ((4 ** 2) <= (10 * 17) <= (25 % 4))) or ((-12 - 20) != (-11 + 1)))\nD. not not (((A bee is a fish.) or ((48 % 10) < (29 % 5) < (3 ** 3))) and ((The chemical symbol for Silver is Ag.) and (The Moon orbits the Earth.)))\nE. not not (((-17 - -3) < (2 ** 1) < (5 ** 2)) and (not not (The currency of Nigeria is the Naira.)))\nF. (not not (((20 - -7) >= (-3 - 5)) or ((19 - -2) >= (-12 - -1)))) and ((5 - -18) >= (-19 * -9)) and (Uranus is the 7th planet from the Sun.)\nG. (The currency of Russia is the Yuan.) and (not not (((-17 - 11) < (-13 * -3)) and ((2 * -2 * -10 * 7) != (25 % 9))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 87408360,
"true_count": 3
},
"seed": 87408360,
"task_id": 687408360,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((((10 + -5) >= (13 + 14)) and ((-5 * 5) <= (18 + -2) <= (-2 * 2 + -2 * -9))) or (not (水星是距离太阳第1近的行星。))) or ((not not (现代奥运会首届举办发生在1896年。)) or (not not (人类只使用了大脑的10%。)))
B. not not (新加坡的首都是阿布贾。)
C. ((not not (水星是距离太阳第1近的行星。)) or (((14 + 15) < (2 ** 3) < (8 * -10 * 0 * 5)) and (鲨鱼是哺乳动物。))) or (((2 ** 3) == (12 * 11)) and ((1 * 4 - 4 * 2) >= (1 ** 1))) or (not ((19 + 0) != (5 ** 3)))
D. ((-6 + 0) > (-6 * 4 - 9 * 10)) and (not ((冰在常温下是固体。) or (摩洛哥位于非洲。)))
E. not not (((韩国的货币是韩元。) or (四月有28天。)) and (氧气在常温下是气体。))
F. (((太平洋是最大的海洋。) or (氧气在常温下是气体。)) and (((17 + 6) < (-17 + 9)) and (巴西位于南美洲。))) and (((8 * 1 + -2 * 4) < (28 % 5)) or (沙特阿拉伯位于亚洲。))
G. ((((6 + -1) >= (2 - 4)) and (地球是距离太阳第4近的行星。)) or (声音无法在真空中传播。)) or ((8小于等于27。) or ((11 - -8) <= (2 + -7) <= (19 + -19)))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,C,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 56335264,
"true_count": 4
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. ((((10 + -5) >= (13 + 14)) and ((-5 * 5) <= (18 + -2) <= (-2 * 2 + -2 * -9))) or (not (水星是距离太阳第1近的行星。))) or ((not not (现代奥运会首届举办发生在1896年。)) or (not not (人类只使用了大脑的10%。)))\nB. not not (新加坡的首都是阿布贾。)\nC. ((not not (水星是距离太阳第1近的行星。)) or (((14 + 15) < (2 ** 3) < (8 * -10 * 0 * 5)) and (鲨鱼是哺乳动物。))) or (((2 ** 3) == (12 * 11)) and ((1 * 4 - 4 * 2) >= (1 ** 1))) or (not ((19 + 0) != (5 ** 3)))\nD. ((-6 + 0) > (-6 * 4 - 9 * 10)) and (not ((冰在常温下是固体。) or (摩洛哥位于非洲。)))\nE. not not (((韩国的货币是韩元。) or (四月有28天。)) and (氧气在常温下是气体。))\nF. (((太平洋是最大的海洋。) or (氧气在常温下是气体。)) and (((17 + 6) < (-17 + 9)) and (巴西位于南美洲。))) and (((8 * 1 + -2 * 4) < (28 % 5)) or (沙特阿拉伯位于亚洲。))\nG. ((((6 + -1) >= (2 - 4)) and (地球是距离太阳第4近的行星。)) or (声音无法在真空中传播。)) or ((8小于等于27。) or ((11 - -8) <= (2 + -7) <= (19 + -19)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 56335264,
"true_count": 4
},
"seed": 56335264,
"task_id": 656335264,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. not not ((加拿大位于北美洲。) or (2011年是闰年。))
B. ((((-4 + -15) != (1 - -5)) or (钙的化学符号是Ca。)) or ((植物通过光合作用产生氧气。) and ((-13 - -13) < (-10 + -14)))) and (((-1 * 4) < (14 + 4)) or (波兰的货币是兹罗提。)) and (not ((水在海平面上的沸点是100摄氏度。) and (第一次世界大战结束发生在1918年。)))
C. (摩洛哥的首都是拉巴特。) or ((12 + -12) != (5 * 17)) or (现代奥运会首届举办发生在1895年。)
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 78233877,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. not not ((加拿大位于北美洲。) or (2011年是闰年。))\nB. ((((-4 + -15) != (1 - -5)) or (钙的化学符号是Ca。)) or ((植物通过光合作用产生氧气。) and ((-13 - -13) < (-10 + -14)))) and (((-1 * 4) < (14 + 4)) or (波兰的货币是兹罗提。)) and (not ((水在海平面上的沸点是100摄氏度。) and (第一次世界大战结束发生在1918年。)))\nC. (摩洛哥的首都是拉巴特。) or ((12 + -12) != (5 * 17)) or (现代奥运会首届举办发生在1895年。)\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 78233877,
"true_count": 2
},
"seed": 78233877,
"task_id": 678233877,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((马有4条腿。) and (1980年奥运会在莫斯科举办。)) and ((-4 + -10) <= (-10 * -7 + 0 * -10))
B. not ((-12 * 20) != (-20 + 18))
C. ((-7 + -10) != (19 - 9)) or (not not ((1 + 2) >= (9 - 18)))
D. ((匈牙利的货币是福林。) or ((14 * -7) <= (8 - -7))) or (钙的化学符号是Cu。)
E. not (水蒸气在常温下是气体。)
F. (not (鲨鱼是哺乳动物。)) and ((蜥蜴是昆虫。) or (1976年奥运会在莫斯科举办。))
G. ((0 + -11) <= (-12 * -13)) and ((月球绕地球运转。) or ((7 - 10) == (-5 - -14)))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,C,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 93710758,
"true_count": 4
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. ((马有4条腿。) and (1980年奥运会在莫斯科举办。)) and ((-4 + -10) <= (-10 * -7 + 0 * -10))\nB. not ((-12 * 20) != (-20 + 18))\nC. ((-7 + -10) != (19 - 9)) or (not not ((1 + 2) >= (9 - 18)))\nD. ((匈牙利的货币是福林。) or ((14 * -7) <= (8 - -7))) or (钙的化学符号是Cu。)\nE. not (水蒸气在常温下是气体。)\nF. (not (鲨鱼是哺乳动物。)) and ((蜥蜴是昆虫。) or (1976年奥运会在莫斯科举办。))\nG. ((0 + -11) <= (-12 * -13)) and ((月球绕地球运转。) or ((7 - 10) == (-5 - -14)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 93710758,
"true_count": 4
},
"seed": 93710758,
"task_id": 693710758,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not not (((not (Sound travels faster in a vacuum.)) and ((-16 * -9) < (0 - -1))) and (not not (Japan is in Europe.)) and (The Soviet Union dissolved occurred in 1991.))) and ((((The 1992 Olympics were held in Barcelona.) or ((30 is less than or equal to 96.) and ((15 + 9) <= (12 % 9)))) or ((Uranus is the 7th planet from the Sun.) or ((19 % 5) >= (37 % 8))) or ((43 % 4) == (27 % 4))) or (not not ((6 + -15) <= (10 * -19))))
B. not not (not not (((-20 + -10) <= (-18 * 15)) or (not not ((The 1964 Olympics were held in Atlanta.) and ((20 + -6) < (12 % 5))))))
C. not not ((not ((not not (The capital of Belgium is Caracas.)) and (not not ((34 % 9) == (0 - -16))))) or (not not ((-5 * -19) < (-6 * 1) < (-11 * -12))))
D. (not not (((((5 - 12) == (-8 - 5)) or (Kenya is in Africa.)) and ((6 - 6) < (1 % 5))) and (The 1896 Olympics were held in Athens.) and (((Saturn is the 6th planet from the Sun.) and ((-5 + -1) > (3 ** 3))) and (((5 - 8) > (1 ** 2)) or (The chemical symbol for Potassium is K.))))) or ((not ((-8 * -6 + 3 * 5) != (10 - 4))) or (((-16 * 4) >= (3 * 7)) or (not ((14 + -19) <= (4 ** 2)))))
E. not not ((not ((The chemical symbol for Sodium is Na.) or (not not (Jupiter is the 8th planet from the Sun.)))) and (not ((1902 is a leap year.) and ((Egypt is in Africa.) and ((7 * 19) != (17 % 7))))))
F. ((((2 - -15) <= (1 ** 2)) and (The 1908 Olympics were held in London.)) or (not ((20 % 6) < (6 + 8) < (18 - -5)))) and (not (((((-5 * 6 * -1 * -1) == (5 + 10)) or ((44 % 7) < (4 % 8))) and (The human body has 206 bones.)) and ((not ((6 * -17) <= (4 ** 3))) and ((The chemical symbol for Helium is Au.) and (There are 30 days in April.)))))
G. not (((93 is divisible by 9.) or (116 is a Fibonacci number.)) or (((6 * -4 - 10 * -4) == (1 ** 2)) and (((A cow has 6 legs.) or ((-20 + -6) > (-19 - -14))) and ((Copper is a solid at room temperature.) and (A lobster has 8 legs.)))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 45734964,
"true_count": 2
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (not not (((not (Sound travels faster in a vacuum.)) and ((-16 * -9) < (0 - -1))) and (not not (Japan is in Europe.)) and (The Soviet Union dissolved occurred in 1991.))) and ((((The 1992 Olympics were held in Barcelona.) or ((30 is less than or equal to 96.) and ((15 + 9) <= (12 % 9)))) or ((Uranus is the 7th planet from the Sun.) or ((19 % 5) >= (37 % 8))) or ((43 % 4) == (27 % 4))) or (not not ((6 + -15) <= (10 * -19))))\nB. not not (not not (((-20 + -10) <= (-18 * 15)) or (not not ((The 1964 Olympics were held in Atlanta.) and ((20 + -6) < (12 % 5))))))\nC. not not ((not ((not not (The capital of Belgium is Caracas.)) and (not not ((34 % 9) == (0 - -16))))) or (not not ((-5 * -19) < (-6 * 1) < (-11 * -12))))\nD. (not not (((((5 - 12) == (-8 - 5)) or (Kenya is in Africa.)) and ((6 - 6) < (1 % 5))) and (The 1896 Olympics were held in Athens.) and (((Saturn is the 6th planet from the Sun.) and ((-5 + -1) > (3 ** 3))) and (((5 - 8) > (1 ** 2)) or (The chemical symbol for Potassium is K.))))) or ((not ((-8 * -6 + 3 * 5) != (10 - 4))) or (((-16 * 4) >= (3 * 7)) or (not ((14 + -19) <= (4 ** 2)))))\nE. not not ((not ((The chemical symbol for Sodium is Na.) or (not not (Jupiter is the 8th planet from the Sun.)))) and (not ((1902 is a leap year.) and ((Egypt is in Africa.) and ((7 * 19) != (17 % 7))))))\nF. ((((2 - -15) <= (1 ** 2)) and (The 1908 Olympics were held in London.)) or (not ((20 % 6) < (6 + 8) < (18 - -5)))) and (not (((((-5 * 6 * -1 * -1) == (5 + 10)) or ((44 % 7) < (4 % 8))) and (The human body has 206 bones.)) and ((not ((6 * -17) <= (4 ** 3))) and ((The chemical symbol for Helium is Au.) and (There are 30 days in April.)))))\nG. not (((93 is divisible by 9.) or (116 is a Fibonacci number.)) or (((6 * -4 - 10 * -4) == (1 ** 2)) and (((A cow has 6 legs.) or ((-20 + -6) > (-19 - -14))) and ((Copper is a solid at room temperature.) and (A lobster has 8 legs.)))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 45734964,
"true_count": 2
},
"seed": 45734964,
"task_id": 645734964,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((十一月有30天。) and ((not (日本的货币是瑞士法郎。)) or (not not (摩洛哥的首都是拉巴特。)))) or ((not ((莱特兄弟首次飞行发生在1908年。) or ((13 + 15) != (-10 * 10 + -1 * 5)))) or (not not ((澳大利亚位于大洋洲。) or ((1 * 10 + 1 * 1) == (5 ** 3)))))
B. not (((((28 % 5) < (1 + -7)) or ((1 ** 2) >= (-20 * 1))) or ((火星是距离太阳第2近的行星。) and (德国位于欧洲。))) and ((-1 * -19) < (2 * 3 + 1 * 10) < (34 % 8)))
C. not not (((4 ** 1) <= (-14 + 16)) or ((not not ((-8 * -10 * 1 * 0) > (8 * -9 - 2 * -5))) or (((-14 * -7) == (-12 + -19)) or (硫的化学符号是S。))))
D. ((((12 + -8) != (33 % 3)) or ((1976年奥运会在蒙特利尔举办。) and (人类首次登月发生在1970年。))) or ((镁的化学符号是Cu。) or ((阿根廷的首都是布宜诺斯艾利斯。) and ((-14 - -15) < (4 ** 2))))) or (not (not ((银的化学符号是Ag。) and ((-17 + -3) >= (-8 - 15)))))
E. (((((13 - 5) == (-7 * -10 - 9 * -1)) and (第二次世界大战开始发生在1939年。)) or (not not (蜘蛛有8条腿。))) and (((-6 + 13) != (5 ** 3)) or (十月有29天。)) and (not (((-18 + -8) == (36 % 1)) or (丹麦的货币是克朗。)))) or (((not not (1991年是闰年。)) or ((南非位于非洲。) and ((-6 * 1 - 7 * -8) <= (8 + 12)))) and ((((4 * 4 * 6 * 8) > (14 * 0)) and (智利的首都是圣地亚哥。)) or (not (铝的化学符号是Ag。))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 95997361,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. ((十一月有30天。) and ((not (日本的货币是瑞士法郎。)) or (not not (摩洛哥的首都是拉巴特。)))) or ((not ((莱特兄弟首次飞行发生在1908年。) or ((13 + 15) != (-10 * 10 + -1 * 5)))) or (not not ((澳大利亚位于大洋洲。) or ((1 * 10 + 1 * 1) == (5 ** 3)))))\nB. not (((((28 % 5) < (1 + -7)) or ((1 ** 2) >= (-20 * 1))) or ((火星是距离太阳第2近的行星。) and (德国位于欧洲。))) and ((-1 * -19) < (2 * 3 + 1 * 10) < (34 % 8)))\nC. not not (((4 ** 1) <= (-14 + 16)) or ((not not ((-8 * -10 * 1 * 0) > (8 * -9 - 2 * -5))) or (((-14 * -7) == (-12 + -19)) or (硫的化学符号是S。))))\nD. ((((12 + -8) != (33 % 3)) or ((1976年奥运会在蒙特利尔举办。) and (人类首次登月发生在1970年。))) or ((镁的化学符号是Cu。) or ((阿根廷的首都是布宜诺斯艾利斯。) and ((-14 - -15) < (4 ** 2))))) or (not (not ((银的化学符号是Ag。) and ((-17 + -3) >= (-8 - 15)))))\nE. (((((13 - 5) == (-7 * -10 - 9 * -1)) and (第二次世界大战开始发生在1939年。)) or (not not (蜘蛛有8条腿。))) and (((-6 + 13) != (5 ** 3)) or (十月有29天。)) and (not (((-18 + -8) == (36 % 1)) or (丹麦的货币是克朗。)))) or (((not not (1991年是闰年。)) or ((南非位于非洲。) and ((-6 * 1 - 7 * -8) <= (8 + 12)))) and ((((4 * 4 * 6 * 8) > (14 * 0)) and (智利的首都是圣地亚哥。)) or (not (铝的化学符号是Ag。))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 95997361,
"true_count": 4
},
"seed": 95997361,
"task_id": 695997361,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not (南极洲是最冷的大陆。)
B. (((水星是距离太阳第7近的行星。) and ((28 % 10) <= (11 * -11) <= (-12 - 8))) and ((2016年奥运会在里约热内卢举办。) and (144是完全平方数。))) or (((-2 + 17) > (8 * 8 - -6 * -9)) and (11是偶数。)) or (1959年是闰年。)
C. ((15 * -17) <= (3 ** 2)) and (not ((-3 + -18) <= (9 - -13))) and ((硅的化学符号是Al。) or (((-3 * 4 - -2 * 8) < (-13 - 6)) or ((-18 + 13) >= (5 ** 3))))
D. not (哥伦比亚的首都是布达佩斯。)
E. (((三月有31天。) and (56是质数。)) and (not (2016年奥运会在雅典举办。))) or ((((10 - -17) < (-8 + 13) < (-17 * -10)) or (美国的货币是美元。)) or (not not ((20 + 20) == (5 + -17))))
F. not (not ((韩国的货币是克朗。) or (法国大革命开始发生在1789年。)))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
"game_data": {
"answer": "D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 69244983,
"true_count": 3
},
"question": "给定以下布尔表达式：\n\nA. not (南极洲是最冷的大陆。)\nB. (((水星是距离太阳第7近的行星。) and ((28 % 10) <= (11 * -11) <= (-12 - 8))) and ((2016年奥运会在里约热内卢举办。) and (144是完全平方数。))) or (((-2 + 17) > (8 * 8 - -6 * -9)) and (11是偶数。)) or (1959年是闰年。)\nC. ((15 * -17) <= (3 ** 2)) and (not ((-3 + -18) <= (9 - -13))) and ((硅的化学符号是Al。) or (((-3 * 4 - -2 * 8) < (-13 - 6)) or ((-18 + 13) >= (5 ** 3))))\nD. not (哥伦比亚的首都是布达佩斯。)\nE. (((三月有31天。) and (56是质数。)) and (not (2016年奥运会在雅典举办。))) or ((((10 - -17) < (-8 + 13) < (-17 * -10)) or (美国的货币是美元。)) or (not not ((20 + 20) == (5 + -17))))\nF. not (not ((韩国的货币是克朗。) or (法国大革命开始发生在1789年。)))\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": 3,
"language": "cn",
"num_options": 6,
"seed": 69244983,
"true_count": 3
},
"seed": 69244983,
"task_id": 669244983,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not ((not not ((-10 * 3 * 3 * -4) >= (-13 + -9))) or ((-7 * 12) < (13 % 7) < (3 * -5 - 8 * 7)) or ((not ((2 - 3) <= (15 - 12))) and ((14 + -12) != (2 ** 1))))
B. not (not (((Jupiter is the 5th planet from the Sun.) and ((13 + 17) < (20 * 13))) and (not not ((10 * -10 * 9 * 2) <= (-3 * -15)))))
C. (not not ((not not (A carp is a bird.)) and ((The chemical symbol for Lead is Co.) and (Wood is a liquid at room temperature.)))) or (((There are 29 days in November.) or (The capital of Canada is Ottawa.)) or (((3 * -4 - -5 * 1) >= (31 % 3)) or (Water is a liquid at room temperature.))) or (not not (((5 * 4) < (43 % 10) < (-14 * -20)) and ((Mars is the 8th planet from the Sun.) or (Iron is a solid at room temperature.))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 30906305,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not ((not not ((-10 * 3 * 3 * -4) >= (-13 + -9))) or ((-7 * 12) < (13 % 7) < (3 * -5 - 8 * 7)) or ((not ((2 - 3) <= (15 - 12))) and ((14 + -12) != (2 ** 1))))\nB. not (not (((Jupiter is the 5th planet from the Sun.) and ((13 + 17) < (20 * 13))) and (not not ((10 * -10 * 9 * 2) <= (-3 * -15)))))\nC. (not not ((not not (A carp is a bird.)) and ((The chemical symbol for Lead is Co.) and (Wood is a liquid at room temperature.)))) or (((There are 29 days in November.) or (The capital of Canada is Ottawa.)) or (((3 * -4 - -5 * 1) >= (31 % 3)) or (Water is a liquid at room temperature.))) or (not not (((5 * 4) < (43 % 10) < (-14 * -20)) and ((Mars is the 8th planet from the Sun.) or (Iron is a solid at room temperature.))))\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": 3,
"seed": 30906305,
"true_count": 3
},
"seed": 30906305,
"task_id": 630906305,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (not not (not (not not (A fly is a reptile.)))) and ((((-17 * 15) >= (5 ** 2)) or ((-13 * -19) < (-1 + -4) < (-14 + 5))) and (Spain is in Asia.)) and (not not (((-3 + 7) != (-5 * 2 - -4 * 8)) or ((0 * -6 - 8 * 8) <= (-19 + 5) <= (1 - -19))))
B. ((World War II began occurred in 1939.) or (not not (not ((-14 * -8) > (-5 * 12))))) or ((not (The Great Fire of London occurred in 1666.)) and (((-1 - -10) != (34 % 8)) or (Nitrogen is a gas at room temperature.))) or (((A beetle is an insect.) or (not (The 1988 Olympics were held in Rio de Janeiro.))) and (not (((-19 + 17) <= (-5 * 4 - -7 * -2)) or ((6 * -13) < (-9 * 10 - -9 * -10)))))
C. ((The currency of Malaysia is the Won.) and (The chemical symbol for Tin is Sn.)) or ((not not (not not ((-13 - -4) != (-4 * 2 + 3 * -5)))) and (((The currency of Canada is the Krone.) and (The currency of Malaysia is the Krona.)) and (Iron is a liquid at room temperature.)))
D. ((((30 is a prime number.) and (A ostrich is a mammal.)) and ((Electricity flows faster than light.) and (The chemical symbol for Chromium is Au.))) and (((The 1988 Olympics were held in Seoul.) and (A ostrich is a fish.)) or (not not (The Moon orbits the Earth.)))) or ((The currency of Australia is the Dollar.) or (not ((8 * 9 + 7 * -10) == (16 * 9))) or (not not (((7 + 19) <= (-6 - -2) <= (-12 - -18)) or (India is in Asia.))))
E. not (((Helium is a gas at room temperature.) and ((The 1960 Olympics were held in Rome.) and ((2 * 9 * 1 * -5) <= (6 * 17)))) and (Silver is a solid at room temperature.))
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": 4,
"language": "en",
"num_options": 5,
"seed": 94449786,
"true_count": 2
},
"question": "Given the following boolean expressions:\n\nA. (not not (not (not not (A fly is a reptile.)))) and ((((-17 * 15) >= (5 ** 2)) or ((-13 * -19) < (-1 + -4) < (-14 + 5))) and (Spain is in Asia.)) and (not not (((-3 + 7) != (-5 * 2 - -4 * 8)) or ((0 * -6 - 8 * 8) <= (-19 + 5) <= (1 - -19))))\nB. ((World War II began occurred in 1939.) or (not not (not ((-14 * -8) > (-5 * 12))))) or ((not (The Great Fire of London occurred in 1666.)) and (((-1 - -10) != (34 % 8)) or (Nitrogen is a gas at room temperature.))) or (((A beetle is an insect.) or (not (The 1988 Olympics were held in Rio de Janeiro.))) and (not (((-19 + 17) <= (-5 * 4 - -7 * -2)) or ((6 * -13) < (-9 * 10 - -9 * -10)))))\nC. ((The currency of Malaysia is the Won.) and (The chemical symbol for Tin is Sn.)) or ((not not (not not ((-13 - -4) != (-4 * 2 + 3 * -5)))) and (((The currency of Canada is the Krone.) and (The currency of Malaysia is the Krona.)) and (Iron is a liquid at room temperature.)))\nD. ((((30 is a prime number.) and (A ostrich is a mammal.)) and ((Electricity flows faster than light.) and (The chemical symbol for Chromium is Au.))) and (((The 1988 Olympics were held in Seoul.) and (A ostrich is a fish.)) or (not not (The Moon orbits the Earth.)))) or ((The currency of Australia is the Dollar.) or (not ((8 * 9 + 7 * -10) == (16 * 9))) or (not not (((7 + 19) <= (-6 - -2) <= (-12 - -18)) or (India is in Asia.))))\nE. not (((Helium is a gas at room temperature.) and ((The 1960 Olympics were held in Rome.) and ((2 * 9 * 1 * -5) <= (6 * 17)))) and (Silver is a solid at room temperature.))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 94449786,
"true_count": 2
},
"seed": 94449786,
"task_id": 694449786,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (0 - 8) != (4 * -15)
B. ((氧的化学符号是O。) or (中国位于亚洲。)) or (((12 * 3) >= (3 ** 2)) and (21是质数。))
C. (蚂蚁是爬行动物。) and ((174是偶数。) or (38大于86。))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 36088513,
"true_count": 2
},
"question": "评估以下每个表达式：\n\nA. (0 - 8) != (4 * -15)\nB. ((氧的化学符号是O。) or (中国位于亚洲。)) or (((12 * 3) >= (3 ** 2)) and (21是质数。))\nC. (蚂蚁是爬行动物。) and ((174是偶数。) or (38大于86。))\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": 3,
"seed": 36088513,
"true_count": 2
},
"seed": 36088513,
"task_id": 636088513,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. (not ((17 + -6) <= (5 * -5))) and ((The currency of United States is the Dollar.) and ((not (Jupiter is the 5th planet from the Sun.)) or ((-9 + 14) <= (14 - 12) <= (9 - -1))))
B. ((((17 - -13) >= (-13 + -16)) or (Electricity flows faster than light.)) and (The 1936 Olympics were held in London.) and (((4 - -16) >= (12 + -7)) or (not not ((7 * -5 + 3 * -9) > (-19 - -5))))) or (((((12 * 3) <= (18 - 12) <= (-1 * -7 - 0 * -7)) or ((13 - -16) != (-5 + 11))) or ((-5 + 15) <= (5 ** 1))) and (((2 * -8 + 3 * -5) > (-10 - 5)) or ((The first iPhone was released occurred in 2007.) and (The 1984 Olympics were held in Antwerp.))))
C. not ((not (((4 * -1 * -5 * 10) <= (6 * -12) <= (16 - -8)) or (The 1996 Olympics were held in Amsterdam.))) and (not not (not ((0 * -1 + 2 * -3) < (1 * -9 - 2 * -2)))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 75660882,
"true_count": 1
},
"question": "Examine these expressions:\n\nA. (not ((17 + -6) <= (5 * -5))) and ((The currency of United States is the Dollar.) and ((not (Jupiter is the 5th planet from the Sun.)) or ((-9 + 14) <= (14 - 12) <= (9 - -1))))\nB. ((((17 - -13) >= (-13 + -16)) or (Electricity flows faster than light.)) and (The 1936 Olympics were held in London.) and (((4 - -16) >= (12 + -7)) or (not not ((7 * -5 + 3 * -9) > (-19 - -5))))) or (((((12 * 3) <= (18 - 12) <= (-1 * -7 - 0 * -7)) or ((13 - -16) != (-5 + 11))) or ((-5 + 15) <= (5 ** 1))) and (((2 * -8 + 3 * -5) > (-10 - 5)) or ((The first iPhone was released occurred in 2007.) and (The 1984 Olympics were held in Antwerp.))))\nC. not ((not (((4 * -1 * -5 * 10) <= (6 * -12) <= (16 - -8)) or (The 1996 Olympics were held in Amsterdam.))) and (not not (not ((0 * -1 + 2 * -3) < (1 * -9 - 2 * -2)))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 75660882,
"true_count": 1
},
"seed": 75660882,
"task_id": 675660882,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (((4 * -10 + 8 * 9) < (3 ** 1)) and ((44 % 3) > (-7 * -1 - -7 * -2)) and (((4 ** 3) < (9 * -5 + -3 * 2) < (0 + 12)) and ((Neptune is the 8th planet from the Sun.) or (Oxygen is a gas at room temperature.)))) or (((-6 * 1 - 8 * 6) < (10 - 11)) or ((-2 * 1 * 6 * 5) < (-14 - -12) < (1 * 7 - -5 * 5))) or ((((-12 - -3) > (5 ** 1)) and ((Saturn is the 2nd planet from the Sun.) or (A elephant has 4 legs.))) and (A lizard is a mammal.))
B. ((not ((There are 30 days in February.) or (World War II ended occurred in 1945.))) and (((6 + -20) < (5 ** 3)) and ((5 + -18) <= (-6 * 2))) and ((-12 + 0) < (-9 - -12))) and (not not ((not not ((1 ** 3) < (8 * 9 + 3 * -1))) or (((13 - 0) >= (-7 * -8)) and (A sparrow is a bird.))))
C. (not (A cockroach is a bird.)) or (not ((((-20 + -20) >= (-17 + 8)) or (The chemical symbol for Carbon is C.)) and ((There are 31 days in March.) or ((19 * 3) != (38 % 8)))))
D. ((((A bird has 2 legs.) and ((3 ** 2) != (15 - -17))) or (((-11 - 20) == (0 * 9 * 5 * -1)) or ((-4 * 13) == (3 + -1)))) and (((17 + -4) > (7 * -4 * -9 * -4)) and (not (There are 31 days in January.)))) or ((A fish has 2 legs.) and (not (((-13 * 16) != (14 - -10)) or ((17 + -10) <= (28 % 3)))))
E. not not (not (((-11 * -2) == (16 * -9)) or (World War I began occurred in 1914.)))
F. not ((A butterfly has 0 legs.) or (not (not not ((4 ** 1) > (-7 - 9)))))
G. (not ((((-6 * 6 * -8 * -10) <= (-3 * -10 * -6 * 4) <= (18 - -5)) and ((1 * -6 * 1 * 9) > (-8 * -5 + 2 * -4))) or (((13 + -20) >= (14 - -1)) or ((4 % 6) <= (-10 * -9 * 7 * 9))))) or (((-15 + 12) <= (1 % 5)) or ((The currency of European Union is the Euro.) or (not ((-3 + 14) <= (4 * 2 + 5 * 8)))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,C,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 77366009,
"true_count": 4
},
"question": "Given the following boolean expressions:\n\nA. (((4 * -10 + 8 * 9) < (3 ** 1)) and ((44 % 3) > (-7 * -1 - -7 * -2)) and (((4 ** 3) < (9 * -5 + -3 * 2) < (0 + 12)) and ((Neptune is the 8th planet from the Sun.) or (Oxygen is a gas at room temperature.)))) or (((-6 * 1 - 8 * 6) < (10 - 11)) or ((-2 * 1 * 6 * 5) < (-14 - -12) < (1 * 7 - -5 * 5))) or ((((-12 - -3) > (5 ** 1)) and ((Saturn is the 2nd planet from the Sun.) or (A elephant has 4 legs.))) and (A lizard is a mammal.))\nB. ((not ((There are 30 days in February.) or (World War II ended occurred in 1945.))) and (((6 + -20) < (5 ** 3)) and ((5 + -18) <= (-6 * 2))) and ((-12 + 0) < (-9 - -12))) and (not not ((not not ((1 ** 3) < (8 * 9 + 3 * -1))) or (((13 - 0) >= (-7 * -8)) and (A sparrow is a bird.))))\nC. (not (A cockroach is a bird.)) or (not ((((-20 + -20) >= (-17 + 8)) or (The chemical symbol for Carbon is C.)) and ((There are 31 days in March.) or ((19 * 3) != (38 % 8)))))\nD. ((((A bird has 2 legs.) and ((3 ** 2) != (15 - -17))) or (((-11 - 20) == (0 * 9 * 5 * -1)) or ((-4 * 13) == (3 + -1)))) and (((17 + -4) > (7 * -4 * -9 * -4)) and (not (There are 31 days in January.)))) or ((A fish has 2 legs.) and (not (((-13 * 16) != (14 - -10)) or ((17 + -10) <= (28 % 3)))))\nE. not not (not (((-11 * -2) == (16 * -9)) or (World War I began occurred in 1914.)))\nF. not ((A butterfly has 0 legs.) or (not (not not ((4 ** 1) > (-7 - 9)))))\nG. (not ((((-6 * 6 * -8 * -10) <= (-3 * -10 * -6 * 4) <= (18 - -5)) and ((1 * -6 * 1 * 9) > (-8 * -5 + 2 * -4))) or (((13 + -20) >= (14 - -1)) or ((4 % 6) <= (-10 * -9 * 7 * 9))))) or (((-15 + 12) <= (1 % 5)) or ((The currency of European Union is the Euro.) or (not ((-3 + 14) <= (4 * 2 + 5 * 8)))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 77366009,
"true_count": 4
},
"seed": 77366009,
"task_id": 677366009,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not not (((11 - 9) >= (14 * 1)) and (not (1975年是闰年。)))
B. ((16 * 6) > (7 * -9 - -3 * -10)) and (韩国位于南极洲。)
C. ((((9 % 6) >= (4 ** 2)) or ((-1 + -14) <= (5 ** 2))) or (not (地球是距离太阳第4近的行星。))) and (袋鼠是哺乳动物。)
D. (瑞典的货币是索尔。) and ((((-14 - -8) >= (3 ** 3)) and ((1 ** 2) == (42 % 9))) or (土耳其的首都是加拉加斯。))
E. ((8 * 9 + -10 * 2) >= (2 - -19)) and (((5 ** 1) >= (-16 - 6)) and (not not ((-19 * -11) > (-19 * -10))))
F. (((2 * -10 - 0 * 10) > (-6 + -1)) or ((7 * 7 * -4 * -4) < (4 - 4))) or ((马有4条腿。) or (声音在真空中传播更快。)) or (not not (((18 * -20) > (-2 + 15)) or (氧气在常温下是气体。)))
G. ((not not (加拿大的首都是柏林。)) and (not not ((-10 * -10 * -7 * -4) <= (-17 - 8)))) or ((not (1984年奥运会在圣路易斯举办。)) or (((-7 * 2 + 0 * 10) < (19 + 7) < (-8 * 0 - 3 * -7)) or (1928年奥运会在阿姆斯特丹举办。)))
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": "C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 83298765,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. not not (((11 - 9) >= (14 * 1)) and (not (1975年是闰年。)))\nB. ((16 * 6) > (7 * -9 - -3 * -10)) and (韩国位于南极洲。)\nC. ((((9 % 6) >= (4 ** 2)) or ((-1 + -14) <= (5 ** 2))) or (not (地球是距离太阳第4近的行星。))) and (袋鼠是哺乳动物。)\nD. (瑞典的货币是索尔。) and ((((-14 - -8) >= (3 ** 3)) and ((1 ** 2) == (42 % 9))) or (土耳其的首都是加拉加斯。))\nE. ((8 * 9 + -10 * 2) >= (2 - -19)) and (((5 ** 1) >= (-16 - 6)) and (not not ((-19 * -11) > (-19 * -10))))\nF. (((2 * -10 - 0 * 10) > (-6 + -1)) or ((7 * 7 * -4 * -4) < (4 - 4))) or ((马有4条腿。) or (声音在真空中传播更快。)) or (not not (((18 * -20) > (-2 + 15)) or (氧气在常温下是气体。)))\nG. ((not not (加拿大的首都是柏林。)) and (not not ((-10 * -10 * -7 * -4) <= (-17 - 8)))) or ((not (1984年奥运会在圣路易斯举办。)) or (((-7 * 2 + 0 * 10) < (19 + 7) < (-8 * 0 - 3 * -7)) or (1928年奥运会在阿姆斯特丹举办。)))\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": 3,
"language": "cn",
"num_options": 7,
"seed": 83298765,
"true_count": 4
},
"seed": 83298765,
"task_id": 683298765,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not (((水星是距离太阳第1近的行星。) or (美国宣布独立发生在1774年。)) or ((美国宣布独立发生在1776年。) and (五月有31天。)))
B. (not ((第一部iPhone发布发生在2007年。) and ((20 + -10) <= (21 % 5)))) and (((15 % 6) == (-12 - -5)) and (((-1 * -5) > (13 - -8)) and (乌龟是爬行动物。)))
C. (((秘鲁的货币是索尔。) and ((5 + -7) > (2 ** 1))) and (法国大革命开始发生在1787年。)) or ((埃及的首都是开罗。) and ((-6 * -8 + 10 * -1) == (-4 * 8 + -10 * 5))) or (not ((哥伦比亚的首都是伯尔尼。) or (南极洲是最冷的大陆。)))
D. (not (伦敦大火发生在1671年。)) and (not not ((中国的货币是比索。) and (2074年是闰年。)))
E. not not ((not (光速约为每秒30万公里。)) and ((6 % 10) > (18 + 11)))
F. ((氮气在常温下是气体。) or (((1 ** 1) <= (2 - 19)) or ((1 * 9) <= (-9 * -1 + -7 * 4) <= (3 ** 2)))) and (not not ((3 + 9) <= (8 * 6 * -4 * 6) <= (33 % 2)))
G. not not (尼日利亚的货币是卢比。)
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 6969827,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. not not (((水星是距离太阳第1近的行星。) or (美国宣布独立发生在1774年。)) or ((美国宣布独立发生在1776年。) and (五月有31天。)))\nB. (not ((第一部iPhone发布发生在2007年。) and ((20 + -10) <= (21 % 5)))) and (((15 % 6) == (-12 - -5)) and (((-1 * -5) > (13 - -8)) and (乌龟是爬行动物。)))\nC. (((秘鲁的货币是索尔。) and ((5 + -7) > (2 ** 1))) and (法国大革命开始发生在1787年。)) or ((埃及的首都是开罗。) and ((-6 * -8 + 10 * -1) == (-4 * 8 + -10 * 5))) or (not ((哥伦比亚的首都是伯尔尼。) or (南极洲是最冷的大陆。)))\nD. (not (伦敦大火发生在1671年。)) and (not not ((中国的货币是比索。) and (2074年是闰年。)))\nE. not not ((not (光速约为每秒30万公里。)) and ((6 % 10) > (18 + 11)))\nF. ((氮气在常温下是气体。) or (((1 ** 1) <= (2 - 19)) or ((1 * 9) <= (-9 * -1 + -7 * 4) <= (3 ** 2)))) and (not not ((3 + 9) <= (8 * 6 * -4 * 6) <= (33 % 2)))\nG. not not (尼日利亚的货币是卢比。)\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": 7,
"seed": 6969827,
"true_count": 1
},
"seed": 6969827,
"task_id": 606969827,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not not ((螃蟹有10条腿。) and (not not ((地球是距离太阳第3近的行星。) or ((6 * -14) <= (-15 + 11)))))
B. ((not (((-3 - 2) < (-16 + -12) < (-7 + 13)) and (18是偶数。))) and (((-6 * 8 - 3 * 6) <= (11 * 20)) or (六月有30天。)) and ((氢的化学符号是K。) or ((第一次世界大战结束发生在1920年。) or ((-14 * 12) != (-6 - -17))))) and ((((海王星是距离太阳第7近的行星。) or (蜘蛛有100条腿。)) and ((-3 * -6 * 6 * -9) != (-3 * -9))) and (法国大革命开始发生在1788年。) and (人类每只手有五个手指。))
C. (((59小于等于74。) and ((8 * -3 * 9 * 7) != (4 * 2 - -6 * 10))) and ((-17 + 12) < (5 ** 2))) or ((1 ** 3) < (-10 * 10 - 4 * 6)) or (not not ((((1 * -7 * -2 * -4) >= (6 - -20)) or (氮的化学符号是Ti。)) and ((鱼有10条腿。) or (三月有31天。))))
D. (((((5 ** 3) < (4 ** 2)) or ((-1 * -4) >= (14 - -11))) or (not not (1932年奥运会在洛杉矶举办。))) or (柏林墙倒塌发生在1984年。) or ((-10 + 6) < (5 + 3) < (20 - 12))) and (not ((not (氧气对人类生存是必需的。)) and (((-20 - -8) < (19 * -17)) or ((6 - 1) > (-16 - -16)))))
E. not (((3 ** 3) < (20 + 13) < (2 - 1)) or (((1 * 2 + -7 * -8) < (2 * -5 + 0 * 5) < (2 ** 3)) or (第一次世界大战结束发生在1913年。)) or (not not ((20 + 11) < (1 ** 1))))
F. ((((捷克的首都是布拉格。) and (墨西哥的首都是墨西哥城。)) or ((地球是距离太阳第3近的行星。) and (196的平方根是14。))) and (硫的化学符号是Cl。)) or (金的化学符号是Ne。) or ((not (not not (酒精在常温下是液体。))) and (894是斐波那契数。) and (not not ((第一次世界大战结束发生在1908年。) and (氯的化学符号是Zn。))))
G. not not (((((1 * 9 + 6 * -9) < (-18 * 6)) or ((14 - 6) > (17 + -3))) or ((苏联解体发生在1992年。) and ((20 * 14) != (2 ** 3)))) and ((not not (32是质数。)) and ((植物通过光合作用产生氧气。) or (月球绕地球运转。))))
H. ((((7 + -13) > (34 % 8)) or ((-7 * 10) > (4 ** 2))) or (not not ((银的化学符号是Pt。) or (1932年奥运会在阿姆斯特丹举办。)))) and (not (not ((-5 * -6 * 3 * -3) < (10 % 1)))) and (((387是完全平方数。) and (南极洲是最冷的大陆。)) or ((美国的货币是比索。) or (2004年奥运会在阿姆斯特丹举办。)) or (((瓢虫是爬行动物。) or (人类有三个肺。)) and (第一部iPhone发布发生在2012年。)))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 8,
"seed": 4297960,
"true_count": 4
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not not ((螃蟹有10条腿。) and (not not ((地球是距离太阳第3近的行星。) or ((6 * -14) <= (-15 + 11)))))\nB. ((not (((-3 - 2) < (-16 + -12) < (-7 + 13)) and (18是偶数。))) and (((-6 * 8 - 3 * 6) <= (11 * 20)) or (六月有30天。)) and ((氢的化学符号是K。) or ((第一次世界大战结束发生在1920年。) or ((-14 * 12) != (-6 - -17))))) and ((((海王星是距离太阳第7近的行星。) or (蜘蛛有100条腿。)) and ((-3 * -6 * 6 * -9) != (-3 * -9))) and (法国大革命开始发生在1788年。) and (人类每只手有五个手指。))\nC. (((59小于等于74。) and ((8 * -3 * 9 * 7) != (4 * 2 - -6 * 10))) and ((-17 + 12) < (5 ** 2))) or ((1 ** 3) < (-10 * 10 - 4 * 6)) or (not not ((((1 * -7 * -2 * -4) >= (6 - -20)) or (氮的化学符号是Ti。)) and ((鱼有10条腿。) or (三月有31天。))))\nD. (((((5 ** 3) < (4 ** 2)) or ((-1 * -4) >= (14 - -11))) or (not not (1932年奥运会在洛杉矶举办。))) or (柏林墙倒塌发生在1984年。) or ((-10 + 6) < (5 + 3) < (20 - 12))) and (not ((not (氧气对人类生存是必需的。)) and (((-20 - -8) < (19 * -17)) or ((6 - 1) > (-16 - -16)))))\nE. not (((3 ** 3) < (20 + 13) < (2 - 1)) or (((1 * 2 + -7 * -8) < (2 * -5 + 0 * 5) < (2 ** 3)) or (第一次世界大战结束发生在1913年。)) or (not not ((20 + 11) < (1 ** 1))))\nF. ((((捷克的首都是布拉格。) and (墨西哥的首都是墨西哥城。)) or ((地球是距离太阳第3近的行星。) and (196的平方根是14。))) and (硫的化学符号是Cl。)) or (金的化学符号是Ne。) or ((not (not not (酒精在常温下是液体。))) and (894是斐波那契数。) and (not not ((第一次世界大战结束发生在1908年。) and (氯的化学符号是Zn。))))\nG. not not (((((1 * 9 + 6 * -9) < (-18 * 6)) or ((14 - 6) > (17 + -3))) or ((苏联解体发生在1992年。) and ((20 * 14) != (2 ** 3)))) and ((not not (32是质数。)) and ((植物通过光合作用产生氧气。) or (月球绕地球运转。))))\nH. ((((7 + -13) > (34 % 8)) or ((-7 * 10) > (4 ** 2))) or (not not ((银的化学符号是Pt。) or (1932年奥运会在阿姆斯特丹举办。)))) and (not (not ((-5 * -6 * 3 * -3) < (10 % 1)))) and (((387是完全平方数。) and (南极洲是最冷的大陆。)) or ((美国的货币是比索。) or (2004年奥运会在阿姆斯特丹举办。)) or (((瓢虫是爬行动物。) or (人类有三个肺。)) and (第一部iPhone发布发生在2012年。)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 8,
"seed": 4297960,
"true_count": 4
},
"seed": 4297960,
"task_id": 604297960,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (-10 * 0 - -5 * -5) == (-8 * -12)
B. 南极洲是最冷的大陆。
C. (-6 - 9) > (-3 + 16)
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 15067215,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. (-10 * 0 - -5 * -5) == (-8 * -12)\nB. 南极洲是最冷的大陆。\nC. (-6 - 9) > (-3 + 16)\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 15067215,
"true_count": 1
},
"seed": 15067215,
"task_id": 615067215,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. not (not not (833是斐波那契数。))
B. ((-18 * 15) == (0 * 12)) or (六月有30天。)
C. (((英国位于欧洲。) and (土星是距离太阳第6近的行星。)) or (not not ((1 * -7 * 4 * 6) <= (3 ** 3)))) and ((-17 + -14) < (9 % 10) < (19 * 11)) and (not (not not ((-4 * -4 + -6 * -8) >= (-4 * -8 + 2 * -6))))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 74471690,
"true_count": 2
},
"question": "考虑以下布尔表达式：\n\nA. not (not not (833是斐波那契数。))\nB. ((-18 * 15) == (0 * 12)) or (六月有30天。)\nC. (((英国位于欧洲。) and (土星是距离太阳第6近的行星。)) or (not not ((1 * -7 * 4 * 6) <= (3 ** 3)))) and ((-17 + -14) < (9 % 10) < (19 * 11)) and (not (not not ((-4 * -4 + -6 * -8) >= (-4 * -8 + 2 * -6))))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 74471690,
"true_count": 2
},
"seed": 74471690,
"task_id": 674471690,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (13 * 19) >= (-2 * 0 + -7 * -9)
B. not not ((94 is an even number.) and ((10 - -14) > (50 % 4)))
C. The chemical symbol for Oxygen is Zn.
D. (The chemical symbol for Mercury is Cu.) or (((2 ** 1) != (-1 * 0 * -4 * 1)) or (Oxygen is necessary for human survival.))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 16730625,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. (13 * 19) >= (-2 * 0 + -7 * -9)\nB. not not ((94 is an even number.) and ((10 - -14) > (50 % 4)))\nC. The chemical symbol for Oxygen is Zn.\nD. (The chemical symbol for Mercury is Cu.) or (((2 ** 1) != (-1 * 0 * -4 * 1)) or (Oxygen is necessary for human survival.))\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": 16730625,
"true_count": 3
},
"seed": 16730625,
"task_id": 616730625,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not (((法国大革命开始发生在1789年。) and (匈牙利的首都是新德里。)) or (not (加拿大位于北美洲。)))
B. ((蚂蚁有6条腿。) or (南非的货币是兰特。)) or (((18 + 15) < (14 % 8)) or (波兰的货币是克朗。)) or ((not not (1936年奥运会在巴黎举办。)) or ((1 ** 3) <= (18 * 12) <= (20 - -3)))
C. ((-1 * 11) < (-9 - 4) < (32 % 3)) and ((25 % 5) <= (-9 * -4 * 1 * 3))
D. (((水在常温下是液体。) or ((18 + 20) <= (-17 - -11))) or ((天王星是距离太阳第3近的行星。) or (金星是距离太阳第8近的行星。))) or (((铅的化学符号是Zn。) or ((3 ** 1) == (49 % 3))) and (((-8 * 8 - 10 * -5) >= (39 % 4)) or ((4 * -14) < (3 - 8))))
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": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 90136639,
"true_count": 3
},
"question": "给定以下布尔表达式：\n\nA. not (((法国大革命开始发生在1789年。) and (匈牙利的首都是新德里。)) or (not (加拿大位于北美洲。)))\nB. ((蚂蚁有6条腿。) or (南非的货币是兰特。)) or (((18 + 15) < (14 % 8)) or (波兰的货币是克朗。)) or ((not not (1936年奥运会在巴黎举办。)) or ((1 ** 3) <= (18 * 12) <= (20 - -3)))\nC. ((-1 * 11) < (-9 - 4) < (32 % 3)) and ((25 % 5) <= (-9 * -4 * 1 * 3))\nD. (((水在常温下是液体。) or ((18 + 20) <= (-17 - -11))) or ((天王星是距离太阳第3近的行星。) or (金星是距离太阳第8近的行星。))) or (((铅的化学符号是Zn。) or ((3 ** 1) == (49 % 3))) and (((-8 * 8 - 10 * -5) >= (39 % 4)) or ((4 * -14) < (3 - 8))))\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": 3,
"language": "cn",
"num_options": 4,
"seed": 90136639,
"true_count": 3
},
"seed": 90136639,
"task_id": 690136639,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (not (((汞在常温下是液体。) or ((23 % 3) >= (12 - 0)) or (二氧化碳在常温下是气体。)) or (匈牙利的货币是福林。) or (not not (人体有150块骨头。)))) or (not not (((月球自己发光。) and (((金的化学符号是Cr。) or (氧气在常温下是液体。)) and (not (欧盟的货币是克朗。)))) or (((1932年奥运会在洛杉矶举办。) or (((-5 * 1 * 10 * -4) != (16 + 19)) or (澳大利亚的货币是澳元。))) and ((-15 + -19) <= (-6 + 4) <= (-3 * -7 - 9 * 6)))))
B. not not (not ((not ((1 % 5) > (-3 * 0 + -9 * -3))) or (not (((3 * 17) != (16 % 3)) and (空气在常温下是液体。))) or (not not (not not (not (火星是距离太阳第8近的行星。))))))
C. (not ((((not not (韩国位于亚洲。)) and (1968年奥运会在伦敦举办。)) or (((-2 * 1 + -2 * 10) != (-5 - 20)) or ((-10 - 3) > (17 * 12))) or (((1964年奥运会在东京举办。) and (六月有30天。)) or (((23 % 10) == (15 + 17)) or (奥地利的首都是维也纳。)))) or (not not (not not ((瑞典的货币是加元。) or (人类首次登月发生在1969年。)))))) or (not ((not ((((10 - -7) >= (5 * 0)) or (土星是距离太阳第4近的行星。)) or (越南的货币是卢布。))) and (((-15 - 11) != (18 + 1)) and (油在常温下是液体。))))
D. (not not (((not not (((0 - -8) >= (3 ** 2)) or ((-2 * 12) == (-14 - 4)))) and (柏林墙倒塌发生在1979年。) and ((not not (钻石在常温下是固体。)) and ((2 ** 3) == (12 + 2)))) or (not not (火星是距离太阳第4近的行星。)))) and (not (((印度的首都是新德里。) and ((1900年奥运会在巴黎举办。) or ((-15 - -16) > (0 + -4)))) and (((19 + 15) != (-19 * 4)) and ((4 ** 1) <= (-7 * -6 * 0 * 7) <= (2 ** 3))))) and (not not ((not not ((not ((10 + 0) < (3 + -20))) and ((2012年奥运会在伦敦举办。) and (2075年是闰年。)))) and ((not (汞在常温下是液体。)) and ((-12 * -15) >= (-10 * 2)))))
E. not (not not ((not not (not (((1 % 4) <= (6 - 11) <= (-15 + -16)) or (457是斐波那契数。)))) and ((not ((3 ** 3) <= (-6 * -4 * -8 * 3))) and (((-4 * 2 - 4 * -3) < (39 % 3)) and ((7 + 4) != (22 % 4)))) and (not (((41小于等于79。) and ((-1 * 6 * -5 * -9) <= (-8 * -12))) and ((-4 * -16) == (12 * -16))))))
F. not not ((not ((not not ((14 - 14) != (-16 - 12))) and ((-3 + -4) < (-12 + 15)))) or (((袋鼠是鸟类。) and ((地球是距离太阳第4近的行星。) or (1980年奥运会在伦敦举办。))) and (not not ((17 % 6) < (7 + -8)))) or (not not (((柏林墙倒塌发生在1984年。) or (not not (1968年奥运会在墨西哥城举办。))) and (韩国的首都是首尔。))))
G. (not not (not not (((18 * 8) <= (9 - -16) <= (1 % 7)) or ((not not ((9 - 14) > (7 * 5 + 9 * 5))) or ((大象有4条腿。) and (86小于等于100。)))))) or (not (not (((丹麦的货币是克朗。) and (巴西位于南美洲。)) or (not not (中国的货币是人民币。))))) or ((not ((希腊的首都是雅典。) or (not not (光速约为每秒30万公里。)))) and (not not ((((秘鲁位于欧洲。) or (秘鲁位于南极洲。)) or ((5 ** 2) <= (31 % 5) <= (-11 * 5))) and (((钻石由碳元素组成。) and (英国的货币是英镑。)) and (((20 + 0) >= (5 - 20)) and (水在海平面上的沸点是100摄氏度。))))))
H. not not (((((肯尼亚的首都是内罗毕。) or (((5 ** 3) > (36 % 3)) and (月球自己发光。))) or ((鸟有10条腿。) or (南极洲是最冷的大陆。))) or (not (((-11 * -10) > (14 * -17)) and (((-2 - 0) <= (46 % 8)) and (地球是距离太阳第3近的行星。))))) and (not not (not not ((((0 - -13) <= (47 % 7)) and ((-8 * 2 - 6 * 6) <= (9 * -20))) and (((16 % 3) >= (16 * -20)) or ((3 ** 2) <= (-20 - 11)))))))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"question": "这里有一些需要评估的布尔表达式：\n\nA. (not (((汞在常温下是液体。) or ((23 % 3) >= (12 - 0)) or (二氧化碳在常温下是气体。)) or (匈牙利的货币是福林。) or (not not (人体有150块骨头。)))) or (not not (((月球自己发光。) and (((金的化学符号是Cr。) or (氧气在常温下是液体。)) and (not (欧盟的货币是克朗。)))) or (((1932年奥运会在洛杉矶举办。) or (((-5 * 1 * 10 * -4) != (16 + 19)) or (澳大利亚的货币是澳元。))) and ((-15 + -19) <= (-6 + 4) <= (-3 * -7 - 9 * 6)))))\nB. not not (not ((not ((1 % 5) > (-3 * 0 + -9 * -3))) or (not (((3 * 17) != (16 % 3)) and (空气在常温下是液体。))) or (not not (not not (not (火星是距离太阳第8近的行星。))))))\nC. (not ((((not not (韩国位于亚洲。)) and (1968年奥运会在伦敦举办。)) or (((-2 * 1 + -2 * 10) != (-5 - 20)) or ((-10 - 3) > (17 * 12))) or (((1964年奥运会在东京举办。) and (六月有30天。)) or (((23 % 10) == (15 + 17)) or (奥地利的首都是维也纳。)))) or (not not (not not ((瑞典的货币是加元。) or (人类首次登月发生在1969年。)))))) or (not ((not ((((10 - -7) >= (5 * 0)) or (土星是距离太阳第4近的行星。)) or (越南的货币是卢布。))) and (((-15 - 11) != (18 + 1)) and (油在常温下是液体。))))\nD. (not not (((not not (((0 - -8) >= (3 ** 2)) or ((-2 * 12) == (-14 - 4)))) and (柏林墙倒塌发生在1979年。) and ((not not (钻石在常温下是固体。)) and ((2 ** 3) == (12 + 2)))) or (not not (火星是距离太阳第4近的行星。)))) and (not (((印度的首都是新德里。) and ((1900年奥运会在巴黎举办。) or ((-15 - -16) > (0 + -4)))) and (((19 + 15) != (-19 * 4)) and ((4 ** 1) <= (-7 * -6 * 0 * 7) <= (2 ** 3))))) and (not not ((not not ((not ((10 + 0) < (3 + -20))) and ((2012年奥运会在伦敦举办。) and (2075年是闰年。)))) and ((not (汞在常温下是液体。)) and ((-12 * -15) >= (-10 * 2)))))\nE. not (not not ((not not (not (((1 % 4) <= (6 - 11) <= (-15 + -16)) or (457是斐波那契数。)))) and ((not ((3 ** 3) <= (-6 * -4 * -8 * 3))) and (((-4 * 2 - 4 * -3) < (39 % 3)) and ((7 + 4) != (22 % 4)))) and (not (((41小于等于79。) and ((-1 * 6 * -5 * -9) <= (-8 * -12))) and ((-4 * -16) == (12 * -16))))))\nF. not not ((not ((not not ((14 - 14) != (-16 - 12))) and ((-3 + -4) < (-12 + 15)))) or (((袋鼠是鸟类。) and ((地球是距离太阳第4近的行星。) or (1980年奥运会在伦敦举办。))) and (not not ((17 % 6) < (7 + -8)))) or (not not (((柏林墙倒塌发生在1984年。) or (not not (1968年奥运会在墨西哥城举办。))) and (韩国的首都是首尔。))))\nG. (not not (not not (((18 * 8) <= (9 - -16) <= (1 % 7)) or ((not not ((9 - 14) > (7 * 5 + 9 * 5))) or ((大象有4条腿。) and (86小于等于100。)))))) or (not (not (((丹麦的货币是克朗。) and (巴西位于南美洲。)) or (not not (中国的货币是人民币。))))) or ((not ((希腊的首都是雅典。) or (not not (光速约为每秒30万公里。)))) and (not not ((((秘鲁位于欧洲。) or (秘鲁位于南极洲。)) or ((5 ** 2) <= (31 % 5) <= (-11 * 5))) and (((钻石由碳元素组成。) and (英国的货币是英镑。)) and (((20 + 0) >= (5 - 20)) and (水在海平面上的沸点是100摄氏度。))))))\nH. not not (((((肯尼亚的首都是内罗毕。) or (((5 ** 3) > (36 % 3)) and (月球自己发光。))) or ((鸟有10条腿。) or (南极洲是最冷的大陆。))) or (not (((-11 * -10) > (14 * -17)) and (((-2 - 0) <= (46 % 8)) and (地球是距离太阳第3近的行星。))))) and (not not (not not ((((0 - -13) <= (47 % 7)) and ((-8 * 2 - 6 * 6) <= (9 * -20))) and (((16 % 3) >= (16 * -20)) or ((3 ** 2) <= (-20 - 11)))))))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
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logic-v2 | 考虑以下布尔表达式：
A. not ((((15 + 18) >= (19 + 16)) and ((7 - 14) >= (-4 * 10 - 10 * 6))) and ((2003年是闰年。) or (狮子是哺乳动物。)))
B. not not ((人类只使用了大脑的10%。) and ((丹麦的货币是克朗。) and (匈牙利的首都是渥太华。)))
C. ((酒精在常温下是液体。) and ((-14 - 11) <= (2 ** 3))) or ((柏林墙倒塌发生在1989年。) or ((蝙蝠是瞎的。) or (十二月有30天。)))
D. ((1 ** 1) < (-3 * -17)) and (((钾的化学符号是Zn。) or ((8 * -9 - 10 * -3) <= (17 * -18))) and (氖的化学符号是Ne。))
E. ((鸭子是鸟类。) or ((10 * -2 + 2 * -10) > (16 * -2))) or (not not ((四月有28天。) or ((17 * 2) <= (7 * 4 - -6 * 10))))
F. (not not (((4 + -14) != (2 - 2)) and ((1 + 2) >= (3 ** 2)))) or (not (((5 ** 3) > (1 * -9)) and (伦敦大火发生在1664年。)))
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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"question": "考虑以下布尔表达式：\n\nA. not ((((15 + 18) >= (19 + 16)) and ((7 - 14) >= (-4 * 10 - 10 * 6))) and ((2003年是闰年。) or (狮子是哺乳动物。)))\nB. not not ((人类只使用了大脑的10%。) and ((丹麦的货币是克朗。) and (匈牙利的首都是渥太华。)))\nC. ((酒精在常温下是液体。) and ((-14 - 11) <= (2 ** 3))) or ((柏林墙倒塌发生在1989年。) or ((蝙蝠是瞎的。) or (十二月有30天。)))\nD. ((1 ** 1) < (-3 * -17)) and (((钾的化学符号是Zn。) or ((8 * -9 - 10 * -3) <= (17 * -18))) and (氖的化学符号是Ne。))\nE. ((鸭子是鸟类。) or ((10 * -2 + 2 * -10) > (16 * -2))) or (not not ((四月有28天。) or ((17 * 2) <= (7 * 4 - -6 * 10))))\nF. (not not (((4 + -14) != (2 - 2)) and ((1 + 2) >= (3 ** 2)))) or (not (((5 ** 3) > (1 * -9)) and (伦敦大火发生在1664年。)))\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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logic-v2 | Examine these expressions:
A. (not ((not ((5 ** 2) <= (36 % 4))) and ((There are 29 days in October.) and (Penguins can fly.)))) and (not not ((1 ** 2) <= (-10 * 9 + 0 * 3)))
B. (not not ((not not (A lobster has 2 legs.)) and (((-15 * -11) <= (-12 + 17)) or (2051 is a leap year.)))) and (((((10 + 20) != (-4 + 7)) or ((-13 + 7) < (-19 - -5))) or (The capital of Kenya is Nairobi.)) and ((2 % 9) <= (-5 * 5 - 7 * -4) <= (-8 * 1 - 7 * -9)) and (not not (not (86 is divisible by 6.))))
C. ((Neptune is the 3rd planet from the Sun.) or (not not ((7 + -8) <= (1 ** 1))) or ((((9 + -6) < (-6 * -1 * 6 * -7) < (3 * -10 - 3 * -3)) and ((-6 - 20) < (12 * -16) < (11 - 1))) and (not not ((-5 * 0 - 5 * -3) >= (14 + 0))))) and (not not (((-7 * 9 * -3 * -1) == (-4 * 3)) or ((-13 * 20) > (50 % 4)))) and (((United States is in North America.) and (((1 * 6 + 4 * 2) >= (-4 + -5)) or ((3 ** 3) <= (-3 * -6)))) and (not (not (A pig has 4 legs.))))
D. (not not ((((6 + 7) <= (-3 - -14) <= (2 - -19)) and (The 1976 Olympics were held in Montreal.)) or (not not (There are 31 days in June.)))) and (((((10 * 0) == (48 % 5)) or (There are 30 days in February.)) and ((79 is a prime number.) and (The chemical symbol for Chromium is Ne.))) and (((The capital of Kenya is Cairo.) and ((-5 + 19) <= (7 * 8 - 6 * 5))) and (not not (The capital of France is Paris.))))
E. Diamonds are made of carbon.
F. ((New Zealand is in Oceania.) and (((The square root of 225 is 1.) or ((-5 * -4 - -10 * -7) <= (-4 * -3 - -7 * -2))) or ((The 2000 Olympics were held in Athens.) or ((16 + -5) <= (1 - 8))))) and (((Air is a solid at room temperature.) and ((17 * -4) < (7 - 2))) and (The chemical symbol for Calcium is Ca.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
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"question": "Examine these expressions:\n\nA. (not ((not ((5 ** 2) <= (36 % 4))) and ((There are 29 days in October.) and (Penguins can fly.)))) and (not not ((1 ** 2) <= (-10 * 9 + 0 * 3)))\nB. (not not ((not not (A lobster has 2 legs.)) and (((-15 * -11) <= (-12 + 17)) or (2051 is a leap year.)))) and (((((10 + 20) != (-4 + 7)) or ((-13 + 7) < (-19 - -5))) or (The capital of Kenya is Nairobi.)) and ((2 % 9) <= (-5 * 5 - 7 * -4) <= (-8 * 1 - 7 * -9)) and (not not (not (86 is divisible by 6.))))\nC. ((Neptune is the 3rd planet from the Sun.) or (not not ((7 + -8) <= (1 ** 1))) or ((((9 + -6) < (-6 * -1 * 6 * -7) < (3 * -10 - 3 * -3)) and ((-6 - 20) < (12 * -16) < (11 - 1))) and (not not ((-5 * 0 - 5 * -3) >= (14 + 0))))) and (not not (((-7 * 9 * -3 * -1) == (-4 * 3)) or ((-13 * 20) > (50 % 4)))) and (((United States is in North America.) and (((1 * 6 + 4 * 2) >= (-4 + -5)) or ((3 ** 3) <= (-3 * -6)))) and (not (not (A pig has 4 legs.))))\nD. (not not ((((6 + 7) <= (-3 - -14) <= (2 - -19)) and (The 1976 Olympics were held in Montreal.)) or (not not (There are 31 days in June.)))) and (((((10 * 0) == (48 % 5)) or (There are 30 days in February.)) and ((79 is a prime number.) and (The chemical symbol for Chromium is Ne.))) and (((The capital of Kenya is Cairo.) and ((-5 + 19) <= (7 * 8 - 6 * 5))) and (not not (The capital of France is Paris.))))\nE. Diamonds are made of carbon.\nF. ((New Zealand is in Oceania.) and (((The square root of 225 is 1.) or ((-5 * -4 - -10 * -7) <= (-4 * -3 - -7 * -2))) or ((The 2000 Olympics were held in Athens.) or ((16 + -5) <= (1 - 8))))) and (((Air is a solid at room temperature.) and ((17 * -4) < (7 - 2))) and (The chemical symbol for Calcium is Ca.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
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logic-v2 | 评估以下每个表达式：
A. ((not (not not ((not not ((4 - 10) < (-8 * -14) < (-10 * -7 + 7 * -2))) or (not (埃及的货币是韩元。))))) or (not (not ((((-5 - 16) > (-13 + -11)) or (铅的化学符号是Pb。)) and (((3 - -10) >= (1 ** 3)) and (越南的首都是伯尔尼。)))))) or (not ((not not ((not ((-16 + 3) <= (-2 + 11) <= (-1 * -17))) and (铜在常温下是气体。))) or ((1956年奥运会在悉尼举办。) and (南非的货币是兰特。))))
B. not not ((((not (((12 % 7) <= (10 + 19) <= (11 - -16)) and ((-4 * 9) != (8 * 10 * 0 * 5)))) or ((1996年奥运会在莫斯科举办。) and (((20 - 8) < (23 % 4)) or (锌的化学符号是Ag。)))) or (not not (钛的化学符号是Mg。))) or ((阿根廷位于南美洲。) and (not not ((-15 + 0) > (7 * -8 - -6 * 10)))) or ((((三月有28天。) or (匈牙利的货币是福林。)) or ((31 % 1) < (-20 * 1))) and ((第二次世界大战结束发生在1945年。) or ((((-14 * -20) <= (7 - 0)) or ((-2 - 15) < (-12 * 10))) or (冰在常温下是气体。)))))
C. not (not not (not (((((5 + 5) == (42 % 1)) or ((-19 * 9) <= (16 + 7) <= (20 - 18))) and (水蒸气在常温下是气体。)) and (((银在常温下是固体。) and ((6 * 9 * 0 * 10) < (3 * -1 * 1 * 9) < (-7 * -9 * 5 * 1))) or (智利的货币是比索。)))))
D. ((not ((澳大利亚的首都是堪培拉。) or ((4 ** 2) <= (-14 + 7) <= (1 ** 1)) or (not (((6 + 3) <= (-6 + 11) <= (8 + -1)) and (大象有4条腿。))))) and (not not ((not not (现代奥运会首届举办发生在1894年。)) and (印度的货币是越南盾。) and ((not (1984年奥运会在伦敦举办。)) or ((224是完全平方数。) or (57能被4整除。)))))) or (not not ((not (((1972年奥运会在巴黎举办。) and (空气在常温下是液体。)) and (((5 * 5 + 7 * 6) < (-19 + 17)) and (美国宣布独立发生在1771年。)))) and ((not (not not (火星是距离太阳第2近的行星。))) and ((not not (一月有30天。)) or (not not (2063年是闰年。))))))
E. (not not (not not (((2052年是闰年。) or ((5 ** 2) <= (-12 * -2) <= (-15 * -12))) or (not not (((13 - 6) == (8 * 12)) and (捷克的货币是兰特。)))))) and (((((((33 % 6) <= (7 * 7 - 7 * 5) <= (17 * 4)) or ((-9 * -1 * -1 * 5) > (13 % 4))) or ((水星是距离太阳第1近的行星。) or ((37 % 7) <= (0 - 2)))) or (钻石由碳元素组成。)) or (not not ((40 % 5) > (4 * -13)))) and (not ((not ((现代奥运会首届举办发生在1896年。) or (秘鲁的首都是内罗毕。))) or (not not (not not ((2 - 15) != (-7 * -10 * -7 * -8)))))))
F. ((not not (not not ((((-19 * 2) < (-2 + -16) < (-6 * 1)) or (铀的化学符号是Pt。)) and (瑞典的货币是比索。)))) or ((not ((3 ** 2) < (-6 * 6))) or (((((-5 * -8) > (-13 * -9)) or ((18 - 10) <= (-8 * -4 * -5 * 2))) or ((钻石由碳元素组成。) and (2020年奥运会在东京举办。))) or ((3 ** 1) <= (15 * -4))))) or ((not ((泰坦尼克号沉没发生在1912年。) and ((3 + 2) < (16 + 3)))) and (not not (((加拿大位于南极洲。) or (((3 - -5) == (5 ** 1)) or (氧气在常温下是气体。))) or (水蒸气在常温下是气体。))))
G. not not (not not ((not ((4 * -9 * 0 * 4) >= (2 ** 1))) and ((1908年奥运会在伦敦举办。) and (not not ((0 * -6) != (-18 - 20))) and (捷克的货币是美元。))))
H. (not not ((not not ((not not ((2 ** 1) > (1 ** 2))) or ((木星是距离太阳第5近的行星。) and ((15 * -11) > (-3 * -19))))) and ((龙虾有10条腿。) and ((五月有29天。) and (((7 - -2) == (2 ** 1)) and (英国位于欧洲。)))))) or (not (((2024年奥运会在蒙特利尔举办。) or (((-8 * -5 + -2 * 5) < (15 * 14) < (3 ** 1)) and (鲨鱼是哺乳动物。)) or (not (((-11 + 18) < (43 % 9)) and (28能被5整除。)))) or (((4 ** 1) >= (3 ** 1)) and ((not not ((5 * -14) < (1 ** 1) < (18 - -7))) and ((哥伦布到达美洲发生在1492年。) and (1904年奥运会在北京举办。))))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
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"true_count": 3
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"question": "评估以下每个表达式：\n\nA. ((not (not not ((not not ((4 - 10) < (-8 * -14) < (-10 * -7 + 7 * -2))) or (not (埃及的货币是韩元。))))) or (not (not ((((-5 - 16) > (-13 + -11)) or (铅的化学符号是Pb。)) and (((3 - -10) >= (1 ** 3)) and (越南的首都是伯尔尼。)))))) or (not ((not not ((not ((-16 + 3) <= (-2 + 11) <= (-1 * -17))) and (铜在常温下是气体。))) or ((1956年奥运会在悉尼举办。) and (南非的货币是兰特。))))\nB. not not ((((not (((12 % 7) <= (10 + 19) <= (11 - -16)) and ((-4 * 9) != (8 * 10 * 0 * 5)))) or ((1996年奥运会在莫斯科举办。) and (((20 - 8) < (23 % 4)) or (锌的化学符号是Ag。)))) or (not not (钛的化学符号是Mg。))) or ((阿根廷位于南美洲。) and (not not ((-15 + 0) > (7 * -8 - -6 * 10)))) or ((((三月有28天。) or (匈牙利的货币是福林。)) or ((31 % 1) < (-20 * 1))) and ((第二次世界大战结束发生在1945年。) or ((((-14 * -20) <= (7 - 0)) or ((-2 - 15) < (-12 * 10))) or (冰在常温下是气体。)))))\nC. not (not not (not (((((5 + 5) == (42 % 1)) or ((-19 * 9) <= (16 + 7) <= (20 - 18))) and (水蒸气在常温下是气体。)) and (((银在常温下是固体。) and ((6 * 9 * 0 * 10) < (3 * -1 * 1 * 9) < (-7 * -9 * 5 * 1))) or (智利的货币是比索。)))))\nD. ((not ((澳大利亚的首都是堪培拉。) or ((4 ** 2) <= (-14 + 7) <= (1 ** 1)) or (not (((6 + 3) <= (-6 + 11) <= (8 + -1)) and (大象有4条腿。))))) and (not not ((not not (现代奥运会首届举办发生在1894年。)) and (印度的货币是越南盾。) and ((not (1984年奥运会在伦敦举办。)) or ((224是完全平方数。) or (57能被4整除。)))))) or (not not ((not (((1972年奥运会在巴黎举办。) and (空气在常温下是液体。)) and (((5 * 5 + 7 * 6) < (-19 + 17)) and (美国宣布独立发生在1771年。)))) and ((not (not not (火星是距离太阳第2近的行星。))) and ((not not (一月有30天。)) or (not not (2063年是闰年。))))))\nE. (not not (not not (((2052年是闰年。) or ((5 ** 2) <= (-12 * -2) <= (-15 * -12))) or (not not (((13 - 6) == (8 * 12)) and (捷克的货币是兰特。)))))) and (((((((33 % 6) <= (7 * 7 - 7 * 5) <= (17 * 4)) or ((-9 * -1 * -1 * 5) > (13 % 4))) or ((水星是距离太阳第1近的行星。) or ((37 % 7) <= (0 - 2)))) or (钻石由碳元素组成。)) or (not not ((40 % 5) > (4 * -13)))) and (not ((not ((现代奥运会首届举办发生在1896年。) or (秘鲁的首都是内罗毕。))) or (not not (not not ((2 - 15) != (-7 * -10 * -7 * -8)))))))\nF. ((not not (not not ((((-19 * 2) < (-2 + -16) < (-6 * 1)) or (铀的化学符号是Pt。)) and (瑞典的货币是比索。)))) or ((not ((3 ** 2) < (-6 * 6))) or (((((-5 * -8) > (-13 * -9)) or ((18 - 10) <= (-8 * -4 * -5 * 2))) or ((钻石由碳元素组成。) and (2020年奥运会在东京举办。))) or ((3 ** 1) <= (15 * -4))))) or ((not ((泰坦尼克号沉没发生在1912年。) and ((3 + 2) < (16 + 3)))) and (not not (((加拿大位于南极洲。) or (((3 - -5) == (5 ** 1)) or (氧气在常温下是气体。))) or (水蒸气在常温下是气体。))))\nG. not not (not not ((not ((4 * -9 * 0 * 4) >= (2 ** 1))) and ((1908年奥运会在伦敦举办。) and (not not ((0 * -6) != (-18 - 20))) and (捷克的货币是美元。))))\nH. (not not ((not not ((not not ((2 ** 1) > (1 ** 2))) or ((木星是距离太阳第5近的行星。) and ((15 * -11) > (-3 * -19))))) and ((龙虾有10条腿。) and ((五月有29天。) and (((7 - -2) == (2 ** 1)) and (英国位于欧洲。)))))) or (not (((2024年奥运会在蒙特利尔举办。) or (((-8 * -5 + -2 * 5) < (15 * 14) < (3 ** 1)) and (鲨鱼是哺乳动物。)) or (not (((-11 + 18) < (43 % 9)) and (28能被5整除。)))) or (((4 ** 1) >= (3 ** 1)) and ((not not ((5 * -14) < (1 ** 1) < (18 - -7))) and ((哥伦布到达美洲发生在1492年。) and (1904年奥运会在北京举办。))))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 75327670,
"true_count": 3
},
"seed": 75327670,
"task_id": 675327670,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not ((33 % 2) != (16 * -10))
B. (((-9 - -10) > (2 * 8 + -4 * -9)) and (not not (Mercury is the 1st planet from the Sun.))) or (((Spain is in Europe.) or (Humans have three lungs.)) and ((The currency of Philippines is the Peso.) and (The currency of Chile is the Peso.)))
C. (((World War II began occurred in 1939.) and (Water is a liquid at room temperature.)) or (Earth is the 6th planet from the Sun.)) or (not (Air is a gas at room temperature.)) or (not ((The 2000 Olympics were held in Tokyo.) and ((1 ** 1) < (13 + 4))))
D. (There are 30 days in February.) and (((5 * -18) >= (-14 - -18)) or (Ice is less dense than liquid water.)) and ((((20 * 7) != (16 + -8)) or ((5 % 3) <= (-2 * -1 - -7 * -9))) or (((16 * -12) != (-9 + 12)) and (There are 30 days in June.)))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 53539536,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not ((33 % 2) != (16 * -10))\nB. (((-9 - -10) > (2 * 8 + -4 * -9)) and (not not (Mercury is the 1st planet from the Sun.))) or (((Spain is in Europe.) or (Humans have three lungs.)) and ((The currency of Philippines is the Peso.) and (The currency of Chile is the Peso.)))\nC. (((World War II began occurred in 1939.) and (Water is a liquid at room temperature.)) or (Earth is the 6th planet from the Sun.)) or (not (Air is a gas at room temperature.)) or (not ((The 2000 Olympics were held in Tokyo.) and ((1 ** 1) < (13 + 4))))\nD. (There are 30 days in February.) and (((5 * -18) >= (-14 - -18)) or (Ice is less dense than liquid water.)) and ((((20 * 7) != (16 + -8)) or ((5 % 3) <= (-2 * -1 - -7 * -9))) or (((16 * -12) != (-9 + 12)) and (There are 30 days in June.)))\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": 4,
"seed": 53539536,
"true_count": 3
},
"seed": 53539536,
"task_id": 653539536,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (-11 * 18) != (36 % 9)
B. (not ((-19 * 1) <= (4 * 14))) or (((1 % 1) == (-2 * -20)) or (镁的化学符号是Mg。))
C. (-9 * -3 + 8 * -4) < (7 * -9 - 10 * 3)
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 19694496,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. (-11 * 18) != (36 % 9)\nB. (not ((-19 * 1) <= (4 * 14))) or (((1 % 1) == (-2 * -20)) or (镁的化学符号是Mg。))\nC. (-9 * -3 + 8 * -4) < (7 * -9 - 10 * 3)\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 19694496,
"true_count": 2
},
"seed": 19694496,
"task_id": 619694496,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (not (not not (((声音在真空中传播更快。) or ((-15 + -6) == (43 % 4))) or ((-16 + 6) <= (18 * 11))))) or (not (not ((((1 * 5 - -10 * -3) != (2 + 20)) or ((9 * 2 + 9 * -10) != (20 * -19))) or (((-17 + 18) != (12 + -12)) and (伦敦大火发生在1666年。)))))
B. (not (not not ((not not (海王星是距离太阳第3近的行星。)) and ((1976年奥运会在蒙特利尔举办。) or (人类有三个肺。))))) or (not not (not not (not ((金的化学符号是Au。) or ((1 * -1) < (17 + 5) < (19 * 3))))))
C. (not (not not ((not not (1990年是闰年。)) or ((2 ** 3) < (45 % 4) < (1 ** 1))))) or (((not ((日本位于欧洲。) and ((4 * 2 - -8 * 4) != (20 * -7)))) and (not not ((18 - -13) < (3 * -9 * -1 * 10)))) and (((not (袋鼠有10条腿。)) or (not ((3 * -8 * -7 * 1) < (1 ** 3) < (6 * 2 + 10 * 10)))) or (沙特阿拉伯位于亚洲。)))
D. not ((((九月有30天。) or (not ((-13 - 4) < (-3 * 4 + 0 * 8)))) and (第二次世界大战开始发生在1940年。)) and ((((11 + 11) <= (31 % 10) <= (-10 * 18)) or (((-17 + -8) == (7 - 6)) or (猫头鹰是鸟类。))) or (五月有31天。)))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 26430539,
"true_count": 4
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (not (not not (((声音在真空中传播更快。) or ((-15 + -6) == (43 % 4))) or ((-16 + 6) <= (18 * 11))))) or (not (not ((((1 * 5 - -10 * -3) != (2 + 20)) or ((9 * 2 + 9 * -10) != (20 * -19))) or (((-17 + 18) != (12 + -12)) and (伦敦大火发生在1666年。)))))\nB. (not (not not ((not not (海王星是距离太阳第3近的行星。)) and ((1976年奥运会在蒙特利尔举办。) or (人类有三个肺。))))) or (not not (not not (not ((金的化学符号是Au。) or ((1 * -1) < (17 + 5) < (19 * 3))))))\nC. (not (not not ((not not (1990年是闰年。)) or ((2 ** 3) < (45 % 4) < (1 ** 1))))) or (((not ((日本位于欧洲。) and ((4 * 2 - -8 * 4) != (20 * -7)))) and (not not ((18 - -13) < (3 * -9 * -1 * 10)))) and (((not (袋鼠有10条腿。)) or (not ((3 * -8 * -7 * 1) < (1 ** 3) < (6 * 2 + 10 * 10)))) or (沙特阿拉伯位于亚洲。)))\nD. not ((((九月有30天。) or (not ((-13 - 4) < (-3 * 4 + 0 * 8)))) and (第二次世界大战开始发生在1940年。)) and ((((11 + 11) <= (31 % 10) <= (-10 * 18)) or (((-17 + -8) == (7 - 6)) or (猫头鹰是鸟类。))) or (五月有31天。)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 26430539,
"true_count": 4
},
"seed": 26430539,
"task_id": 626430539,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. (not not (A alligator is a reptile.)) or ((-5 * -5 * -4 * -8) <= (5 ** 2))
B. (1 * -8) < (13 * 0) < (14 + 8)
C. (-1 * -10 * -9 * -5) <= (2 - 3) <= (2 ** 2)
D. ((-4 - 18) >= (10 * -2 * -2 * 4)) or (((-16 * -20) == (-3 * -11)) or ((5 * -10 + -7 * -2) != (8 * 3 * -9 * -7)))
E. 265 is a Fibonacci number.
F. (716 is a Fibonacci number.) or (A bee is a mammal.)
G. not (((-14 - -14) < (5 * 3 * -7 * -1)) and ((-8 * -9 - 5 * -5) > (6 * 4)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 79591027,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. (not not (A alligator is a reptile.)) or ((-5 * -5 * -4 * -8) <= (5 ** 2))\nB. (1 * -8) < (13 * 0) < (14 + 8)\nC. (-1 * -10 * -9 * -5) <= (2 - 3) <= (2 ** 2)\nD. ((-4 - 18) >= (10 * -2 * -2 * 4)) or (((-16 * -20) == (-3 * -11)) or ((5 * -10 + -7 * -2) != (8 * 3 * -9 * -7)))\nE. 265 is a Fibonacci number.\nF. (716 is a Fibonacci number.) or (A bee is a mammal.)\nG. not (((-14 - -14) < (5 * 3 * -7 * -1)) and ((-8 * -9 - 5 * -5) > (6 * 4)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 79591027,
"true_count": 3
},
"seed": 79591027,
"task_id": 679591027,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. ((Oxygen is a solid at room temperature.) and ((2 ** 1) != (8 + -19))) and (not not ((9 * 3 - 3 * -4) != (-2 * -7 + 2 * -10)))
B. The chemical symbol for Carbon is C.
C. (The capital of Hungary is Budapest.) and (The chemical symbol for Aluminum is Sn.)
D. A cat has 4 legs.
E. (-10 * 9 * 0 * -7) >= (11 * 9)
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 20564655,
"true_count": 2
},
"question": "Here are some boolean expressions to evaluate:\n\nA. ((Oxygen is a solid at room temperature.) and ((2 ** 1) != (8 + -19))) and (not not ((9 * 3 - 3 * -4) != (-2 * -7 + 2 * -10)))\nB. The chemical symbol for Carbon is C.\nC. (The capital of Hungary is Budapest.) and (The chemical symbol for Aluminum is Sn.)\nD. A cat has 4 legs.\nE. (-10 * 9 * 0 * -7) >= (11 * 9)\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 20564655,
"true_count": 2
},
"seed": 20564655,
"task_id": 620564655,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not (not not ((Jupiter is the 5th planet from the Sun.) and (not not ((7 * -4) >= (8 * 4 - 9 * 2))) and (((The 1952 Olympics were held in Helsinki.) and ((-1 * 9) > (3 ** 3))) or ((The chemical symbol for Helium is S.) and (Whales are fish.)))))
B. not not (((((The capital of Cuba is Helsinki.) or (A dog has 8 legs.)) and ((72 is an odd number.) and (Indonesia is in Asia.))) or (not not (((9 * 6 - 4 * -5) < (48 % 2)) or (Mars is the 4th planet from the Sun.)))) and ((The speed of light is approximately 300,000 km/s.) and (not ((Silver is a solid at room temperature.) or ((17 % 9) != (4 * -8 - -3 * 7))))))
C. (not ((not not (((5 ** 3) < (2 ** 3) < (-8 * 2 * 8 * 1)) or (Morocco is in Africa.))) and (((2087 is a leap year.) and (The French Revolution began occurred in 1789.)) or (Mercury is a liquid at room temperature.)))) or (not not ((not ((A tuna is a fish.) or ((5 - 12) > (-2 + -15)))) or ((-3 - -10) >= (4 + 11))))
D. (not (not ((not not (Venus is the 6th planet from the Sun.)) and ((-1 * -8) <= (3 ** 1) <= (-4 * 2 + 2 * 6))))) and ((not (not not ((1956 is a leap year.) and ((0 * 10 + 3 * -3) < (35 % 10))))) or (((There are 28 days in August.) and (The square root of 4 is 1.)) and (((-11 * 11) > (-9 * -7 - -9 * 3)) or ((12 - -19) == (-9 * 16)))) or ((not ((The currency of Israel is the Krone.) and ((14 * -5) < (4 + -16) < (-9 * 0)))) or (not not (((10 - 8) <= (-17 - 20)) and (France is in Europe.)))))
E. not ((not not (((1903 is a leap year.) and (The Titanic sank occurred in 1912.)) or (There are 30 days in September.))) and (not (((19 % 8) != (1 ** 1)) or ((A horse has 4 legs.) or (The chemical symbol for Carbon is Na.)))))
F. not not ((((not (Helium is a gas at room temperature.)) or (((-8 * -18) <= (-14 + 7)) or (Chile is in South America.))) and ((((12 * 7) < (-6 - -16) < (6 * -3 - -10 * -5)) or (Uranus is the 7th planet from the Sun.)) and ((A horse has 0 legs.) or (The capital of Argentina is Lima.)))) and (not (not not ((-10 * 2 * 6 * -7) > (1 * -9 - -5 * 0)))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 2081574,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. not not (not not ((Jupiter is the 5th planet from the Sun.) and (not not ((7 * -4) >= (8 * 4 - 9 * 2))) and (((The 1952 Olympics were held in Helsinki.) and ((-1 * 9) > (3 ** 3))) or ((The chemical symbol for Helium is S.) and (Whales are fish.)))))\nB. not not (((((The capital of Cuba is Helsinki.) or (A dog has 8 legs.)) and ((72 is an odd number.) and (Indonesia is in Asia.))) or (not not (((9 * 6 - 4 * -5) < (48 % 2)) or (Mars is the 4th planet from the Sun.)))) and ((The speed of light is approximately 300,000 km/s.) and (not ((Silver is a solid at room temperature.) or ((17 % 9) != (4 * -8 - -3 * 7))))))\nC. (not ((not not (((5 ** 3) < (2 ** 3) < (-8 * 2 * 8 * 1)) or (Morocco is in Africa.))) and (((2087 is a leap year.) and (The French Revolution began occurred in 1789.)) or (Mercury is a liquid at room temperature.)))) or (not not ((not ((A tuna is a fish.) or ((5 - 12) > (-2 + -15)))) or ((-3 - -10) >= (4 + 11))))\nD. (not (not ((not not (Venus is the 6th planet from the Sun.)) and ((-1 * -8) <= (3 ** 1) <= (-4 * 2 + 2 * 6))))) and ((not (not not ((1956 is a leap year.) and ((0 * 10 + 3 * -3) < (35 % 10))))) or (((There are 28 days in August.) and (The square root of 4 is 1.)) and (((-11 * 11) > (-9 * -7 - -9 * 3)) or ((12 - -19) == (-9 * 16)))) or ((not ((The currency of Israel is the Krone.) and ((14 * -5) < (4 + -16) < (-9 * 0)))) or (not not (((10 - 8) <= (-17 - 20)) and (France is in Europe.)))))\nE. not ((not not (((1903 is a leap year.) and (The Titanic sank occurred in 1912.)) or (There are 30 days in September.))) and (not (((19 % 8) != (1 ** 1)) or ((A horse has 4 legs.) or (The chemical symbol for Carbon is Na.)))))\nF. not not ((((not (Helium is a gas at room temperature.)) or (((-8 * -18) <= (-14 + 7)) or (Chile is in South America.))) and ((((12 * 7) < (-6 - -16) < (6 * -3 - -10 * -5)) or (Uranus is the 7th planet from the Sun.)) and ((A horse has 0 legs.) or (The capital of Argentina is Lima.)))) and (not (not not ((-10 * 2 * 6 * -7) > (1 * -9 - -5 * 0)))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 2081574,
"true_count": 1
},
"seed": 2081574,
"task_id": 602081574,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (-17 - 8) > (-12 * -12)
B. ((16 % 1) < (3 ** 3)) and ((2 ** 3) <= (8 - 20))
C. (-6 - 18) >= (-17 + -20)
D. (29 % 9) <= (-14 + -20) <= (18 - -9)
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 82206201,
"true_count": 1
},
"question": "Analyze these boolean expressions:\n\nA. (-17 - 8) > (-12 * -12)\nB. ((16 % 1) < (3 ** 3)) and ((2 ** 3) <= (8 - 20))\nC. (-6 - 18) >= (-17 + -20)\nD. (29 % 9) <= (-14 + -20) <= (18 - -9)\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 82206201,
"true_count": 1
},
"seed": 82206201,
"task_id": 682206201,
"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 ((2060年是闰年。) and (新加坡的货币是新加坡元。)))
B. not ((3 * 10) >= (-7 * 1))
C. 声音无法在真空中传播。
D. not not ((not not ((17 - -17) <= (4 ** 1) <= (-2 * 0 - 3 * -1))) and (not (2094年是闰年。)))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 46356550,
"true_count": 1
},
"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 ((2060年是闰年。) and (新加坡的货币是新加坡元。)))\nB. not ((3 * 10) >= (-7 * 1))\nC. 声音无法在真空中传播。\nD. not not ((not not ((17 - -17) <= (4 ** 1) <= (-2 * 0 - 3 * -1))) and (not (2094年是闰年。)))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 46356550,
"true_count": 1
},
"seed": 46356550,
"task_id": 646356550,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. (not (not (Whales are fish.))) or ((((Spiders are insects.) and ((17 + -20) == (28 % 1))) and ((The chemical symbol for Carbon is C.) and ((-15 * 5) != (5 * -8 + 10 * -4)))) or (Spain is in Europe.)) or (((Wood is a solid at room temperature.) or ((The Moon produces its own light.) and ((The currency of Australia is the Dollar.) and (65 is divisible by 10.)))) or ((not not ((7 % 9) > (-13 * 1))) or ((China is in Asia.) and (A human has 2 legs.)) or (New Zealand is in Oceania.)))
B. not (not not (not ((((10 % 6) < (4 * -5 + -10 * 8) < (8 * 10 + -6 * -10)) or (Venus is the 2nd planet from the Sun.)) and ((Alcohol is a liquid at room temperature.) and ((3 * -5 - 0 * -9) >= (5 + 20))))))
C. not ((not ((31 % 9) < (-11 + -6))) and (((((-7 * -19) == (-17 - 20)) and (United Kingdom is in Asia.)) and ((6 * 9 - 5 * 10) <= (-3 * -16))) and ((not not (The currency of European Union is the Euro.)) and ((World War II ended occurred in 1945.) and ((-10 * -5) < (1 ** 3))))))
D. not not ((((not ((11 - -17) <= (-4 - 9) <= (0 * -8 * -1 * 9))) or (not not ((18 - 10) == (-6 * -6)))) or (not not ((A crocodile is a mammal.) or (The currency of Sweden is the Krona.)))) and ((27 is divisible by 12.) and (not not (The first Olympic Games of modern era occurred in 1896.))))
E. not (not not (((not ((4 ** 3) < (11 + -11))) or ((Thailand is in North America.) and (The 1948 Olympics were held in Mexico City.))) or (The currency of India is the Rupee.)))
F. ((not ((((-10 * 9 + -5 * -2) > (20 + -3)) and ((-9 * 7 - 1 * 2) < (12 - 14))) and ((The currency of New Zealand is the Dollar.) and (A chicken is a fish.)))) and (not not (((The Sun revolves around the Earth.) and (62 is a prime number.)) or ((-7 * -8 * -6 * 5) != (17 * -5))))) and (not not (not not ((Jupiter is the 5th planet from the Sun.) or ((The 1908 Olympics were held in Munich.) or (A cat has 6 legs.)))))
G. not not ((((18 - -6) >= (6 + 20)) or ((((17 - 7) >= (-10 * -16)) and (Thailand is in Antarctica.)) and ((Saudi Arabia is in Asia.) and (World War II ended occurred in 1945.)))) or ((The currency of Chile is the Rupee.) or (188 is an odd number.) or (Silver is a gas at room temperature.)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 68815485,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. (not (not (Whales are fish.))) or ((((Spiders are insects.) and ((17 + -20) == (28 % 1))) and ((The chemical symbol for Carbon is C.) and ((-15 * 5) != (5 * -8 + 10 * -4)))) or (Spain is in Europe.)) or (((Wood is a solid at room temperature.) or ((The Moon produces its own light.) and ((The currency of Australia is the Dollar.) and (65 is divisible by 10.)))) or ((not not ((7 % 9) > (-13 * 1))) or ((China is in Asia.) and (A human has 2 legs.)) or (New Zealand is in Oceania.)))\nB. not (not not (not ((((10 % 6) < (4 * -5 + -10 * 8) < (8 * 10 + -6 * -10)) or (Venus is the 2nd planet from the Sun.)) and ((Alcohol is a liquid at room temperature.) and ((3 * -5 - 0 * -9) >= (5 + 20))))))\nC. not ((not ((31 % 9) < (-11 + -6))) and (((((-7 * -19) == (-17 - 20)) and (United Kingdom is in Asia.)) and ((6 * 9 - 5 * 10) <= (-3 * -16))) and ((not not (The currency of European Union is the Euro.)) and ((World War II ended occurred in 1945.) and ((-10 * -5) < (1 ** 3))))))\nD. not not ((((not ((11 - -17) <= (-4 - 9) <= (0 * -8 * -1 * 9))) or (not not ((18 - 10) == (-6 * -6)))) or (not not ((A crocodile is a mammal.) or (The currency of Sweden is the Krona.)))) and ((27 is divisible by 12.) and (not not (The first Olympic Games of modern era occurred in 1896.))))\nE. not (not not (((not ((4 ** 3) < (11 + -11))) or ((Thailand is in North America.) and (The 1948 Olympics were held in Mexico City.))) or (The currency of India is the Rupee.)))\nF. ((not ((((-10 * 9 + -5 * -2) > (20 + -3)) and ((-9 * 7 - 1 * 2) < (12 - 14))) and ((The currency of New Zealand is the Dollar.) and (A chicken is a fish.)))) and (not not (((The Sun revolves around the Earth.) and (62 is a prime number.)) or ((-7 * -8 * -6 * 5) != (17 * -5))))) and (not not (not not ((Jupiter is the 5th planet from the Sun.) or ((The 1908 Olympics were held in Munich.) or (A cat has 6 legs.)))))\nG. not not ((((18 - -6) >= (6 + 20)) or ((((17 - 7) >= (-10 * -16)) and (Thailand is in Antarctica.)) and ((Saudi Arabia is in Asia.) and (World War II ended occurred in 1945.)))) or ((The currency of Chile is the Rupee.) or (188 is an odd number.) or (Silver is a gas at room temperature.)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 68815485,
"true_count": 3
},
"seed": 68815485,
"task_id": 668815485,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (((not not (((17 - -14) <= (20 * -4)) and ((-13 - -12) != (-18 * -3)))) or (not not (((8 * -9 + 1 * 4) != (-16 - 4)) or ((10 * 9 + 5 * 9) <= (2 % 8))))) or (((17 * 10) != (1 ** 2)) or ((not not (The capital of Vietnam is Rabat.)) or ((-3 * -7 - -4 * -6) != (5 ** 2)))))
B. (not not (not ((not not (There are 31 days in October.)) and (not not ((-14 - -20) >= (-1 * 7 * 3 * -9)))))) and (not (not not ((((11 - 5) >= (24 % 3)) or (The human body has 150 bones.)) or (not not (The chemical symbol for Silicon is Si.)))))
C. not not (not (((-15 + 2) != (2 * 1 * 8 * -5)) and (A dragonfly is a bird.)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 40340303,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not not (((not not (((17 - -14) <= (20 * -4)) and ((-13 - -12) != (-18 * -3)))) or (not not (((8 * -9 + 1 * 4) != (-16 - 4)) or ((10 * 9 + 5 * 9) <= (2 % 8))))) or (((17 * 10) != (1 ** 2)) or ((not not (The capital of Vietnam is Rabat.)) or ((-3 * -7 - -4 * -6) != (5 ** 2)))))\nB. (not not (not ((not not (There are 31 days in October.)) and (not not ((-14 - -20) >= (-1 * 7 * 3 * -9)))))) and (not (not not ((((11 - 5) >= (24 % 3)) or (The human body has 150 bones.)) or (not not (The chemical symbol for Silicon is Si.)))))\nC. not not (not (((-15 + 2) != (2 * 1 * 8 * -5)) and (A dragonfly is a bird.)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 40340303,
"true_count": 2
},
"seed": 40340303,
"task_id": 640340303,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (not ((5 ** 2) == (17 * 14))) or (((-5 - 12) != (-5 * 3)) and (((4 ** 2) <= (17 + -10)) and ((-10 + -9) <= (-7 * 5 * -5 * 7))))
B. not (not ((西班牙的首都是奥斯陆。) and ((9 * 7 - -1 * 3) < (16 * 0) < (-9 - -6))))
C. not not (not not (((-15 - 6) == (42 % 5)) and (710是斐波那契数。)))
D. not ((-8 + 12) == (8 * -9 + -8 * -7))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 20400468,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. (not ((5 ** 2) == (17 * 14))) or (((-5 - 12) != (-5 * 3)) and (((4 ** 2) <= (17 + -10)) and ((-10 + -9) <= (-7 * 5 * -5 * 7))))\nB. not (not ((西班牙的首都是奥斯陆。) and ((9 * 7 - -1 * 3) < (16 * 0) < (-9 - -6))))\nC. not not (not not (((-15 - 6) == (42 % 5)) and (710是斐波那契数。)))\nD. not ((-8 + 12) == (8 * -9 + -8 * -7))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 20400468,
"true_count": 2
},
"seed": 20400468,
"task_id": 620400468,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((not ((Nigeria is in Europe.) and ((15 + 7) != (2 - 15)))) or (((-3 * -14) == (-7 - 16)) and (not not ((Carbon dioxide is a gas at room temperature.) and (The chemical symbol for Iron is He.))))) and (not not ((((-18 + 13) < (-15 - -8) < (5 ** 2)) or (((6 % 10) < (1 * -8 * 9 * 0)) and (The chemical symbol for Silicon is P.))) and ((A chicken has 2 legs.) or (There are 31 days in September.))))
B. (((not not (The currency of Vietnam is the Rand.)) and (((3 ** 2) >= (-10 + 13)) and ((4 ** 1) <= (0 - -20) <= (-20 + 9)))) and ((A bird has 2 legs.) and (not (((8 % 1) != (3 * 1)) or ((2 ** 3) != (-19 - -14)))))) and ((not ((The chemical symbol for Chromium is P.) or (((-13 - 13) >= (-10 * 5 * 4 * 9)) and (The 1908 Olympics were held in Moscow.)))) or (not not ((14 * 14) <= (-17 * 7))))
C. (not not (not not (((1970 is a leap year.) or (Neptune is the 8th planet from the Sun.)) and (((-14 + 16) >= (1 * -9 - 8 * 8)) or (1931 is a leap year.))))) or (not (((-13 + -15) == (-20 - -18)) or (Nigeria is in Africa.)))
D. not not ((not ((50 % 6) <= (43 % 1))) and ((25 % 8) <= (-3 * -9 * -9 * 4) <= (-8 * 10 - 4 * 4)) and ((A frog has 4 legs.) and ((Argentina is in South America.) and (2005 is a leap year.)) and (((The 1896 Olympics were held in Los Angeles.) and ((5 - -8) <= (14 + -12))) and (not ((7 * -9 - 0 * 7) == (2 - -14))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 99162062,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. ((not ((Nigeria is in Europe.) and ((15 + 7) != (2 - 15)))) or (((-3 * -14) == (-7 - 16)) and (not not ((Carbon dioxide is a gas at room temperature.) and (The chemical symbol for Iron is He.))))) and (not not ((((-18 + 13) < (-15 - -8) < (5 ** 2)) or (((6 % 10) < (1 * -8 * 9 * 0)) and (The chemical symbol for Silicon is P.))) and ((A chicken has 2 legs.) or (There are 31 days in September.))))\nB. (((not not (The currency of Vietnam is the Rand.)) and (((3 ** 2) >= (-10 + 13)) and ((4 ** 1) <= (0 - -20) <= (-20 + 9)))) and ((A bird has 2 legs.) and (not (((8 % 1) != (3 * 1)) or ((2 ** 3) != (-19 - -14)))))) and ((not ((The chemical symbol for Chromium is P.) or (((-13 - 13) >= (-10 * 5 * 4 * 9)) and (The 1908 Olympics were held in Moscow.)))) or (not not ((14 * 14) <= (-17 * 7))))\nC. (not not (not not (((1970 is a leap year.) or (Neptune is the 8th planet from the Sun.)) and (((-14 + 16) >= (1 * -9 - 8 * 8)) or (1931 is a leap year.))))) or (not (((-13 + -15) == (-20 - -18)) or (Nigeria is in Africa.)))\nD. not not ((not ((50 % 6) <= (43 % 1))) and ((25 % 8) <= (-3 * -9 * -9 * 4) <= (-8 * 10 - 4 * 4)) and ((A frog has 4 legs.) and ((Argentina is in South America.) and (2005 is a leap year.)) and (((The 1896 Olympics were held in Los Angeles.) and ((5 - -8) <= (14 + -12))) and (not ((7 * -9 - 0 * 7) == (2 - -14))))))\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": 99162062,
"true_count": 1
},
"seed": 99162062,
"task_id": 699162062,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. (not not (Whales are fish.)) or (((5 * -2 + -8 * 1) <= (-9 * -12) <= (11 + 1)) or (((-10 * -10) >= (16 * 4)) and (Penguins can fly.)))
B. (not ((2069 is a leap year.) or ((13 - -12) < (6 * 7 - 9 * -5)))) and (not not ((Oil is a liquid at room temperature.) or ((-20 - 10) != (5 ** 1))))
C. not ((not not ((12 * 7) <= (5 ** 3) <= (-9 - 5))) and (not ((-3 - 4) < (2 ** 2))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 25296577,
"true_count": 1
},
"question": "Evaluate each expression below:\n\nA. (not not (Whales are fish.)) or (((5 * -2 + -8 * 1) <= (-9 * -12) <= (11 + 1)) or (((-10 * -10) >= (16 * 4)) and (Penguins can fly.)))\nB. (not ((2069 is a leap year.) or ((13 - -12) < (6 * 7 - 9 * -5)))) and (not not ((Oil is a liquid at room temperature.) or ((-20 - 10) != (5 ** 1))))\nC. not ((not not ((12 * 7) <= (5 ** 3) <= (-9 - 5))) and (not ((-3 - 4) < (2 ** 2))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 25296577,
"true_count": 1
},
"seed": 25296577,
"task_id": 625296577,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. ((not not ((17 + -1) != (-2 * 17))) or (莱特兄弟首次飞行发生在1903年。)) or ((not (2是质数。)) or ((美国宣布独立发生在1776年。) and ((-20 * 9) == (-10 * -5 - -3 * -9))))
B. ((25 % 1) < (-16 * 12)) or ((美国宣布独立发生在1766年。) or ((氯的化学符号是U。) or (金在常温下是固体。)))
C. ((3 ** 2) == (13 - 17)) or (((1 ** 2) <= (5 - -20) <= (-18 + -13)) and (电流比光速更快。)) or (((10 * -2 * -10 * 3) == (20 + -6)) or ((-2 * 9 + 10 * 2) > (-2 + 8)))
D. (((5 ** 3) >= (-1 - 3)) and (匈牙利的货币是加元。)) and ((第二次世界大战结束发生在1943年。) and (汞在常温下是液体。))
E. ((not ((-18 - 3) <= (5 ** 3) <= (18 + 5))) or ((太阳绕地球运转。) or ((-18 * -20) <= (4 + -12)))) or ((3 ** 3) < (44 % 10))
F. (土星是距离太阳第3近的行星。) and ((31 % 2) == (7 - -14))
G. (((-20 - 7) <= (4 - -15)) or (not not (加拿大位于北美洲。))) or ((not (七月有31天。)) and (((1 - -8) < (18 - -10)) or ((4 - -6) == (1 ** 1))))
H. ((not (印度的首都是新德里。)) and (((3 * -18) <= (9 * 8 - 5 * 0) <= (10 * -8 - 8 * -7)) or (蟑螂是昆虫。))) and (not not ((法国大革命开始发生在1789年。) and (现代奥运会首届举办发生在1896年。)))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,B,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 90183073,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. ((not not ((17 + -1) != (-2 * 17))) or (莱特兄弟首次飞行发生在1903年。)) or ((not (2是质数。)) or ((美国宣布独立发生在1776年。) and ((-20 * 9) == (-10 * -5 - -3 * -9))))\nB. ((25 % 1) < (-16 * 12)) or ((美国宣布独立发生在1766年。) or ((氯的化学符号是U。) or (金在常温下是固体。)))\nC. ((3 ** 2) == (13 - 17)) or (((1 ** 2) <= (5 - -20) <= (-18 + -13)) and (电流比光速更快。)) or (((10 * -2 * -10 * 3) == (20 + -6)) or ((-2 * 9 + 10 * 2) > (-2 + 8)))\nD. (((5 ** 3) >= (-1 - 3)) and (匈牙利的货币是加元。)) and ((第二次世界大战结束发生在1943年。) and (汞在常温下是液体。))\nE. ((not ((-18 - 3) <= (5 ** 3) <= (18 + 5))) or ((太阳绕地球运转。) or ((-18 * -20) <= (4 + -12)))) or ((3 ** 3) < (44 % 10))\nF. (土星是距离太阳第3近的行星。) and ((31 % 2) == (7 - -14))\nG. (((-20 - 7) <= (4 - -15)) or (not not (加拿大位于北美洲。))) or ((not (七月有31天。)) and (((1 - -8) < (18 - -10)) or ((4 - -6) == (1 ** 1))))\nH. ((not (印度的首都是新德里。)) and (((3 * -18) <= (9 * 8 - 5 * 0) <= (10 * -8 - 8 * -7)) or (蟑螂是昆虫。))) and (not not ((法国大革命开始发生在1789年。) and (现代奥运会首届举办发生在1896年。)))\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": 8,
"seed": 90183073,
"true_count": 4
},
"seed": 90183073,
"task_id": 690183073,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (((47 % 10) != (-12 * 5)) and ((Sharks are mammals.) and ((21 % 8) <= (4 * -18))))
B. (Bats are blind.) and (not ((A sparrow is a bird.) or ((1 - -9) < (3 ** 2) < (10 + 3))))
C. ((not not ((14 * 15) != (10 * -8 + 1 * 5))) and (((8 * 3 + 1 * -4) <= (5 - -1)) or (The capital of Cuba is Havana.))) or (not ((-15 * -18) > (-19 - -7))) or (Neptune is the 2nd planet from the Sun.)
D. not not (161 is a perfect square.)
E. (233 is a perfect square.) or ((-17 + -11) >= (-7 - 4))
F. ((((14 - -20) <= (20 + 12)) or ((-2 * -16) != (11 + -18))) and ((The capital of Saudi Arabia is Copenhagen.) and (A day on Earth is 24 hours.))) and (not not (There are 30 days in July.)) and ((3 * -2 + -2 * -4) <= (2 + 8))
G. ((((-20 + -5) == (-2 * 2 + -2 * 0)) or (The currency of Turkey is the Yuan.)) and (The 1988 Olympics were held in Seoul.)) and (The Pacific Ocean is the largest ocean.)
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": 7,
"seed": 98311997,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (((47 % 10) != (-12 * 5)) and ((Sharks are mammals.) and ((21 % 8) <= (4 * -18))))\nB. (Bats are blind.) and (not ((A sparrow is a bird.) or ((1 - -9) < (3 ** 2) < (10 + 3))))\nC. ((not not ((14 * 15) != (10 * -8 + 1 * 5))) and (((8 * 3 + 1 * -4) <= (5 - -1)) or (The capital of Cuba is Havana.))) or (not ((-15 * -18) > (-19 - -7))) or (Neptune is the 2nd planet from the Sun.)\nD. not not (161 is a perfect square.)\nE. (233 is a perfect square.) or ((-17 + -11) >= (-7 - 4))\nF. ((((14 - -20) <= (20 + 12)) or ((-2 * -16) != (11 + -18))) and ((The capital of Saudi Arabia is Copenhagen.) and (A day on Earth is 24 hours.))) and (not not (There are 30 days in July.)) and ((3 * -2 + -2 * -4) <= (2 + 8))\nG. ((((-20 + -5) == (-2 * 2 + -2 * 0)) or (The currency of Turkey is the Yuan.)) and (The 1988 Olympics were held in Seoul.)) and (The Pacific Ocean is the largest ocean.)\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": 7,
"seed": 98311997,
"true_count": 1
},
"seed": 98311997,
"task_id": 698311997,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not (not ((((-3 - 17) < (9 * -9 + 5 * -6)) and ((Nitrogen is a gas at room temperature.) and (The chemical symbol for Calcium is S.)) and (((Plants produce oxygen through photosynthesis.) and (A duck is an insect.)) and (((-16 + 20) <= (2 * 9 + 6 * -9)) and ((22 % 2) <= (4 ** 1))))) or ((2080 is a leap year.) and ((-4 * 7 + -8 * -10) >= (15 % 10)))))
B. ((((not ((11 % 4) != (16 + -11))) and (The currency of United States is the Dollar.)) and (((1 + -19) < (12 - -12)) and (not not (not not (A dog has 10 legs.))))) and (not not (not ((2 ** 2) >= (7 % 4))))) and (not (not (not ((((-1 * -2 + 10 * -6) >= (0 + 5)) or (There are 31 days in July.)) or (((12 - -18) >= (0 * -3 + -9 * 5)) and ((2 ** 2) >= (-17 * -19)))))))
C. not (not not (not not ((((The speed of light is approximately 300,000 km/s.) or ((4 ** 1) < (4 - 13) < (15 - 13))) or (((22 % 7) != (-17 + 8)) and ((4 ** 1) == (4 ** 1)))) and ((18 % 10) != (-18 * -9)))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 59042460,
"true_count": 1
},
"question": "Consider the following logical expressions:\n\nA. not (not ((((-3 - 17) < (9 * -9 + 5 * -6)) and ((Nitrogen is a gas at room temperature.) and (The chemical symbol for Calcium is S.)) and (((Plants produce oxygen through photosynthesis.) and (A duck is an insect.)) and (((-16 + 20) <= (2 * 9 + 6 * -9)) and ((22 % 2) <= (4 ** 1))))) or ((2080 is a leap year.) and ((-4 * 7 + -8 * -10) >= (15 % 10)))))\nB. ((((not ((11 % 4) != (16 + -11))) and (The currency of United States is the Dollar.)) and (((1 + -19) < (12 - -12)) and (not not (not not (A dog has 10 legs.))))) and (not not (not ((2 ** 2) >= (7 % 4))))) and (not (not (not ((((-1 * -2 + 10 * -6) >= (0 + 5)) or (There are 31 days in July.)) or (((12 - -18) >= (0 * -3 + -9 * 5)) and ((2 ** 2) >= (-17 * -19)))))))\nC. not (not not (not not ((((The speed of light is approximately 300,000 km/s.) or ((4 ** 1) < (4 - 13) < (15 - 13))) or (((22 % 7) != (-17 + 8)) and ((4 ** 1) == (4 ** 1)))) and ((18 % 10) != (-18 * -9)))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 59042460,
"true_count": 1
},
"seed": 59042460,
"task_id": 659042460,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. ((((1 * 5 * -4 * 8) < (-10 * 8) < (4 % 10)) and (United Kingdom is in Europe.)) or (1991 is a leap year.)) or ((Alcohol is a solid at room temperature.) or (2049 is a leap year.)) or ((not ((1 - 7) >= (4 ** 3))) or ((The capital of Ireland is Oslo.) or ((-2 * -12) < (-6 * -2 * -4 * -3) < (-18 + 3))))
B. (The Great Wall of China was built in one year.) and ((Oil is a gas at room temperature.) or ((-1 * 4 - 9 * -2) >= (14 * 19))) and ((10 * -6 * -10 * 2) < (-13 - -16))
C. (((A beetle is an insect.) and ((-3 - 14) <= (2 ** 3))) and (not ((0 * 8 + -2 * 3) < (-9 + 8) < (12 * 18)))) and (((9 * 10 + 4 * -4) != (-7 - -20)) or (not (349 is a Fibonacci number.)))
D. not not (((Steam is a solid at room temperature.) and (The capital of Finland is Rome.)) and (((-5 * -4 * 0 * 0) == (17 + 4)) and ((34 % 10) <= (5 * -1 * 8 * -2) <= (9 * -7 * -1 * 0))))
E. ((not (There are 29 days in July.)) or (((23 % 2) == (19 * -13)) or ((-2 - 11) != (-4 - -9)))) or (((Humans only use 10% of their brain.) or ((7 * 20) > (-7 * 10 - 5 * -7))) or (not not (Diamond is a solid at room temperature.)))
F. (There are 30 days in January.) and ((not (Water is a liquid at room temperature.)) and (((-5 * 10) != (-9 * -2 + 0 * 6)) or (A duck has 2 legs.)))
G. not not (not not ((The capital of Netherlands is Hanoi.) and ((1 ** 2) != (-9 + 20))))
H. (not ((103 is an odd number.) and ((3 * 5 * -7 * -3) == (6 * 2 + 0 * 2)))) and ((-2 - 15) >= (7 * 4 - -3 * 9))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 41919152,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. ((((1 * 5 * -4 * 8) < (-10 * 8) < (4 % 10)) and (United Kingdom is in Europe.)) or (1991 is a leap year.)) or ((Alcohol is a solid at room temperature.) or (2049 is a leap year.)) or ((not ((1 - 7) >= (4 ** 3))) or ((The capital of Ireland is Oslo.) or ((-2 * -12) < (-6 * -2 * -4 * -3) < (-18 + 3))))\nB. (The Great Wall of China was built in one year.) and ((Oil is a gas at room temperature.) or ((-1 * 4 - 9 * -2) >= (14 * 19))) and ((10 * -6 * -10 * 2) < (-13 - -16))\nC. (((A beetle is an insect.) and ((-3 - 14) <= (2 ** 3))) and (not ((0 * 8 + -2 * 3) < (-9 + 8) < (12 * 18)))) and (((9 * 10 + 4 * -4) != (-7 - -20)) or (not (349 is a Fibonacci number.)))\nD. not not (((Steam is a solid at room temperature.) and (The capital of Finland is Rome.)) and (((-5 * -4 * 0 * 0) == (17 + 4)) and ((34 % 10) <= (5 * -1 * 8 * -2) <= (9 * -7 * -1 * 0))))\nE. ((not (There are 29 days in July.)) or (((23 % 2) == (19 * -13)) or ((-2 - 11) != (-4 - -9)))) or (((Humans only use 10% of their brain.) or ((7 * 20) > (-7 * 10 - 5 * -7))) or (not not (Diamond is a solid at room temperature.)))\nF. (There are 30 days in January.) and ((not (Water is a liquid at room temperature.)) and (((-5 * 10) != (-9 * -2 + 0 * 6)) or (A duck has 2 legs.)))\nG. not not (not not ((The capital of Netherlands is Hanoi.) and ((1 ** 2) != (-9 + 20))))\nH. (not ((103 is an odd number.) and ((3 * 5 * -7 * -3) == (6 * 2 + 0 * 2)))) and ((-2 - 15) >= (7 * 4 - -3 * 9))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 41919152,
"true_count": 2
},
"seed": 41919152,
"task_id": 641919152,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not (not ((-11 - -8) <= (10 * -1 - 4 * -2)))
B. (not not ((-2 * -1) < (9 * -1 + -10 * 7))) and (((11 + -8) <= (-2 - -5) <= (46 % 9)) and ((Humans only use 10% of their brain.) and ((-17 * -6) >= (-15 * 17)))) and (not not ((14 + 6) == (5 ** 2)))
C. not ((not (not ((1 ** 1) <= (3 ** 1)))) and (not not (((18 % 7) == (2 * -2 * -5 * 2)) or ((-5 * 3 - -10 * -3) == (17 - 1)))))
D. (((((31 % 1) == (19 + -6)) or (Japan is in Africa.)) and (not (The first Olympic Games of modern era occurred in 1896.))) and (not ((The currency of Philippines is the Peso.) or (Water is a gas at room temperature.)))) and ((not (not ((-1 * 9) < (24 % 5)))) or (((The 2008 Olympics were held in Beijing.) or ((3 ** 2) == (-5 * 1 - 6 * 1))) or (Carbon dioxide is a gas at room temperature.)))
E. not (not (The currency of Peru is the Sol.))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 31462983,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. not (not ((-11 - -8) <= (10 * -1 - 4 * -2)))\nB. (not not ((-2 * -1) < (9 * -1 + -10 * 7))) and (((11 + -8) <= (-2 - -5) <= (46 % 9)) and ((Humans only use 10% of their brain.) and ((-17 * -6) >= (-15 * 17)))) and (not not ((14 + 6) == (5 ** 2)))\nC. not ((not (not ((1 ** 1) <= (3 ** 1)))) and (not not (((18 % 7) == (2 * -2 * -5 * 2)) or ((-5 * 3 - -10 * -3) == (17 - 1)))))\nD. (((((31 % 1) == (19 + -6)) or (Japan is in Africa.)) and (not (The first Olympic Games of modern era occurred in 1896.))) and (not ((The currency of Philippines is the Peso.) or (Water is a gas at room temperature.)))) and ((not (not ((-1 * 9) < (24 % 5)))) or (((The 2008 Olympics were held in Beijing.) or ((3 ** 2) == (-5 * 1 - 6 * 1))) or (Carbon dioxide is a gas at room temperature.)))\nE. not (not (The currency of Peru is the Sol.))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 31462983,
"true_count": 3
},
"seed": 31462983,
"task_id": 631462983,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. 瑞典的货币是韩元。
B. (((19 * -18) == (6 * 6 + 7 * 3)) or ((-18 + 10) >= (10 * 2))) and ((152是奇数。) or (苏联解体发生在1991年。))
C. not not (印度的首都是巴黎。)
D. ((1912年奥运会在柏林举办。) or (德国的首都是柏林。)) and ((-13 * -20) >= (5 + -5))
E. 蜘蛛有8条腿。
F. ((金星是距离太阳第6近的行星。) or ((-20 - 17) != (12 - 16))) and (中国的首都是曼谷。)
G. ((墨西哥位于亚洲。) and ((-2 + -7) <= (-14 + 9))) or ((磷的化学符号是P。) or ((-1 - 7) != (25 % 7)))
H. ((泰坦尼克号沉没发生在1914年。) and ((5 ** 2) < (11 + 1) < (18 - 20))) and ((46能被10整除。) and ((20 + 3) < (4 - 16)))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 13844741,
"true_count": 3
},
"question": "研究以下逻辑语句：\n\nA. 瑞典的货币是韩元。\nB. (((19 * -18) == (6 * 6 + 7 * 3)) or ((-18 + 10) >= (10 * 2))) and ((152是奇数。) or (苏联解体发生在1991年。))\nC. not not (印度的首都是巴黎。)\nD. ((1912年奥运会在柏林举办。) or (德国的首都是柏林。)) and ((-13 * -20) >= (5 + -5))\nE. 蜘蛛有8条腿。\nF. ((金星是距离太阳第6近的行星。) or ((-20 - 17) != (12 - 16))) and (中国的首都是曼谷。)\nG. ((墨西哥位于亚洲。) and ((-2 + -7) <= (-14 + 9))) or ((磷的化学符号是P。) or ((-1 - 7) != (25 % 7)))\nH. ((泰坦尼克号沉没发生在1914年。) and ((5 ** 2) < (11 + 1) < (18 - 20))) and ((46能被10整除。) and ((20 + 3) < (4 - 16)))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 13844741,
"true_count": 3
},
"seed": 13844741,
"task_id": 613844741,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not not (((1927年是闰年。) and (大象有8条腿。)) or ((18 * 1) != (-3 * 8 + 10 * -6)))
B. not (大象有0条腿。)
C. (not (not not ((10 * 8 * 5 * 0) <= (-14 - 17) <= (20 * 15)))) and (not not (人类有0条腿。))
D. not ((17 % 10) <= (4 ** 3))
E. (蜘蛛有10条腿。) or (((20 * 19) <= (23 % 1)) and (((-7 * 0) != (-11 - 16)) or ((-11 + -2) > (7 - 0))))
F. ((not ((13 - -5) > (5 ** 3))) and ((1908年奥运会在伦敦举办。) and (沙特阿拉伯的货币是里亚尔。))) and ((0 * -9 - -7 * -7) == (5 ** 1))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 65148414,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not not (((1927年是闰年。) and (大象有8条腿。)) or ((18 * 1) != (-3 * 8 + 10 * -6)))\nB. not (大象有0条腿。)\nC. (not (not not ((10 * 8 * 5 * 0) <= (-14 - 17) <= (20 * 15)))) and (not not (人类有0条腿。))\nD. not ((17 % 10) <= (4 ** 3))\nE. (蜘蛛有10条腿。) or (((20 * 19) <= (23 % 1)) and (((-7 * 0) != (-11 - 16)) or ((-11 + -2) > (7 - 0))))\nF. ((not ((13 - -5) > (5 ** 3))) and ((1908年奥运会在伦敦举办。) and (沙特阿拉伯的货币是里亚尔。))) and ((0 * -9 - -7 * -7) == (5 ** 1))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 65148414,
"true_count": 2
},
"seed": 65148414,
"task_id": 665148414,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (The chemical symbol for Iron is Fe.)
B. not not (((2 ** 1) < (0 * 4)) and ((2 + -16) != (-9 + -20)))
C. The first moon landing occurred in 1964.
D. (not not ((14 + 3) <= (4 ** 1))) or ((2 * -9 * -10 * -8) >= (1 ** 2))
E. (not not (The 1952 Olympics were held in Montreal.)) or (not (47 is a prime number.))
F. (The chemical symbol for Aluminum is Al.) and (((1 * 2 * -4 * -2) >= (-2 * -7)) and (A salmon is a fish.))
G. (not not ((19 % 5) >= (3 % 9))) or (((12 * -20) <= (18 + -7)) or ((-2 + 19) >= (3 * 1 * -1 * 0)))
H. ((4 * 4) >= (-7 * -6 * 1 * 1)) or (((-9 * -6 - -1 * -10) != (-5 * -2 * 10 * -7)) or (7 is greater than 79.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 35448655,
"true_count": 4
},
"question": "Examine these expressions:\n\nA. not not (The chemical symbol for Iron is Fe.)\nB. not not (((2 ** 1) < (0 * 4)) and ((2 + -16) != (-9 + -20)))\nC. The first moon landing occurred in 1964.\nD. (not not ((14 + 3) <= (4 ** 1))) or ((2 * -9 * -10 * -8) >= (1 ** 2))\nE. (not not (The 1952 Olympics were held in Montreal.)) or (not (47 is a prime number.))\nF. (The chemical symbol for Aluminum is Al.) and (((1 * 2 * -4 * -2) >= (-2 * -7)) and (A salmon is a fish.))\nG. (not not ((19 % 5) >= (3 % 9))) or (((12 * -20) <= (18 + -7)) or ((-2 + 19) >= (3 * 1 * -1 * 0)))\nH. ((4 * 4) >= (-7 * -6 * 1 * 1)) or (((-9 * -6 - -1 * -10) != (-5 * -2 * 10 * -7)) or (7 is greater than 79.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 35448655,
"true_count": 4
},
"seed": 35448655,
"task_id": 635448655,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not not ((埃及位于非洲。) and ((-2 - 14) != (-9 * -7 * 6 * 10)))
B. not ((9 + -10) < (-9 + -3) < (27 % 2))
C. ((((1 ** 2) <= (4 * 8 - -5 * -8)) and ((8 * 10) <= (-9 + 17))) and (not (甲虫是鸟类。))) or ((((20 * 17) <= (-7 + 5)) and (99小于等于18。)) and ((天王星是距离太阳第6近的行星。) and ((-12 * 17) <= (50 % 3) <= (-3 * 5 + 6 * -5))))
D. (not ((酒精在常温下是液体。) or (越南位于南极洲。))) or ((-15 - -1) != (36 % 4)) or (not not (((50 % 7) >= (2 + -1)) and ((7 + -3) <= (7 - -4))))
E. (1904年奥运会在巴黎举办。) and (火星是距离太阳第4近的行星。)
F. ((not (菲律宾的首都是柏林。)) and (((-17 - 6) <= (10 - 8)) and (65是偶数。))) or ((11 + 16) >= (5 ** 3))
G. ((not not ((-1 - -14) <= (-2 * 1 + 6 * 5))) and (((6 % 10) != (1 * -8 - 8 * -10)) and ((21 % 10) > (2 ** 2)))) and ((17 * -10) <= (-20 - -18) <= (-3 * -5 * -9 * -8))
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,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 91359861,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. not not ((埃及位于非洲。) and ((-2 - 14) != (-9 * -7 * 6 * 10)))\nB. not ((9 + -10) < (-9 + -3) < (27 % 2))\nC. ((((1 ** 2) <= (4 * 8 - -5 * -8)) and ((8 * 10) <= (-9 + 17))) and (not (甲虫是鸟类。))) or ((((20 * 17) <= (-7 + 5)) and (99小于等于18。)) and ((天王星是距离太阳第6近的行星。) and ((-12 * 17) <= (50 % 3) <= (-3 * 5 + 6 * -5))))\nD. (not ((酒精在常温下是液体。) or (越南位于南极洲。))) or ((-15 - -1) != (36 % 4)) or (not not (((50 % 7) >= (2 + -1)) and ((7 + -3) <= (7 - -4))))\nE. (1904年奥运会在巴黎举办。) and (火星是距离太阳第4近的行星。)\nF. ((not (菲律宾的首都是柏林。)) and (((-17 - 6) <= (10 - 8)) and (65是偶数。))) or ((11 + 16) >= (5 ** 3))\nG. ((not not ((-1 - -14) <= (-2 * 1 + 6 * 5))) and (((6 % 10) != (1 * -8 - 8 * -10)) and ((21 % 10) > (2 ** 2)))) and ((17 * -10) <= (-20 - -18) <= (-3 * -5 * -9 * -8))\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": 7,
"seed": 91359861,
"true_count": 3
},
"seed": 91359861,
"task_id": 691359861,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. not (((光速约为每秒30万公里。) and (柏林墙倒塌发生在1989年。)) and ((捷克的货币是克朗。) or (蛇有6条腿。)))
B. (第二次世界大战开始发生在1939年。) or ((not not (十二月有31天。)) and (((-19 * 15) < (16 - -9) < (6 - -18)) or ((-6 * 2 + 7 * 7) < (-9 * 7 * -3 * 3) < (5 % 9))))
C. ((not not ((-15 * 15) < (3 + 4))) and ((-20 - -6) <= (-10 + -20))) and (苏联解体发生在1991年。) and (not (((0 * 6 + 0 * -3) >= (-17 + -10)) or (芬兰的首都是赫尔辛基。)))
D. (((0 * -16) != (1 ** 2)) or (not not (德国位于北美洲。))) and (not not ((7 % 4) <= (-15 * 9) <= (3 * -9 * -2 * 3))) and (五月有31天。)
E. ((not not (硫的化学符号是N。)) and (((19 % 1) >= (4 ** 3)) and (75是完全平方数。))) or ((((15 + -20) <= (30 % 10)) or (新加坡的货币是印尼盾。)) or (1955年是闰年。))
F. (not not (not not (1956年奥运会在墨尔本举办。))) and ((-15 - 7) == (4 ** 1))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 27946119,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. not (((光速约为每秒30万公里。) and (柏林墙倒塌发生在1989年。)) and ((捷克的货币是克朗。) or (蛇有6条腿。)))\nB. (第二次世界大战开始发生在1939年。) or ((not not (十二月有31天。)) and (((-19 * 15) < (16 - -9) < (6 - -18)) or ((-6 * 2 + 7 * 7) < (-9 * 7 * -3 * 3) < (5 % 9))))\nC. ((not not ((-15 * 15) < (3 + 4))) and ((-20 - -6) <= (-10 + -20))) and (苏联解体发生在1991年。) and (not (((0 * 6 + 0 * -3) >= (-17 + -10)) or (芬兰的首都是赫尔辛基。)))\nD. (((0 * -16) != (1 ** 2)) or (not not (德国位于北美洲。))) and (not not ((7 % 4) <= (-15 * 9) <= (3 * -9 * -2 * 3))) and (五月有31天。)\nE. ((not not (硫的化学符号是N。)) and (((19 % 1) >= (4 ** 3)) and (75是完全平方数。))) or ((((15 + -20) <= (30 % 10)) or (新加坡的货币是印尼盾。)) or (1955年是闰年。))\nF. (not not (not not (1956年奥运会在墨尔本举办。))) and ((-15 - 7) == (4 ** 1))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 27946119,
"true_count": 2
},
"seed": 27946119,
"task_id": 627946119,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not (Helium is a gas at room temperature.)) and (not not (Thailand is in Oceania.)) and (((((-6 * -7 + -3 * -4) == (-20 * 11)) and ((11 * 6) <= (-13 * 12))) and (not ((16 + -5) > (32 % 4)))) and (The currency of Mexico is the Dollar.))
B. not not (((20 * 15) <= (-16 + -7)) or (((4 ** 3) > (4 * 12)) and (Humans only use 10% of their brain.)) or ((3 * -5) < (5 * -1 * 10 * -2)))
C. (((((0 + -3) <= (-10 - 7)) and (The chemical symbol for Mercury is Hg.)) and ((-10 + 5) < (-1 * -2 + -8 * -8) < (-9 + -5))) or (2 is less than or equal to 48.)) or ((The currency of European Union is the Won.) and (((18 - 12) > (11 * -19)) and ((8 * -14) <= (-13 + -16)))) or (not not (Uranus is the 4th planet from the Sun.))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 88271447,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. (not (Helium is a gas at room temperature.)) and (not not (Thailand is in Oceania.)) and (((((-6 * -7 + -3 * -4) == (-20 * 11)) and ((11 * 6) <= (-13 * 12))) and (not ((16 + -5) > (32 % 4)))) and (The currency of Mexico is the Dollar.))\nB. not not (((20 * 15) <= (-16 + -7)) or (((4 ** 3) > (4 * 12)) and (Humans only use 10% of their brain.)) or ((3 * -5) < (5 * -1 * 10 * -2)))\nC. (((((0 + -3) <= (-10 - 7)) and (The chemical symbol for Mercury is Hg.)) and ((-10 + 5) < (-1 * -2 + -8 * -8) < (-9 + -5))) or (2 is less than or equal to 48.)) or ((The currency of European Union is the Won.) and (((18 - 12) > (11 * -19)) and ((8 * -14) <= (-13 + -16)))) or (not not (Uranus is the 4th planet from the Sun.))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 88271447,
"true_count": 2
},
"seed": 88271447,
"task_id": 688271447,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not not (((175是斐波那契数。) and (企鹅能飞翔。)) or (((-10 - -9) > (13 + -17)) and (新加坡的货币是新加坡元。)))
B. ((四月有30天。) or (德国位于亚洲。)) and (not (not not (水在海平面上的沸点是100摄氏度。)))
C. ((((1 % 7) > (1 * 20)) and ((1 * 10 + -5 * 0) >= (10 * 7 * -4 * -9))) or ((5 * -15) >= (20 * 7))) or (((1 ** 3) < (-13 * -3)) or (((7 + 10) > (4 * -8 + 7 * 6)) and ((0 * 1 + 8 * -9) != (-12 * -19))))
D. (((尼日利亚的货币是奈拉。) and ((6 % 5) == (10 + -17))) and ((氧气在常温下是气体。) or ((14 - 18) != (10 - 13)))) or ((十一月有30天。) or (1960年奥运会在罗马举办。)) or (((氧气在常温下是液体。) or ((2 ** 2) == (-6 + 6))) or (not (南非的货币是克朗。)))
E. ((氢的化学符号是P。) and (((1 ** 1) == (-5 * 9 + -8 * -10)) or ((3 + 15) == (1 ** 1)))) or ((12 * -6) != (33 % 3)) or (1932年奥运会在巴黎举办。)
F. (鳕鱼是鱼类。) and ((((5 ** 3) > (1 * -7)) and ((8 * -5 + 3 * 2) > (3 ** 1))) or ((0 * 18) != (15 + -10)))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 69439170,
"true_count": 5
},
"question": "检验这些表达式：\n\nA. not not (((175是斐波那契数。) and (企鹅能飞翔。)) or (((-10 - -9) > (13 + -17)) and (新加坡的货币是新加坡元。)))\nB. ((四月有30天。) or (德国位于亚洲。)) and (not (not not (水在海平面上的沸点是100摄氏度。)))\nC. ((((1 % 7) > (1 * 20)) and ((1 * 10 + -5 * 0) >= (10 * 7 * -4 * -9))) or ((5 * -15) >= (20 * 7))) or (((1 ** 3) < (-13 * -3)) or (((7 + 10) > (4 * -8 + 7 * 6)) and ((0 * 1 + 8 * -9) != (-12 * -19))))\nD. (((尼日利亚的货币是奈拉。) and ((6 % 5) == (10 + -17))) and ((氧气在常温下是气体。) or ((14 - 18) != (10 - 13)))) or ((十一月有30天。) or (1960年奥运会在罗马举办。)) or (((氧气在常温下是液体。) or ((2 ** 2) == (-6 + 6))) or (not (南非的货币是克朗。)))\nE. ((氢的化学符号是P。) and (((1 ** 1) == (-5 * 9 + -8 * -10)) or ((3 + 15) == (1 ** 1)))) or ((12 * -6) != (33 % 3)) or (1932年奥运会在巴黎举办。)\nF. (鳕鱼是鱼类。) and ((((5 ** 3) > (1 * -7)) and ((8 * -5 + 3 * 2) > (3 ** 1))) or ((0 * 18) != (15 + -10)))\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": 6,
"seed": 69439170,
"true_count": 5
},
"seed": 69439170,
"task_id": 669439170,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not (Australia is in South America.)
B. ((not ((0 * -4) >= (19 * -12))) or ((54 is less than or equal to 66.) or (The capital of Sweden is Stockholm.))) and ((20 - 20) < (-20 + 5) < (1 ** 3))
C. not not (not (((-3 * -19) <= (24 % 9) <= (-9 - 16)) and (Neptune is the 5th planet from the Sun.)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 64850463,
"true_count": 2
},
"question": "Given the following boolean expressions:\n\nA. not (Australia is in South America.)\nB. ((not ((0 * -4) >= (19 * -12))) or ((54 is less than or equal to 66.) or (The capital of Sweden is Stockholm.))) and ((20 - 20) < (-20 + 5) < (1 ** 3))\nC. not not (not (((-3 * -19) <= (24 % 9) <= (-9 - 16)) and (Neptune is the 5th planet from the Sun.)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 64850463,
"true_count": 2
},
"seed": 64850463,
"task_id": 664850463,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not not (not ((India is in South America.) or (A duck is a bird.)))
B. (244 is a perfect square.) and (The 1920 Olympics were held in Antwerp.)
C. not not (The chemical symbol for Manganese is Mn.)
D. (not not (((-8 * -20) >= (4 - 19)) and (Spiders are insects.))) or ((10 * -4) <= (-9 * 19) <= (-5 * 9 + 3 * 2)) or (A cockroach is an insect.)
E. ((not (Saudi Arabia is in Antarctica.)) or ((The 1928 Olympics were held in Amsterdam.) and (90 is an odd number.))) and ((not not ((6 * -2 - -9 * 10) < (1 ** 1) < (-9 * -3 - -3 * 9))) and (not not (The capital of France is Paris.)))
F. (There are 29 days in July.) or (((7 * -9 * 3 * 2) != (11 + 11)) or (There are 28 days in February.)) or ((((9 * 9) != (12 * -18)) or ((19 * 0) < (6 + -18))) and (((1 * 5 * 0 * -7) < (19 - -17)) and (2042 is a leap year.)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 52491268,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. not not (not ((India is in South America.) or (A duck is a bird.)))\nB. (244 is a perfect square.) and (The 1920 Olympics were held in Antwerp.)\nC. not not (The chemical symbol for Manganese is Mn.)\nD. (not not (((-8 * -20) >= (4 - 19)) and (Spiders are insects.))) or ((10 * -4) <= (-9 * 19) <= (-5 * 9 + 3 * 2)) or (A cockroach is an insect.)\nE. ((not (Saudi Arabia is in Antarctica.)) or ((The 1928 Olympics were held in Amsterdam.) and (90 is an odd number.))) and ((not not ((6 * -2 - -9 * 10) < (1 ** 1) < (-9 * -3 - -3 * 9))) and (not not (The capital of France is Paris.)))\nF. (There are 29 days in July.) or (((7 * -9 * 3 * 2) != (11 + 11)) or (There are 28 days in February.)) or ((((9 * 9) != (12 * -18)) or ((19 * 0) < (6 + -18))) and (((1 * 5 * 0 * -7) < (19 - -17)) and (2042 is a leap year.)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 52491268,
"true_count": 3
},
"seed": 52491268,
"task_id": 652491268,
"task_type": "boolean_expressions"
} |
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