env stringclasses 1
value | prompt stringlengths 85 3.69k | extra dict |
|---|---|---|
logic-v2 | Consider the following logical expressions:
A. (6 - -2) < (35 % 9) < (-17 * -14)
B. not not ((There are 30 days in September.) and (Morocco is in Africa.))
C. not not (not not ((-5 * 8 * -4 * 3) >= (9 * 10 - -1 * 1)))
D. (not not (The capital of Saudi Arabia is Lisbon.)) or (((18 + -8) <= (1 ** 3) <= (19 * -16)) and (The chemical symbol for Calcium is Ag.))
E. ((133 is an odd number.) and (A lobster has 10 legs.)) or (((8 * 9 + 4 * -6) < (1 ** 3) < (-10 * -8 + 9 * 1)) and (The capital of Morocco is Rabat.))
F. (-7 + -9) >= (7 * -8 - 0 * 1)
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 55354421,
"true_count": 4
},
"question": "Consider the following logical expressions:\n\nA. (6 - -2) < (35 % 9) < (-17 * -14)\nB. not not ((There are 30 days in September.) and (Morocco is in Africa.))\nC. not not (not not ((-5 * 8 * -4 * 3) >= (9 * 10 - -1 * 1)))\nD. (not not (The capital of Saudi Arabia is Lisbon.)) or (((18 + -8) <= (1 ** 3) <= (19 * -16)) and (The chemical symbol for Calcium is Ag.))\nE. ((133 is an odd number.) and (A lobster has 10 legs.)) or (((8 * 9 + 4 * -6) < (1 ** 3) < (-10 * -8 + 9 * 1)) and (The capital of Morocco is Rabat.))\nF. (-7 + -9) >= (7 * -8 - 0 * 1)\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 55354421,
"true_count": 4
},
"seed": 55354421,
"task_id": 655354421,
"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. 地球上一天是24小时。
B. not ((8 * 20) > (4 ** 3))
C. ((1968年奥运会在北京举办。) and ((-14 * 0) < (-12 + -7))) and (六月有29天。)
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 24424075,
"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. 地球上一天是24小时。\nB. not ((8 * 20) > (4 ** 3))\nC. ((1968年奥运会在北京举办。) and ((-14 * 0) < (-12 + -7))) and (六月有29天。)\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 24424075,
"true_count": 1
},
"seed": 24424075,
"task_id": 624424075,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not (not not (((The chemical symbol for Mercury is Pt.) or ((-19 * -1) < (4 - -7))) and ((Oil is a liquid at room temperature.) or ((15 - -8) < (15 - -18) < (-15 - 11)))))) and (((((The 1936 Olympics were held in London.) or ((19 * 1) != (2 * -15))) and (not (27 is divisible by 6.))) and ((-11 * 11) > (11 % 8)) and (The 1964 Olympics were held in Munich.)) or (not ((((-5 - -11) < (16 * 2)) or ((38 % 1) <= (18 * 5))) or ((15 + -12) < (-4 + -11) < (37 % 6)))))
B. (not not (not (((The capital of Egypt is Singapore.) or (World War I ended occurred in 1918.)) or ((Water is a liquid at room temperature.) and (The French Revolution began occurred in 1789.))))) or (not not (Electricity flows faster than light.)) or (((902 is a Fibonacci number.) or ((-8 * 3 - -10 * 7) >= (4 ** 1))) or ((The chemical symbol for Chlorine is Cl.) or ((not (The 1968 Olympics were held in Mexico City.)) and (The 1936 Olympics were held in Berlin.))))
C. (not (not ((not ((15 - -16) < (-2 * -1 - -4 * -1) < (-16 + 5))) and (not (Brazil is in South America.))))) or ((((-1 - -2) != (1 ** 3)) and (not ((14 * 0) <= (10 * 0 + -6 * 10))) and ((-20 * -11) != (7 + 9))) and ((not ((Jupiter is the 3rd planet from the Sun.) and (Earth is the 3rd planet from the Sun.))) and ((1 ** 3) <= (40 % 2) <= (-3 - 18)) and ((not ((-6 - -13) < (2 ** 2) < (5 ** 1))) or (not not (China is in Asia.)))))
D. not not (not (not not (not ((Helium is a liquid at room temperature.) and (The chemical symbol for Platinum is Hg.)))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 60777603,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. (not (not not (((The chemical symbol for Mercury is Pt.) or ((-19 * -1) < (4 - -7))) and ((Oil is a liquid at room temperature.) or ((15 - -8) < (15 - -18) < (-15 - 11)))))) and (((((The 1936 Olympics were held in London.) or ((19 * 1) != (2 * -15))) and (not (27 is divisible by 6.))) and ((-11 * 11) > (11 % 8)) and (The 1964 Olympics were held in Munich.)) or (not ((((-5 - -11) < (16 * 2)) or ((38 % 1) <= (18 * 5))) or ((15 + -12) < (-4 + -11) < (37 % 6)))))\nB. (not not (not (((The capital of Egypt is Singapore.) or (World War I ended occurred in 1918.)) or ((Water is a liquid at room temperature.) and (The French Revolution began occurred in 1789.))))) or (not not (Electricity flows faster than light.)) or (((902 is a Fibonacci number.) or ((-8 * 3 - -10 * 7) >= (4 ** 1))) or ((The chemical symbol for Chlorine is Cl.) or ((not (The 1968 Olympics were held in Mexico City.)) and (The 1936 Olympics were held in Berlin.))))\nC. (not (not ((not ((15 - -16) < (-2 * -1 - -4 * -1) < (-16 + 5))) and (not (Brazil is in South America.))))) or ((((-1 - -2) != (1 ** 3)) and (not ((14 * 0) <= (10 * 0 + -6 * 10))) and ((-20 * -11) != (7 + 9))) and ((not ((Jupiter is the 3rd planet from the Sun.) and (Earth is the 3rd planet from the Sun.))) and ((1 ** 3) <= (40 % 2) <= (-3 - 18)) and ((not ((-6 - -13) < (2 ** 2) < (5 ** 1))) or (not not (China is in Asia.)))))\nD. not not (not (not not (not ((Helium is a liquid at room temperature.) and (The chemical symbol for Platinum is Hg.)))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 60777603,
"true_count": 1
},
"seed": 60777603,
"task_id": 660777603,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (((-8 * -8) != (7 - -5)) and (United States is in North America.) and ((not not ((-8 - 11) <= (2 * 0 + -6 * -7))) and (not (Russia is in Europe.)))) and (not ((((18 % 7) != (9 + 11)) or (The French Revolution began occurred in 1789.)) and ((A turtle is an insect.) and (Earth is the 6th planet from the Sun.))))
B. not not (((6 + -6) <= (-7 + -3)) or (Air is a solid at room temperature.))
C. ((((-3 - 4) != (1 ** 3)) and (The currency of Egypt is the Peso.)) and (The 2000 Olympics were held in Sydney.) and (The capital of Cuba is New Delhi.)) or (((2 - -9) < (6 - 6)) and ((((-2 * 13) <= (29 % 1)) and ((-3 + 7) <= (-10 * -7 * -1 * 1) <= (4 * 3 + -1 * 6))) and (((2 ** 3) < (19 * -5)) or ((5 - 10) == (6 + 20)))))
D. not ((not ((-9 * -15) <= (11 + -16))) or ((13 * -18) >= (-14 + 18)))
E. not ((1905 is a leap year.) and (not not (((10 * 9 + 1 * -8) == (8 - -8)) and (The 1988 Olympics were held in Berlin.))))
F. (not not (not not ((9 * 0 * -4 * -6) <= (-12 - -6)))) or (not (not not (((12 + 2) == (2 ** 1)) or ((11 * -4) < (11 * -12)))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 33591203,
"true_count": 2
},
"question": "Below are several boolean expressions:\n\nA. (((-8 * -8) != (7 - -5)) and (United States is in North America.) and ((not not ((-8 - 11) <= (2 * 0 + -6 * -7))) and (not (Russia is in Europe.)))) and (not ((((18 % 7) != (9 + 11)) or (The French Revolution began occurred in 1789.)) and ((A turtle is an insect.) and (Earth is the 6th planet from the Sun.))))\nB. not not (((6 + -6) <= (-7 + -3)) or (Air is a solid at room temperature.))\nC. ((((-3 - 4) != (1 ** 3)) and (The currency of Egypt is the Peso.)) and (The 2000 Olympics were held in Sydney.) and (The capital of Cuba is New Delhi.)) or (((2 - -9) < (6 - 6)) and ((((-2 * 13) <= (29 % 1)) and ((-3 + 7) <= (-10 * -7 * -1 * 1) <= (4 * 3 + -1 * 6))) and (((2 ** 3) < (19 * -5)) or ((5 - 10) == (6 + 20)))))\nD. not ((not ((-9 * -15) <= (11 + -16))) or ((13 * -18) >= (-14 + 18)))\nE. not ((1905 is a leap year.) and (not not (((10 * 9 + 1 * -8) == (8 - -8)) and (The 1988 Olympics were held in Berlin.))))\nF. (not not (not not ((9 * 0 * -4 * -6) <= (-12 - -6)))) or (not (not not (((12 + 2) == (2 ** 1)) or ((11 * -4) < (11 * -12)))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 33591203,
"true_count": 2
},
"seed": 33591203,
"task_id": 633591203,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. 207是完全平方数。
B. not not (not ((-14 + -11) == (16 * 15)))
C. (-1 * 9 * 8 * 6) != (0 - 19)
D. not (not ((3 % 1) <= (1 * -11)))
E. 五月有31天。
F. not not ((19 - 10) <= (1 * -2 + -10 * 2) <= (17 + 7))
G. (((10 + -10) < (-1 * 7 + 7 * 0)) and (乌鸦是鸟类。)) or (not not (水星是距离太阳第1近的行星。))
H. not not (摩洛哥位于非洲。)
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,C,E,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 51430841,
"true_count": 5
},
"question": "考虑以下布尔表达式：\n\nA. 207是完全平方数。\nB. not not (not ((-14 + -11) == (16 * 15)))\nC. (-1 * 9 * 8 * 6) != (0 - 19)\nD. not (not ((3 % 1) <= (1 * -11)))\nE. 五月有31天。\nF. not not ((19 - 10) <= (1 * -2 + -10 * 2) <= (17 + 7))\nG. (((10 + -10) < (-1 * 7 + 7 * 0)) and (乌鸦是鸟类。)) or (not not (水星是距离太阳第1近的行星。))\nH. not not (摩洛哥位于非洲。)\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 51430841,
"true_count": 5
},
"seed": 51430841,
"task_id": 651430841,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (((1 ** 1) == (10 + -19)) and ((6 + -9) == (-9 + 4))) or (((1912 is a leap year.) or ((-5 * 5 - -6 * 4) <= (5 * -14))) and ((-19 * -3) > (0 * -11)))
B. not (Brazil is in Antarctica.)
C. (The square root of 225 is 15.) and ((not (The capital of Philippines is Manila.)) and (not not ((13 - -19) != (-15 + -13))))
D. (((The capital of South Korea is Havana.) or ((6 * -3 - -5 * -9) <= (6 * 20) <= (4 * 8 + 0 * 4))) or ((The chemical symbol for Helium is Zn.) or (The chemical symbol for Carbon is C.))) or ((Mars is the 7th planet from the Sun.) or (Venus is the 5th planet from the Sun.)) or (((The capital of Venezuela is Caracas.) or (Mercury is the 1st planet from the Sun.)) and (Helium is a gas at room temperature.))
E. not not ((not not (A octopus has 4 legs.)) or ((-9 * -9 - 3 * 8) != (14 - 14)))
F. not (not (not not ((-7 + -10) < (8 * 9) < (7 * -11))))
G. ((not (Mars is the 1st planet from the Sun.)) or ((The capital of Indonesia is Jakarta.) or (Sharks are mammals.))) or (((Air is a gas at room temperature.) or (The currency of Nigeria is the Sol.)) and (not ((10 * 4 + -5 * 2) <= (-17 * -12))))
H. (((5 * 4) >= (-7 + 1)) and ((30 % 8) != (18 * -2))) or ((((15 + 10) >= (-16 + -16)) and ((0 + -18) == (2 - -15))) and ((The chemical symbol for Nitrogen is Al.) and (The capital of Cuba is Cairo.)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,D,E,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 6364066,
"true_count": 6
},
"question": "Study the following logical statements:\n\nA. (((1 ** 1) == (10 + -19)) and ((6 + -9) == (-9 + 4))) or (((1912 is a leap year.) or ((-5 * 5 - -6 * 4) <= (5 * -14))) and ((-19 * -3) > (0 * -11)))\nB. not (Brazil is in Antarctica.)\nC. (The square root of 225 is 15.) and ((not (The capital of Philippines is Manila.)) and (not not ((13 - -19) != (-15 + -13))))\nD. (((The capital of South Korea is Havana.) or ((6 * -3 - -5 * -9) <= (6 * 20) <= (4 * 8 + 0 * 4))) or ((The chemical symbol for Helium is Zn.) or (The chemical symbol for Carbon is C.))) or ((Mars is the 7th planet from the Sun.) or (Venus is the 5th planet from the Sun.)) or (((The capital of Venezuela is Caracas.) or (Mercury is the 1st planet from the Sun.)) and (Helium is a gas at room temperature.))\nE. not not ((not not (A octopus has 4 legs.)) or ((-9 * -9 - 3 * 8) != (14 - 14)))\nF. not (not (not not ((-7 + -10) < (8 * 9) < (7 * -11))))\nG. ((not (Mars is the 1st planet from the Sun.)) or ((The capital of Indonesia is Jakarta.) or (Sharks are mammals.))) or (((Air is a gas at room temperature.) or (The currency of Nigeria is the Sol.)) and (not ((10 * 4 + -5 * 2) <= (-17 * -12))))\nH. (((5 * 4) >= (-7 + 1)) and ((30 % 8) != (18 * -2))) or ((((15 + 10) >= (-16 + -16)) and ((0 + -18) == (2 - -15))) and ((The chemical symbol for Nitrogen is Al.) and (The capital of Cuba is Cairo.)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 6364066,
"true_count": 6
},
"seed": 6364066,
"task_id": 606364066,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not not ((not ((-16 + 4) < (4 ** 1))) and (((-6 - 2) < (-8 - -9)) or (蛇有2条腿。)))
B. ((not not (not ((-1 - 13) >= (32 % 3)))) and (1956年奥运会在墨尔本举办。)) and (((32 % 3) <= (-19 + -15) <= (2 ** 2)) and (not not ((5 ** 3) >= (-6 * -1 + 0 * 10))) and (((泰国的首都是曼谷。) and ((-15 * 17) < (-6 * -9 * -7 * -8) < (-1 * 8 + -2 * 6))) and ((镍的化学符号是Al。) and ((-6 * -2 * 0 * 10) != (-4 * -1 + 0 * -8)))))
C. (not (not (not not (鹦鹉是鸟类。)))) or ((not ((硅的化学符号是Si。) or ((19 * -2) >= (-8 * -14)))) and (not not ((伦敦大火发生在1666年。) or ((9 + 14) == (-18 + 6)))))
D. ((not not ((汞在常温下是液体。) and ((1 + -8) != (-12 - 15)))) and (((巴西的货币是雷亚尔。) or (澳大利亚的货币是雷亚尔。)) or ((37能被9整除。) and ((20 % 1) != (5 - 5))))) or ((196是完全平方数。) or (人体有150块骨头。)) or ((2012年奥运会在伦敦举办。) or (not ((龙虾有6条腿。) and (汞在常温下是液体。))))
E. (not not ((匈牙利的首都是吉隆坡。) or (not (土星是距离太阳第6近的行星。)))) or ((((钻石在常温下是固体。) and (水星是距离太阳第1近的行星。)) or ((莱特兄弟首次飞行发生在1903年。) or ((3 - -2) > (-3 + -19)))) and ((丹麦的首都是都柏林。) and (((-1 + 6) >= (-7 * -6 * -5 * 7)) and (1952年奥运会在赫尔辛基举办。))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 17294348,
"true_count": 2
},
"question": "评估以下每个表达式：\n\nA. not not ((not ((-16 + 4) < (4 ** 1))) and (((-6 - 2) < (-8 - -9)) or (蛇有2条腿。)))\nB. ((not not (not ((-1 - 13) >= (32 % 3)))) and (1956年奥运会在墨尔本举办。)) and (((32 % 3) <= (-19 + -15) <= (2 ** 2)) and (not not ((5 ** 3) >= (-6 * -1 + 0 * 10))) and (((泰国的首都是曼谷。) and ((-15 * 17) < (-6 * -9 * -7 * -8) < (-1 * 8 + -2 * 6))) and ((镍的化学符号是Al。) and ((-6 * -2 * 0 * 10) != (-4 * -1 + 0 * -8)))))\nC. (not (not (not not (鹦鹉是鸟类。)))) or ((not ((硅的化学符号是Si。) or ((19 * -2) >= (-8 * -14)))) and (not not ((伦敦大火发生在1666年。) or ((9 + 14) == (-18 + 6)))))\nD. ((not not ((汞在常温下是液体。) and ((1 + -8) != (-12 - 15)))) and (((巴西的货币是雷亚尔。) or (澳大利亚的货币是雷亚尔。)) or ((37能被9整除。) and ((20 % 1) != (5 - 5))))) or ((196是完全平方数。) or (人体有150块骨头。)) or ((2012年奥运会在伦敦举办。) or (not ((龙虾有6条腿。) and (汞在常温下是液体。))))\nE. (not not ((匈牙利的首都是吉隆坡。) or (not (土星是距离太阳第6近的行星。)))) or ((((钻石在常温下是固体。) and (水星是距离太阳第1近的行星。)) or ((莱特兄弟首次飞行发生在1903年。) or ((3 - -2) > (-3 + -19)))) and ((丹麦的首都是都柏林。) and (((-1 + 6) >= (-7 * -6 * -5 * 7)) and (1952年奥运会在赫尔辛基举办。))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 17294348,
"true_count": 2
},
"seed": 17294348,
"task_id": 617294348,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (not (((36 % 1) != (5 * -8 * -2 * -8)) or ((The currency of Thailand is the Baht.) and (70 is a prime number.)))) and (The chemical symbol for Hydrogen is Co.) and ((((190 is a Fibonacci number.) and (Brazil is in South America.)) or (((9 - 5) <= (8 + 12)) or (The chemical symbol for Tin is Sn.))) or (not not (not not ((-12 * 4) < (17 * 20)))))
B. not (((((-17 * 12) == (40 % 3)) and ((-7 + -19) > (-10 - -1))) and (((-9 - -3) > (5 ** 2)) or (China is in Asia.))) and (not (((-8 * 2 + -1 * -3) > (5 ** 1)) or ((-2 * 9) > (9 - 20)))))
C. ((((The currency of Colombia is the Rand.) and ((15 * -8) < (32 % 2) < (8 * -4 + -3 * 8))) or (not not (The chemical symbol for Nickel is Ni.))) and ((2055 is a leap year.) and ((The chemical symbol for Zinc is Cu.) and (The 2012 Olympics were held in London.)))) and ((((-9 + -2) != (5 % 9)) or (not (Oxygen is a gas at room temperature.))) and ((The chemical symbol for Titanium is Ti.) and ((Spiders are insects.) or ((2 ** 2) == (-15 - 8)))))
D. (((((6 * 8 + 10 * 10) < (14 - 0)) and ((2 ** 1) != (-2 * 2))) or (((-6 - -14) > (-7 + -19)) or (The chemical symbol for Platinum is Pt.))) and ((not ((-19 * -11) <= (-10 * 11))) and (not (The Soviet Union dissolved occurred in 1991.)))) or (((-13 + 16) != (4 + -5)) or ((The 1956 Olympics were held in Melbourne.) and ((-18 + -9) >= (4 - -12)))) or ((Nigeria is in Africa.) and (((The 1996 Olympics were held in Atlanta.) or (Iron is a gas at room temperature.)) or ((3 ** 2) > (-12 - 20))))
E. (((((15 + -6) == (39 % 3)) or (The capital of Chile is Lisbon.)) and (not not ((41 % 10) >= (-1 - 0)))) and ((not (The chemical symbol for Phosphorus is P.)) or (202 is a perfect square.))) and (((((11 * 18) <= (9 * -4 + 2 * -6)) or (The 1984 Olympics were held in Los Angeles.)) or (Nigeria is in Oceania.)) and ((3 * 4 + 1 * 3) < (18 + 14) < (0 * 7 + -7 * 5)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 16348183,
"true_count": 2
},
"question": "Review these logical expressions:\n\nA. (not (((36 % 1) != (5 * -8 * -2 * -8)) or ((The currency of Thailand is the Baht.) and (70 is a prime number.)))) and (The chemical symbol for Hydrogen is Co.) and ((((190 is a Fibonacci number.) and (Brazil is in South America.)) or (((9 - 5) <= (8 + 12)) or (The chemical symbol for Tin is Sn.))) or (not not (not not ((-12 * 4) < (17 * 20)))))\nB. not (((((-17 * 12) == (40 % 3)) and ((-7 + -19) > (-10 - -1))) and (((-9 - -3) > (5 ** 2)) or (China is in Asia.))) and (not (((-8 * 2 + -1 * -3) > (5 ** 1)) or ((-2 * 9) > (9 - 20)))))\nC. ((((The currency of Colombia is the Rand.) and ((15 * -8) < (32 % 2) < (8 * -4 + -3 * 8))) or (not not (The chemical symbol for Nickel is Ni.))) and ((2055 is a leap year.) and ((The chemical symbol for Zinc is Cu.) and (The 2012 Olympics were held in London.)))) and ((((-9 + -2) != (5 % 9)) or (not (Oxygen is a gas at room temperature.))) and ((The chemical symbol for Titanium is Ti.) and ((Spiders are insects.) or ((2 ** 2) == (-15 - 8)))))\nD. (((((6 * 8 + 10 * 10) < (14 - 0)) and ((2 ** 1) != (-2 * 2))) or (((-6 - -14) > (-7 + -19)) or (The chemical symbol for Platinum is Pt.))) and ((not ((-19 * -11) <= (-10 * 11))) and (not (The Soviet Union dissolved occurred in 1991.)))) or (((-13 + 16) != (4 + -5)) or ((The 1956 Olympics were held in Melbourne.) and ((-18 + -9) >= (4 - -12)))) or ((Nigeria is in Africa.) and (((The 1996 Olympics were held in Atlanta.) or (Iron is a gas at room temperature.)) or ((3 ** 2) > (-12 - 20))))\nE. (((((15 + -6) == (39 % 3)) or (The capital of Chile is Lisbon.)) and (not not ((41 % 10) >= (-1 - 0)))) and ((not (The chemical symbol for Phosphorus is P.)) or (202 is a perfect square.))) and (((((11 * 18) <= (9 * -4 + 2 * -6)) or (The 1984 Olympics were held in Los Angeles.)) or (Nigeria is in Oceania.)) and ((3 * 4 + 1 * 3) < (18 + 14) < (0 * 7 + -7 * 5)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
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"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not not (not ((((not not ((10 - 15) >= (-15 * -14))) or (((-14 * 6) != (12 % 1)) and (The 1956 Olympics were held in Munich.))) and (not (Iron is a solid at room temperature.))) and ((not not (((13 * 19) < (16 - 18)) and (A sheep is a mammal.))) and ((not not ((2 * -8) <= (-2 * 0 + -6 * -9))) and (not (A horse has 8 legs.))))))
B. not not (not not ((((((6 - -6) <= (5 ** 1)) or ((0 + 1) > (-9 + 18))) and (((20 + 20) <= (2 ** 2)) or (The 1928 Olympics were held in Amsterdam.))) and ((Copper is a solid at room temperature.) or (A bear is a reptile.)) and (not not ((The chemical symbol for Gold is Mn.) and ((10 * 4 + -8 * -6) <= (8 * 0))))) or (Earth is the 3rd planet from the Sun.) or (((5 ** 2) > (15 - -14)) or (((6 + 1) == (45 % 5)) or (The currency of Vietnam is the Shekel.)) or ((9 * 2) > (-16 * -8)))))
C. not (not not (((not not (not not ((12 + 11) < (39 % 1)))) or ((not not (Plants produce oxygen through photosynthesis.)) and (not ((14 - -17) == (-8 * -6))))) or ((The chemical symbol for Neon is Ne.) or ((((6 * 11) == (3 ** 3)) and ((-18 - -2) <= (-20 - -19) <= (-7 * 4 + 8 * 2))) or ((18 - 13) >= (-3 - -20))))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
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"answer": "A,B",
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"question": "Analyze these boolean expressions:\n\nA. not not (not ((((not not ((10 - 15) >= (-15 * -14))) or (((-14 * 6) != (12 % 1)) and (The 1956 Olympics were held in Munich.))) and (not (Iron is a solid at room temperature.))) and ((not not (((13 * 19) < (16 - 18)) and (A sheep is a mammal.))) and ((not not ((2 * -8) <= (-2 * 0 + -6 * -9))) and (not (A horse has 8 legs.))))))\nB. not not (not not ((((((6 - -6) <= (5 ** 1)) or ((0 + 1) > (-9 + 18))) and (((20 + 20) <= (2 ** 2)) or (The 1928 Olympics were held in Amsterdam.))) and ((Copper is a solid at room temperature.) or (A bear is a reptile.)) and (not not ((The chemical symbol for Gold is Mn.) and ((10 * 4 + -8 * -6) <= (8 * 0))))) or (Earth is the 3rd planet from the Sun.) or (((5 ** 2) > (15 - -14)) or (((6 + 1) == (45 % 5)) or (The currency of Vietnam is the Shekel.)) or ((9 * 2) > (-16 * -8)))))\nC. not (not not (((not not (not not ((12 + 11) < (39 % 1)))) or ((not not (Plants produce oxygen through photosynthesis.)) and (not ((14 - -17) == (-8 * -6))))) or ((The chemical symbol for Neon is Ne.) or ((((6 * 11) == (3 ** 3)) and ((-18 - -2) <= (-20 - -19) <= (-7 * 4 + 8 * 2))) or ((18 - 13) >= (-3 - -20))))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
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"language": "en",
"num_options": 3,
"seed": 67172124,
"true_count": 2
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"seed": 67172124,
"task_id": 667172124,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. (((5 * -1 - -2 * -8) >= (-18 - 19)) or (not ((-6 * -7 - 10 * 4) > (-4 - -4))) or ((19 - -2) > (2 * -3 + -10 * 8))) and (((((13 - 20) <= (0 * -8 - 2 * -3)) and (The currency of Brazil is the Real.)) and ((The 1908 Olympics were held in Amsterdam.) or (The 1936 Olympics were held in Sydney.))) or (not (not (The 1992 Olympics were held in Barcelona.))))
B. not not ((not not (((-5 * 16) != (3 ** 1)) or (The chemical symbol for Hydrogen is H.))) and ((Plants produce oxygen through photosynthesis.) and ((3 ** 3) <= (1 + 4) <= (-16 - -2))) and ((20 + -6) < (8 * 2)))
C. (not not (((384 is a perfect square.) or (Egypt is in Africa.)) and (not not ((-19 + -8) > (-18 - 10))))) and (not not (The 1964 Olympics were held in Tokyo.))
D. (not ((-7 + -3) == (-4 * 5 + 6 * -2))) or ((The currency of Peru is the Dollar.) or (not not (not ((10 + -9) > (-16 - -10)))))
E. not (((-13 + 8) == (3 - 5)) or ((((-14 - 10) <= (2 ** 1)) or ((5 ** 1) == (18 - 20))) and (not not (The currency of India is the Lira.))))
F. (not ((7 * -7 + 2 * 5) != (-7 * -7 - 3 * 0))) or (not ((-4 + 20) != (1 * -4 + 5 * 2))) or ((not not ((Morocco is in Africa.) and ((15 + 12) != (29 % 6)))) and (not (not (Christopher Columbus reached America occurred in 1492.))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
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"answer": "A,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
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"question": "Evaluate each expression below:\n\nA. (((5 * -1 - -2 * -8) >= (-18 - 19)) or (not ((-6 * -7 - 10 * 4) > (-4 - -4))) or ((19 - -2) > (2 * -3 + -10 * 8))) and (((((13 - 20) <= (0 * -8 - 2 * -3)) and (The currency of Brazil is the Real.)) and ((The 1908 Olympics were held in Amsterdam.) or (The 1936 Olympics were held in Sydney.))) or (not (not (The 1992 Olympics were held in Barcelona.))))\nB. not not ((not not (((-5 * 16) != (3 ** 1)) or (The chemical symbol for Hydrogen is H.))) and ((Plants produce oxygen through photosynthesis.) and ((3 ** 3) <= (1 + 4) <= (-16 - -2))) and ((20 + -6) < (8 * 2)))\nC. (not not (((384 is a perfect square.) or (Egypt is in Africa.)) and (not not ((-19 + -8) > (-18 - 10))))) and (not not (The 1964 Olympics were held in Tokyo.))\nD. (not ((-7 + -3) == (-4 * 5 + 6 * -2))) or ((The currency of Peru is the Dollar.) or (not not (not ((10 + -9) > (-16 - -10)))))\nE. not (((-13 + 8) == (3 - 5)) or ((((-14 - 10) <= (2 ** 1)) or ((5 ** 1) == (18 - 20))) and (not not (The currency of India is the Lira.))))\nF. (not ((7 * -7 + 2 * 5) != (-7 * -7 - 3 * 0))) or (not ((-4 + 20) != (1 * -4 + 5 * 2))) or ((not not ((Morocco is in Africa.) and ((15 + 12) != (29 % 6)))) and (not (not (Christopher Columbus reached America occurred in 1492.))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
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"true_count": 5
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"seed": 65322053,
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"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. 2086 is a leap year.
B. (-11 * 1) == (1 ** 2)
C. (((-8 + 6) >= (-18 + -14)) and ((6 * -2 - 10 * 2) > (19 - -1))) or (not ((-4 - -16) != (4 ** 2)))
D. not (((14 * 18) < (-19 * -8)) or ((2 ** 1) == (3 ** 1)))
E. ((The chemical symbol for Cobalt is Co.) or (Neptune is the 8th planet from the Sun.)) and ((-18 + -16) >= (7 - -3))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
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"answer": "D",
"difficulty": 1,
"gpt_response": "",
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"true_count": 1
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"question": "Given the following boolean expressions:\n\nA. 2086 is a leap year.\nB. (-11 * 1) == (1 ** 2)\nC. (((-8 + 6) >= (-18 + -14)) and ((6 * -2 - 10 * 2) > (19 - -1))) or (not ((-4 - -16) != (4 ** 2)))\nD. not (((14 * 18) < (-19 * -8)) or ((2 ** 1) == (3 ** 1)))\nE. ((The chemical symbol for Cobalt is Co.) or (Neptune is the 8th planet from the Sun.)) and ((-18 + -16) >= (7 - -3))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 12527121,
"true_count": 1
},
"seed": 12527121,
"task_id": 612527121,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (((((-11 * 6) < (-15 * -4)) or ((2 * -15) < (-2 * 8 + 4 * -10) < (-10 * -10 * -10 * 4))) or ((17 + 5) == (-20 * -17))) and (莱特兄弟首次飞行发生在1903年。) and (not ((埃及的首都是赫尔辛基。) and (47是质数。)))) or (((not (柏林墙倒塌发生在1979年。)) and ((3 - 6) != (5 - -1))) and (丹麦的货币是克朗。))
B. (((not ((15 * -15) < (-6 * 8 + 2 * 4))) and ((-3 * 11) == (1 ** 2))) or ((海王星是距离太阳第5近的行星。) or (not not (镁的化学符号是Mg。)))) or ((((20 % 6) >= (15 - -19)) and (not (鲸鱼是鱼类。))) and ((not ((-1 * 7 - -5 * 1) >= (-1 * 10 + -1 * 0))) and ((6 * -2 * -9 * 4) <= (10 - 16) <= (1 ** 3))))
C. (not (((1964年奥运会在东京举办。) or (中国的首都是北京。)) or (鸭子有2条腿。))) or (not not (not not (((-11 + -17) > (8 + 8)) or ((6 % 4) <= (3 ** 1) <= (-1 - -8)))))
D. not not ((三文鱼是鱼类。) and ((-6 * 2 * -2 * 1) <= (-8 - -10)))
E. not ((((四月有30天。) and (2033年是闰年。)) and (((-2 + 20) <= (-5 - 0)) and (鲸鱼是鱼类。))) and ((2 ** 2) == (39 % 2)))
F. ((海王星是距离太阳第4近的行星。) and ((((12 % 7) <= (-2 * -9 + -7 * 2)) or ((-5 * -1) <= (-19 - 2))) and (钙的化学符号是Sn。))) or ((not not ((尼日利亚位于非洲。) and (蝙蝠是瞎的。))) or (not not ((章鱼有8条腿。) or ((12 * 4) != (7 + -4)))))
G. (((((8 * 0 - -6 * -8) > (4 ** 1)) or (天王星是距离太阳第6近的行星。)) or (not not ((5 * -6 + 10 * 1) != (6 * 1 + -9 * -10)))) or (not (((5 ** 1) > (-16 + 16)) or (袋鼠有10条腿。)))) or ((越南的首都是内罗毕。) or (((12 - 6) < (12 % 8)) and (11是质数。))) or ((加拿大位于北美洲。) and (not not ((南非位于非洲。) or ((-4 * 4 - -2 * -6) <= (3 * -2) <= (5 ** 1)))))
H. (((1968年奥运会在墨西哥城举办。) and ((-12 + -1) > (6 * 10 * -7 * 7))) and (六月有31天。)) or ((((欧盟的货币是欧元。) and (莱特兄弟首次飞行发生在1902年。)) and (not not (氢的化学符号是H。))) and (((14 - -9) < (4 - 18) < (25 % 7)) and (伦敦大火发生在1666年。)) and ((((3 + 6) > (-2 * -18)) or ((-13 * 14) < (0 * -6 - 7 * -10))) and (((13 + -17) <= (22 % 3)) and (84是质数。))))
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": "A,B,C,E,F,G",
"difficulty": 1,
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"question": "这里有一些需要评估的布尔表达式：\n\nA. (((((-11 * 6) < (-15 * -4)) or ((2 * -15) < (-2 * 8 + 4 * -10) < (-10 * -10 * -10 * 4))) or ((17 + 5) == (-20 * -17))) and (莱特兄弟首次飞行发生在1903年。) and (not ((埃及的首都是赫尔辛基。) and (47是质数。)))) or (((not (柏林墙倒塌发生在1979年。)) and ((3 - 6) != (5 - -1))) and (丹麦的货币是克朗。))\nB. (((not ((15 * -15) < (-6 * 8 + 2 * 4))) and ((-3 * 11) == (1 ** 2))) or ((海王星是距离太阳第5近的行星。) or (not not (镁的化学符号是Mg。)))) or ((((20 % 6) >= (15 - -19)) and (not (鲸鱼是鱼类。))) and ((not ((-1 * 7 - -5 * 1) >= (-1 * 10 + -1 * 0))) and ((6 * -2 * -9 * 4) <= (10 - 16) <= (1 ** 3))))\nC. (not (((1964年奥运会在东京举办。) or (中国的首都是北京。)) or (鸭子有2条腿。))) or (not not (not not (((-11 + -17) > (8 + 8)) or ((6 % 4) <= (3 ** 1) <= (-1 - -8)))))\nD. not not ((三文鱼是鱼类。) and ((-6 * 2 * -2 * 1) <= (-8 - -10)))\nE. not ((((四月有30天。) and (2033年是闰年。)) and (((-2 + 20) <= (-5 - 0)) and (鲸鱼是鱼类。))) and ((2 ** 2) == (39 % 2)))\nF. ((海王星是距离太阳第4近的行星。) and ((((12 % 7) <= (-2 * -9 + -7 * 2)) or ((-5 * -1) <= (-19 - 2))) and (钙的化学符号是Sn。))) or ((not not ((尼日利亚位于非洲。) and (蝙蝠是瞎的。))) or (not not ((章鱼有8条腿。) or ((12 * 4) != (7 + -4)))))\nG. (((((8 * 0 - -6 * -8) > (4 ** 1)) or (天王星是距离太阳第6近的行星。)) or (not not ((5 * -6 + 10 * 1) != (6 * 1 + -9 * -10)))) or (not (((5 ** 1) > (-16 + 16)) or (袋鼠有10条腿。)))) or ((越南的首都是内罗毕。) or (((12 - 6) < (12 % 8)) and (11是质数。))) or ((加拿大位于北美洲。) and (not not ((南非位于非洲。) or ((-4 * 4 - -2 * -6) <= (3 * -2) <= (5 ** 1)))))\nH. (((1968年奥运会在墨西哥城举办。) and ((-12 + -1) > (6 * 10 * -7 * 7))) and (六月有31天。)) or ((((欧盟的货币是欧元。) and (莱特兄弟首次飞行发生在1902年。)) and (not not (氢的化学符号是H。))) and (((14 - -9) < (4 - 18) < (25 % 7)) and (伦敦大火发生在1666年。)) and ((((3 + 6) > (-2 * -18)) or ((-13 * 14) < (0 * -6 - 7 * -10))) and (((13 + -17) <= (22 % 3)) and (84是质数。))))\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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"seed": 65972595,
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"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((((2020年奥运会在东京举办。) and (((-1 * -3) <= (1 * 8 + 1 * 3)) and ((-10 * 2 + 8 * -4) < (-3 * -6 - 2 * 4) < (8 + -7)))) and (((秘鲁位于南美洲。) and (807是斐波那契数。)) and (not not (古巴的首都是哈瓦那。)))) or ((not (not not (124是偶数。))) or ((not not ((-8 + 1) != (-20 * 0))) and (((28 % 5) != (17 % 6)) and (九月有31天。))))) or (((136是斐波那契数。) or ((13 - -15) >= (6 + 2)) or ((((10 % 10) < (-13 + -16)) and (埃及的货币是埃及镑。)) or (((1 * 15) > (6 + 10)) or (法国大革命开始发生在1789年。)))) and ((菲律宾的首都是渥太华。) and (not not (澳大利亚的货币是里亚尔。))))
B. ((not ((not not ((9 + 4) > (-19 + 20))) or ((地球上一天是24小时。) and (龙虾有100条腿。)))) and ((not (not ((-18 - -20) != (-9 + 5)))) and (((10 * -2 + 4 * 2) <= (-14 + -15)) or (not ((5 * 2) != (-3 + 8)))))) or ((((((45 % 6) < (14 - -9) < (15 + -13)) or (水星是距离太阳第5近的行星。)) and ((3 * -11) != (-12 * -15))) and (土耳其的首都是安卡拉。)) or ((((二月有28天。) and ((18 - -14) < (1 * -3))) and (1927年是闰年。)) and (丹麦的货币是索尔。) and ((((1 ** 1) != (9 * 6)) or ((-2 * -20) <= (9 + -16))) and ((乌龟是昆虫。) or (泰国的首都是首尔。)))))
C. ((((二氧化碳在常温下是气体。) and (氖的化学符号是Mn。)) and (((1943年是闰年。) or (莱特兄弟首次飞行发生在1898年。)) and ((3 * -3) < (-3 * -20) < (3 + 0)))) and (not not (32是质数。))) and ((((-2 * -1) <= (-3 * 6 - -3 * 8)) and (((阿根廷位于大洋洲。) or ((-20 - 14) <= (-3 * 6 + -4 * 6))) and (not (1984年奥运会在洛杉矶举办。)))) and (not not (((钙的化学符号是He。) and ((6 % 2) > (8 * -10 * -3 * -1))) or (not not (印度尼西亚的货币是印尼盾。)))))
D. not not (((((氧气在常温下是气体。) and (哥伦布到达美洲发生在1497年。)) or ((印度的货币是卢比。) or ((6 - -15) == (24 % 6)))) or ((汞的化学符号是K。) or (肯尼亚位于非洲。)) or (((伦敦大火发生在1664年。) and (氧气在常温下是气体。)) or (not not ((5 * -7 - 7 * 9) <= (5 * -6 + 8 * 6) <= (13 + -9))))) and (not (not not ((金鱼是爬行动物。) or ((1 * -9 * 9 * 1) < (10 * -9 * -10 * 6) < (-18 - -19))))))
E. not ((((9 - 4) == (-6 + -9)) and ((泰坦尼克号沉没发生在1911年。) and ((320是斐波那契数。) or (海王星是距离太阳第1近的行星。)))) or ((not (尼日利亚位于南美洲。)) and ((2016年奥运会在里约热内卢举办。) and ((-7 * -20) != (7 * 6 - -2 * 10)))) or (not ((铅的化学符号是Ag。) or (((19 - -12) < (2 * -10 * 8 * 3)) or (人类每只手有五个手指。)))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
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"true_count": 1
},
"question": "检验这些表达式：\n\nA. ((((2020年奥运会在东京举办。) and (((-1 * -3) <= (1 * 8 + 1 * 3)) and ((-10 * 2 + 8 * -4) < (-3 * -6 - 2 * 4) < (8 + -7)))) and (((秘鲁位于南美洲。) and (807是斐波那契数。)) and (not not (古巴的首都是哈瓦那。)))) or ((not (not not (124是偶数。))) or ((not not ((-8 + 1) != (-20 * 0))) and (((28 % 5) != (17 % 6)) and (九月有31天。))))) or (((136是斐波那契数。) or ((13 - -15) >= (6 + 2)) or ((((10 % 10) < (-13 + -16)) and (埃及的货币是埃及镑。)) or (((1 * 15) > (6 + 10)) or (法国大革命开始发生在1789年。)))) and ((菲律宾的首都是渥太华。) and (not not (澳大利亚的货币是里亚尔。))))\nB. ((not ((not not ((9 + 4) > (-19 + 20))) or ((地球上一天是24小时。) and (龙虾有100条腿。)))) and ((not (not ((-18 - -20) != (-9 + 5)))) and (((10 * -2 + 4 * 2) <= (-14 + -15)) or (not ((5 * 2) != (-3 + 8)))))) or ((((((45 % 6) < (14 - -9) < (15 + -13)) or (水星是距离太阳第5近的行星。)) and ((3 * -11) != (-12 * -15))) and (土耳其的首都是安卡拉。)) or ((((二月有28天。) and ((18 - -14) < (1 * -3))) and (1927年是闰年。)) and (丹麦的货币是索尔。) and ((((1 ** 1) != (9 * 6)) or ((-2 * -20) <= (9 + -16))) and ((乌龟是昆虫。) or (泰国的首都是首尔。)))))\nC. ((((二氧化碳在常温下是气体。) and (氖的化学符号是Mn。)) and (((1943年是闰年。) or (莱特兄弟首次飞行发生在1898年。)) and ((3 * -3) < (-3 * -20) < (3 + 0)))) and (not not (32是质数。))) and ((((-2 * -1) <= (-3 * 6 - -3 * 8)) and (((阿根廷位于大洋洲。) or ((-20 - 14) <= (-3 * 6 + -4 * 6))) and (not (1984年奥运会在洛杉矶举办。)))) and (not not (((钙的化学符号是He。) and ((6 % 2) > (8 * -10 * -3 * -1))) or (not not (印度尼西亚的货币是印尼盾。)))))\nD. not not (((((氧气在常温下是气体。) and (哥伦布到达美洲发生在1497年。)) or ((印度的货币是卢比。) or ((6 - -15) == (24 % 6)))) or ((汞的化学符号是K。) or (肯尼亚位于非洲。)) or (((伦敦大火发生在1664年。) and (氧气在常温下是气体。)) or (not not ((5 * -7 - 7 * 9) <= (5 * -6 + 8 * 6) <= (13 + -9))))) and (not (not not ((金鱼是爬行动物。) or ((1 * -9 * 9 * 1) < (10 * -9 * -10 * 6) < (-18 - -19))))))\nE. not ((((9 - 4) == (-6 + -9)) and ((泰坦尼克号沉没发生在1911年。) and ((320是斐波那契数。) or (海王星是距离太阳第1近的行星。)))) or ((not (尼日利亚位于南美洲。)) and ((2016年奥运会在里约热内卢举办。) and ((-7 * -20) != (7 * 6 - -2 * 10)))) or (not ((铅的化学符号是Ag。) or (((19 - -12) < (2 * -10 * 8 * 3)) or (人类每只手有五个手指。)))))\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": {
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"language": "cn",
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"seed": 63708241,
"true_count": 1
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"seed": 63708241,
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"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (not (The first airplane flight by the Wright Brothers occurred in 1903.)) or (Mercury is the 7th planet from the Sun.)
B. The chemical symbol for Oxygen is Au.
C. Water is a liquid at room temperature.
D. ((4 * 0 + -1 * -1) >= (-7 * -1 - 10 * -4)) and ((The capital of New Zealand is Stockholm.) and ((-17 + 7) == (-1 + 15)))
E. ((1903 is a leap year.) or (2045 is a leap year.)) and ((54 is an odd number.) and ((-19 + 15) != (8 * -10)))
F. There are 31 days in December.
G. not not (2093 is a leap year.)
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "C,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
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"question": "Review these logical expressions:\n\nA. (not (The first airplane flight by the Wright Brothers occurred in 1903.)) or (Mercury is the 7th planet from the Sun.)\nB. The chemical symbol for Oxygen is Au.\nC. Water is a liquid at room temperature.\nD. ((4 * 0 + -1 * -1) >= (-7 * -1 - 10 * -4)) and ((The capital of New Zealand is Stockholm.) and ((-17 + 7) == (-1 + 15)))\nE. ((1903 is a leap year.) or (2045 is a leap year.)) and ((54 is an odd number.) and ((-19 + 15) != (8 * -10)))\nF. There are 31 days in December.\nG. not not (2093 is a leap year.)\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 74556686,
"true_count": 2
},
"seed": 74556686,
"task_id": 674556686,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not (((-13 * 14) > (-1 * 18)) and (1996年奥运会在亚特兰大举办。))
B. 马来西亚的首都是赫尔辛基。
C. ((九月有28天。) or (702是斐波那契数。)) and (南非位于非洲。)
D. (((1 * -5 * 10 * -5) > (5 - 2)) or ((16 + -5) > (-2 * -1))) and ((氧气对人类生存是必需的。) or (鳄鱼是爬行动物。))
E. (9 * 7 - -5 * 1) < (-18 + 16)
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
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"seed": 56039215,
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"question": "审视以下逻辑表达式：\n\nA. not not (((-13 * 14) > (-1 * 18)) and (1996年奥运会在亚特兰大举办。))\nB. 马来西亚的首都是赫尔辛基。\nC. ((九月有28天。) or (702是斐波那契数。)) and (南非位于非洲。)\nD. (((1 * -5 * 10 * -5) > (5 - 2)) or ((16 + -5) > (-2 * -1))) and ((氧气对人类生存是必需的。) or (鳄鱼是爬行动物。))\nE. (9 * 7 - -5 * 1) < (-18 + 16)\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
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"language": "cn",
"num_options": 5,
"seed": 56039215,
"true_count": 1
},
"seed": 56039215,
"task_id": 656039215,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not ((-17 * -10) <= (-4 * 3))) and (not (((-15 + 1) < (-6 * 1 - -10 * -6) < (12 * -12)) or (not (There are 31 days in January.))))
B. (not not (1956 is a leap year.)) or ((4 - 3) != (3 ** 2)) or (not (A frog has 4 legs.))
C. (((Ice is less dense than liquid water.) or ((Earth is the 3rd planet from the Sun.) or (The currency of Malaysia is the Ringgit.))) or ((17 + -5) >= (10 - 12))) or (not not ((2 ** 1) != (0 * -6 * 6 * -2))) or ((((Helium is a gas at room temperature.) or (The capital of Cuba is Cairo.)) and (((18 + 15) < (-19 + -12) < (2 * 1 + -5 * 5)) or ((2 ** 2) < (2 * 10 + 6 * -2)))) or ((not (Mercury is the 4th planet from the Sun.)) and (not not ((-7 - -6) != (-19 * 1)))))
D. (not (not (((13 * -7) <= (11 + 15)) or (Mars is the 4th planet from the Sun.)))) or (((-1 - 5) < (1 * -6 - -7 * 9)) or ((-19 + -2) >= (27 % 7))) or (((not not ((-1 * -6 - -8 * -2) < (20 * 17))) or (((-7 + -6) >= (-10 * 5)) and ((15 - 15) < (0 * 0 * -5 * -6) < (5 * 2 * 6 * -8)))) and (not ((The 1936 Olympics were held in Paris.) or ((5 + 19) < (10 * -9 * 0 * -4) < (-5 + 11)))))
E. (((5 - -15) < (-5 + -16)) or ((The capital of Venezuela is Tokyo.) or (2032 is a leap year.)) or (((Alcohol is a liquid at room temperature.) or ((16 + -4) >= (-9 + 2))) and (Saturn is the 6th planet from the Sun.))) and (not (((The capital of France is Bern.) and ((2 ** 2) <= (14 % 8))) or ((7 - -13) <= (-12 * -1))))
F. (not not (not not ((14 + -4) <= (-16 + 16)))) and (not (((79 is divisible by 5.) or ((15 - -12) != (-6 + -9))) or (not ((48 % 6) >= (6 - -8)))))
G. (not not (The currency of United States is the Dollar.)) and (not (((15 * -2) >= (3 ** 3)) or (not ((-13 - 8) >= (10 + 18)))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
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"question": "Analyze these boolean expressions:\n\nA. (not ((-17 * -10) <= (-4 * 3))) and (not (((-15 + 1) < (-6 * 1 - -10 * -6) < (12 * -12)) or (not (There are 31 days in January.))))\nB. (not not (1956 is a leap year.)) or ((4 - 3) != (3 ** 2)) or (not (A frog has 4 legs.))\nC. (((Ice is less dense than liquid water.) or ((Earth is the 3rd planet from the Sun.) or (The currency of Malaysia is the Ringgit.))) or ((17 + -5) >= (10 - 12))) or (not not ((2 ** 1) != (0 * -6 * 6 * -2))) or ((((Helium is a gas at room temperature.) or (The capital of Cuba is Cairo.)) and (((18 + 15) < (-19 + -12) < (2 * 1 + -5 * 5)) or ((2 ** 2) < (2 * 10 + 6 * -2)))) or ((not (Mercury is the 4th planet from the Sun.)) and (not not ((-7 - -6) != (-19 * 1)))))\nD. (not (not (((13 * -7) <= (11 + 15)) or (Mars is the 4th planet from the Sun.)))) or (((-1 - 5) < (1 * -6 - -7 * 9)) or ((-19 + -2) >= (27 % 7))) or (((not not ((-1 * -6 - -8 * -2) < (20 * 17))) or (((-7 + -6) >= (-10 * 5)) and ((15 - 15) < (0 * 0 * -5 * -6) < (5 * 2 * 6 * -8)))) and (not ((The 1936 Olympics were held in Paris.) or ((5 + 19) < (10 * -9 * 0 * -4) < (-5 + 11)))))\nE. (((5 - -15) < (-5 + -16)) or ((The capital of Venezuela is Tokyo.) or (2032 is a leap year.)) or (((Alcohol is a liquid at room temperature.) or ((16 + -4) >= (-9 + 2))) and (Saturn is the 6th planet from the Sun.))) and (not (((The capital of France is Bern.) and ((2 ** 2) <= (14 % 8))) or ((7 - -13) <= (-12 * -1))))\nF. (not not (not not ((14 + -4) <= (-16 + 16)))) and (not (((79 is divisible by 5.) or ((15 - -12) != (-6 + -9))) or (not ((48 % 6) >= (6 - -8)))))\nG. (not not (The currency of United States is the Dollar.)) and (not (((15 * -2) >= (3 ** 3)) or (not ((-13 - 8) >= (10 + 18)))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 60186989,
"true_count": 5
},
"seed": 60186989,
"task_id": 660186989,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (not ((not (((4 * 6) < (-15 - -19)) or (瑞典的货币是克朗。))) or (not not ((79是质数。) or (钻石在常温下是固体。))))) or (((((墨西哥的货币是比索。) and ((40 % 9) == (-9 + 1))) and (硫的化学符号是Si。)) or (not not ((4是斐波那契数。) or ((13 + 20) != (18 - 0))))) or (not ((7 + 1) == (9 * 16))))
B. ((((((18 + 16) < (26 % 1) < (9 * -5)) and (印度尼西亚的货币是林吉特。)) or (not ((50 % 5) < (-3 * -7)))) or (not not (not not (金星是距离太阳第7近的行星。)))) or ((5 ** 1) < (-17 * 6)) or (((((3 * -7 * 2 * -5) == (-17 - -8)) or (尼日利亚的首都是华沙。)) and (not ((0 * 5) != (38 % 2)))) and (章鱼有6条腿。))) and (((氧的化学符号是U。) or (1936年是闰年。)) and (((十一月有30天。) or (not ((-16 + 2) != (-16 - -20)))) and (((16 * -17) != (10 + 5)) and (((19 % 2) > (8 * 0 - -10 * 5)) and (中国位于北美洲。)))))
C. ((((9 * 16) < (-1 + 9) < (-7 * -1 * 5 * 6)) or ((德国位于欧洲。) or (以色列的货币是里拉。)) or (not ((芬兰的首都是赫尔辛基。) or (德国的首都是巴黎。)))) and ((((-9 * -12) <= (16 + 16)) and (汞的化学符号是Mn。)) or ((not ((19 * 16) != (19 * 19))) and (not not (196是偶数。))))) and (not (((0 * 1 + 6 * 6) <= (10 + 3)) and (not ((7 * 1 - 6 * -3) > (15 + -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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 7896191,
"true_count": 1
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (not ((not (((4 * 6) < (-15 - -19)) or (瑞典的货币是克朗。))) or (not not ((79是质数。) or (钻石在常温下是固体。))))) or (((((墨西哥的货币是比索。) and ((40 % 9) == (-9 + 1))) and (硫的化学符号是Si。)) or (not not ((4是斐波那契数。) or ((13 + 20) != (18 - 0))))) or (not ((7 + 1) == (9 * 16))))\nB. ((((((18 + 16) < (26 % 1) < (9 * -5)) and (印度尼西亚的货币是林吉特。)) or (not ((50 % 5) < (-3 * -7)))) or (not not (not not (金星是距离太阳第7近的行星。)))) or ((5 ** 1) < (-17 * 6)) or (((((3 * -7 * 2 * -5) == (-17 - -8)) or (尼日利亚的首都是华沙。)) and (not ((0 * 5) != (38 % 2)))) and (章鱼有6条腿。))) and (((氧的化学符号是U。) or (1936年是闰年。)) and (((十一月有30天。) or (not ((-16 + 2) != (-16 - -20)))) and (((16 * -17) != (10 + 5)) and (((19 % 2) > (8 * 0 - -10 * 5)) and (中国位于北美洲。)))))\nC. ((((9 * 16) < (-1 + 9) < (-7 * -1 * 5 * 6)) or ((德国位于欧洲。) or (以色列的货币是里拉。)) or (not ((芬兰的首都是赫尔辛基。) or (德国的首都是巴黎。)))) and ((((-9 * -12) <= (16 + 16)) and (汞的化学符号是Mn。)) or ((not ((19 * 16) != (19 * 19))) and (not not (196是偶数。))))) and (not (((0 * 1 + 6 * 6) <= (10 + 3)) and (not ((7 * 1 - 6 * -3) > (15 + -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": 5,
"language": "cn",
"num_options": 3,
"seed": 7896191,
"true_count": 1
},
"seed": 7896191,
"task_id": 607896191,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not (((俄罗斯的首都是莫斯科。) or (1992年奥运会在圣路易斯举办。)) and (not not ((20 % 3) <= (2 ** 2))))
B. ((not ((-12 + 10) < (50 % 4))) or ((铁在常温下是固体。) or (锌的化学符号是Ca。))) or ((((9 * -5 - -3 * 9) < (12 - 5) < (10 * 2)) and (羊是哺乳动物。)) and (not ((-3 * 5 * 0 * -5) >= (2 ** 3))))
C. (五月有31天。) and (((58是奇数。) or (南非的货币是兰特。)) and ((美国宣布独立发生在1776年。) and (79小于等于46。)))
D. (not not ((2036年是闰年。) and ((10 - -15) <= (5 * -5 + 6 * -10)))) or ((2024年奥运会在墨尔本举办。) or ((-9 - 9) >= (-2 - -1)))
E. ((((45 % 5) != (-5 * -7 + 10 * 4)) and (水蒸气在常温下是气体。)) and (钛的化学符号是Ti。)) or ((-17 - 1) < (7 + -4)) or (((巴西位于北美洲。) or (海王星是距离太阳第8近的行星。)) or (not (火星是距离太阳最近的行星。)))
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,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 90837498,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. not (((俄罗斯的首都是莫斯科。) or (1992年奥运会在圣路易斯举办。)) and (not not ((20 % 3) <= (2 ** 2))))\nB. ((not ((-12 + 10) < (50 % 4))) or ((铁在常温下是固体。) or (锌的化学符号是Ca。))) or ((((9 * -5 - -3 * 9) < (12 - 5) < (10 * 2)) and (羊是哺乳动物。)) and (not ((-3 * 5 * 0 * -5) >= (2 ** 3))))\nC. (五月有31天。) and (((58是奇数。) or (南非的货币是兰特。)) and ((美国宣布独立发生在1776年。) and (79小于等于46。)))\nD. (not not ((2036年是闰年。) and ((10 - -15) <= (5 * -5 + 6 * -10)))) or ((2024年奥运会在墨尔本举办。) or ((-9 - 9) >= (-2 - -1)))\nE. ((((45 % 5) != (-5 * -7 + 10 * 4)) and (水蒸气在常温下是气体。)) and (钛的化学符号是Ti。)) or ((-17 - 1) < (7 + -4)) or (((巴西位于北美洲。) or (海王星是距离太阳第8近的行星。)) or (not (火星是距离太阳最近的行星。)))\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": 90837498,
"true_count": 2
},
"seed": 90837498,
"task_id": 690837498,
"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 ((((39 % 3) < (-10 + -16)) and (((1908年奥运会在伦敦举办。) or ((-9 + -2) <= (-18 + 14))) or (((-15 - -6) > (8 - 2)) and (土星是距离太阳第6近的行星。)))) and (not (not not ((鲨鱼是哺乳动物。) and (鳄鱼是爬行动物。)))))) and (not not (not ((((印度位于非洲。) or (土星是距离太阳第3近的行星。)) or (not (南非位于非洲。))) or (意大利的首都是布鲁塞尔。))))
B. not not ((not not (not (((-2 * 15) != (-17 - -4)) and (not (锰的化学符号是Si。))))) and ((((((-16 - -9) > (-10 * 3 + -8 * -9)) or ((-5 * 3 - -1 * 8) == (10 * -2 * 8 * 7))) and ((埃及位于南极洲。) or ((-10 * 5 - 2 * 1) <= (5 + 8) <= (7 - -5)))) and (not (比利时的首都是加拉加斯。)) and ((3 * -19) <= (14 - 3))) or ((not (not not (1976年奥运会在蒙特利尔举办。))) and (一月有29天。))))
C. (not (not not ((not (埃及的首都是哈瓦那。)) and ((5 - -19) == (1 + 3))))) or (((not ((not not ((3 ** 2) <= (7 * -16))) or (not (第一部iPhone发布发生在2007年。)))) or ((not ((36 % 2) > (-4 + -4))) and (1896年奥运会在北京举办。) and (not not (((-18 + -15) <= (-7 + 17)) or ((-2 - -20) > (13 + -20)))))) or (((not ((德国的首都是安卡拉。) or ((-7 * 2 - -3 * 1) == (-5 * 6 * 6 * 2)))) and (((袋鼠有2条腿。) or (日本位于亚洲。)) and ((第一次世界大战结束发生在1913年。) or ((39 % 3) > (5 ** 3))))) or ((铂的化学符号是Co。) or ((94大于73。) and ((闪电不会两次击中同一个地方。) and (2005年是闰年。))))))
D. ((not (((not not ((1 - -8) == (14 % 6))) and (法国位于南美洲。)) and (八月有31天。))) or ((((((0 * 10) > (-20 - -20)) or (1932年奥运会在洛杉矶举办。)) and (not ((-1 - 12) == (11 + -3)))) and ((((3 - -1) < (4 * -3 - 9 * 5) < (-7 + 19)) or (冰在常温下是固体。)) and ((法国位于大洋洲。) or (阿根廷的货币是人民币。)))) and ((not ((氧气在常温下是液体。) and ((8 - 2) == (25 % 2)))) or ((18 * -10) <= (8 + 15)) or (2008年奥运会在莫斯科举办。)))) and (not not (not ((((20 * -9) == (5 * -6)) and (not not (泰国的货币是泰铢。))) or ((not not (美国位于亚洲。)) and (59小于等于51。)))))
E. not (not not (((氧气在常温下是液体。) and (铜在常温下是气体。) and (((69是质数。) and (巴西的首都是巴西利亚。)) and (not not ((2 * 16) < (42 % 10) < (-9 - 18))))) or ((2 * -3 - 3 * 3) <= (7 * 8 * -10 * -8)) or (((not not (沙特阿拉伯位于亚洲。)) and (地球是距离太阳第3近的行星。)) or (not (((18 + -4) == (3 ** 2)) and ((-15 - 8) >= (17 + -15)))))))
F. (((((14 * -16) <= (-2 * -8 - 3 * -4)) and (88小于等于53。)) and ((((-5 * -10 + 7 * 1) >= (15 - 9)) and (氧气在常温下是固体。)) and (地球是距离太阳第3近的行星。)) and ((莱特兄弟首次飞行发生在1902年。) or (((铁的化学符号是Fe。) or ((9 * 3) >= (-19 + -19))) and (((2 * -5) > (7 + 18)) or ((4 * 10 + 8 * 1) <= (18 % 6)))))) or (not not ((((巴西的货币是雷亚尔。) and (哥伦比亚的首都是阿姆斯特丹。)) and (人体有150块骨头。)) and ((20 + 20) < (15 % 9) < (12 * -19))))) or (not not (((1998年是闰年。) or ((11 + 1) < (-7 - 10) < (-13 - -2))) or (not (声音在真空中传播更快。))))
G. (not not (not (((7 + -4) <= (4 % 2) <= (-14 * 10)) and ((摩洛哥位于非洲。) or (((-6 + 6) != (19 - 16)) and (九月有30天。)))))) and ((not (not (not (118是完全平方数。)))) and (((not not (2024年奥运会在巴黎举办。)) or (希腊的首都是巴黎。)) and ((((6 - 4) <= (3 ** 2) <= (-6 * 9)) and ((5 ** 2) > (6 - 13))) or (not not (火星是距离太阳第4近的行星。))))) and (not not (not (not (((2097年是闰年。) and (第一次世界大战开始发生在1916年。)) or ((-7 + 11) < (-8 * 0 + 7 * 10))))))
H. not not ((((not ((-13 * 1) <= (3 ** 3))) and ((not (火星是距离太阳最近的行星。)) and ((-13 * -12) == (20 * 14)))) and ((((17 % 1) >= (-3 + -1)) or ((-12 * -3) != (-7 * -5 - -2 * 6))) or (((-3 * -13) < (-7 * 4)) and ((11 * -16) < (3 ** 3)))) and (not not (not ((17 % 5) >= (2 ** 1))))) and ((not (not not (1938年是闰年。))) and (((冰在常温下是固体。) and (((2 ** 3) > (13 % 4)) or (冰在常温下是液体。))) or ((((-16 * -19) >= (3 ** 3)) or (植物通过光合作用产生氧气。)) and ((氖的化学符号是N。) and (蝴蝶有6条腿。))))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A,C,D,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 73216650,
"true_count": 5
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. (not ((((39 % 3) < (-10 + -16)) and (((1908年奥运会在伦敦举办。) or ((-9 + -2) <= (-18 + 14))) or (((-15 - -6) > (8 - 2)) and (土星是距离太阳第6近的行星。)))) and (not (not not ((鲨鱼是哺乳动物。) and (鳄鱼是爬行动物。)))))) and (not not (not ((((印度位于非洲。) or (土星是距离太阳第3近的行星。)) or (not (南非位于非洲。))) or (意大利的首都是布鲁塞尔。))))\nB. not not ((not not (not (((-2 * 15) != (-17 - -4)) and (not (锰的化学符号是Si。))))) and ((((((-16 - -9) > (-10 * 3 + -8 * -9)) or ((-5 * 3 - -1 * 8) == (10 * -2 * 8 * 7))) and ((埃及位于南极洲。) or ((-10 * 5 - 2 * 1) <= (5 + 8) <= (7 - -5)))) and (not (比利时的首都是加拉加斯。)) and ((3 * -19) <= (14 - 3))) or ((not (not not (1976年奥运会在蒙特利尔举办。))) and (一月有29天。))))\nC. (not (not not ((not (埃及的首都是哈瓦那。)) and ((5 - -19) == (1 + 3))))) or (((not ((not not ((3 ** 2) <= (7 * -16))) or (not (第一部iPhone发布发生在2007年。)))) or ((not ((36 % 2) > (-4 + -4))) and (1896年奥运会在北京举办。) and (not not (((-18 + -15) <= (-7 + 17)) or ((-2 - -20) > (13 + -20)))))) or (((not ((德国的首都是安卡拉。) or ((-7 * 2 - -3 * 1) == (-5 * 6 * 6 * 2)))) and (((袋鼠有2条腿。) or (日本位于亚洲。)) and ((第一次世界大战结束发生在1913年。) or ((39 % 3) > (5 ** 3))))) or ((铂的化学符号是Co。) or ((94大于73。) and ((闪电不会两次击中同一个地方。) and (2005年是闰年。))))))\nD. ((not (((not not ((1 - -8) == (14 % 6))) and (法国位于南美洲。)) and (八月有31天。))) or ((((((0 * 10) > (-20 - -20)) or (1932年奥运会在洛杉矶举办。)) and (not ((-1 - 12) == (11 + -3)))) and ((((3 - -1) < (4 * -3 - 9 * 5) < (-7 + 19)) or (冰在常温下是固体。)) and ((法国位于大洋洲。) or (阿根廷的货币是人民币。)))) and ((not ((氧气在常温下是液体。) and ((8 - 2) == (25 % 2)))) or ((18 * -10) <= (8 + 15)) or (2008年奥运会在莫斯科举办。)))) and (not not (not ((((20 * -9) == (5 * -6)) and (not not (泰国的货币是泰铢。))) or ((not not (美国位于亚洲。)) and (59小于等于51。)))))\nE. not (not not (((氧气在常温下是液体。) and (铜在常温下是气体。) and (((69是质数。) and (巴西的首都是巴西利亚。)) and (not not ((2 * 16) < (42 % 10) < (-9 - 18))))) or ((2 * -3 - 3 * 3) <= (7 * 8 * -10 * -8)) or (((not not (沙特阿拉伯位于亚洲。)) and (地球是距离太阳第3近的行星。)) or (not (((18 + -4) == (3 ** 2)) and ((-15 - 8) >= (17 + -15)))))))\nF. (((((14 * -16) <= (-2 * -8 - 3 * -4)) and (88小于等于53。)) and ((((-5 * -10 + 7 * 1) >= (15 - 9)) and (氧气在常温下是固体。)) and (地球是距离太阳第3近的行星。)) and ((莱特兄弟首次飞行发生在1902年。) or (((铁的化学符号是Fe。) or ((9 * 3) >= (-19 + -19))) and (((2 * -5) > (7 + 18)) or ((4 * 10 + 8 * 1) <= (18 % 6)))))) or (not not ((((巴西的货币是雷亚尔。) and (哥伦比亚的首都是阿姆斯特丹。)) and (人体有150块骨头。)) and ((20 + 20) < (15 % 9) < (12 * -19))))) or (not not (((1998年是闰年。) or ((11 + 1) < (-7 - 10) < (-13 - -2))) or (not (声音在真空中传播更快。))))\nG. (not not (not (((7 + -4) <= (4 % 2) <= (-14 * 10)) and ((摩洛哥位于非洲。) or (((-6 + 6) != (19 - 16)) and (九月有30天。)))))) and ((not (not (not (118是完全平方数。)))) and (((not not (2024年奥运会在巴黎举办。)) or (希腊的首都是巴黎。)) and ((((6 - 4) <= (3 ** 2) <= (-6 * 9)) and ((5 ** 2) > (6 - 13))) or (not not (火星是距离太阳第4近的行星。))))) and (not not (not (not (((2097年是闰年。) and (第一次世界大战开始发生在1916年。)) or ((-7 + 11) < (-8 * 0 + 7 * 10))))))\nH. not not ((((not ((-13 * 1) <= (3 ** 3))) and ((not (火星是距离太阳最近的行星。)) and ((-13 * -12) == (20 * 14)))) and ((((17 % 1) >= (-3 + -1)) or ((-12 * -3) != (-7 * -5 - -2 * 6))) or (((-3 * -13) < (-7 * 4)) and ((11 * -16) < (3 ** 3)))) and (not not (not ((17 % 5) >= (2 ** 1))))) and ((not (not not (1938年是闰年。))) and (((冰在常温下是固体。) and (((2 ** 3) > (13 % 4)) or (冰在常温下是液体。))) or ((((-16 * -19) >= (3 ** 3)) or (植物通过光合作用产生氧气。)) and ((氖的化学符号是N。) and (蝴蝶有6条腿。))))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 73216650,
"true_count": 5
},
"seed": 73216650,
"task_id": 673216650,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. ((not ((美国宣布独立发生在1776年。) or (美国宣布独立发生在1776年。) or ((鳟鱼是鸟类。) or (哥伦布到达美洲发生在1492年。)))) or (not ((not ((109是偶数。) and (冰在常温下是气体。))) and (蟑螂是昆虫。)))) and (((((((1 % 1) > (-11 - -17)) and (金在常温下是液体。)) or (((1 * -4 + -5 * -6) > (10 - -19)) and ((12 + 17) <= (11 * 0)))) and (土星是距离太阳第6近的行星。)) or (not ((41能被6整除。) and (三月有28天。)))) or ((地球绕太阳运转。) or ((-6 - -2) < (0 * 14)) or (西班牙位于大洋洲。)) or (not not (not (((-10 * -7 - -1 * 4) >= (1 ** 2)) and (油在常温下是液体。)))))
B. not not (not ((not not ((2013年是闰年。) or ((22 % 1) <= (-7 * 12)))) and ((not ((-18 * -14) >= (10 % 1))) and ((9 - -2) <= (1 * -6 - -7 * 9))) and (not (加拿大的首都是首尔。))))
C. (not (not (not not ((12 + 13) < (15 * 3) < (2 + -10))))) or ((not (((-7 - 14) == (2 + 14)) and (((-10 * -1 + -9 * 9) <= (1 ** 3) <= (8 * 10)) and (((18 - 2) <= (-8 * -3)) and (柏林墙倒塌发生在1989年。))))) or ((((加拿大的货币是克朗。) or (阿根廷的货币是欧元。)) and ((10 + 10) != (-10 * -5 - 7 * -4))) or ((秘鲁位于南美洲。) or (乌鸦是爬行动物。)) or ((not ((6 - -13) > (5 ** 2))) and ((美国的货币是美元。) and (沙特阿拉伯的货币是里亚尔。)))) or (not ((柏林墙倒塌发生在1979年。) or ((-3 * 1 * -7 * -3) <= (2 ** 1) <= (29 % 1)))))
D. not not (((((((-10 * -4 * -4 * -3) != (-11 * -10)) and ((-8 * 10 + 2 * 9) < (12 - 20))) or ((2042年是闰年。) or (希腊的首都是维也纳。))) and ((金在常温下是固体。) or (摩洛哥的首都是拉巴特。))) and (not not ((-5 * 4 - -2 * -3) == (-7 - -1)))) or ((((4 ** 1) >= (-4 * 9 * -10 * 10)) and (法国大革命开始发生在1799年。)) or ((not not ((-8 + -4) >= (-1 * 14))) or (not ((22 % 2) != (14 - -5))))) or (not ((火星是距离太阳第4近的行星。) or (((3 ** 2) < (3 * 3 + -6 * 0)) and ((-2 * 19) < (-19 - 17) < (-18 - 4))) or (油在常温下是液体。))))
E. not (((not (not not (922是斐波那契数。))) or (not not (not not (第一部iPhone发布发生在2007年。))) or (((-14 - 19) >= (10 + 13)) or ((((-20 * -1) < (-1 - 15) < (-1 - -7)) or (五月有31天。)) or (希腊的首都是布加勒斯特。)))) and ((((not (蜘蛛是昆虫。)) or ((匈牙利的首都是渥太华。) and (1900年奥运会在巴黎举办。))) and (not (not not (龙虾有8条腿。)))) or (((16 - 17) != (18 - -1)) or (十二月有31天。))))
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,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 5,
"seed": 10226,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. ((not ((美国宣布独立发生在1776年。) or (美国宣布独立发生在1776年。) or ((鳟鱼是鸟类。) or (哥伦布到达美洲发生在1492年。)))) or (not ((not ((109是偶数。) and (冰在常温下是气体。))) and (蟑螂是昆虫。)))) and (((((((1 % 1) > (-11 - -17)) and (金在常温下是液体。)) or (((1 * -4 + -5 * -6) > (10 - -19)) and ((12 + 17) <= (11 * 0)))) and (土星是距离太阳第6近的行星。)) or (not ((41能被6整除。) and (三月有28天。)))) or ((地球绕太阳运转。) or ((-6 - -2) < (0 * 14)) or (西班牙位于大洋洲。)) or (not not (not (((-10 * -7 - -1 * 4) >= (1 ** 2)) and (油在常温下是液体。)))))\nB. not not (not ((not not ((2013年是闰年。) or ((22 % 1) <= (-7 * 12)))) and ((not ((-18 * -14) >= (10 % 1))) and ((9 - -2) <= (1 * -6 - -7 * 9))) and (not (加拿大的首都是首尔。))))\nC. (not (not (not not ((12 + 13) < (15 * 3) < (2 + -10))))) or ((not (((-7 - 14) == (2 + 14)) and (((-10 * -1 + -9 * 9) <= (1 ** 3) <= (8 * 10)) and (((18 - 2) <= (-8 * -3)) and (柏林墙倒塌发生在1989年。))))) or ((((加拿大的货币是克朗。) or (阿根廷的货币是欧元。)) and ((10 + 10) != (-10 * -5 - 7 * -4))) or ((秘鲁位于南美洲。) or (乌鸦是爬行动物。)) or ((not ((6 - -13) > (5 ** 2))) and ((美国的货币是美元。) and (沙特阿拉伯的货币是里亚尔。)))) or (not ((柏林墙倒塌发生在1979年。) or ((-3 * 1 * -7 * -3) <= (2 ** 1) <= (29 % 1)))))\nD. not not (((((((-10 * -4 * -4 * -3) != (-11 * -10)) and ((-8 * 10 + 2 * 9) < (12 - 20))) or ((2042年是闰年。) or (希腊的首都是维也纳。))) and ((金在常温下是固体。) or (摩洛哥的首都是拉巴特。))) and (not not ((-5 * 4 - -2 * -3) == (-7 - -1)))) or ((((4 ** 1) >= (-4 * 9 * -10 * 10)) and (法国大革命开始发生在1799年。)) or ((not not ((-8 + -4) >= (-1 * 14))) or (not ((22 % 2) != (14 - -5))))) or (not ((火星是距离太阳第4近的行星。) or (((3 ** 2) < (3 * 3 + -6 * 0)) and ((-2 * 19) < (-19 - 17) < (-18 - 4))) or (油在常温下是液体。))))\nE. not (((not (not not (922是斐波那契数。))) or (not not (not not (第一部iPhone发布发生在2007年。))) or (((-14 - 19) >= (10 + 13)) or ((((-20 * -1) < (-1 - 15) < (-1 - -7)) or (五月有31天。)) or (希腊的首都是布加勒斯特。)))) and ((((not (蜘蛛是昆虫。)) or ((匈牙利的首都是渥太华。) and (1900年奥运会在巴黎举办。))) and (not (not not (龙虾有8条腿。)))) or (((16 - 17) != (18 - -1)) or (十二月有31天。))))\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": 5,
"seed": 10226,
"true_count": 3
},
"seed": 10226,
"task_id": 600010226,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((not (瑞典的首都是赫尔辛基。)) or ((220是完全平方数。) or (比利时的首都是曼谷。))) or (巴西的货币是雷亚尔。) or ((7 % 4) == (-4 - -11))
B. (not ((印度尼西亚位于亚洲。) and (螃蟹有10条腿。))) or ((not not (锰的化学符号是Co。)) and (not (智利的货币是泰铢。)))
C. (铜的化学符号是Cu。) and (((二月有28天。) and ((31 % 10) <= (0 - 15))) and ((2016年是闰年。) or (十二月有30天。)))
D. not ((10 * 10 * 3 * -9) < (-10 * -9))
E. ((电流比光速更快。) or (not not (硫的化学符号是S。))) and (not not (not ((43 % 3) >= (5 * 8 * 2 * 5))))
F. ((not not ((6 + 18) >= (-2 * 1 - 7 * 0))) or (not not (新西兰位于大洋洲。))) and (not not ((墨西哥的货币是韩元。) or (地球上一天是24小时。)))
G. (捷克的货币是埃及镑。) or ((not not (英国的货币是卢比。)) or (not not (澳大利亚位于欧洲。)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 29766377,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. ((not (瑞典的首都是赫尔辛基。)) or ((220是完全平方数。) or (比利时的首都是曼谷。))) or (巴西的货币是雷亚尔。) or ((7 % 4) == (-4 - -11))\nB. (not ((印度尼西亚位于亚洲。) and (螃蟹有10条腿。))) or ((not not (锰的化学符号是Co。)) and (not (智利的货币是泰铢。)))\nC. (铜的化学符号是Cu。) and (((二月有28天。) and ((31 % 10) <= (0 - 15))) and ((2016年是闰年。) or (十二月有30天。)))\nD. not ((10 * 10 * 3 * -9) < (-10 * -9))\nE. ((电流比光速更快。) or (not not (硫的化学符号是S。))) and (not not (not ((43 % 3) >= (5 * 8 * 2 * 5))))\nF. ((not not ((6 + 18) >= (-2 * 1 - 7 * 0))) or (not not (新西兰位于大洋洲。))) and (not not ((墨西哥的货币是韩元。) or (地球上一天是24小时。)))\nG. (捷克的货币是埃及镑。) or ((not not (英国的货币是卢比。)) or (not not (澳大利亚位于欧洲。)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 29766377,
"true_count": 3
},
"seed": 29766377,
"task_id": 629766377,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (5 - 3) >= (-2 * -7 - -3 * -4)
B. not (((1 * 4 * 7 * -6) < (1 ** 2) < (21 % 4)) or ((1 * 16) > (-7 - 9)))
C. 木星是距离太阳第8近的行星。
D. (((20 * 6) > (-6 * 6)) or ((17 - -19) == (-14 + 11))) or ((八月有29天。) and (49大于51。))
E. (((3 + 6) != (-20 - -18)) or (哥伦布到达美洲发生在1492年。)) or ((氦的化学符号是He。) or ((4 - -8) != (-10 * 0 + 8 * 7)))
F. (not not ((-10 + -13) <= (-14 - -15) <= (0 * -1))) and ((1 * 3 + -7 * 4) == (1 ** 3))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 62269587,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. (5 - 3) >= (-2 * -7 - -3 * -4)\nB. not (((1 * 4 * 7 * -6) < (1 ** 2) < (21 % 4)) or ((1 * 16) > (-7 - 9)))\nC. 木星是距离太阳第8近的行星。\nD. (((20 * 6) > (-6 * 6)) or ((17 - -19) == (-14 + 11))) or ((八月有29天。) and (49大于51。))\nE. (((3 + 6) != (-20 - -18)) or (哥伦布到达美洲发生在1492年。)) or ((氦的化学符号是He。) or ((4 - -8) != (-10 * 0 + 8 * 7)))\nF. (not not ((-10 + -13) <= (-14 - -15) <= (0 * -1))) and ((1 * 3 + -7 * 4) == (1 ** 3))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 62269587,
"true_count": 3
},
"seed": 62269587,
"task_id": 662269587,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. 火烈鸟是鱼类。
B. not ((95小于等于37。) or (19是完全平方数。))
C. not (墨西哥的货币是韩元。)
D. 莱特兄弟首次飞行发生在1913年。
E. 荷兰的首都是墨西哥城。
F. (((-8 * 3 + 3 * 5) < (-10 - 7)) and (中国长城是在一年内建成的。)) or (((28 % 6) == (7 * -8 * -5 * -1)) or (委内瑞拉的首都是加拉加斯。))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "B,C,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 16351379,
"true_count": 3
},
"question": "评估以下每个表达式：\n\nA. 火烈鸟是鱼类。\nB. not ((95小于等于37。) or (19是完全平方数。))\nC. not (墨西哥的货币是韩元。)\nD. 莱特兄弟首次飞行发生在1913年。\nE. 荷兰的首都是墨西哥城。\nF. (((-8 * 3 + 3 * 5) < (-10 - 7)) and (中国长城是在一年内建成的。)) or (((28 % 6) == (7 * -8 * -5 * -1)) or (委内瑞拉的首都是加拉加斯。))\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": 6,
"seed": 16351379,
"true_count": 3
},
"seed": 16351379,
"task_id": 616351379,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not (not ((not ((-17 * 14) != (-9 * -3 + 5 * 8))) and ((not not ((7 * 10 * -9 * 9) >= (1 + 10))) or ((8 * 11) == (-10 - 19))) and ((2012年奥运会在伦敦举办。) and (冰在常温下是固体。))))
B. not ((not not (not not ((葡萄牙的首都是里斯本。) and ((冰在常温下是液体。) and ((-7 * 0 + 2 * -10) == (-14 * 5)))))) or (not not ((5 ** 1) <= (-12 * 13) <= (13 + -8))) or ((not (((2 ** 2) > (5 ** 1)) and (((-1 - -18) > (8 + -2)) and (柏林墙倒塌发生在1989年。)))) and (((9 * 10 * 2 * 1) > (-13 - 4)) and ((地球上一天是24小时。) and ((新西兰的货币是日元。) or ((-1 * -6 * 6 * -7) >= (37 % 7)))))))
C. not not (not (((((天王星是距离太阳第2近的行星。) and ((-19 - -8) == (9 * -2 + -1 * 1))) or (not (铝的化学符号是Sn。))) and ((2004年奥运会在北京举办。) or (二氧化碳在常温下是气体。)) and (not ((三月有31天。) or (1988年奥运会在洛杉矶举办。)))) and (((莱特兄弟首次飞行发生在1904年。) and (not not ((2 * -3 * -2 * -2) >= (13 + -14)))) or (not not ((3 * 2 * -1 * -10) < (-16 + -1))) or ((((-9 * -6 - -3 * -10) >= (-10 * 0 * -6 * -6)) or (地球绕太阳运转。)) or ((地球是距离太阳第1近的行星。) and (沙特阿拉伯的首都是利雅得。))))))
D. ((((1964年奥运会在东京举办。) and ((8 + -12) < (5 * -5) < (16 + 2)) and (((-3 * -9 * -3 * 4) == (-6 + 7)) or (尼日利亚的货币是奈拉。))) and (((((5 + -2) <= (-1 * -10 + -7 * 0) <= (-8 * -7 + -7 * 5)) or (1956年奥运会在墨尔本举办。)) or (250是完全平方数。)) or (((鲸鱼是鱼类。) or ((33 % 7) <= (13 - -3))) or (not not ((3 * 5) < (2 ** 2)))))) and ((not not ((4 ** 3) < (-9 + -5))) and (not not ((1 ** 2) <= (-6 * 7 + 1 * 1) <= (2 ** 1))))) and (not not (not not (not not ((not not (捷克的货币是克朗。)) or (not (土耳其的货币是谢克尔。))))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 39424713,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. not (not ((not ((-17 * 14) != (-9 * -3 + 5 * 8))) and ((not not ((7 * 10 * -9 * 9) >= (1 + 10))) or ((8 * 11) == (-10 - 19))) and ((2012年奥运会在伦敦举办。) and (冰在常温下是固体。))))\nB. not ((not not (not not ((葡萄牙的首都是里斯本。) and ((冰在常温下是液体。) and ((-7 * 0 + 2 * -10) == (-14 * 5)))))) or (not not ((5 ** 1) <= (-12 * 13) <= (13 + -8))) or ((not (((2 ** 2) > (5 ** 1)) and (((-1 - -18) > (8 + -2)) and (柏林墙倒塌发生在1989年。)))) and (((9 * 10 * 2 * 1) > (-13 - 4)) and ((地球上一天是24小时。) and ((新西兰的货币是日元。) or ((-1 * -6 * 6 * -7) >= (37 % 7)))))))\nC. not not (not (((((天王星是距离太阳第2近的行星。) and ((-19 - -8) == (9 * -2 + -1 * 1))) or (not (铝的化学符号是Sn。))) and ((2004年奥运会在北京举办。) or (二氧化碳在常温下是气体。)) and (not ((三月有31天。) or (1988年奥运会在洛杉矶举办。)))) and (((莱特兄弟首次飞行发生在1904年。) and (not not ((2 * -3 * -2 * -2) >= (13 + -14)))) or (not not ((3 * 2 * -1 * -10) < (-16 + -1))) or ((((-9 * -6 - -3 * -10) >= (-10 * 0 * -6 * -6)) or (地球绕太阳运转。)) or ((地球是距离太阳第1近的行星。) and (沙特阿拉伯的首都是利雅得。))))))\nD. ((((1964年奥运会在东京举办。) and ((8 + -12) < (5 * -5) < (16 + 2)) and (((-3 * -9 * -3 * 4) == (-6 + 7)) or (尼日利亚的货币是奈拉。))) and (((((5 + -2) <= (-1 * -10 + -7 * 0) <= (-8 * -7 + -7 * 5)) or (1956年奥运会在墨尔本举办。)) or (250是完全平方数。)) or (((鲸鱼是鱼类。) or ((33 % 7) <= (13 - -3))) or (not not ((3 * 5) < (2 ** 2)))))) and ((not not ((4 ** 3) < (-9 + -5))) and (not not ((1 ** 2) <= (-6 * 7 + 1 * 1) <= (2 ** 1))))) and (not not (not not (not not ((not not (捷克的货币是克朗。)) or (not (土耳其的货币是谢克尔。))))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 39424713,
"true_count": 2
},
"seed": 39424713,
"task_id": 639424713,
"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 not (not not (((-17 + -7) <= (16 + -2) <= (18 + -8)) or (氧气在常温下是气体。)))) and (((((2 ** 2) < (-15 + -17)) and ((-9 * -10 * 7 * 3) >= (10 + 12))) or (蝙蝠是瞎的。)) and ((39 % 2) > (11 * 17)))) or (((智利位于非洲。) and (not not ((31 % 1) > (1 * -8 * -8 * 4)))) and ((not (not not (2008年是闰年。))) and (二氧化碳在常温下是固体。))))
B. not not (not (((not not (马来西亚的首都是吉隆坡。)) and ((((1 + 19) != (11 * 6)) and ((17 - 7) >= (6 * 0 + 0 * 2))) and (not (水星是距离太阳第1近的行星。)))) and ((((-18 - 15) > (-14 * 17)) or (瑞典的货币是克朗。)) and (((-15 + -10) != (15 + -18)) and ((-8 + -18) != (-5 + 4)))) and ((not (火星是距离太阳第4近的行星。)) and ((12 + 3) > (11 + 4)))))
C. not not ((not not ((新加坡的货币是新加坡元。) or (not (71是偶数。)) or (not (((-11 + -18) < (9 + -3) < (3 * -8 * -9 * -7)) or (海王星是距离太阳第1近的行星。))))) or (not ((((水在常温下是固体。) or (197是偶数。)) and (((-4 * 6 + 8 * -1) < (-4 * 10 * -10 * 7)) and (三月有28天。))) or ((18 + -14) == (32 % 5)))))
D. not not (((not not ((16 + -1) > (14 * -5))) and ((波兰的首都是堪培拉。) and (((越南的货币是越南盾。) and (光速比声速快。)) and ((硅的化学符号是Si。) and ((5 ** 3) <= (4 * 9 - -1 * -7)))))) or ((((((11 - -17) == (2 ** 2)) and (121的平方根是10。)) and (not (比利时的首都是奥斯陆。))) and (not not (越南的货币是日元。))) and ((七月有30天。) or ((十一月有30天。) and ((1 * 5 + 4 * -1) < (3 ** 3) < (-16 + 10))))))
E. not not ((((2024年奥运会在巴黎举办。) or (not not (秘鲁的首都是利马。)) or ((9 + -19) > (-16 + -7))) or (not (2020年奥运会在伦敦举办。))) and (not not ((((1948年奥运会在伦敦举办。) or (铜在常温下是气体。)) or ((-2 + -12) != (2 * -5 - -4 * 9))) or (麻雀是鸟类。))))
F. not not ((not not ((not ((金星是距离太阳第2近的行星。) or (猫有6条腿。))) or (((铝的化学符号是O。) or (企鹅能飞翔。)) and (现代奥运会首届举办发生在1895年。)))) or (((中国长城是在一年内建成的。) or (((变色龙是哺乳动物。) and ((-5 * 7) > (3 * 7 - 4 * -9))) or (not not ((-1 * 3) < (3 ** 2) < (7 * 3 * -6 * -9))))) and (not not ((11是质数。) or ((15 - 14) <= (-13 - 2) <= (0 * 5 * -6 * -6)))) and (not (第一次世界大战结束发生在1918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": "B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 82222738,
"true_count": 3
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. not not (((not not (not not (((-17 + -7) <= (16 + -2) <= (18 + -8)) or (氧气在常温下是气体。)))) and (((((2 ** 2) < (-15 + -17)) and ((-9 * -10 * 7 * 3) >= (10 + 12))) or (蝙蝠是瞎的。)) and ((39 % 2) > (11 * 17)))) or (((智利位于非洲。) and (not not ((31 % 1) > (1 * -8 * -8 * 4)))) and ((not (not not (2008年是闰年。))) and (二氧化碳在常温下是固体。))))\nB. not not (not (((not not (马来西亚的首都是吉隆坡。)) and ((((1 + 19) != (11 * 6)) and ((17 - 7) >= (6 * 0 + 0 * 2))) and (not (水星是距离太阳第1近的行星。)))) and ((((-18 - 15) > (-14 * 17)) or (瑞典的货币是克朗。)) and (((-15 + -10) != (15 + -18)) and ((-8 + -18) != (-5 + 4)))) and ((not (火星是距离太阳第4近的行星。)) and ((12 + 3) > (11 + 4)))))\nC. not not ((not not ((新加坡的货币是新加坡元。) or (not (71是偶数。)) or (not (((-11 + -18) < (9 + -3) < (3 * -8 * -9 * -7)) or (海王星是距离太阳第1近的行星。))))) or (not ((((水在常温下是固体。) or (197是偶数。)) and (((-4 * 6 + 8 * -1) < (-4 * 10 * -10 * 7)) and (三月有28天。))) or ((18 + -14) == (32 % 5)))))\nD. not not (((not not ((16 + -1) > (14 * -5))) and ((波兰的首都是堪培拉。) and (((越南的货币是越南盾。) and (光速比声速快。)) and ((硅的化学符号是Si。) and ((5 ** 3) <= (4 * 9 - -1 * -7)))))) or ((((((11 - -17) == (2 ** 2)) and (121的平方根是10。)) and (not (比利时的首都是奥斯陆。))) and (not not (越南的货币是日元。))) and ((七月有30天。) or ((十一月有30天。) and ((1 * 5 + 4 * -1) < (3 ** 3) < (-16 + 10))))))\nE. not not ((((2024年奥运会在巴黎举办。) or (not not (秘鲁的首都是利马。)) or ((9 + -19) > (-16 + -7))) or (not (2020年奥运会在伦敦举办。))) and (not not ((((1948年奥运会在伦敦举办。) or (铜在常温下是气体。)) or ((-2 + -12) != (2 * -5 - -4 * 9))) or (麻雀是鸟类。))))\nF. not not ((not not ((not ((金星是距离太阳第2近的行星。) or (猫有6条腿。))) or (((铝的化学符号是O。) or (企鹅能飞翔。)) and (现代奥运会首届举办发生在1895年。)))) or (((中国长城是在一年内建成的。) or (((变色龙是哺乳动物。) and ((-5 * 7) > (3 * 7 - 4 * -9))) or (not not ((-1 * 3) < (3 ** 2) < (7 * 3 * -6 * -9))))) and (not not ((11是质数。) or ((15 - 14) <= (-13 - 2) <= (0 * 5 * -6 * -6)))) and (not (第一次世界大战结束发生在1918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": 6,
"language": "cn",
"num_options": 6,
"seed": 82222738,
"true_count": 3
},
"seed": 82222738,
"task_id": 682222738,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not (((not not (not not (not ((14 + 17) <= (9 * 6 * 10 * -10))))) or (not ((((-5 * 18) >= (-10 * -1 + -3 * 5)) and (187是偶数。)) or ((空气在常温下是气体。) or ((5 ** 2) >= (1 + 13)))))) and (((((土耳其的货币是里拉。) and ((-2 * 1 + 7 * 1) != (27 % 4))) or ((1912年奥运会在伦敦举办。) or ((-6 + 2) >= (-10 * 16)))) and ((电流比光速更快。) and (印度的货币是埃及镑。)) and (法国位于欧洲。)) and ((月球自己发光。) and ((钴的化学符号是Fe。) or ((-6 * 5 + 2 * -5) > (17 % 4))) and ((-10 * 15) <= (5 * 20) <= (2 - -20)))))
B. not not ((not not (not (丹麦的货币是克朗。))) and ((((not not ((-16 + -14) > (13 - -4))) or (((-6 * 3 - 0 * 4) == (-3 - 13)) and (1968年奥运会在墨西哥城举办。))) and (氦的化学符号是Mn。)) or ((297是完全平方数。) and ((-3 * -3 + 8 * -7) < (50 % 9)))))
C. not not ((not (((-2 * -10 + -5 * 2) == (-1 * -8 + -7 * 6)) or (((-17 + -14) < (4 ** 1) < (-4 * 16)) and (植物通过光合作用产生氧气。)) or ((not (银的化学符号是Ag。)) and ((21 % 1) <= (-8 - 3) <= (9 % 9))))) or (not not ((9 * -8 * 4 * 8) >= (-7 * -1))) or (not not ((((2008年奥运会在洛杉矶举办。) or (澳大利亚的首都是堪培拉。)) and (法国位于欧洲。)) or (not not ((2 % 4) < (-3 + 14) < (-10 * -4 + -3 * 2))))))
D. not not (((not (((智利的货币是比索。) and ((-5 * -5) >= (4 * 5 + -6 * 10))) and ((鲸鱼是鱼类。) and (秘鲁位于南美洲。)))) and (not ((22是奇数。) and ((氧气对人类生存是必需的。) or (人类只使用了大脑的10%。))))) or ((not not ((火星是距离太阳第4近的行星。) or ((-3 * -12) == (-10 * -2 - -6 * 7)))) or (((意大利的首都是阿布贾。) and (1992年奥运会在洛杉矶举办。)) and ((比利时的首都是布鲁塞尔。) and (2012年奥运会在东京举办。)))) or ((((8 % 1) != (-2 + -18)) and ((-12 * 2) < (1 + 8))) or ((33 % 3) < (9 * 10 + -3 * -5)) or (not not (not ((2004年奥运会在雅典举办。) or ((-12 * 6) <= (1 ** 1)))))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 65844386,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. not (((not not (not not (not ((14 + 17) <= (9 * 6 * 10 * -10))))) or (not ((((-5 * 18) >= (-10 * -1 + -3 * 5)) and (187是偶数。)) or ((空气在常温下是气体。) or ((5 ** 2) >= (1 + 13)))))) and (((((土耳其的货币是里拉。) and ((-2 * 1 + 7 * 1) != (27 % 4))) or ((1912年奥运会在伦敦举办。) or ((-6 + 2) >= (-10 * 16)))) and ((电流比光速更快。) and (印度的货币是埃及镑。)) and (法国位于欧洲。)) and ((月球自己发光。) and ((钴的化学符号是Fe。) or ((-6 * 5 + 2 * -5) > (17 % 4))) and ((-10 * 15) <= (5 * 20) <= (2 - -20)))))\nB. not not ((not not (not (丹麦的货币是克朗。))) and ((((not not ((-16 + -14) > (13 - -4))) or (((-6 * 3 - 0 * 4) == (-3 - 13)) and (1968年奥运会在墨西哥城举办。))) and (氦的化学符号是Mn。)) or ((297是完全平方数。) and ((-3 * -3 + 8 * -7) < (50 % 9)))))\nC. not not ((not (((-2 * -10 + -5 * 2) == (-1 * -8 + -7 * 6)) or (((-17 + -14) < (4 ** 1) < (-4 * 16)) and (植物通过光合作用产生氧气。)) or ((not (银的化学符号是Ag。)) and ((21 % 1) <= (-8 - 3) <= (9 % 9))))) or (not not ((9 * -8 * 4 * 8) >= (-7 * -1))) or (not not ((((2008年奥运会在洛杉矶举办。) or (澳大利亚的首都是堪培拉。)) and (法国位于欧洲。)) or (not not ((2 % 4) < (-3 + 14) < (-10 * -4 + -3 * 2))))))\nD. not not (((not (((智利的货币是比索。) and ((-5 * -5) >= (4 * 5 + -6 * 10))) and ((鲸鱼是鱼类。) and (秘鲁位于南美洲。)))) and (not ((22是奇数。) and ((氧气对人类生存是必需的。) or (人类只使用了大脑的10%。))))) or ((not not ((火星是距离太阳第4近的行星。) or ((-3 * -12) == (-10 * -2 - -6 * 7)))) or (((意大利的首都是阿布贾。) and (1992年奥运会在洛杉矶举办。)) and ((比利时的首都是布鲁塞尔。) and (2012年奥运会在东京举办。)))) or ((((8 % 1) != (-2 + -18)) and ((-12 * 2) < (1 + 8))) or ((33 % 3) < (9 * 10 + -3 * -5)) or (not not (not ((2004年奥运会在雅典举办。) or ((-12 * 6) <= (1 ** 1)))))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 65844386,
"true_count": 3
},
"seed": 65844386,
"task_id": 665844386,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (((A iguana is a reptile.) or ((-12 + -1) < (5 + 4) < (-1 - -6))) or (The chemical symbol for Copper is Cu.)) and (not ((17 + 7) < (2 ** 2)))
B. (The 1984 Olympics were held in Los Angeles.) and ((((-14 * 12) == (-9 * -8 - -7 * 0)) or (The first iPhone was released occurred in 2007.)) or (The capital of South Korea is Manila.))
C. not (((19 * -12) >= (5 * 1 + -6 * 10)) and ((7 is less than or equal to 54.) or (The speed of light is approximately 300,000 km/s.)))
D. (((1935 is a leap year.) or ((-4 * 20) >= (19 * -1))) and ((5 * 5) != (-4 * 6))) or (((Ice is a gas at room temperature.) or ((-1 * 10) >= (10 * 0 + -9 * -1))) or (((-13 + 16) <= (50 % 8) <= (3 ** 3)) and (The currency of Egypt is the Pound.)))
E. (not ((Australia is in Oceania.) or (30 is a perfect square.))) and ((3 ** 1) > (4 + -20))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 18556457,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. (((A iguana is a reptile.) or ((-12 + -1) < (5 + 4) < (-1 - -6))) or (The chemical symbol for Copper is Cu.)) and (not ((17 + 7) < (2 ** 2)))\nB. (The 1984 Olympics were held in Los Angeles.) and ((((-14 * 12) == (-9 * -8 - -7 * 0)) or (The first iPhone was released occurred in 2007.)) or (The capital of South Korea is Manila.))\nC. not (((19 * -12) >= (5 * 1 + -6 * 10)) and ((7 is less than or equal to 54.) or (The speed of light is approximately 300,000 km/s.)))\nD. (((1935 is a leap year.) or ((-4 * 20) >= (19 * -1))) and ((5 * 5) != (-4 * 6))) or (((Ice is a gas at room temperature.) or ((-1 * 10) >= (10 * 0 + -9 * -1))) or (((-13 + 16) <= (50 % 8) <= (3 ** 3)) and (The currency of Egypt is the Pound.)))\nE. (not ((Australia is in Oceania.) or (30 is a perfect square.))) and ((3 ** 1) > (4 + -20))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 18556457,
"true_count": 3
},
"seed": 18556457,
"task_id": 618556457,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((((印度尼西亚的首都是雅加达。) or ((44 % 9) != (-9 * 10 * 10 * -9))) and ((not not (氮气在常温下是气体。)) and ((水在常温下是液体。) or (氮气在常温下是固体。)))) and (((not not (铅的化学符号是Au。)) and (not not (中国位于北美洲。))) and (not ((4 ** 3) >= (16 + 19))))) or ((((8 + 3) != (9 - 7)) and ((-13 + -14) < (-4 - 2) < (19 - 6))) and (((-17 * 12) <= (8 * 11) <= (15 * 18)) and (((4 * 5 * 3 * 2) <= (14 - -12)) and (2020年奥运会在东京举办。))) and (not not (酒精在常温下是液体。)))
B. (((not not (not not ((5 ** 2) != (-17 * -18)))) or ((-8 * 14) < (10 - 1))) or (((智利的首都是开罗。) or ((8 - -13) <= (4 * 8))) or ((748是斐波那契数。) or ((16 + -7) >= (-13 - 14)))) or (not not ((not (美国宣布独立发生在1776年。)) and (((0 * 9 + 3 * -3) >= (-3 * -4 * -4 * -9)) and (铜的化学符号是Cu。))))) and (((鲸鱼是哺乳动物。) and (2067年是闰年。) and (not not ((九月有30天。) or ((2 % 5) == (-14 * 17))))) and (not not (((埃及的货币是谢克尔。) or (356是完全平方数。)) and (((9 * 8 + -7 * -3) < (10 * 5 * -1 * -9)) and (意大利位于欧洲。)))))
C. (not not ((6是质数。) or (not (not (印度的货币是克朗。))))) and ((((7 * -10 * -4 * 10) >= (6 * 9 + -3 * 1)) and (not ((2 ** 1) == (-12 + -10)))) and (((2 * -9 * 9 * -1) == (1 ** 2)) or (not ((-9 * 10) <= (-17 + -1))))) and (not (((越南的首都是河内。) and ((1928年奥运会在阿姆斯特丹举办。) or (阿根廷的货币是比索。))) and ((((16 + -3) >= (15 + -12)) or ((1 * 8 - -7 * -5) >= (18 % 7))) and (二月有28天。))))
D. (not ((((1 * -1 + -9 * -2) >= (-13 * 7)) and (1984年奥运会在亚特兰大举办。)) or ((氖的化学符号是Hg。) and ((-8 * -10 + 2 * 7) >= (18 * -11))))) and (not (((27 % 2) <= (3 - -16) <= (-4 + 6)) and (人类只使用了大脑的10%。)))
E. not ((not not ((((10 + -11) > (4 * -3 * -1 * -9)) or ((1 - -20) >= (5 ** 1))) or ((秘鲁的货币是比索。) or ((15 - -14) >= (-16 * 5))))) or (((-15 * -2) <= (9 * 2 * 1 * -9)) and (not ((-20 * -4) <= (8 * 1 + 4 * -10)))) or (not not ((-12 + 4) != (17 - 6))))
F. (((三文鱼是昆虫。) or ((英国的货币是兹罗提。) and ((-4 * -7 * 1 * 7) > (5 * -7 * 5 * 5))) or ((((27 % 3) >= (-1 * -18)) and (木星是距离太阳第5近的行星。)) and (比利时的首都是渥太华。))) and ((not not ((49 % 5) < (17 + 16))) and (((1 * -14) <= (16 - -13)) or (猫头鹰是鸟类。))) and (not not ((1984年奥运会在斯德哥尔摩举办。) or ((南极洲是最冷的大陆。) and ((-5 * 1 - 9 * -7) != (-3 - 13)))))) or (((not not (((-3 - 13) >= (17 - 13)) and (1953年是闰年。))) or ((-10 + -1) > (4 - -15))) and ((not (not not ((-8 * -6) != (7 * -10 - -9 * 7)))) and (金星是距离太阳第2近的行星。)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 48186671,
"true_count": 1
},
"question": "检验这些表达式：\n\nA. ((((印度尼西亚的首都是雅加达。) or ((44 % 9) != (-9 * 10 * 10 * -9))) and ((not not (氮气在常温下是气体。)) and ((水在常温下是液体。) or (氮气在常温下是固体。)))) and (((not not (铅的化学符号是Au。)) and (not not (中国位于北美洲。))) and (not ((4 ** 3) >= (16 + 19))))) or ((((8 + 3) != (9 - 7)) and ((-13 + -14) < (-4 - 2) < (19 - 6))) and (((-17 * 12) <= (8 * 11) <= (15 * 18)) and (((4 * 5 * 3 * 2) <= (14 - -12)) and (2020年奥运会在东京举办。))) and (not not (酒精在常温下是液体。)))\nB. (((not not (not not ((5 ** 2) != (-17 * -18)))) or ((-8 * 14) < (10 - 1))) or (((智利的首都是开罗。) or ((8 - -13) <= (4 * 8))) or ((748是斐波那契数。) or ((16 + -7) >= (-13 - 14)))) or (not not ((not (美国宣布独立发生在1776年。)) and (((0 * 9 + 3 * -3) >= (-3 * -4 * -4 * -9)) and (铜的化学符号是Cu。))))) and (((鲸鱼是哺乳动物。) and (2067年是闰年。) and (not not ((九月有30天。) or ((2 % 5) == (-14 * 17))))) and (not not (((埃及的货币是谢克尔。) or (356是完全平方数。)) and (((9 * 8 + -7 * -3) < (10 * 5 * -1 * -9)) and (意大利位于欧洲。)))))\nC. (not not ((6是质数。) or (not (not (印度的货币是克朗。))))) and ((((7 * -10 * -4 * 10) >= (6 * 9 + -3 * 1)) and (not ((2 ** 1) == (-12 + -10)))) and (((2 * -9 * 9 * -1) == (1 ** 2)) or (not ((-9 * 10) <= (-17 + -1))))) and (not (((越南的首都是河内。) and ((1928年奥运会在阿姆斯特丹举办。) or (阿根廷的货币是比索。))) and ((((16 + -3) >= (15 + -12)) or ((1 * 8 - -7 * -5) >= (18 % 7))) and (二月有28天。))))\nD. (not ((((1 * -1 + -9 * -2) >= (-13 * 7)) and (1984年奥运会在亚特兰大举办。)) or ((氖的化学符号是Hg。) and ((-8 * -10 + 2 * 7) >= (18 * -11))))) and (not (((27 % 2) <= (3 - -16) <= (-4 + 6)) and (人类只使用了大脑的10%。)))\nE. not ((not not ((((10 + -11) > (4 * -3 * -1 * -9)) or ((1 - -20) >= (5 ** 1))) or ((秘鲁的货币是比索。) or ((15 - -14) >= (-16 * 5))))) or (((-15 * -2) <= (9 * 2 * 1 * -9)) and (not ((-20 * -4) <= (8 * 1 + 4 * -10)))) or (not not ((-12 + 4) != (17 - 6))))\nF. (((三文鱼是昆虫。) or ((英国的货币是兹罗提。) and ((-4 * -7 * 1 * 7) > (5 * -7 * 5 * 5))) or ((((27 % 3) >= (-1 * -18)) and (木星是距离太阳第5近的行星。)) and (比利时的首都是渥太华。))) and ((not not ((49 % 5) < (17 + 16))) and (((1 * -14) <= (16 - -13)) or (猫头鹰是鸟类。))) and (not not ((1984年奥运会在斯德哥尔摩举办。) or ((南极洲是最冷的大陆。) and ((-5 * 1 - 9 * -7) != (-3 - 13)))))) or (((not not (((-3 - 13) >= (17 - 13)) and (1953年是闰年。))) or ((-10 + -1) > (4 - -15))) and ((not (not not ((-8 * -6) != (7 * -10 - -9 * 7)))) and (金星是距离太阳第2近的行星。)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 48186671,
"true_count": 1
},
"seed": 48186671,
"task_id": 648186671,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (((2 ** 2) > (2 * 4 - -8 * 6)) or ((火烈鸟是鸟类。) or ((10 * 18) > (-1 * -5 - -10 * 1))) or (天王星是距离太阳第3近的行星。)) and (((-11 - -2) < (5 % 5)) or (木星是距离太阳第4近的行星。))
B. ((not not (not (土星是距离太阳第8近的行星。))) or (not ((尼日利亚的货币是奈拉。) and (1980年奥运会在莫斯科举办。)))) and ((((企鹅能飞翔。) or (埃及的首都是开罗。)) or (西班牙位于南美洲。)) or (莱特兄弟首次飞行发生在1904年。))
C. ((not not ((1922年是闰年。) or ((1 ** 2) == (12 + -3)))) and (火星是距离太阳第4近的行星。) and (not not (天王星是距离太阳第7近的行星。))) or (((新加坡的货币是比索。) or (not not (1900年奥运会在伦敦举办。))) or (2008年奥运会在巴黎举办。))
D. ((((-17 * 1) > (7 + 12)) or ((-7 + -15) == (-13 + 2))) and (not not (1956年奥运会在墨尔本举办。)) and (not (柏林墙倒塌发生在1999年。))) and (((6 * -4) < (4 * 4 * 9 * -7) < (11 * 8)) or ((((-8 * 3 + 6 * -5) >= (15 + -4)) and ((-16 - 0) >= (0 * 4 * -5 * -6))) or (not not ((-19 - -3) <= (-2 * -3 - 10 * 5)))))
E. not not ((((法国大革命开始发生在1789年。) and (地球是距离太阳第4近的行星。)) or ((-11 + 1) >= (9 * -1))) or ((not (81能被10整除。)) and (((15 + 17) > (0 * 5)) and (198是完全平方数。))))
F. (not not (not not ((木头在常温下是液体。) or (26是完全平方数。)))) or (((2 ** 1) < (16 + -18)) or ((not (韩国位于亚洲。)) or (((1 ** 2) == (-1 * 5 - -2 * -4)) and ((1 * -3 * -6 * 3) >= (0 + -1)))))
G. ((((美国宣布独立发生在1776年。) and (智利的货币是福林。)) or ((螃蟹有10条腿。) and ((13 - -16) >= (5 ** 1)))) or ((-1 * 7 + 10 * -5) < (-20 - 18))) or ((-10 * -7) > (18 - -18)) or ((((7 - -3) <= (-19 - 9)) and (((6 * 1) > (16 * -15)) and ((12 % 10) > (4 - 11)))) and ((not not (2037年是闰年。)) and ((木头在常温下是液体。) and ((4 ** 2) == (-20 - -14)))))
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,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 80118086,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. (((2 ** 2) > (2 * 4 - -8 * 6)) or ((火烈鸟是鸟类。) or ((10 * 18) > (-1 * -5 - -10 * 1))) or (天王星是距离太阳第3近的行星。)) and (((-11 - -2) < (5 % 5)) or (木星是距离太阳第4近的行星。))\nB. ((not not (not (土星是距离太阳第8近的行星。))) or (not ((尼日利亚的货币是奈拉。) and (1980年奥运会在莫斯科举办。)))) and ((((企鹅能飞翔。) or (埃及的首都是开罗。)) or (西班牙位于南美洲。)) or (莱特兄弟首次飞行发生在1904年。))\nC. ((not not ((1922年是闰年。) or ((1 ** 2) == (12 + -3)))) and (火星是距离太阳第4近的行星。) and (not not (天王星是距离太阳第7近的行星。))) or (((新加坡的货币是比索。) or (not not (1900年奥运会在伦敦举办。))) or (2008年奥运会在巴黎举办。))\nD. ((((-17 * 1) > (7 + 12)) or ((-7 + -15) == (-13 + 2))) and (not not (1956年奥运会在墨尔本举办。)) and (not (柏林墙倒塌发生在1999年。))) and (((6 * -4) < (4 * 4 * 9 * -7) < (11 * 8)) or ((((-8 * 3 + 6 * -5) >= (15 + -4)) and ((-16 - 0) >= (0 * 4 * -5 * -6))) or (not not ((-19 - -3) <= (-2 * -3 - 10 * 5)))))\nE. not not ((((法国大革命开始发生在1789年。) and (地球是距离太阳第4近的行星。)) or ((-11 + 1) >= (9 * -1))) or ((not (81能被10整除。)) and (((15 + 17) > (0 * 5)) and (198是完全平方数。))))\nF. (not not (not not ((木头在常温下是液体。) or (26是完全平方数。)))) or (((2 ** 1) < (16 + -18)) or ((not (韩国位于亚洲。)) or (((1 ** 2) == (-1 * 5 - -2 * -4)) and ((1 * -3 * -6 * 3) >= (0 + -1)))))\nG. ((((美国宣布独立发生在1776年。) and (智利的货币是福林。)) or ((螃蟹有10条腿。) and ((13 - -16) >= (5 ** 1)))) or ((-1 * 7 + 10 * -5) < (-20 - 18))) or ((-10 * -7) > (18 - -18)) or ((((7 - -3) <= (-19 - 9)) and (((6 * 1) > (16 * -15)) and ((12 % 10) > (4 - 11)))) and ((not not (2037年是闰年。)) and ((木头在常温下是液体。) and ((4 ** 2) == (-20 - -14)))))\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": 80118086,
"true_count": 3
},
"seed": 80118086,
"task_id": 680118086,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. 土耳其的货币是里拉。
B. (1904年奥运会在圣路易斯举办。) or ((10 * 1 * -10 * -9) == (15 + 2))
C. not not (((3 + 2) != (-19 - -19)) and ((-19 + 9) > (-9 + 15)))
D. not not ((古巴的首都是莫斯科。) and ((3 * 0 - 2 * 7) <= (19 * 5)))
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": 4,
"seed": 19907379,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. 土耳其的货币是里拉。\nB. (1904年奥运会在圣路易斯举办。) or ((10 * 1 * -10 * -9) == (15 + 2))\nC. not not (((3 + 2) != (-19 - -19)) and ((-19 + 9) > (-9 + 15)))\nD. not not ((古巴的首都是莫斯科。) and ((3 * 0 - 2 * 7) <= (19 * 5)))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 19907379,
"true_count": 2
},
"seed": 19907379,
"task_id": 619907379,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (There are 28 days in February.)
B. (not not (The capital of Germany is Berlin.)) and (((2083 is a leap year.) and ((13 - 7) != (12 + 11))) and ((134 is an odd number.) or (A swan is a mammal.)))
C. (not not ((There are 31 days in August.) or ((-18 - 2) == (13 + 7)))) or (The capital of New Zealand is Buenos Aires.) or (not not (((15 * -14) > (-20 * -20)) or (Alcohol is a liquid 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,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 5738844,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (There are 28 days in February.)\nB. (not not (The capital of Germany is Berlin.)) and (((2083 is a leap year.) and ((13 - 7) != (12 + 11))) and ((134 is an odd number.) or (A swan is a mammal.)))\nC. (not not ((There are 31 days in August.) or ((-18 - 2) == (13 + 7)))) or (The capital of New Zealand is Buenos Aires.) or (not not (((15 * -14) > (-20 * -20)) or (Alcohol is a liquid 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": 3,
"language": "en",
"num_options": 3,
"seed": 5738844,
"true_count": 2
},
"seed": 5738844,
"task_id": 605738844,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. The square root of 196 is 12.
B. not not ((The chemical symbol for Platinum is Pt.) or ((-18 - -8) == (-1 * 10 * 5 * 8)))
C. (not (World War II ended occurred in 1945.)) and (((5 * -5 * 9 * -5) > (4 * -10 + -10 * 5)) or (The Sun revolves around the Earth.))
D. ((-1 * -8) <= (3 ** 2)) and (((3 * 0 * 6 * 8) > (0 * -11)) or ((39 % 3) >= (-19 * -13)))
E. not ((140 is an odd number.) or ((24 % 5) > (-12 - -8)))
F. (3 * 2 + 4 * 1) < (3 + 16) < (18 - 12)
G. ((-15 * 8) < (-7 * -9 * -1 * 7)) and ((The chemical symbol for Sodium is Ag.) and (There are 30 days in December.))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 71564129,
"true_count": 1
},
"question": "Analyze these boolean expressions:\n\nA. The square root of 196 is 12.\nB. not not ((The chemical symbol for Platinum is Pt.) or ((-18 - -8) == (-1 * 10 * 5 * 8)))\nC. (not (World War II ended occurred in 1945.)) and (((5 * -5 * 9 * -5) > (4 * -10 + -10 * 5)) or (The Sun revolves around the Earth.))\nD. ((-1 * -8) <= (3 ** 2)) and (((3 * 0 * 6 * 8) > (0 * -11)) or ((39 % 3) >= (-19 * -13)))\nE. not ((140 is an odd number.) or ((24 % 5) > (-12 - -8)))\nF. (3 * 2 + 4 * 1) < (3 + 16) < (18 - 12)\nG. ((-15 * 8) < (-7 * -9 * -1 * 7)) and ((The chemical symbol for Sodium is Ag.) and (There are 30 days in December.))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 71564129,
"true_count": 1
},
"seed": 71564129,
"task_id": 671564129,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. 太平洋是最大的海洋。
B. (银的化学符号是Ag。) and (not not (258是完全平方数。))
C. not not (not (袋鼠有2条腿。))
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": 2,
"language": "cn",
"num_options": 3,
"seed": 51273654,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. 太平洋是最大的海洋。\nB. (银的化学符号是Ag。) and (not not (258是完全平方数。))\nC. not not (not (袋鼠有2条腿。))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 51273654,
"true_count": 1
},
"seed": 51273654,
"task_id": 651273654,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (5 * -11) > (2 ** 1)
B. not not (((-20 * 0) >= (6 % 1)) or (World War I ended occurred in 1918.))
C. (not (Sound cannot travel through a vacuum.)) or (not not ((39 % 5) != (-16 - 17)))
D. not (not not ((-3 - 18) <= (5 * -20)))
E. not not (((2 ** 1) < (-5 + 1) < (-12 + 6)) or (The 1936 Olympics were held in Berlin.))
F. (not not (The currency of Poland is the Ruble.)) and ((World War II began occurred in 1939.) or ((18 - 13) == (8 * -5)))
G. ((-11 - -2) != (3 ** 1)) and (((2 * 18) != (16 - 18)) and (Jupiter is the 3rd planet from the Sun.))
H. Spain is in Europe.
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "B,C,D,E,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 49032294,
"true_count": 5
},
"question": "Given the following boolean expressions:\n\nA. (5 * -11) > (2 ** 1)\nB. not not (((-20 * 0) >= (6 % 1)) or (World War I ended occurred in 1918.))\nC. (not (Sound cannot travel through a vacuum.)) or (not not ((39 % 5) != (-16 - 17)))\nD. not (not not ((-3 - 18) <= (5 * -20)))\nE. not not (((2 ** 1) < (-5 + 1) < (-12 + 6)) or (The 1936 Olympics were held in Berlin.))\nF. (not not (The currency of Poland is the Ruble.)) and ((World War II began occurred in 1939.) or ((18 - 13) == (8 * -5)))\nG. ((-11 - -2) != (3 ** 1)) and (((2 * 18) != (16 - 18)) and (Jupiter is the 3rd planet from the Sun.))\nH. Spain is in Europe.\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 49032294,
"true_count": 5
},
"seed": 49032294,
"task_id": 649032294,
"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 ((人体有150块骨头。) or (地球是距离太阳第3近的行星。))
B. (((1 ** 1) <= (1 * 0 + -5 * 5)) or (65能被7整除。)) and ((43是奇数。) and (氧气对人类生存是必需的。))
C. not not ((16的平方根是4。) or (1948年奥运会在伦敦举办。))
D. not not ((0 + 3) != (3 * -9 + -5 * -1))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 53911621,
"true_count": 3
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. not not ((人体有150块骨头。) or (地球是距离太阳第3近的行星。))\nB. (((1 ** 1) <= (1 * 0 + -5 * 5)) or (65能被7整除。)) and ((43是奇数。) and (氧气对人类生存是必需的。))\nC. not not ((16的平方根是4。) or (1948年奥运会在伦敦举办。))\nD. not not ((0 + 3) != (3 * -9 + -5 * -1))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 53911621,
"true_count": 3
},
"seed": 53911621,
"task_id": 653911621,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (((((-10 + -2) < (3 ** 3) < (-15 - -11)) or (111是斐波那契数。)) or (((38 % 4) <= (-5 * -17)) or (油在常温下是液体。))) or (阿根廷位于南美洲。)) or (2004年奥运会在亚特兰大举办。) or ((五月有31天。) and (not not (美国宣布独立发生在1776年。)) and (not not (伦敦大火发生在1667年。)))
B. (not not (((荷兰的首都是阿姆斯特丹。) or (英国的货币是新加坡元。)) and (((40 % 4) < (-15 * 16) < (-10 - -18)) or (土星是距离太阳第6近的行星。)))) and ((not ((3 * -6 * 3 * 1) < (-2 * 5 * 6 * 8))) and (((12 + -18) <= (-10 * -16)) and (瑞士的首都是墨西哥城。))) and ((((鹦鹉是鸟类。) and (加拿大的首都是布拉格。)) and ((六月有30天。) and (1984年奥运会在洛杉矶举办。))) and (((-20 + -20) < (-18 + 0) < (1 ** 3)) or (not (第一部iPhone发布发生在2007年。))))
C. (not not (not not ((天王星是距离太阳第7近的行星。) or ((3 * -7) > (-3 - 3))))) and (not (not not (1996年奥运会在洛杉矶举办。)))
D. ((not (((10 * 0) <= (5 ** 3)) or (墨西哥位于北美洲。))) or (((-15 - 16) < (3 ** 1)) and ((氧气对人类生存是必需的。) and (土星是距离太阳第6近的行星。)))) and (not not (not not ((柏林墙倒塌发生在1989年。) and (水在常温下是液体。))))
E. (not not ((not not ((-6 * 5 * -4 * 2) < (7 + -11))) or ((瑞典的首都是斯德哥尔摩。) or ((9 * 8) != (-14 - -13))))) and ((not not (蜥蜴是爬行动物。)) or (not ((火星是距离太阳最近的行星。) and (蛇有0条腿。))))
F. (((not not ((-18 + -15) <= (-9 * -4 - -6 * -7))) or ((磷的化学符号是S。) and ((10 - 1) >= (2 ** 1)))) and ((not not ((-8 * -7) != (-9 - -7))) and (not not (钻石在常温下是气体。)))) or (((3 ** 1) < (10 + 16) < (5 ** 3)) or ((铝的化学符号是Al。) or (莱特兄弟首次飞行发生在1903年。))) or (not not (((1896年奥运会在伦敦举办。) and (15是质数。)) and (not ((1 ** 3) >= (16 - 5)))))
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": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 8472106,
"true_count": 5
},
"question": "分析以下逻辑表达式：\n\nA. (((((-10 + -2) < (3 ** 3) < (-15 - -11)) or (111是斐波那契数。)) or (((38 % 4) <= (-5 * -17)) or (油在常温下是液体。))) or (阿根廷位于南美洲。)) or (2004年奥运会在亚特兰大举办。) or ((五月有31天。) and (not not (美国宣布独立发生在1776年。)) and (not not (伦敦大火发生在1667年。)))\nB. (not not (((荷兰的首都是阿姆斯特丹。) or (英国的货币是新加坡元。)) and (((40 % 4) < (-15 * 16) < (-10 - -18)) or (土星是距离太阳第6近的行星。)))) and ((not ((3 * -6 * 3 * 1) < (-2 * 5 * 6 * 8))) and (((12 + -18) <= (-10 * -16)) and (瑞士的首都是墨西哥城。))) and ((((鹦鹉是鸟类。) and (加拿大的首都是布拉格。)) and ((六月有30天。) and (1984年奥运会在洛杉矶举办。))) and (((-20 + -20) < (-18 + 0) < (1 ** 3)) or (not (第一部iPhone发布发生在2007年。))))\nC. (not not (not not ((天王星是距离太阳第7近的行星。) or ((3 * -7) > (-3 - 3))))) and (not (not not (1996年奥运会在洛杉矶举办。)))\nD. ((not (((10 * 0) <= (5 ** 3)) or (墨西哥位于北美洲。))) or (((-15 - 16) < (3 ** 1)) and ((氧气对人类生存是必需的。) and (土星是距离太阳第6近的行星。)))) and (not not (not not ((柏林墙倒塌发生在1989年。) and (水在常温下是液体。))))\nE. (not not ((not not ((-6 * 5 * -4 * 2) < (7 + -11))) or ((瑞典的首都是斯德哥尔摩。) or ((9 * 8) != (-14 - -13))))) and ((not not (蜥蜴是爬行动物。)) or (not ((火星是距离太阳最近的行星。) and (蛇有0条腿。))))\nF. (((not not ((-18 + -15) <= (-9 * -4 - -6 * -7))) or ((磷的化学符号是S。) and ((10 - 1) >= (2 ** 1)))) and ((not not ((-8 * -7) != (-9 - -7))) and (not not (钻石在常温下是气体。)))) or (((3 ** 1) < (10 + 16) < (5 ** 3)) or ((铝的化学符号是Al。) or (莱特兄弟首次飞行发生在1903年。))) or (not not (((1896年奥运会在伦敦举办。) and (15是质数。)) and (not ((1 ** 3) >= (16 - 5)))))\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": 4,
"language": "cn",
"num_options": 6,
"seed": 8472106,
"true_count": 5
},
"seed": 8472106,
"task_id": 608472106,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not (((The chemical symbol for Titanium is Co.) or ((26 is a prime number.) or ((-3 * 6 + 10 * -9) > (3 ** 2)))) or (((-10 * 6) <= (-6 - -7)) and ((-14 * 7) < (-14 - -7) < (-15 - -2))) or (((There are 29 days in March.) and (Helium is a gas at room temperature.)) and ((South Korea is in Asia.) and (Air is a gas at room temperature.))))
B. not not ((((A cat has 4 legs.) and ((13 - -8) == (9 * -7 + 4 * 4))) and (((3 - 15) == (-13 + -5)) and (A bird has 4 legs.))) or (not not (Earth is the 3rd planet from the Sun.)) or (((16 - -20) <= (-10 * 7 * 3 * 9)) or (not ((-8 + 14) < (2 + 10)))))
C. ((A cow has 10 legs.) or (not not (Uranus is the 7th planet from the Sun.))) and (((Diamond is a solid at room temperature.) or ((The chemical symbol for Mercury is Pb.) or ((-3 * -4 + 3 * 6) < (-10 * 4 - 7 * 2)))) or (not (The square root of 121 is 1.)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 14113230,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. not not (((The chemical symbol for Titanium is Co.) or ((26 is a prime number.) or ((-3 * 6 + 10 * -9) > (3 ** 2)))) or (((-10 * 6) <= (-6 - -7)) and ((-14 * 7) < (-14 - -7) < (-15 - -2))) or (((There are 29 days in March.) and (Helium is a gas at room temperature.)) and ((South Korea is in Asia.) and (Air is a gas at room temperature.))))\nB. not not ((((A cat has 4 legs.) and ((13 - -8) == (9 * -7 + 4 * 4))) and (((3 - 15) == (-13 + -5)) and (A bird has 4 legs.))) or (not not (Earth is the 3rd planet from the Sun.)) or (((16 - -20) <= (-10 * 7 * 3 * 9)) or (not ((-8 + 14) < (2 + 10)))))\nC. ((A cow has 10 legs.) or (not not (Uranus is the 7th planet from the Sun.))) and (((Diamond is a solid at room temperature.) or ((The chemical symbol for Mercury is Pb.) or ((-3 * -4 + 3 * 6) < (-10 * 4 - 7 * 2)))) or (not (The square root of 121 is 1.)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 14113230,
"true_count": 2
},
"seed": 14113230,
"task_id": 614113230,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not not (((Russia is in North America.) and (The first airplane flight by the Wright Brothers occurred in 1903.)) and (The Great Fire of London occurred in 1666.))) and (not not (((4 % 1) <= (1 % 3)) and ((9 * 2) <= (5 ** 2)))) and (((-18 + -14) < (4 ** 3) < (-5 * -5 + 5 * -6)) or ((((8 * -7 + 10 * 7) == (5 ** 1)) and ((25 % 7) < (18 - 7))) and (((18 - 16) != (-17 * -9)) or ((4 ** 1) != (-5 - 8)))))
B. ((((Sharks are mammals.) and (209 is a Fibonacci number.)) and ((The 1964 Olympics were held in Tokyo.) or ((-6 + 13) < (-9 + 0) < (5 * -8)))) and (not not ((Steam is a liquid at room temperature.) and ((-11 * -19) <= (-10 + 16))))) or (not (not not (Oxygen is a gas at room temperature.))) or ((The chemical symbol for Calcium is Zn.) or (China is in Asia.))
C. ((not ((17 - 2) <= (29 % 9))) or (not not (A ladybug is a reptile.)) or ((-5 - -17) > (7 % 1))) or (not ((Humans have five fingers on each hand.) or ((-1 * 5 - 7 * 0) <= (5 * 6))))
D. (((13 - -19) < (-3 + -13) < (3 * -1 - 0 * 10)) or (The square root of 81 is 9.)) and ((-7 * -9 + 1 * 0) > (4 * 2 + -9 * -10)) and ((not ((10 + 20) >= (13 + -18))) or (85 is less than or equal to 91.))
E. (((((9 * -3 + 9 * -9) >= (-10 * 2)) and (A elephant has 6 legs.)) and ((The currency of India is the Rupee.) and ((5 % 3) > (-3 - 2)))) or (((Penguins can fly.) and (The chemical symbol for Silver is S.)) or ((2 ** 3) < (12 - -16) < (2 ** 3)))) or ((1 ** 3) >= (-10 * -19)) or (((29 is divisible by 9.) or (not not ((-4 * 10 + 10 * 7) <= (-11 - 2)))) or ((not not ((-5 * -2 + 1 * 6) < (14 + -12))) or ((The 1956 Olympics were held in Rome.) or (27 is divisible by 3.))))
F. ((((The chemical symbol for Gold is Cl.) or ((-1 * 7 + -10 * 5) >= (2 ** 1))) or (Whales are fish.)) or (Electricity flows faster than light.)) or (not not (Mercury is a gas at room temperature.))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 11310696,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. (not not (((Russia is in North America.) and (The first airplane flight by the Wright Brothers occurred in 1903.)) and (The Great Fire of London occurred in 1666.))) and (not not (((4 % 1) <= (1 % 3)) and ((9 * 2) <= (5 ** 2)))) and (((-18 + -14) < (4 ** 3) < (-5 * -5 + 5 * -6)) or ((((8 * -7 + 10 * 7) == (5 ** 1)) and ((25 % 7) < (18 - 7))) and (((18 - 16) != (-17 * -9)) or ((4 ** 1) != (-5 - 8)))))\nB. ((((Sharks are mammals.) and (209 is a Fibonacci number.)) and ((The 1964 Olympics were held in Tokyo.) or ((-6 + 13) < (-9 + 0) < (5 * -8)))) and (not not ((Steam is a liquid at room temperature.) and ((-11 * -19) <= (-10 + 16))))) or (not (not not (Oxygen is a gas at room temperature.))) or ((The chemical symbol for Calcium is Zn.) or (China is in Asia.))\nC. ((not ((17 - 2) <= (29 % 9))) or (not not (A ladybug is a reptile.)) or ((-5 - -17) > (7 % 1))) or (not ((Humans have five fingers on each hand.) or ((-1 * 5 - 7 * 0) <= (5 * 6))))\nD. (((13 - -19) < (-3 + -13) < (3 * -1 - 0 * 10)) or (The square root of 81 is 9.)) and ((-7 * -9 + 1 * 0) > (4 * 2 + -9 * -10)) and ((not ((10 + 20) >= (13 + -18))) or (85 is less than or equal to 91.))\nE. (((((9 * -3 + 9 * -9) >= (-10 * 2)) and (A elephant has 6 legs.)) and ((The currency of India is the Rupee.) and ((5 % 3) > (-3 - 2)))) or (((Penguins can fly.) and (The chemical symbol for Silver is S.)) or ((2 ** 3) < (12 - -16) < (2 ** 3)))) or ((1 ** 3) >= (-10 * -19)) or (((29 is divisible by 9.) or (not not ((-4 * 10 + 10 * 7) <= (-11 - 2)))) or ((not not ((-5 * -2 + 1 * 6) < (14 + -12))) or ((The 1956 Olympics were held in Rome.) or (27 is divisible by 3.))))\nF. ((((The chemical symbol for Gold is Cl.) or ((-1 * 7 + -10 * 5) >= (2 ** 1))) or (Whales are fish.)) or (Electricity flows faster than light.)) or (not not (Mercury is a gas at room temperature.))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 11310696,
"true_count": 3
},
"seed": 11310696,
"task_id": 611310696,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not (((意大利位于大洋洲。) or (氯的化学符号是U。)) and ((汞在常温下是液体。) or (地球是距离太阳第5近的行星。)))
B. (not not (not not (墨西哥位于北美洲。))) and (not (((-13 * -5) > (8 * 9 + -4 * 1)) or (1948年奥运会在东京举办。)))
C. (铝的化学符号是Al。) or (not (not (钙的化学符号是P。)))
D. ((((4 ** 2) == (10 - 12)) or (64的平方根是8。)) or ((1904年奥运会在圣路易斯举办。) or (葡萄牙的首都是里斯本。))) or ((not not (菲律宾的首都是马尼拉。)) or (((-5 * 9) >= (0 * 1 + 2 * 3)) and (埃及的货币是埃及镑。)))
E. (2055年是闰年。) and ((not ((17 + 11) <= (5 * -9 * 3 * 3))) and (((-10 + -2) >= (-6 + -14)) and ((5 - -18) >= (-3 - -19))))
F. ((((10 + -6) <= (-13 + -10) <= (-16 - 9)) or ((-10 + 18) >= (1 ** 1))) or ((氯的化学符号是Cl。) and ((-3 + 20) >= (-1 + 11)))) and (巴西的首都是巴西利亚。)
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,B,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 25547079,
"true_count": 5
},
"question": "评估以下每个表达式：\n\nA. not (((意大利位于大洋洲。) or (氯的化学符号是U。)) and ((汞在常温下是液体。) or (地球是距离太阳第5近的行星。)))\nB. (not not (not not (墨西哥位于北美洲。))) and (not (((-13 * -5) > (8 * 9 + -4 * 1)) or (1948年奥运会在东京举办。)))\nC. (铝的化学符号是Al。) or (not (not (钙的化学符号是P。)))\nD. ((((4 ** 2) == (10 - 12)) or (64的平方根是8。)) or ((1904年奥运会在圣路易斯举办。) or (葡萄牙的首都是里斯本。))) or ((not not (菲律宾的首都是马尼拉。)) or (((-5 * 9) >= (0 * 1 + 2 * 3)) and (埃及的货币是埃及镑。)))\nE. (2055年是闰年。) and ((not ((17 + 11) <= (5 * -9 * 3 * 3))) and (((-10 + -2) >= (-6 + -14)) and ((5 - -18) >= (-3 - -19))))\nF. ((((10 + -6) <= (-13 + -10) <= (-16 - 9)) or ((-10 + 18) >= (1 ** 1))) or ((氯的化学符号是Cl。) and ((-3 + 20) >= (-1 + 11)))) and (巴西的首都是巴西利亚。)\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 25547079,
"true_count": 5
},
"seed": 25547079,
"task_id": 625547079,
"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 ((1896年奥运会在里约热内卢举办。) or (七月有31天。))) and ((3 % 2) < (6 + -20) < (-19 + -11))) and (((地球绕太阳运转。) or (中国的货币是人民币。)) or ((酒精在常温下是液体。) or (185是完全平方数。))) and (((((13 - 19) >= (0 * -6 - 9 * 5)) and (1968年奥运会在北京举办。)) or (((-9 + -18) <= (4 * 4 * -5 * -3)) or (瑞典的货币是雷亚尔。))) and (五月有31天。) and (not (not not (水在海平面上的沸点是100摄氏度。))))
B. (not (((4 ** 2) == (0 - 4)) or (not not ((-9 - 14) < (48 % 7))))) and ((((-16 + 0) < (-13 * 20)) and (越南的货币是克朗。)) and (磷的化学符号是P。)) and ((169的平方根是13。) or (not (((-14 - -7) >= (3 * -10)) or (马来西亚的货币是澳元。))))
C. ((not not (硫的化学符号是Pb。)) and ((6 * 1) > (-7 - -8))) and (not not ((法国大革命开始发生在1789年。) and ((-3 - -8) > (-2 * 5 - 1 * 10)))) and (not (not ((鱼有8条腿。) or (人类首次登月发生在1969年。))))
D. (not (2020年奥运会在东京举办。)) and ((蛇有10条腿。) or ((not (1936年奥运会在柏林举办。)) and (((42 % 9) != (3 % 6)) or ((5 ** 3) == (2 ** 1)))))
E. (((7 * 5 - -4 * -2) == (11 + -17)) or (法国大革命开始发生在1789年。) or (鸵鸟是鸟类。)) and (not not (not ((2 * -11) < (4 ** 3) < (7 + -7))))
F. ((not not (not not ((11 - 18) > (16 * -1)))) and ((四月有28天。) and ((5 ** 2) > (1 ** 2))) and ((8 % 9) != (-7 * -2 * 7 * -1))) or ((((7 * 0 + 4 * -5) == (-2 * -8)) or (((-5 - -9) >= (20 + -1)) and ((13 + -19) <= (2 ** 1)))) or ((-18 + -9) >= (17 - 1)))
G. not (not not (not not ((天王星是距离太阳第7近的行星。) and ((45 % 1) <= (-14 - 20)))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 71669960,
"true_count": 2
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. ((not ((1896年奥运会在里约热内卢举办。) or (七月有31天。))) and ((3 % 2) < (6 + -20) < (-19 + -11))) and (((地球绕太阳运转。) or (中国的货币是人民币。)) or ((酒精在常温下是液体。) or (185是完全平方数。))) and (((((13 - 19) >= (0 * -6 - 9 * 5)) and (1968年奥运会在北京举办。)) or (((-9 + -18) <= (4 * 4 * -5 * -3)) or (瑞典的货币是雷亚尔。))) and (五月有31天。) and (not (not not (水在海平面上的沸点是100摄氏度。))))\nB. (not (((4 ** 2) == (0 - 4)) or (not not ((-9 - 14) < (48 % 7))))) and ((((-16 + 0) < (-13 * 20)) and (越南的货币是克朗。)) and (磷的化学符号是P。)) and ((169的平方根是13。) or (not (((-14 - -7) >= (3 * -10)) or (马来西亚的货币是澳元。))))\nC. ((not not (硫的化学符号是Pb。)) and ((6 * 1) > (-7 - -8))) and (not not ((法国大革命开始发生在1789年。) and ((-3 - -8) > (-2 * 5 - 1 * 10)))) and (not (not ((鱼有8条腿。) or (人类首次登月发生在1969年。))))\nD. (not (2020年奥运会在东京举办。)) and ((蛇有10条腿。) or ((not (1936年奥运会在柏林举办。)) and (((42 % 9) != (3 % 6)) or ((5 ** 3) == (2 ** 1)))))\nE. (((7 * 5 - -4 * -2) == (11 + -17)) or (法国大革命开始发生在1789年。) or (鸵鸟是鸟类。)) and (not not (not ((2 * -11) < (4 ** 3) < (7 + -7))))\nF. ((not not (not not ((11 - 18) > (16 * -1)))) and ((四月有28天。) and ((5 ** 2) > (1 ** 2))) and ((8 % 9) != (-7 * -2 * 7 * -1))) or ((((7 * 0 + 4 * -5) == (-2 * -8)) or (((-5 - -9) >= (20 + -1)) and ((13 + -19) <= (2 ** 1)))) or ((-18 + -9) >= (17 - 1)))\nG. not (not not (not not ((天王星是距离太阳第7近的行星。) and ((45 % 1) <= (-14 - 20)))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 71669960,
"true_count": 2
},
"seed": 71669960,
"task_id": 671669960,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not (((not not ((-5 * -5 * -6 * 9) == (17 - 0))) and (((-8 + 17) == (19 * 7)) or (埃及的货币是兹罗提。))) and (((油在常温下是液体。) or (锰的化学符号是Mn。)) and (((3 * 7 - 6 * -10) > (9 * -15)) or (月球自己发光。))))
B. not ((not (十一月有30天。)) or (瑞士的货币是越南盾。) or (捷克的货币是比索。))
C. ((not not (((-8 - -12) != (-20 * 15)) and ((-4 - -12) > (-16 * -19)))) and ((第二次世界大战结束发生在1945年。) and (铁在常温下是液体。)) and (((捷克的货币是卢布。) and (空气在常温下是气体。)) and ((2004年奥运会在墨尔本举办。) and ((-18 + -12) == (4 * -6 - -9 * -8))))) and (not (((2 * -4 - -7 * -9) == (-9 * -12)) or (乌鸦是鱼类。))) and (not not (肯尼亚的首都是雅加达。))
D. (((not (海王星是距离太阳第8近的行星。)) or (((40 % 3) <= (11 - 18) <= (-6 - -8)) and ((1 ** 2) != (13 - -8)))) and (50大于15。) and (阿根廷的货币是比索。)) or ((not not ((六月有30天。) or ((8 % 10) <= (7 + 14) <= (7 * -13)))) and (not not ((埃及的货币是埃及镑。) or (牛是哺乳动物。))))
E. not not (((((18 * -15) < (10 * -1 - -8 * -2) < (-7 * -9 + 1 * 0)) or (1908年奥运会在伦敦举办。)) and (not ((-12 * -2) <= (17 * 20) <= (15 - 20)))) and ((1996年奥运会在亚特兰大举办。) or ((钻石在常温下是气体。) or (1992年奥运会在安特卫普举办。))))
F. (not (not (((9 - -20) <= (-19 + -2) <= (3 ** 1)) and (意大利的首都是布鲁塞尔。)))) or (not not (1952年奥运会在赫尔辛基举办。))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 11271268,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. not not (((not not ((-5 * -5 * -6 * 9) == (17 - 0))) and (((-8 + 17) == (19 * 7)) or (埃及的货币是兹罗提。))) and (((油在常温下是液体。) or (锰的化学符号是Mn。)) and (((3 * 7 - 6 * -10) > (9 * -15)) or (月球自己发光。))))\nB. not ((not (十一月有30天。)) or (瑞士的货币是越南盾。) or (捷克的货币是比索。))\nC. ((not not (((-8 - -12) != (-20 * 15)) and ((-4 - -12) > (-16 * -19)))) and ((第二次世界大战结束发生在1945年。) and (铁在常温下是液体。)) and (((捷克的货币是卢布。) and (空气在常温下是气体。)) and ((2004年奥运会在墨尔本举办。) and ((-18 + -12) == (4 * -6 - -9 * -8))))) and (not (((2 * -4 - -7 * -9) == (-9 * -12)) or (乌鸦是鱼类。))) and (not not (肯尼亚的首都是雅加达。))\nD. (((not (海王星是距离太阳第8近的行星。)) or (((40 % 3) <= (11 - 18) <= (-6 - -8)) and ((1 ** 2) != (13 - -8)))) and (50大于15。) and (阿根廷的货币是比索。)) or ((not not ((六月有30天。) or ((8 % 10) <= (7 + 14) <= (7 * -13)))) and (not not ((埃及的货币是埃及镑。) or (牛是哺乳动物。))))\nE. not not (((((18 * -15) < (10 * -1 - -8 * -2) < (-7 * -9 + 1 * 0)) or (1908年奥运会在伦敦举办。)) and (not ((-12 * -2) <= (17 * 20) <= (15 - 20)))) and ((1996年奥运会在亚特兰大举办。) or ((钻石在常温下是气体。) or (1992年奥运会在安特卫普举办。))))\nF. (not (not (((9 - -20) <= (-19 + -2) <= (3 ** 1)) and (意大利的首都是布鲁塞尔。)))) or (not not (1952年奥运会在赫尔辛基举办。))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 11271268,
"true_count": 4
},
"seed": 11271268,
"task_id": 611271268,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (((not not (((-8 - -5) >= (-8 - -18)) and (1920年奥运会在安特卫普举办。))) and (((22是质数。) and (十月有31天。)) or ((33 % 2) == (4 ** 3)))) and (not not (not ((1948年奥运会在伦敦举办。) and ((4 ** 3) <= (12 + -2)))))) or (((((2024年奥运会在巴黎举办。) and ((40 % 9) < (8 * -2 * 6 * 6))) and ((6 * -2 * 4 * -4) > (10 * -5 - -6 * 9))) or ((-4 * 5) >= (11 - 10))) and (not (not not (not ((33 % 6) == (11 * -4))))))
B. not not (not not (not not (not not (((-9 * -7 * 6 * 6) >= (5 ** 1)) or ((0 * 3 + 9 * -7) == (50 % 2))))))
C. not (not not ((((16 + 0) < (-6 + 7)) and (not (氮气在常温下是气体。))) or (not not (((-20 - 14) <= (14 - 0)) or (1968年奥运会在墨尔本举办。)))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 21743059,
"true_count": 1
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (((not not (((-8 - -5) >= (-8 - -18)) and (1920年奥运会在安特卫普举办。))) and (((22是质数。) and (十月有31天。)) or ((33 % 2) == (4 ** 3)))) and (not not (not ((1948年奥运会在伦敦举办。) and ((4 ** 3) <= (12 + -2)))))) or (((((2024年奥运会在巴黎举办。) and ((40 % 9) < (8 * -2 * 6 * 6))) and ((6 * -2 * 4 * -4) > (10 * -5 - -6 * 9))) or ((-4 * 5) >= (11 - 10))) and (not (not not (not ((33 % 6) == (11 * -4))))))\nB. not not (not not (not not (not not (((-9 * -7 * 6 * 6) >= (5 ** 1)) or ((0 * 3 + 9 * -7) == (50 % 2))))))\nC. not (not not ((((16 + 0) < (-6 + 7)) and (not (氮气在常温下是气体。))) or (not not (((-20 - 14) <= (14 - 0)) or (1968年奥运会在墨尔本举办。)))))\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": 3,
"seed": 21743059,
"true_count": 1
},
"seed": 21743059,
"task_id": 621743059,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (not (((Bats are blind.) and (79 is greater than 21.)) and ((The capital of Turkey is Ankara.) and ((12 - 1) <= (9 - 4)))))
B. not ((A tiger is a mammal.) and ((-10 + 7) <= (10 * -2 - -1 * -10) <= (-6 + -1)))
C. (((-20 + -3) >= (14 + -9)) or (((The capital of New Zealand is Bangkok.) or ((1 - -12) < (-19 + -12))) and (((-10 - -11) > (-10 + 6)) or (The currency of Indonesia is the Dollar.)))) and ((-8 - -10) <= (-4 * -6 - 10 * 6) <= (2 ** 1)) and (((The chemical symbol for Sulfur is S.) or ((World War I began occurred in 1914.) or (Neptune is the 8th planet from the Sun.))) or (Neptune is the 7th planet from the Sun.) or (A duck has 2 legs.))
D. (not (Mars is the 8th planet from the Sun.)) or ((The currency of Japan is the Dollar.) or (not ((-13 + -15) >= (-11 - -17))))
E. ((((The capital of Russia is Budapest.) and (Mars is the 4th planet from the Sun.)) and (((-6 * -16) <= (-10 - -2)) or (The capital of Portugal is New Delhi.))) and (((9 + -16) == (8 - -13)) or ((16 * -3) < (16 + 16))) and (((The 1936 Olympics were held in Berlin.) or (There are 28 days in February.)) or (not not (There are 31 days in October.)))) and (not not ((not (The currency of Singapore is the Koruna.)) or ((The capital of Venezuela is Dublin.) and (There are 31 days in October.))))
F. ((not (((6 - -13) > (9 * 3 - -10 * 10)) and ((5 ** 1) == (10 * 7)))) and ((not not (The first moon landing occurred in 1969.)) and (((10 - 12) > (15 + -6)) and (The human body has 150 bones.)))) or ((((4 - 19) < (-17 * 18) < (48 % 6)) and ((Sound travels faster in a vacuum.) or (There are 31 days in September.))) or (The Great Fire of London occurred in 1666.))
G. ((((Christopher Columbus reached America occurred in 1492.) and ((12 + -13) >= (-20 - 16))) and (Jupiter is the 5th planet from the Sun.)) and (The capital of China is Tokyo.)) and (Russia is in Europe.) and (((((-2 + 10) >= (3 + -17)) or (A human has 2 legs.)) and (((9 * -1 + -4 * 8) > (3 ** 3)) and (337 is a perfect square.))) and (((Russia is in Oceania.) or (Mercury is the 4th planet from the Sun.)) or (((-9 * 3 - -9 * 2) == (1 ** 1)) or ((17 + 14) <= (18 + -16)))))
H. not not (((((0 * -9 * -5 * 1) != (17 - 14)) and (A lizard is a reptile.)) or (The capital of Colombia is Kyiv.)) or (not not (not (103 is an even number.))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,D,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 65221120,
"true_count": 5
},
"question": "Examine these expressions:\n\nA. not not (not (((Bats are blind.) and (79 is greater than 21.)) and ((The capital of Turkey is Ankara.) and ((12 - 1) <= (9 - 4)))))\nB. not ((A tiger is a mammal.) and ((-10 + 7) <= (10 * -2 - -1 * -10) <= (-6 + -1)))\nC. (((-20 + -3) >= (14 + -9)) or (((The capital of New Zealand is Bangkok.) or ((1 - -12) < (-19 + -12))) and (((-10 - -11) > (-10 + 6)) or (The currency of Indonesia is the Dollar.)))) and ((-8 - -10) <= (-4 * -6 - 10 * 6) <= (2 ** 1)) and (((The chemical symbol for Sulfur is S.) or ((World War I began occurred in 1914.) or (Neptune is the 8th planet from the Sun.))) or (Neptune is the 7th planet from the Sun.) or (A duck has 2 legs.))\nD. (not (Mars is the 8th planet from the Sun.)) or ((The currency of Japan is the Dollar.) or (not ((-13 + -15) >= (-11 - -17))))\nE. ((((The capital of Russia is Budapest.) and (Mars is the 4th planet from the Sun.)) and (((-6 * -16) <= (-10 - -2)) or (The capital of Portugal is New Delhi.))) and (((9 + -16) == (8 - -13)) or ((16 * -3) < (16 + 16))) and (((The 1936 Olympics were held in Berlin.) or (There are 28 days in February.)) or (not not (There are 31 days in October.)))) and (not not ((not (The currency of Singapore is the Koruna.)) or ((The capital of Venezuela is Dublin.) and (There are 31 days in October.))))\nF. ((not (((6 - -13) > (9 * 3 - -10 * 10)) and ((5 ** 1) == (10 * 7)))) and ((not not (The first moon landing occurred in 1969.)) and (((10 - 12) > (15 + -6)) and (The human body has 150 bones.)))) or ((((4 - 19) < (-17 * 18) < (48 % 6)) and ((Sound travels faster in a vacuum.) or (There are 31 days in September.))) or (The Great Fire of London occurred in 1666.))\nG. ((((Christopher Columbus reached America occurred in 1492.) and ((12 + -13) >= (-20 - 16))) and (Jupiter is the 5th planet from the Sun.)) and (The capital of China is Tokyo.)) and (Russia is in Europe.) and (((((-2 + 10) >= (3 + -17)) or (A human has 2 legs.)) and (((9 * -1 + -4 * 8) > (3 ** 3)) and (337 is a perfect square.))) and (((Russia is in Oceania.) or (Mercury is the 4th planet from the Sun.)) or (((-9 * 3 - -9 * 2) == (1 ** 1)) or ((17 + 14) <= (18 + -16)))))\nH. not not (((((0 * -9 * -5 * 1) != (17 - 14)) and (A lizard is a reptile.)) or (The capital of Colombia is Kyiv.)) or (not not (not (103 is an even number.))))\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": 65221120,
"true_count": 5
},
"seed": 65221120,
"task_id": 665221120,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (not not (not (The chemical symbol for Lead is Pb.)))
B. not ((not (((4 + 7) == (-4 * 7 - -8 * -5)) or (not ((-11 + -1) == (3 ** 3))))) or (((The chemical symbol for Phosphorus is Co.) or ((0 * -6) < (-8 * 2))) or (((1 ** 2) > (4 ** 1)) and (95 is greater than 24.))) or ((((13 * -20) >= (-12 * -14)) and ((Russia is in North America.) or (Copper is a solid at room temperature.))) and (((4 ** 3) <= (7 * 6 + 6 * -7)) or (2096 is a leap year.)) and (not ((Humans only use 10% of their brain.) and ((12 + 5) > (-10 * 0 - -6 * -6))))))
C. not not (((not (((19 % 5) <= (-19 - 19)) or ((-12 * -10) == (-9 - 13)))) or (((-10 + 7) < (8 * 0)) and (The capital of Canada is Wellington.)) or (not not (((4 + -14) <= (10 * -12)) and (The chemical symbol for Nitrogen is N.)))) or (((8 * 3 - -8 * -10) <= (11 + -19) <= (3 - -9)) or (((A bee is a fish.) and ((-1 * 1 * -8 * 10) <= (9 * 7 - 5 * 4))) or (((3 ** 2) >= (3 ** 2)) or (The chemical symbol for Aluminum is Al.)))))
D. not (not not (((21 % 7) == (-2 - -13)) and (Japan is in Asia.)))
E. (not (((((-6 * 8 * -2 * 2) != (-19 * -16)) and ((-13 * 1) == (2 * -9))) or (((25 % 5) < (-8 * -13)) and ((-5 + 19) < (4 * 6 + 6 * -2) < (1 * 11)))) and ((-9 * 3 * -6 * -3) >= (5 ** 2)))) and (not not ((((Humans have five fingers on each hand.) or (A kangaroo has 2 legs.)) or ((A penguin is a reptile.) and (The 1900 Olympics were held in Paris.))) and ((((22 % 6) == (-20 - -13)) or ((4 * -8) != (-17 + 8))) or (Electricity flows faster than light.))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 8034714,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (not not (not (The chemical symbol for Lead is Pb.)))\nB. not ((not (((4 + 7) == (-4 * 7 - -8 * -5)) or (not ((-11 + -1) == (3 ** 3))))) or (((The chemical symbol for Phosphorus is Co.) or ((0 * -6) < (-8 * 2))) or (((1 ** 2) > (4 ** 1)) and (95 is greater than 24.))) or ((((13 * -20) >= (-12 * -14)) and ((Russia is in North America.) or (Copper is a solid at room temperature.))) and (((4 ** 3) <= (7 * 6 + 6 * -7)) or (2096 is a leap year.)) and (not ((Humans only use 10% of their brain.) and ((12 + 5) > (-10 * 0 - -6 * -6))))))\nC. not not (((not (((19 % 5) <= (-19 - 19)) or ((-12 * -10) == (-9 - 13)))) or (((-10 + 7) < (8 * 0)) and (The capital of Canada is Wellington.)) or (not not (((4 + -14) <= (10 * -12)) and (The chemical symbol for Nitrogen is N.)))) or (((8 * 3 - -8 * -10) <= (11 + -19) <= (3 - -9)) or (((A bee is a fish.) and ((-1 * 1 * -8 * 10) <= (9 * 7 - 5 * 4))) or (((3 ** 2) >= (3 ** 2)) or (The chemical symbol for Aluminum is Al.)))))\nD. not (not not (((21 % 7) == (-2 - -13)) and (Japan is in Asia.)))\nE. (not (((((-6 * 8 * -2 * 2) != (-19 * -16)) and ((-13 * 1) == (2 * -9))) or (((25 % 5) < (-8 * -13)) and ((-5 + 19) < (4 * 6 + 6 * -2) < (1 * 11)))) and ((-9 * 3 * -6 * -3) >= (5 ** 2)))) and (not not ((((Humans have five fingers on each hand.) or (A kangaroo has 2 legs.)) or ((A penguin is a reptile.) and (The 1900 Olympics were held in Paris.))) and ((((22 % 6) == (-20 - -13)) or ((4 * -8) != (-17 + 8))) or (Electricity flows faster than light.))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 8034714,
"true_count": 4
},
"seed": 8034714,
"task_id": 608034714,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. ((((-2 * 10 + -5 * -1) == (-4 * 9)) or ((3 ** 2) == (-2 - 16))) or (((-7 * 3 + 6 * 2) == (-16 * -19)) and ((-10 * 7 * -3 * 1) <= (-3 * -1 - 9 * 3) <= (24 % 6)))) or (The currency of Colombia is the Baht.) or ((-2 - -11) > (11 * 19))
B. not not (((Colombia is in South America.) and ((16 - 14) <= (-10 - -3))) and ((Helium is a liquid at room temperature.) or ((6 * 8 + -9 * 3) < (-20 - 13))))
C. ((not ((8 - 14) <= (-9 * 10 - -1 * -6))) and (Uranus is the 2nd planet from the Sun.)) and (not not (The currency of Brazil is the Dollar.))
D. ((((2 + -12) <= (-2 + -13)) and (Italy is in Africa.)) or (The currency of Turkey is the Lira.)) or (96 is divisible by 8.) or (((A human is a mammal.) and (The currency of South Africa is the Rand.)) and (The chemical symbol for Magnesium is U.))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 49505127,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. ((((-2 * 10 + -5 * -1) == (-4 * 9)) or ((3 ** 2) == (-2 - 16))) or (((-7 * 3 + 6 * 2) == (-16 * -19)) and ((-10 * 7 * -3 * 1) <= (-3 * -1 - 9 * 3) <= (24 % 6)))) or (The currency of Colombia is the Baht.) or ((-2 - -11) > (11 * 19))\nB. not not (((Colombia is in South America.) and ((16 - 14) <= (-10 - -3))) and ((Helium is a liquid at room temperature.) or ((6 * 8 + -9 * 3) < (-20 - 13))))\nC. ((not ((8 - 14) <= (-9 * 10 - -1 * -6))) and (Uranus is the 2nd planet from the Sun.)) and (not not (The currency of Brazil is the Dollar.))\nD. ((((2 + -12) <= (-2 + -13)) and (Italy is in Africa.)) or (The currency of Turkey is the Lira.)) or (96 is divisible by 8.) or (((A human is a mammal.) and (The currency of South Africa is the Rand.)) and (The chemical symbol for Magnesium is U.))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 49505127,
"true_count": 1
},
"seed": 49505127,
"task_id": 649505127,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not ((not ((not not (There are 28 days in February.)) and ((-20 * -11) <= (4 + 6)))) or ((not (((9 * -2 + 3 * -7) >= (-2 * 11)) and ((3 * 2 + 8 * 10) != (13 - -6)))) or (((6 * 5 * -6 * 8) > (0 * -14)) or ((-3 * -9 + 1 * 4) > (8 + 2))) or ((((16 * -3) < (-7 * 8 - 1 * -5) < (-11 - -20)) or (The chemical symbol for Oxygen is O.)) and ((-6 + -17) != (19 % 10)))))
B. (not ((The United States declared independence occurred in 1776.) and ((not not ((-5 + 4) >= (-13 - 0))) or (2022 is a leap year.)))) or (not (((((5 * -10) <= (-4 + -1)) or ((-6 + -3) < (47 % 6) < (-14 - -14))) or ((The capital of Ukraine is Bucharest.) and ((0 * 4 + 6 * -6) == (-8 - 20)))) or (The capital of Belgium is Brussels.) or (not (((-11 + 14) <= (0 - -20)) or (South Korea is in Asia.)))))
C. ((not ((12 * -5) > (46 % 8))) or (624 is a Fibonacci number.) or ((((1927 is a leap year.) and (Ice is less dense than liquid water.)) and (((14 + -9) <= (-12 - -20)) or (Carbon dioxide is a gas at room temperature.))) or (The 1984 Olympics were held in Los Angeles.))) or ((not not (not not (The 1920 Olympics were held in London.))) and (not ((-13 - -17) <= (5 * -10 - -9 * -5) <= (3 ** 1))))
D. not not (((not not ((The 1912 Olympics were held in Stockholm.) and ((-4 * -2 * 9 * -8) >= (-5 + -10)))) and (Oxygen is necessary for human survival.)) and (not not (not not ((Christopher Columbus reached America occurred in 1492.) or ((0 + -20) == (-3 * 13))))))
E. not (not (((not not (The 1936 Olympics were held in Antwerp.)) or ((-12 + -8) != (-3 - 19))) or (((0 * 9 - -1 * 8) <= (-10 * 9 - 8 * 0)) or (The chemical symbol for Sulfur is S.))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
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"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not ((not ((not not (There are 28 days in February.)) and ((-20 * -11) <= (4 + 6)))) or ((not (((9 * -2 + 3 * -7) >= (-2 * 11)) and ((3 * 2 + 8 * 10) != (13 - -6)))) or (((6 * 5 * -6 * 8) > (0 * -14)) or ((-3 * -9 + 1 * 4) > (8 + 2))) or ((((16 * -3) < (-7 * 8 - 1 * -5) < (-11 - -20)) or (The chemical symbol for Oxygen is O.)) and ((-6 + -17) != (19 % 10)))))\nB. (not ((The United States declared independence occurred in 1776.) and ((not not ((-5 + 4) >= (-13 - 0))) or (2022 is a leap year.)))) or (not (((((5 * -10) <= (-4 + -1)) or ((-6 + -3) < (47 % 6) < (-14 - -14))) or ((The capital of Ukraine is Bucharest.) and ((0 * 4 + 6 * -6) == (-8 - 20)))) or (The capital of Belgium is Brussels.) or (not (((-11 + 14) <= (0 - -20)) or (South Korea is in Asia.)))))\nC. ((not ((12 * -5) > (46 % 8))) or (624 is a Fibonacci number.) or ((((1927 is a leap year.) and (Ice is less dense than liquid water.)) and (((14 + -9) <= (-12 - -20)) or (Carbon dioxide is a gas at room temperature.))) or (The 1984 Olympics were held in Los Angeles.))) or ((not not (not not (The 1920 Olympics were held in London.))) and (not ((-13 - -17) <= (5 * -10 - -9 * -5) <= (3 ** 1))))\nD. not not (((not not ((The 1912 Olympics were held in Stockholm.) and ((-4 * -2 * 9 * -8) >= (-5 + -10)))) and (Oxygen is necessary for human survival.)) and (not not (not not ((Christopher Columbus reached America occurred in 1492.) or ((0 + -20) == (-3 * 13))))))\nE. not (not (((not not (The 1936 Olympics were held in Antwerp.)) or ((-12 + -8) != (-3 - 19))) or (((0 * 9 - -1 * 8) <= (-10 * 9 - 8 * 0)) or (The chemical symbol for Sulfur is S.))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 13373222,
"true_count": 2
},
"seed": 13373222,
"task_id": 613373222,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not not (not ((The capital of Ukraine is Buenos Aires.) or ((1930 is a leap year.) and ((-19 - 3) > (-4 + 12)))))
B. not not (not ((not not (The chemical symbol for Oxygen is Na.)) or (not not (There are 29 days in June.))))
C. (not not (((The 1968 Olympics were held in Mexico City.) and ((-4 * 0 - -3 * -6) < (-9 * -1 * -7 * 8))) and ((8 * 5) <= (0 * -2 + 2 * -4)))) and ((The French Revolution began occurred in 1789.) or ((-7 - -8) != (7 * -3)))
D. (not ((18 * 2) <= (5 ** 2))) or ((not not (The capital of Ireland is Dublin.)) or ((Venus is the 2nd planet from the Sun.) and (The chemical symbol for Calcium is Au.))) or (((((1 - 14) >= (-17 * 0)) and ((-2 * -3 + -6 * 9) <= (-4 * -2 - -10 * 5) <= (14 - 20))) and ((0 + 19) <= (38 % 3))) or (Gold is a gas at room temperature.))
E. ((The currency of Japan is the Yen.) or ((The Moon orbits the Earth.) and (World War I began occurred in 1914.)) or (not ((The Soviet Union dissolved occurred in 1991.) and ((-19 * -5) > (7 * -7 + -2 * -7))))) and (((((1 * -8 + 6 * 4) >= (46 % 7)) or (The 1936 Olympics were held in Berlin.)) and (1915 is a leap year.)) or (((12 - -17) <= (4 ** 1)) and ((1 * 9 + 3 * -4) == (-17 + -6))) or (((-12 + 15) != (4 * 1 * 1 * 0)) and (((28 % 9) >= (26 % 2)) and ((-16 * 11) < (-5 + -8)))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 2007308,
"true_count": 4
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not not (not ((The capital of Ukraine is Buenos Aires.) or ((1930 is a leap year.) and ((-19 - 3) > (-4 + 12)))))\nB. not not (not ((not not (The chemical symbol for Oxygen is Na.)) or (not not (There are 29 days in June.))))\nC. (not not (((The 1968 Olympics were held in Mexico City.) and ((-4 * 0 - -3 * -6) < (-9 * -1 * -7 * 8))) and ((8 * 5) <= (0 * -2 + 2 * -4)))) and ((The French Revolution began occurred in 1789.) or ((-7 - -8) != (7 * -3)))\nD. (not ((18 * 2) <= (5 ** 2))) or ((not not (The capital of Ireland is Dublin.)) or ((Venus is the 2nd planet from the Sun.) and (The chemical symbol for Calcium is Au.))) or (((((1 - 14) >= (-17 * 0)) and ((-2 * -3 + -6 * 9) <= (-4 * -2 - -10 * 5) <= (14 - 20))) and ((0 + 19) <= (38 % 3))) or (Gold is a gas at room temperature.))\nE. ((The currency of Japan is the Yen.) or ((The Moon orbits the Earth.) and (World War I began occurred in 1914.)) or (not ((The Soviet Union dissolved occurred in 1991.) and ((-19 * -5) > (7 * -7 + -2 * -7))))) and (((((1 * -8 + 6 * 4) >= (46 % 7)) or (The 1936 Olympics were held in Berlin.)) and (1915 is a leap year.)) or (((12 - -17) <= (4 ** 1)) and ((1 * 9 + 3 * -4) == (-17 + -6))) or (((-12 + 15) != (4 * 1 * 1 * 0)) and (((28 % 9) >= (26 % 2)) and ((-16 * 11) < (-5 + -8)))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 2007308,
"true_count": 4
},
"seed": 2007308,
"task_id": 602007308,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not (not (not not (月球自己发光。)))
B. not not (((第二次世界大战结束发生在1950年。) or (钴的化学符号是Co。)) and ((-6 * 14) > (8 * 5 + 5 * -1)))
C. ((((12 + -11) != (2 ** 3)) or (捷克的首都是布拉格。)) and ((8 * 8 * 1 * 2) != (30 % 7))) and (((地球是距离太阳第3近的行星。) and (委内瑞拉的首都是加拉加斯。)) and (not (莱特兄弟首次飞行发生在1905年。)))
D. ((((-13 + 5) != (-13 + -18)) and (匈牙利的货币是福林。)) or (英国的货币是英镑。)) and (蜘蛛有100条腿。)
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 40352283,
"true_count": 2
},
"question": "审视以下逻辑表达式：\n\nA. not not (not (not not (月球自己发光。)))\nB. not not (((第二次世界大战结束发生在1950年。) or (钴的化学符号是Co。)) and ((-6 * 14) > (8 * 5 + 5 * -1)))\nC. ((((12 + -11) != (2 ** 3)) or (捷克的首都是布拉格。)) and ((8 * 8 * 1 * 2) != (30 % 7))) and (((地球是距离太阳第3近的行星。) and (委内瑞拉的首都是加拉加斯。)) and (not (莱特兄弟首次飞行发生在1905年。)))\nD. ((((-13 + 5) != (-13 + -18)) and (匈牙利的货币是福林。)) or (英国的货币是英镑。)) and (蜘蛛有100条腿。)\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": 4,
"seed": 40352283,
"true_count": 2
},
"seed": 40352283,
"task_id": 640352283,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. Canada is in North America.
B. not not (((5 * 4) < (4 - 11)) and ((6 + 5) >= (6 - 2)))
C. not ((Bats are blind.) or (The capital of Finland is Helsinki.))
D. Nitrogen is a gas at room temperature.
E. (-6 * 10 + -7 * -3) != (-2 + 5)
F. not (A sheep is a fish.)
G. ((The chemical symbol for Sodium is Mg.) or (A pig has 4 legs.)) or (((8 * 7 * 4 * 8) == (16 + -15)) or ((-18 + -20) > (9 * -3)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,D,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 40150679,
"true_count": 5
},
"question": "Review these logical expressions:\n\nA. Canada is in North America.\nB. not not (((5 * 4) < (4 - 11)) and ((6 + 5) >= (6 - 2)))\nC. not ((Bats are blind.) or (The capital of Finland is Helsinki.))\nD. Nitrogen is a gas at room temperature.\nE. (-6 * 10 + -7 * -3) != (-2 + 5)\nF. not (A sheep is a fish.)\nG. ((The chemical symbol for Sodium is Mg.) or (A pig has 4 legs.)) or (((8 * 7 * 4 * 8) == (16 + -15)) or ((-18 + -20) > (9 * -3)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 40150679,
"true_count": 5
},
"seed": 40150679,
"task_id": 640150679,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not not (((2 - -17) != (6 * 0 * 2 * -9)) and (((-3 * 20) != (1 ** 3)) or (The 1976 Olympics were held in Montreal.)))) or ((not not ((The chemical symbol for Neon is Sn.) or (The chemical symbol for Silicon is Si.))) or (not not ((The capital of Greece is Rome.) or ((7 * 9) > (-3 * -10)))))
B. (((((8 * -1 + 10 * 7) < (-18 * -12)) or (The 1976 Olympics were held in Rome.)) or ((The capital of Kenya is Nairobi.) and (The square root of 4 is 4.))) and ((-11 * -4) < (13 * -3))) or (((not not ((5 - -13) >= (1 ** 2))) or (not not (The 1912 Olympics were held in Stockholm.))) and ((Italy is in North America.) or ((5 ** 3) <= (2 - -16))) and (((Silver is a solid at room temperature.) and ((39 % 3) == (-2 * -14))) and (The capital of India is New Delhi.)))
C. (((((0 + 17) == (-13 + -20)) or ((4 % 8) == (-4 * 4 + -8 * 5))) or ((Mars is the 4th planet from the Sun.) or (Oxygen is a gas at room temperature.))) and (not (The first airplane flight by the Wright Brothers occurred in 1903.)) and (1909 is a leap year.)) or (((-3 * 10 + 1 * -9) == (4 ** 2)) and (Alcohol is a liquid at room temperature.) and (The capital of Philippines is Bangkok.))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 922442,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. (not not (((2 - -17) != (6 * 0 * 2 * -9)) and (((-3 * 20) != (1 ** 3)) or (The 1976 Olympics were held in Montreal.)))) or ((not not ((The chemical symbol for Neon is Sn.) or (The chemical symbol for Silicon is Si.))) or (not not ((The capital of Greece is Rome.) or ((7 * 9) > (-3 * -10)))))\nB. (((((8 * -1 + 10 * 7) < (-18 * -12)) or (The 1976 Olympics were held in Rome.)) or ((The capital of Kenya is Nairobi.) and (The square root of 4 is 4.))) and ((-11 * -4) < (13 * -3))) or (((not not ((5 - -13) >= (1 ** 2))) or (not not (The 1912 Olympics were held in Stockholm.))) and ((Italy is in North America.) or ((5 ** 3) <= (2 - -16))) and (((Silver is a solid at room temperature.) and ((39 % 3) == (-2 * -14))) and (The capital of India is New Delhi.)))\nC. (((((0 + 17) == (-13 + -20)) or ((4 % 8) == (-4 * 4 + -8 * 5))) or ((Mars is the 4th planet from the Sun.) or (Oxygen is a gas at room temperature.))) and (not (The first airplane flight by the Wright Brothers occurred in 1903.)) and (1909 is a leap year.)) or (((-3 * 10 + 1 * -9) == (4 ** 2)) and (Alcohol is a liquid at room temperature.) and (The capital of Philippines is Bangkok.))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 922442,
"true_count": 1
},
"seed": 922442,
"task_id": 600922442,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not not (not ((Jupiter is the 2nd planet from the Sun.) or ((The chemical symbol for Zinc is Pb.) and (The capital of Singapore is Bogota.))))
B. ((((-5 * 3 + -9 * 9) < (40 % 9) < (-13 + -16)) and ((-15 * -9) != (4 ** 3))) and ((5 ** 2) < (15 - 12))) or (not (1929 is a leap year.)) or ((not not ((-15 * 18) <= (48 % 8) <= (5 * 7 - -8 * 5))) and (((Mars is the 4th planet from the Sun.) and (The square root of 81 is 9.)) and (not not (The currency of Philippines is the Riyal.))))
C. (not ((The currency of Japan is the Yen.) or (((-6 * 14) < (41 % 6)) and ((-10 * 9 - -2 * 3) > (16 - -16))))) or (not not ((not not (Argentina is in Antarctica.)) or (not not (Neptune is the 8th planet from the Sun.))))
D. not not (((((-1 + -9) <= (24 % 9)) or (There are 30 days in September.)) or (((2 * 9 - 8 * 9) > (-4 * 10 + 7 * -7)) and ((-3 + 7) <= (48 % 7)))) or (not ((4 - 17) < (3 ** 2) < (6 * -13))) or (((The square root of 36 is 9.) and ((3 - 19) != (-5 * -10 * 3 * -1))) and ((The currency of Russia is the Dollar.) or ((-4 + -8) != (-11 * -5)))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 45549699,
"true_count": 4
},
"question": "Analyze these boolean expressions:\n\nA. not not (not ((Jupiter is the 2nd planet from the Sun.) or ((The chemical symbol for Zinc is Pb.) and (The capital of Singapore is Bogota.))))\nB. ((((-5 * 3 + -9 * 9) < (40 % 9) < (-13 + -16)) and ((-15 * -9) != (4 ** 3))) and ((5 ** 2) < (15 - 12))) or (not (1929 is a leap year.)) or ((not not ((-15 * 18) <= (48 % 8) <= (5 * 7 - -8 * 5))) and (((Mars is the 4th planet from the Sun.) and (The square root of 81 is 9.)) and (not not (The currency of Philippines is the Riyal.))))\nC. (not ((The currency of Japan is the Yen.) or (((-6 * 14) < (41 % 6)) and ((-10 * 9 - -2 * 3) > (16 - -16))))) or (not not ((not not (Argentina is in Antarctica.)) or (not not (Neptune is the 8th planet from the Sun.))))\nD. not not (((((-1 + -9) <= (24 % 9)) or (There are 30 days in September.)) or (((2 * 9 - 8 * 9) > (-4 * 10 + 7 * -7)) and ((-3 + 7) <= (48 % 7)))) or (not ((4 - 17) < (3 ** 2) < (6 * -13))) or (((The square root of 36 is 9.) and ((3 - 19) != (-5 * -10 * 3 * -1))) and ((The currency of Russia is the Dollar.) or ((-4 + -8) != (-11 * -5)))))\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": 45549699,
"true_count": 4
},
"seed": 45549699,
"task_id": 645549699,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not not (((2 ** 2) <= (4 - 8)) and (1984年奥运会在巴黎举办。))
B. (-12 * -5) <= (-8 - -9) <= (-9 * 11)
C. ((酒精在常温下是气体。) or ((8 * 5 + 6 * -4) >= (-9 - 4))) or ((铀的化学符号是U。) or ((-15 * 7) < (2 ** 1)))
D. 人体有206块骨头。
E. (not not (2000年奥运会在巴塞罗那举办。)) and (not (91是奇数。))
F. (十二月有31天。) or ((1996年奥运会在慕尼黑举办。) or (俄罗斯的货币是卢布。))
G. 墨西哥位于非洲。
H. ((3 ** 3) != (1 * -16)) and (((15 - -16) <= (8 + -3)) and (壁虎是爬行动物。))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 75659143,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. not not (((2 ** 2) <= (4 - 8)) and (1984年奥运会在巴黎举办。))\nB. (-12 * -5) <= (-8 - -9) <= (-9 * 11)\nC. ((酒精在常温下是气体。) or ((8 * 5 + 6 * -4) >= (-9 - 4))) or ((铀的化学符号是U。) or ((-15 * 7) < (2 ** 1)))\nD. 人体有206块骨头。\nE. (not not (2000年奥运会在巴塞罗那举办。)) and (not (91是奇数。))\nF. (十二月有31天。) or ((1996年奥运会在慕尼黑举办。) or (俄罗斯的货币是卢布。))\nG. 墨西哥位于非洲。\nH. ((3 ** 3) != (1 * -16)) and (((15 - -16) <= (8 + -3)) and (壁虎是爬行动物。))\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": 8,
"seed": 75659143,
"true_count": 3
},
"seed": 75659143,
"task_id": 675659143,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. ((not (not ((Earth is the 3rd planet from the Sun.) and ((-6 - -3) > (13 * 8))))) or ((The Great Fire of London occurred in 1666.) and ((3 ** 2) != (3 * -5 + 8 * 10)))) and ((not ((11 + -2) == (19 - 13))) or (((((-9 - -7) < (3 * -8 + 4 * -3) < (16 + -7)) or ((-8 * 18) != (13 * 14))) and (Neptune is the 7th planet from the Sun.)) or ((11 - 5) < (3 ** 2))))
B. ((not not ((1945 is a leap year.) and (A horse has 4 legs.))) and ((The 1964 Olympics were held in Tokyo.) or (Argentina is in Europe.) or (not not (not not (2084 is a leap year.))))) or ((((not not (Chile is in Antarctica.)) and ((A lobster has 2 legs.) and (A whale is a mammal.))) or ((2 + -12) > (16 * -11)) or (1984 is a leap year.)) or (Saudi Arabia is in Asia.) or ((Vietnam is in Asia.) and ((0 + 7) < (-8 + -13) < (-11 * -8))))
C. ((not (New Zealand is in Oceania.)) or (((2027 is a leap year.) or ((1 ** 2) <= (2 * -3 * 2 * -9))) or ((The 1932 Olympics were held in Los Angeles.) or ((10 - 1) == (1 * 5 * 6 * -2)))) or ((((-6 * 9 * 4 * 0) >= (-11 - -12)) or ((The Moon produces its own light.) and (The currency of Australia is the Pound.))) and (((Mercury is the 1st planet from the Sun.) or (The 2016 Olympics were held in Rio de Janeiro.)) or (not ((-13 - 7) > (16 % 3)))))) or (not not (not not (1975 is a leap year.)))
D. not not (not not ((not (not (Vietnam is in North America.))) and (The capital of Mexico is Mexico City.)))
E. not (not not ((((The Great Fire of London occurred in 1666.) and (1903 is a leap year.)) and (not not (2039 is a leap year.))) and (not ((The currency of Nigeria is the Naira.) or ((15 * -18) <= (16 % 6))))))
F. (not not (((not not (The 1984 Olympics were held in Los Angeles.)) and (((-10 - 8) <= (5 * 7 - -4 * 5) <= (2 - 13)) and (Ice is a gas at room temperature.))) and ((((3 ** 3) > (5 - -18)) or (There are 31 days in January.)) and (not not ((12 * 20) != (3 ** 3)))))) and (not not ((((The capital of Denmark is New Delhi.) or (Iron is a solid at room temperature.)) or ((16 * 16) < (14 + 7))) and (A ostrich is a mammal.)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 95400843,
"true_count": 4
},
"question": "Below are several boolean expressions:\n\nA. ((not (not ((Earth is the 3rd planet from the Sun.) and ((-6 - -3) > (13 * 8))))) or ((The Great Fire of London occurred in 1666.) and ((3 ** 2) != (3 * -5 + 8 * 10)))) and ((not ((11 + -2) == (19 - 13))) or (((((-9 - -7) < (3 * -8 + 4 * -3) < (16 + -7)) or ((-8 * 18) != (13 * 14))) and (Neptune is the 7th planet from the Sun.)) or ((11 - 5) < (3 ** 2))))\nB. ((not not ((1945 is a leap year.) and (A horse has 4 legs.))) and ((The 1964 Olympics were held in Tokyo.) or (Argentina is in Europe.) or (not not (not not (2084 is a leap year.))))) or ((((not not (Chile is in Antarctica.)) and ((A lobster has 2 legs.) and (A whale is a mammal.))) or ((2 + -12) > (16 * -11)) or (1984 is a leap year.)) or (Saudi Arabia is in Asia.) or ((Vietnam is in Asia.) and ((0 + 7) < (-8 + -13) < (-11 * -8))))\nC. ((not (New Zealand is in Oceania.)) or (((2027 is a leap year.) or ((1 ** 2) <= (2 * -3 * 2 * -9))) or ((The 1932 Olympics were held in Los Angeles.) or ((10 - 1) == (1 * 5 * 6 * -2)))) or ((((-6 * 9 * 4 * 0) >= (-11 - -12)) or ((The Moon produces its own light.) and (The currency of Australia is the Pound.))) and (((Mercury is the 1st planet from the Sun.) or (The 2016 Olympics were held in Rio de Janeiro.)) or (not ((-13 - 7) > (16 % 3)))))) or (not not (not not (1975 is a leap year.)))\nD. not not (not not ((not (not (Vietnam is in North America.))) and (The capital of Mexico is Mexico City.)))\nE. not (not not ((((The Great Fire of London occurred in 1666.) and (1903 is a leap year.)) and (not not (2039 is a leap year.))) and (not ((The currency of Nigeria is the Naira.) or ((15 * -18) <= (16 % 6))))))\nF. (not not (((not not (The 1984 Olympics were held in Los Angeles.)) and (((-10 - 8) <= (5 * 7 - -4 * 5) <= (2 - 13)) and (Ice is a gas at room temperature.))) and ((((3 ** 3) > (5 - -18)) or (There are 31 days in January.)) and (not not ((12 * 20) != (3 ** 3)))))) and (not not ((((The capital of Denmark is New Delhi.) or (Iron is a solid at room temperature.)) or ((16 * 16) < (14 + 7))) and (A ostrich is a mammal.)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
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"seed": 95400843,
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"task_id": 695400843,
"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 ((丹麦的货币是索尔。) or (尼日利亚的货币是奈拉。) or ((8 + 5) <= (-1 * -6) <= (0 * -19))))) or (not not (((木头在常温下是固体。) and ((-7 * -10 - 6 * -1) < (10 * 8 + -4 * 7) < (-8 * 9 - 9 * -4))) or (not (铬的化学符号是Sn。))))
B. ((not ((not not (((9 % 2) <= (-20 - 18)) and (第一部iPhone发布发生在2005年。))) or (伦敦大火发生在1664年。))) and ((not not (not not ((1908年奥运会在斯德哥尔摩举办。) and ((40 % 4) < (6 * -2 - 6 * -2) < (3 ** 3))))) or (not not (((154是偶数。) or (2020年奥运会在东京举办。)) and (氮气在常温下是气体。))))) or (not not ((not not (not not (((1 * 17) == (4 - -9)) or (人类首次登月发生在1969年。)))) and ((镁的化学符号是Ag。) or (not (not not (1960年奥运会在雅典举办。))))))
C. not not ((not not (((((-10 - 11) < (31 % 5) < (-8 * -6 + -8 * -2)) or (铀的化学符号是Ca。)) and (((3 * 8 - 2 * 10) < (-17 - -16)) and (蝙蝠是瞎的。))) or ((秘鲁的首都是罗马。) or ((-9 - -8) < (6 * 8 + -5 * -2) < (-5 * -6 - -8 * -5))) or ((-9 * 20) < (-13 + -8)))) and (((39 % 7) <= (6 + -14)) and (((太阳绕地球运转。) or (铁在常温下是液体。)) and ((-10 * -7 - -10 * -8) <= (6 % 1) <= (14 - -17)))) and (not not (not ((2 ** 3) > (8 + -12)))))
D. ((not not (not not (铜在常温下是液体。))) and ((not (金枪鱼是鱼类。)) and (((-2 * 16) < (12 + -8) < (6 - 2)) or (not not (蜥蜴是爬行动物。))))) or ((not ((not ((-2 * 0 - 2 * -2) < (15 - 3))) or (not (日本的首都是东京。)))) or (not not (1904年奥运会在圣路易斯举办。))) or (not (((not (not not (铝的化学符号是Al。))) and (not (505是斐波那契数。))) or (芬兰的首都是北京。) or (((not not ((-10 * 3 - -1 * -7) < (-9 + 1) < (-8 * -5))) or (人类首次登月发生在1974年。)) and (not not (十一月有31天。)))))
E. not ((((铁在常温下是气体。) and ((九月有30天。) and ((-4 * 20) > (-8 * 1 - 8 * -1))) and (not not (((50 % 5) != (3 ** 3)) or ((5 ** 3) <= (-19 - 11))))) or (not (((秘鲁位于南美洲。) and ((43 % 1) == (-18 + -1))) or ((80是质数。) or (阿根廷位于南美洲。))))) and (not not (((第二次世界大战结束发生在1945年。) or ((-5 - 0) >= (-10 * -1 - 8 * -8))) and ((((-8 - -1) > (-1 - 16)) or ((-2 * -3 - -2 * -7) != (50 % 1))) or (not not ((1 ** 3) <= (19 + -4)))))))
F. ((((not not (not not ((1 + -12) < (1 ** 1)))) and (蝙蝠是瞎的。)) or (((7 - -10) < (10 * 4 * -10 * 7)) and (not (not (海王星是距离太阳第8近的行星。))))) and (not (not (((3 ** 1) <= (-8 * 7 + -7 * -3)) and ((1900年奥运会在洛杉矶举办。) and (钻石在常温下是液体。)))))) and (not (not (((-20 * -18) < (7 * 3) < (2 + -13)) or (2012年奥运会在东京举办。) or (((声音无法在真空中传播。) or ((16 % 2) != (-20 - -3))) and ((7 * 5) != (-10 + -16))))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
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"difficulty": 1,
"gpt_response": "",
"metadata": {
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"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. (not (not not ((丹麦的货币是索尔。) or (尼日利亚的货币是奈拉。) or ((8 + 5) <= (-1 * -6) <= (0 * -19))))) or (not not (((木头在常温下是固体。) and ((-7 * -10 - 6 * -1) < (10 * 8 + -4 * 7) < (-8 * 9 - 9 * -4))) or (not (铬的化学符号是Sn。))))\nB. ((not ((not not (((9 % 2) <= (-20 - 18)) and (第一部iPhone发布发生在2005年。))) or (伦敦大火发生在1664年。))) and ((not not (not not ((1908年奥运会在斯德哥尔摩举办。) and ((40 % 4) < (6 * -2 - 6 * -2) < (3 ** 3))))) or (not not (((154是偶数。) or (2020年奥运会在东京举办。)) and (氮气在常温下是气体。))))) or (not not ((not not (not not (((1 * 17) == (4 - -9)) or (人类首次登月发生在1969年。)))) and ((镁的化学符号是Ag。) or (not (not not (1960年奥运会在雅典举办。))))))\nC. not not ((not not (((((-10 - 11) < (31 % 5) < (-8 * -6 + -8 * -2)) or (铀的化学符号是Ca。)) and (((3 * 8 - 2 * 10) < (-17 - -16)) and (蝙蝠是瞎的。))) or ((秘鲁的首都是罗马。) or ((-9 - -8) < (6 * 8 + -5 * -2) < (-5 * -6 - -8 * -5))) or ((-9 * 20) < (-13 + -8)))) and (((39 % 7) <= (6 + -14)) and (((太阳绕地球运转。) or (铁在常温下是液体。)) and ((-10 * -7 - -10 * -8) <= (6 % 1) <= (14 - -17)))) and (not not (not ((2 ** 3) > (8 + -12)))))\nD. ((not not (not not (铜在常温下是液体。))) and ((not (金枪鱼是鱼类。)) and (((-2 * 16) < (12 + -8) < (6 - 2)) or (not not (蜥蜴是爬行动物。))))) or ((not ((not ((-2 * 0 - 2 * -2) < (15 - 3))) or (not (日本的首都是东京。)))) or (not not (1904年奥运会在圣路易斯举办。))) or (not (((not (not not (铝的化学符号是Al。))) and (not (505是斐波那契数。))) or (芬兰的首都是北京。) or (((not not ((-10 * 3 - -1 * -7) < (-9 + 1) < (-8 * -5))) or (人类首次登月发生在1974年。)) and (not not (十一月有31天。)))))\nE. not ((((铁在常温下是气体。) and ((九月有30天。) and ((-4 * 20) > (-8 * 1 - 8 * -1))) and (not not (((50 % 5) != (3 ** 3)) or ((5 ** 3) <= (-19 - 11))))) or (not (((秘鲁位于南美洲。) and ((43 % 1) == (-18 + -1))) or ((80是质数。) or (阿根廷位于南美洲。))))) and (not not (((第二次世界大战结束发生在1945年。) or ((-5 - 0) >= (-10 * -1 - 8 * -8))) and ((((-8 - -1) > (-1 - 16)) or ((-2 * -3 - -2 * -7) != (50 % 1))) or (not not ((1 ** 3) <= (19 + -4)))))))\nF. ((((not not (not not ((1 + -12) < (1 ** 1)))) and (蝙蝠是瞎的。)) or (((7 - -10) < (10 * 4 * -10 * 7)) and (not (not (海王星是距离太阳第8近的行星。))))) and (not (not (((3 ** 1) <= (-8 * 7 + -7 * -3)) and ((1900年奥运会在洛杉矶举办。) and (钻石在常温下是液体。)))))) and (not (not (((-20 * -18) < (7 * 3) < (2 + -13)) or (2012年奥运会在东京举办。) or (((声音无法在真空中传播。) or ((16 % 2) != (-20 - -3))) and ((7 * 5) != (-10 + -16))))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
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"language": "cn",
"num_options": 6,
"seed": 2411958,
"true_count": 4
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"seed": 2411958,
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"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not (54 is greater than 14.)
B. (((13 - -20) >= (-1 - 16)) and (((17 * 0) >= (8 * -5 - 6 * 4)) and (A gecko is a reptile.))) and (not ((The capital of France is Lima.) and ((-5 * -7) > (-17 + -14))))
C. ((((-7 * -16) < (-15 * 12)) and (The capital of Egypt is Cairo.)) and ((A human is a mammal.) or (Bats are blind.))) and ((10 * 2 + -7 * -4) < (-16 + -10) < (18 % 5))
D. ((-12 * 2) > (-13 + -18)) or (There are 29 days in February.)
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 4565153,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. not (54 is greater than 14.)\nB. (((13 - -20) >= (-1 - 16)) and (((17 * 0) >= (8 * -5 - 6 * 4)) and (A gecko is a reptile.))) and (not ((The capital of France is Lima.) and ((-5 * -7) > (-17 + -14))))\nC. ((((-7 * -16) < (-15 * 12)) and (The capital of Egypt is Cairo.)) and ((A human is a mammal.) or (Bats are blind.))) and ((10 * 2 + -7 * -4) < (-16 + -10) < (18 % 5))\nD. ((-12 * 2) > (-13 + -18)) or (There are 29 days in February.)\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 4565153,
"true_count": 2
},
"seed": 4565153,
"task_id": 604565153,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not not ((((地球上一天是24小时。) and ((-4 * 10 * 1 * 5) > (7 + -8))) and ((第一次世界大战结束发生在1923年。) and (太平洋是最大的海洋。))) and ((第一部iPhone发布发生在2002年。) or (((0 * -6 * 0 * 9) != (-18 + -11)) or (蜘蛛是昆虫。))))
B. not not ((((6 + -16) > (-17 + -17)) and ((11 % 3) < (43 % 5))) and ((2 * -9 * 9 * 4) <= (-6 * 5) <= (9 * -6 + -5 * 1)))
C. ((沙特阿拉伯位于亚洲。) or ((29 % 1) == (1 % 2)) or ((((9 * 9 - 2 * 1) <= (7 - 9)) or (智利的首都是圣地亚哥。)) and (((20 - -14) >= (3 + -12)) and ((8 * 14) >= (-7 + -13))))) and ((not (1964年奥运会在东京举办。)) or (not ((9 + -12) < (2 * -20)))) and (not not ((((-7 * -4 * 8 * 9) < (0 * 1) < (-2 * 8 * 3 * 7)) and (地球是距离太阳第3近的行星。)) and (硫的化学符号是S。)))
D. ((not ((鸡是哺乳动物。) and (羊是哺乳动物。))) and (((0 * 10) <= (-2 * 3 * 4 * -8)) and ((9 * -19) < (-12 - 11))) and (((瓢虫是昆虫。) and (中国长城是在一年内建成的。)) and ((声音无法在真空中传播。) or ((42 % 10) < (15 % 6) < (-9 - 17))))) or ((汞的化学符号是Hg。) or (蜘蛛是昆虫。) or ((铜在常温下是固体。) and ((4 * 11) >= (-9 * 6 - 3 * 1))))
E. (((西班牙的首都是斯德哥尔摩。) and (波兰的首都是华沙。)) or (秘鲁的首都是利马。)) or (((not (1952年奥运会在赫尔辛基举办。)) and (not ((-6 * -19) < (20 * 1)))) and ((5 * 0) <= (13 * 11)))
F. (((not not (水星是距离太阳第1近的行星。)) or (((18 + 5) <= (5 * 5 - 3 * -5) <= (-2 + 9)) and (摩洛哥的首都是里斯本。))) or (第一部iPhone发布发生在2005年。)) or (not ((-5 + -17) >= (1 ** 2)))
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": "D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 95146284,
"true_count": 3
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not not ((((地球上一天是24小时。) and ((-4 * 10 * 1 * 5) > (7 + -8))) and ((第一次世界大战结束发生在1923年。) and (太平洋是最大的海洋。))) and ((第一部iPhone发布发生在2002年。) or (((0 * -6 * 0 * 9) != (-18 + -11)) or (蜘蛛是昆虫。))))\nB. not not ((((6 + -16) > (-17 + -17)) and ((11 % 3) < (43 % 5))) and ((2 * -9 * 9 * 4) <= (-6 * 5) <= (9 * -6 + -5 * 1)))\nC. ((沙特阿拉伯位于亚洲。) or ((29 % 1) == (1 % 2)) or ((((9 * 9 - 2 * 1) <= (7 - 9)) or (智利的首都是圣地亚哥。)) and (((20 - -14) >= (3 + -12)) and ((8 * 14) >= (-7 + -13))))) and ((not (1964年奥运会在东京举办。)) or (not ((9 + -12) < (2 * -20)))) and (not not ((((-7 * -4 * 8 * 9) < (0 * 1) < (-2 * 8 * 3 * 7)) and (地球是距离太阳第3近的行星。)) and (硫的化学符号是S。)))\nD. ((not ((鸡是哺乳动物。) and (羊是哺乳动物。))) and (((0 * 10) <= (-2 * 3 * 4 * -8)) and ((9 * -19) < (-12 - 11))) and (((瓢虫是昆虫。) and (中国长城是在一年内建成的。)) and ((声音无法在真空中传播。) or ((42 % 10) < (15 % 6) < (-9 - 17))))) or ((汞的化学符号是Hg。) or (蜘蛛是昆虫。) or ((铜在常温下是固体。) and ((4 * 11) >= (-9 * 6 - 3 * 1))))\nE. (((西班牙的首都是斯德哥尔摩。) and (波兰的首都是华沙。)) or (秘鲁的首都是利马。)) or (((not (1952年奥运会在赫尔辛基举办。)) and (not ((-6 * -19) < (20 * 1)))) and ((5 * 0) <= (13 * 11)))\nF. (((not not (水星是距离太阳第1近的行星。)) or (((18 + 5) <= (5 * 5 - 3 * -5) <= (-2 + 9)) and (摩洛哥的首都是里斯本。))) or (第一部iPhone发布发生在2005年。)) or (not ((-5 + -17) >= (1 ** 2)))\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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"seed": 95146284,
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"seed": 95146284,
"task_id": 695146284,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (not (((-6 * 3 + -2 * 0) < (4 ** 1)) or ((5 is greater than 62.) or (The 1972 Olympics were held in Barcelona.)) or (not (((6 * 6 * -6 * 4) != (6 + 4)) and ((12 + -11) >= (-18 * -1)))))) and (not (not (434 is a Fibonacci number.)))
B. not ((not (not not (The 1936 Olympics were held in Berlin.))) and (((The capital of Canada is Ottawa.) and ((11 + 14) <= (-12 - 11))) and (not not ((23 % 10) >= (-16 * 15)))) and (((There are 31 days in July.) or ((-16 * 16) <= (2 * -6))) and (Ice is a solid at room temperature.) and (not (The currency of Chile is the Forint.))))
C. not not (((((-10 * 11) >= (-3 * 7 + -1 * -7)) and ((The currency of Egypt is the Peso.) and ((7 * 0 * -7 * 10) >= (8 * 3 + 9 * -7)))) and ((The capital of Ireland is Caracas.) or (not not (The Berlin Wall fell occurred in 1989.)))) or ((((Ice is a liquid at room temperature.) and (Sound travels faster in a vacuum.)) and (((17 * -7) > (-11 + 3)) and (The capital of Switzerland is Bern.))) and ((1987 is a leap year.) or (not not (The chemical symbol for Sulfur is S.)))))
D. not not ((not not (not (not not ((-13 - 19) > (17 - 17))))) or (((37 is an even number.) and (((-4 - 19) != (1 * 4 + -8 * 10)) or ((9 + -2) == (-12 * 2)))) or (((The chemical symbol for Titanium is Co.) and ((-9 * -5 + 5 * -4) <= (17 + -14) <= (1 ** 3))) or ((The currency of Russia is the Lira.) or ((5 ** 3) >= (-2 * 1 + -8 * 5))))))
E. not not (not (not ((The chemical symbol for Helium is He.) and (not (Indonesia is in Europe.)))))
F. not not (not (((((48 % 6) != (12 * 17)) or ((-15 - -20) <= (-10 * 0 + 10 * 9))) or ((-20 + -17) < (-2 - -1))) or (A chicken has 2 legs.)))
G. not (not (((not ((2 ** 1) != (-1 * -7 * -1 * -3))) or ((0 * 15) > (-6 - 14))) or ((Diamond is a solid at room temperature.) or ((There are 30 days in January.) and ((-2 * -8 * -1 * -2) > (-4 + -6))))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"question": "Consider the following logical expressions:\n\nA. (not (((-6 * 3 + -2 * 0) < (4 ** 1)) or ((5 is greater than 62.) or (The 1972 Olympics were held in Barcelona.)) or (not (((6 * 6 * -6 * 4) != (6 + 4)) and ((12 + -11) >= (-18 * -1)))))) and (not (not (434 is a Fibonacci number.)))\nB. not ((not (not not (The 1936 Olympics were held in Berlin.))) and (((The capital of Canada is Ottawa.) and ((11 + 14) <= (-12 - 11))) and (not not ((23 % 10) >= (-16 * 15)))) and (((There are 31 days in July.) or ((-16 * 16) <= (2 * -6))) and (Ice is a solid at room temperature.) and (not (The currency of Chile is the Forint.))))\nC. not not (((((-10 * 11) >= (-3 * 7 + -1 * -7)) and ((The currency of Egypt is the Peso.) and ((7 * 0 * -7 * 10) >= (8 * 3 + 9 * -7)))) and ((The capital of Ireland is Caracas.) or (not not (The Berlin Wall fell occurred in 1989.)))) or ((((Ice is a liquid at room temperature.) and (Sound travels faster in a vacuum.)) and (((17 * -7) > (-11 + 3)) and (The capital of Switzerland is Bern.))) and ((1987 is a leap year.) or (not not (The chemical symbol for Sulfur is S.)))))\nD. not not ((not not (not (not not ((-13 - 19) > (17 - 17))))) or (((37 is an even number.) and (((-4 - 19) != (1 * 4 + -8 * 10)) or ((9 + -2) == (-12 * 2)))) or (((The chemical symbol for Titanium is Co.) and ((-9 * -5 + 5 * -4) <= (17 + -14) <= (1 ** 3))) or ((The currency of Russia is the Lira.) or ((5 ** 3) >= (-2 * 1 + -8 * 5))))))\nE. not not (not (not ((The chemical symbol for Helium is He.) and (not (Indonesia is in Europe.)))))\nF. not not (not (((((48 % 6) != (12 * 17)) or ((-15 - -20) <= (-10 * 0 + 10 * 9))) or ((-20 + -17) < (-2 - -1))) or (A chicken has 2 legs.)))\nG. not (not (((not ((2 ** 1) != (-1 * -7 * -1 * -3))) or ((0 * 15) > (-6 - 14))) or ((Diamond is a solid at room temperature.) or ((There are 30 days in January.) and ((-2 * -8 * -1 * -2) > (-4 + -6))))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
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"language": "en",
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"seed": 60944209,
"true_count": 4
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"seed": 60944209,
"task_id": 660944209,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not not ((16 + 6) <= (5 ** 3))) and ((Nitrogen is a liquid at room temperature.) or ((The chemical symbol for Phosphorus is Na.) or (Colombia is in South America.))) and (not not ((not ((0 * -17) > (18 % 9))) and (((3 * -6 + -1 * -2) <= (20 * 19)) or (The capital of Australia is Wellington.))))
B. ((not not (((-7 + 20) < (4 - 18) < (8 * 8 * 2 * -3)) or (A mosquito is an insect.))) and ((7 * -2 - 3 * -10) < (-3 + 1))) or ((((The chemical symbol for Carbon is C.) and ((8 + 15) == (3 * 9 - 2 * -5))) and (Steam is a gas at room temperature.)) and ((8 * 9 * 6 * 3) < (16 - -14)))
C. (not (Mars is the 1st planet from the Sun.)) and ((A ant is a fish.) and (not not ((The currency of Brazil is the Dollar.) and ((4 % 5) < (-7 + 13) < (20 - 0)))))
D. (not not ((((22 % 5) < (1 ** 1)) and ((-16 * 18) >= (1 + 3))) or ((-11 + 9) == (5 ** 2)))) or (((44 % 4) <= (6 * 9 + 10 * -1)) and (The chemical symbol for Silver is Ag.))
E. (not not (((The capital of Cuba is Havana.) or ((10 + -11) != (9 - -17))) or (not not (Neptune is the 1st planet from the Sun.)))) and (((9 * -10 * -7 * -10) > (-11 * -1)) or (A cat has 6 legs.) or (not ((36 % 3) <= (5 ** 1))))
F. ((The currency of Hungary is the Forint.) or (not not (A sparrow is a bird.)) or (((8 + -17) < (23 % 2)) or ((The 1900 Olympics were held in London.) and ((10 * -5 - -5 * -8) != (6 * 3))))) or ((not (A cow has 4 legs.)) and (not not (The 1980 Olympics were held in Antwerp.))) or (not (((The chemical symbol for Helium is Cu.) and ((14 + -14) <= (-19 - 20))) and (not not (Saudi Arabia is in South America.))))
G. (not not ((not (The square root of 1 is 1.)) and (((4 ** 2) <= (3 ** 3)) and ((-20 - 11) < (9 + -12))))) or (not not (South Africa is in Africa.))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,D,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 25019841,
"true_count": 4
},
"question": "Analyze these boolean expressions:\n\nA. (not not ((16 + 6) <= (5 ** 3))) and ((Nitrogen is a liquid at room temperature.) or ((The chemical symbol for Phosphorus is Na.) or (Colombia is in South America.))) and (not not ((not ((0 * -17) > (18 % 9))) and (((3 * -6 + -1 * -2) <= (20 * 19)) or (The capital of Australia is Wellington.))))\nB. ((not not (((-7 + 20) < (4 - 18) < (8 * 8 * 2 * -3)) or (A mosquito is an insect.))) and ((7 * -2 - 3 * -10) < (-3 + 1))) or ((((The chemical symbol for Carbon is C.) and ((8 + 15) == (3 * 9 - 2 * -5))) and (Steam is a gas at room temperature.)) and ((8 * 9 * 6 * 3) < (16 - -14)))\nC. (not (Mars is the 1st planet from the Sun.)) and ((A ant is a fish.) and (not not ((The currency of Brazil is the Dollar.) and ((4 % 5) < (-7 + 13) < (20 - 0)))))\nD. (not not ((((22 % 5) < (1 ** 1)) and ((-16 * 18) >= (1 + 3))) or ((-11 + 9) == (5 ** 2)))) or (((44 % 4) <= (6 * 9 + 10 * -1)) and (The chemical symbol for Silver is Ag.))\nE. (not not (((The capital of Cuba is Havana.) or ((10 + -11) != (9 - -17))) or (not not (Neptune is the 1st planet from the Sun.)))) and (((9 * -10 * -7 * -10) > (-11 * -1)) or (A cat has 6 legs.) or (not ((36 % 3) <= (5 ** 1))))\nF. ((The currency of Hungary is the Forint.) or (not not (A sparrow is a bird.)) or (((8 + -17) < (23 % 2)) or ((The 1900 Olympics were held in London.) and ((10 * -5 - -5 * -8) != (6 * 3))))) or ((not (A cow has 4 legs.)) and (not not (The 1980 Olympics were held in Antwerp.))) or (not (((The chemical symbol for Helium is Cu.) and ((14 + -14) <= (-19 - 20))) and (not not (Saudi Arabia is in South America.))))\nG. (not not ((not (The square root of 1 is 1.)) and (((4 ** 2) <= (3 ** 3)) and ((-20 - 11) < (9 + -12))))) or (not not (South Africa is in Africa.))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 25019841,
"true_count": 4
},
"seed": 25019841,
"task_id": 625019841,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((not ((((-1 * 1 + 7 * 3) > (25 % 3)) and (木头在常温下是液体。)) and (((47 % 6) >= (5 ** 2)) and (太平洋是最大的海洋。)))) and ((((铝的化学符号是Fe。) and (鱼有0条腿。)) and (钠的化学符号是Na。)) or (not ((4 * -3 - -7 * -1) < (-15 + 2))))) and (not not (((((-1 - -17) == (2 * 13)) or ((5 + -20) >= (24 % 8))) and (太阳绕地球运转。)) and (not (not (海王星是距离太阳第5近的行星。)))))
B. not (((not not (not ((13 + 12) > (3 + 16)))) and (((-6 - -11) != (0 * -14)) and (558是斐波那契数。)) and (not (((-9 * 2 + -3 * 0) < (-14 - -18) < (15 + -4)) and (月球绕地球运转。)))) or (((太阳绕地球运转。) or (not (汞的化学符号是He。))) and (((-6 - -5) != (1 * -3 - 8 * -8)) and (第一次世界大战结束发生在1913年。)) and (((猫有4条腿。) or ((-4 - 13) <= (17 * -18))) and (马来西亚的首都是吉隆坡。))))
C. not ((((8 * -9 + 3 * 6) == (47 % 5)) and (地球是距离太阳第8近的行星。) and (1911年是闰年。)) and ((((0 * 13) == (-18 * -7)) or (印度尼西亚位于亚洲。)) or (((-19 + -6) <= (-20 - -9) <= (20 + 4)) and ((-1 - -20) >= (11 + 17)))) and (not not (not (蝙蝠是瞎的。))))
D. (((not not (not ((-10 * 4 - -4 * 4) >= (-6 * 1 + 2 * -3)))) or ((((-6 * 7 * 9 * -5) <= (9 + 17) <= (10 + -11)) or (木头在常温下是固体。)) and (((1 ** 3) > (16 - 5)) or ((-10 * -10 - 3 * -6) >= (0 * -15))))) or (not not ((6 - 7) < (-11 + 9)))) and (not not (声音在真空中传播更快。)) and (not not (((not ((-9 * -7 + -4 * 3) < (-18 - 15))) or (35是偶数。)) and (((8 * -6 - 6 * -4) >= (25 % 9)) and (火星是距离太阳第4近的行星。)) and ((1952年奥运会在巴黎举办。) or ((8 - 14) >= (-12 - -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": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 72475088,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. ((not ((((-1 * 1 + 7 * 3) > (25 % 3)) and (木头在常温下是液体。)) and (((47 % 6) >= (5 ** 2)) and (太平洋是最大的海洋。)))) and ((((铝的化学符号是Fe。) and (鱼有0条腿。)) and (钠的化学符号是Na。)) or (not ((4 * -3 - -7 * -1) < (-15 + 2))))) and (not not (((((-1 - -17) == (2 * 13)) or ((5 + -20) >= (24 % 8))) and (太阳绕地球运转。)) and (not (not (海王星是距离太阳第5近的行星。)))))\nB. not (((not not (not ((13 + 12) > (3 + 16)))) and (((-6 - -11) != (0 * -14)) and (558是斐波那契数。)) and (not (((-9 * 2 + -3 * 0) < (-14 - -18) < (15 + -4)) and (月球绕地球运转。)))) or (((太阳绕地球运转。) or (not (汞的化学符号是He。))) and (((-6 - -5) != (1 * -3 - 8 * -8)) and (第一次世界大战结束发生在1913年。)) and (((猫有4条腿。) or ((-4 - 13) <= (17 * -18))) and (马来西亚的首都是吉隆坡。))))\nC. not ((((8 * -9 + 3 * 6) == (47 % 5)) and (地球是距离太阳第8近的行星。) and (1911年是闰年。)) and ((((0 * 13) == (-18 * -7)) or (印度尼西亚位于亚洲。)) or (((-19 + -6) <= (-20 - -9) <= (20 + 4)) and ((-1 - -20) >= (11 + 17)))) and (not not (not (蝙蝠是瞎的。))))\nD. (((not not (not ((-10 * 4 - -4 * 4) >= (-6 * 1 + 2 * -3)))) or ((((-6 * 7 * 9 * -5) <= (9 + 17) <= (10 + -11)) or (木头在常温下是固体。)) and (((1 ** 3) > (16 - 5)) or ((-10 * -10 - 3 * -6) >= (0 * -15))))) or (not not ((6 - 7) < (-11 + 9)))) and (not not (声音在真空中传播更快。)) and (not not (((not ((-9 * -7 + -4 * 3) < (-18 - 15))) or (35是偶数。)) and (((8 * -6 - 6 * -4) >= (25 % 9)) and (火星是距离太阳第4近的行星。)) and ((1952年奥运会在巴黎举办。) or ((8 - 14) >= (-12 - -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。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 72475088,
"true_count": 2
},
"seed": 72475088,
"task_id": 672475088,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((1 + 9) < (3 % 1)) and (not ((越南的货币是克朗。) or ((1 * 1 + 1 * -5) < (20 * 9))))) and ((-2 - 11) < (4 * 5 * -2 * -9) < (-10 - 4)) and (((((5 - 5) == (15 - 19)) or (韩国的货币是韩元。)) or ((-1 + 2) <= (12 + 4))) and (((5 ** 3) <= (9 * 7)) and ((7 * -8 + 0 * -4) <= (3 ** 3))) and ((((-6 + 20) < (15 * 14)) or (中国长城是在一年内建成的。)) and (not ((2 * 3) >= (7 - 16)))))
B. (not not ((3 ** 2) >= (9 * 1))) and (not not (not ((24 % 3) <= (26 % 8)))) and (not ((((-18 + -3) < (8 - 2) < (-11 * 19)) and (俄罗斯位于北美洲。)) and (not (钠的化学符号是Na。))))
C. (((not (南非的货币是兰特。)) and ((汞的化学符号是Hg。) and (袋鼠是哺乳动物。))) and ((((44 % 6) <= (8 * -5)) or (2024年奥运会在巴黎举办。)) or (not not (2020年奥运会在东京举办。)))) and (not not (not not (2100年是闰年。))) and ((not ((钻石由碳元素组成。) and (秘鲁的货币是索尔。))) and ((伦敦大火发生在1666年。) and (54是质数。)) and (not not (南非位于非洲。)))
D. not (((not not (新西兰的首都是惠灵顿。)) and ((氧的化学符号是O。) or ((-19 * 8) < (2 * -8 + -1 * 4) < (1 * -7)))) and ((2071年是闰年。) or (美国宣布独立发生在1771年。)) and (((7 * 7) == (7 * 9)) and (not ((-6 * 1 * 7 * 7) >= (3 ** 1)))))
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": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 5108149,
"true_count": 1
},
"question": "考虑以下布尔表达式：\n\nA. (((1 + 9) < (3 % 1)) and (not ((越南的货币是克朗。) or ((1 * 1 + 1 * -5) < (20 * 9))))) and ((-2 - 11) < (4 * 5 * -2 * -9) < (-10 - 4)) and (((((5 - 5) == (15 - 19)) or (韩国的货币是韩元。)) or ((-1 + 2) <= (12 + 4))) and (((5 ** 3) <= (9 * 7)) and ((7 * -8 + 0 * -4) <= (3 ** 3))) and ((((-6 + 20) < (15 * 14)) or (中国长城是在一年内建成的。)) and (not ((2 * 3) >= (7 - 16)))))\nB. (not not ((3 ** 2) >= (9 * 1))) and (not not (not ((24 % 3) <= (26 % 8)))) and (not ((((-18 + -3) < (8 - 2) < (-11 * 19)) and (俄罗斯位于北美洲。)) and (not (钠的化学符号是Na。))))\nC. (((not (南非的货币是兰特。)) and ((汞的化学符号是Hg。) and (袋鼠是哺乳动物。))) and ((((44 % 6) <= (8 * -5)) or (2024年奥运会在巴黎举办。)) or (not not (2020年奥运会在东京举办。)))) and (not not (not not (2100年是闰年。))) and ((not ((钻石由碳元素组成。) and (秘鲁的货币是索尔。))) and ((伦敦大火发生在1666年。) and (54是质数。)) and (not not (南非位于非洲。)))\nD. not (((not not (新西兰的首都是惠灵顿。)) and ((氧的化学符号是O。) or ((-19 * 8) < (2 * -8 + -1 * 4) < (1 * -7)))) and ((2071年是闰年。) or (美国宣布独立发生在1771年。)) and (((7 * 7) == (7 * 9)) and (not ((-6 * 1 * 7 * 7) >= (3 ** 1)))))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 5108149,
"true_count": 1
},
"seed": 5108149,
"task_id": 605108149,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (((九月有30天。) or (蜜蜂是昆虫。)) or ((-2 * -2 + -9 * -4) != (-20 + 2))) or (第二次世界大战开始发生在1929年。)
B. (秘鲁的货币是索尔。) or ((-9 + 14) > (4 + 15))
C. (肯尼亚位于亚洲。) or ((14 - -5) <= (7 * 7 + -3 * -5))
D. not (((八月有31天。) or (韩国的货币是韩元。)) and (not not (39能被8整除。)))
E. (not not (((8 * 6 + 2 * 0) == (6 - 2)) and (秘鲁的首都是里斯本。))) or (((2 ** 1) <= (14 + -16) <= (4 ** 3)) and (not not (五月有31天。)))
F. not (蜘蛛有0条腿。)
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,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 54460595,
"true_count": 5
},
"question": "给定以下布尔表达式：\n\nA. (((九月有30天。) or (蜜蜂是昆虫。)) or ((-2 * -2 + -9 * -4) != (-20 + 2))) or (第二次世界大战开始发生在1929年。)\nB. (秘鲁的货币是索尔。) or ((-9 + 14) > (4 + 15))\nC. (肯尼亚位于亚洲。) or ((14 - -5) <= (7 * 7 + -3 * -5))\nD. not (((八月有31天。) or (韩国的货币是韩元。)) and (not not (39能被8整除。)))\nE. (not not (((8 * 6 + 2 * 0) == (6 - 2)) and (秘鲁的首都是里斯本。))) or (((2 ** 1) <= (14 + -16) <= (4 ** 3)) and (not not (五月有31天。)))\nF. not (蜘蛛有0条腿。)\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": 54460595,
"true_count": 5
},
"seed": 54460595,
"task_id": 654460595,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (((((14 - 13) != (0 + 7)) and (The 2000 Olympics were held in Athens.)) or ((-9 - -20) < (23 % 1))) or (Water is a liquid at room temperature.)) or ((not (The capital of Colombia is Bogota.)) and (not not (The currency of Brazil is the Dong.)))
B. not ((((10 * 2 - -1 * -8) == (-8 - -16)) or (South Korea is in Europe.)) and ((A tiger is a mammal.) or (((-9 + 3) == (-7 * 19)) or ((-19 + 16) < (-11 * -18)))))
C. (not (((The chemical symbol for Aluminum is Al.) and ((2 - 18) <= (19 - -3) <= (-17 - -4))) and ((-2 - 20) >= (1 * 19)))) or (((There are 29 days in April.) or ((The capital of New Zealand is Wellington.) or ((-18 - 14) == (4 * 2 - 9 * 1)))) or ((-5 + -14) == (-15 * 13)))
D. not (((((4 + 12) >= (18 - 11)) or (The 1912 Olympics were held in Stockholm.)) and (((2 * -1 * -3 * 9) > (4 ** 2)) or ((20 - 20) < (15 * 6)))) or (not not (The chemical symbol for Silicon is C.)))
E. not (((((1 * -3 + 3 * -7) <= (2 ** 2) <= (-19 * 0)) and (The capital of Romania is Bucharest.)) or ((1 ** 1) <= (-1 + 7))) or (not not ((The currency of New Zealand is the Dollar.) and (There are 31 days in May.))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 84762668,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. (((((14 - 13) != (0 + 7)) and (The 2000 Olympics were held in Athens.)) or ((-9 - -20) < (23 % 1))) or (Water is a liquid at room temperature.)) or ((not (The capital of Colombia is Bogota.)) and (not not (The currency of Brazil is the Dong.)))\nB. not ((((10 * 2 - -1 * -8) == (-8 - -16)) or (South Korea is in Europe.)) and ((A tiger is a mammal.) or (((-9 + 3) == (-7 * 19)) or ((-19 + 16) < (-11 * -18)))))\nC. (not (((The chemical symbol for Aluminum is Al.) and ((2 - 18) <= (19 - -3) <= (-17 - -4))) and ((-2 - 20) >= (1 * 19)))) or (((There are 29 days in April.) or ((The capital of New Zealand is Wellington.) or ((-18 - 14) == (4 * 2 - 9 * 1)))) or ((-5 + -14) == (-15 * 13)))\nD. not (((((4 + 12) >= (18 - 11)) or (The 1912 Olympics were held in Stockholm.)) and (((2 * -1 * -3 * 9) > (4 ** 2)) or ((20 - 20) < (15 * 6)))) or (not not (The chemical symbol for Silicon is C.)))\nE. not (((((1 * -3 + 3 * -7) <= (2 ** 2) <= (-19 * 0)) and (The capital of Romania is Bucharest.)) or ((1 ** 1) <= (-1 + 7))) or (not not ((The currency of New Zealand is the Dollar.) and (There are 31 days in May.))))\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": 84762668,
"true_count": 3
},
"seed": 84762668,
"task_id": 684762668,
"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 (((-20 + -3) < (5 ** 2)) and (((11 - -14) < (-18 * -3)) or ((5 ** 2) >= (-15 * -5)))))) or (((not not (not not (2080年是闰年。))) or (((碳的化学符号是He。) or ((-4 - 14) != (17 - -7))) or (((4 * -6 - -9 * 10) <= (8 * 0 * 1 * 4)) and ((13 + -10) == (7 - 7))))) or (not (not ((-11 * 14) <= (6 - -13)))) or (not ((((0 * -2 - -4 * -10) <= (-15 - 6)) or ((8 + 20) > (-11 * -10))) or (((-1 + 8) <= (-19 - -12)) or ((1 * -8 + 1 * -1) != (-11 * 9))))))
B. (not ((24能被5整除。) and (not (not not ((-5 * -2 - -4 * -7) > (18 * -18)))))) or (not (泰国的货币是泰铢。)) or (((铜的化学符号是O。) and (not not ((50小于等于67。) and ((-7 * 1) > (3 ** 1))))) or (not not (not (天王星是距离太阳第7近的行星。))) or ((not not ((-3 + -2) != (11 + -17))) or ((((2 ** 3) < (12 + 17)) and ((8 * -6 * 9 * -8) > (8 - -13))) or (((7 - 11) > (5 - -15)) and ((9 * -8 - -1 * 4) < (-6 * -3) < (8 * 1 * 0 * -8))))))
C. (not ((not ((哥伦比亚的首都是布加勒斯特。) and ((0 * 5 * -2 * 9) <= (10 * -7)))) and (土耳其的首都是安卡拉。))) and ((((-13 - 1) == (1 * 12)) and (not not (100的平方根是10。)) and (((鱼有0条腿。) and ((-13 + -4) == (8 - 3))) and ((企鹅能飞翔。) or (现代奥运会首届举办发生在1896年。)))) or (((19 + 11) <= (5 * 11) <= (32 % 3)) or (((9 - -3) != (5 + -20)) or ((10 + 11) <= (-15 * -20)))) or ((((莱特兄弟首次飞行发生在1908年。) or (德国的首都是阿布贾。)) or (not (第一次世界大战结束发生在1918年。))) or (((4 * 6 * 1 * 3) < (6 * 5 - -8 * -3) < (11 + 11)) and ((波兰的货币是奈拉。) or (苏联解体发生在1986年。)))))
D. not ((((((-20 - 0) >= (19 + -8)) or ((1 ** 2) <= (-2 + 16))) and (((10 + -2) <= (12 % 5) <= (-3 * 7 * 2 * -2)) and ((19 - -19) >= (-11 * 3)))) and ((6 % 1) != (8 - -20))) and ((银在常温下是固体。) and (氦的化学符号是Fe。)))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 86905265,
"true_count": 3
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. (not not (not (((-20 + -3) < (5 ** 2)) and (((11 - -14) < (-18 * -3)) or ((5 ** 2) >= (-15 * -5)))))) or (((not not (not not (2080年是闰年。))) or (((碳的化学符号是He。) or ((-4 - 14) != (17 - -7))) or (((4 * -6 - -9 * 10) <= (8 * 0 * 1 * 4)) and ((13 + -10) == (7 - 7))))) or (not (not ((-11 * 14) <= (6 - -13)))) or (not ((((0 * -2 - -4 * -10) <= (-15 - 6)) or ((8 + 20) > (-11 * -10))) or (((-1 + 8) <= (-19 - -12)) or ((1 * -8 + 1 * -1) != (-11 * 9))))))\nB. (not ((24能被5整除。) and (not (not not ((-5 * -2 - -4 * -7) > (18 * -18)))))) or (not (泰国的货币是泰铢。)) or (((铜的化学符号是O。) and (not not ((50小于等于67。) and ((-7 * 1) > (3 ** 1))))) or (not not (not (天王星是距离太阳第7近的行星。))) or ((not not ((-3 + -2) != (11 + -17))) or ((((2 ** 3) < (12 + 17)) and ((8 * -6 * 9 * -8) > (8 - -13))) or (((7 - 11) > (5 - -15)) and ((9 * -8 - -1 * 4) < (-6 * -3) < (8 * 1 * 0 * -8))))))\nC. (not ((not ((哥伦比亚的首都是布加勒斯特。) and ((0 * 5 * -2 * 9) <= (10 * -7)))) and (土耳其的首都是安卡拉。))) and ((((-13 - 1) == (1 * 12)) and (not not (100的平方根是10。)) and (((鱼有0条腿。) and ((-13 + -4) == (8 - 3))) and ((企鹅能飞翔。) or (现代奥运会首届举办发生在1896年。)))) or (((19 + 11) <= (5 * 11) <= (32 % 3)) or (((9 - -3) != (5 + -20)) or ((10 + 11) <= (-15 * -20)))) or ((((莱特兄弟首次飞行发生在1908年。) or (德国的首都是阿布贾。)) or (not (第一次世界大战结束发生在1918年。))) or (((4 * 6 * 1 * 3) < (6 * 5 - -8 * -3) < (11 + 11)) and ((波兰的货币是奈拉。) or (苏联解体发生在1986年。)))))\nD. not ((((((-20 - 0) >= (19 + -8)) or ((1 ** 2) <= (-2 + 16))) and (((10 + -2) <= (12 % 5) <= (-3 * 7 * 2 * -2)) and ((19 - -19) >= (-11 * 3)))) and ((6 % 1) != (8 - -20))) and ((银在常温下是固体。) and (氦的化学符号是Fe。)))\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": 5,
"language": "cn",
"num_options": 4,
"seed": 86905265,
"true_count": 3
},
"seed": 86905265,
"task_id": 686905265,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((((4 ** 1) < (-9 * -12) < (-5 * 0 - 2 * 8)) or ((哥伦比亚的货币是比索。) or ((4 + 11) <= (-8 + -7)))) and (((莱特兄弟首次飞行发生在1903年。) or ((19 + 6) < (2 ** 2) < (-2 * 3 + 7 * 8))) and ((火烈鸟是鸟类。) and (1999年是闰年。)))) or (not not ((((-16 - 6) > (12 - 7)) or ((12 % 6) > (3 ** 1))) and (第一次世界大战结束发生在1916年。)))
B. (not (((-2 * -6 - -3 * 8) <= (3 * 10 - 3 * 2)) and (((-19 - 15) != (49 % 7)) or (第一部iPhone发布发生在2002年。)))) or (not not (土耳其的货币是里亚尔。)) or (not not ((1931年是闰年。) and (((-13 * 3) > (4 ** 1)) and ((12 - -13) >= (1 - 17)))))
C. (((((13 + -5) <= (-4 * -10)) and (第一次世界大战开始发生在1914年。)) or ((20 - -17) < (2 ** 1))) or (韩国位于亚洲。)) or ((英国位于亚洲。) or (((38 % 4) >= (14 - 12)) or ((11 * -14) > (13 + -15))) or (((钠的化学符号是Co。) and ((5 ** 1) == (-5 + -13))) and (((0 * -3 - -9 * -2) != (46 % 9)) or ((0 + -12) > (-9 * 9 - 0 * -5)))))
D. ((火星是距离太阳第1近的行星。) and (1960年奥运会在东京举办。)) and (((not ((4 ** 3) >= (-15 - 9))) and ((荷兰的首都是利马。) or ((-2 - 3) <= (1 + 11)))) and ((not not ((30 % 3) <= (-2 * -1 - 7 * -5))) or (not not (中国位于亚洲。))))
E. (((2 * -10 * 6 * 10) != (-11 + -4)) and (1932年奥运会在东京举办。)) or (马来西亚的货币是谢克尔。) or (not ((((14 + 8) >= (-17 + -16)) or (匈牙利的首都是布达佩斯。)) and ((9 * 3 + 5 * -2) == (11 * -14))))
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,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 18822980,
"true_count": 3
},
"question": "分析以下逻辑表达式：\n\nA. ((((4 ** 1) < (-9 * -12) < (-5 * 0 - 2 * 8)) or ((哥伦比亚的货币是比索。) or ((4 + 11) <= (-8 + -7)))) and (((莱特兄弟首次飞行发生在1903年。) or ((19 + 6) < (2 ** 2) < (-2 * 3 + 7 * 8))) and ((火烈鸟是鸟类。) and (1999年是闰年。)))) or (not not ((((-16 - 6) > (12 - 7)) or ((12 % 6) > (3 ** 1))) and (第一次世界大战结束发生在1916年。)))\nB. (not (((-2 * -6 - -3 * 8) <= (3 * 10 - 3 * 2)) and (((-19 - 15) != (49 % 7)) or (第一部iPhone发布发生在2002年。)))) or (not not (土耳其的货币是里亚尔。)) or (not not ((1931年是闰年。) and (((-13 * 3) > (4 ** 1)) and ((12 - -13) >= (1 - 17)))))\nC. (((((13 + -5) <= (-4 * -10)) and (第一次世界大战开始发生在1914年。)) or ((20 - -17) < (2 ** 1))) or (韩国位于亚洲。)) or ((英国位于亚洲。) or (((38 % 4) >= (14 - 12)) or ((11 * -14) > (13 + -15))) or (((钠的化学符号是Co。) and ((5 ** 1) == (-5 + -13))) and (((0 * -3 - -9 * -2) != (46 % 9)) or ((0 + -12) > (-9 * 9 - 0 * -5)))))\nD. ((火星是距离太阳第1近的行星。) and (1960年奥运会在东京举办。)) and (((not ((4 ** 3) >= (-15 - 9))) and ((荷兰的首都是利马。) or ((-2 - 3) <= (1 + 11)))) and ((not not ((30 % 3) <= (-2 * -1 - 7 * -5))) or (not not (中国位于亚洲。))))\nE. (((2 * -10 * 6 * 10) != (-11 + -4)) and (1932年奥运会在东京举办。)) or (马来西亚的货币是谢克尔。) or (not ((((14 + 8) >= (-17 + -16)) or (匈牙利的首都是布达佩斯。)) and ((9 * 3 + 5 * -2) == (11 * -14))))\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": 4,
"language": "cn",
"num_options": 5,
"seed": 18822980,
"true_count": 3
},
"seed": 18822980,
"task_id": 618822980,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not not (not not ((not not ((((-7 * -5 * 10 * 10) > (11 % 3)) and (149是偶数。)) or ((8 - -4) == (5 ** 2)))) or ((印度尼西亚位于亚洲。) or ((埃及的货币是埃及镑。) or (捷克的货币是奈拉。))) or (((-3 * 15) > (-16 - 5)) or ((尼日利亚位于北美洲。) and ((-5 * -2 + -2 * 7) > (-1 - 0))) or (not not ((波兰的首都是曼谷。) or ((-2 + -15) < (-16 + 3) < (15 + -2)))))))
B. not ((((not (((4 * -10 - 10 * -4) > (4 - -6)) or (2008年奥运会在巴黎举办。))) and ((((27 % 8) == (5 ** 1)) and (乌龟是爬行动物。)) or (((1 ** 3) >= (-13 * 0)) and ((17 - 17) <= (-16 * 4))))) or ((not (not not (2016年是闰年。))) and ((not ((-5 * 16) == (-15 + 10))) and ((日本的首都是东京。) and ((4 - 3) == (33 % 10)))))) or (not ((匈牙利的货币是新西兰元。) or (((6 - -5) == (2 - 7)) or (埃及的首都是开罗。)) or ((-5 * 7 * -1 * -8) <= (3 ** 3)))))
C. not not (not (((((铅的化学符号是Pb。) and ((-9 + -8) > (-20 * -19))) and ((3 ** 3) == (-4 - 15))) or (埃及位于大洋洲。)) or (not not (((匈牙利的货币是克朗。) or (10是质数。)) or (((5 ** 1) > (3 % 2)) and (鲸鱼是鱼类。))))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 35628325,
"true_count": 3
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not not (not not ((not not ((((-7 * -5 * 10 * 10) > (11 % 3)) and (149是偶数。)) or ((8 - -4) == (5 ** 2)))) or ((印度尼西亚位于亚洲。) or ((埃及的货币是埃及镑。) or (捷克的货币是奈拉。))) or (((-3 * 15) > (-16 - 5)) or ((尼日利亚位于北美洲。) and ((-5 * -2 + -2 * 7) > (-1 - 0))) or (not not ((波兰的首都是曼谷。) or ((-2 + -15) < (-16 + 3) < (15 + -2)))))))\nB. not ((((not (((4 * -10 - 10 * -4) > (4 - -6)) or (2008年奥运会在巴黎举办。))) and ((((27 % 8) == (5 ** 1)) and (乌龟是爬行动物。)) or (((1 ** 3) >= (-13 * 0)) and ((17 - 17) <= (-16 * 4))))) or ((not (not not (2016年是闰年。))) and ((not ((-5 * 16) == (-15 + 10))) and ((日本的首都是东京。) and ((4 - 3) == (33 % 10)))))) or (not ((匈牙利的货币是新西兰元。) or (((6 - -5) == (2 - 7)) or (埃及的首都是开罗。)) or ((-5 * 7 * -1 * -8) <= (3 ** 3)))))\nC. not not (not (((((铅的化学符号是Pb。) and ((-9 + -8) > (-20 * -19))) and ((3 ** 3) == (-4 - 15))) or (埃及位于大洋洲。)) or (not not (((匈牙利的货币是克朗。) or (10是质数。)) or (((5 ** 1) > (3 % 2)) and (鲸鱼是鱼类。))))))\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": 6,
"language": "cn",
"num_options": 3,
"seed": 35628325,
"true_count": 3
},
"seed": 35628325,
"task_id": 635628325,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (1903 is a leap year.)
B. (The square root of 36 is 6.) and ((Christopher Columbus reached America occurred in 1492.) or (not ((3 - 0) >= (-10 * -14))))
C. not not (not not ((-5 * 2) < (-9 + -10)))
D. (not (((15 - -11) > (9 % 4)) and (Venus is the 2nd planet from the Sun.))) or ((The currency of European Union is the Peso.) or ((2 * 5) != (-20 + -7))) or ((((-3 * -2 * -6 * 1) == (5 - 15)) or (The chemical symbol for Sodium is S.)) or (not ((18 + -13) < (-1 * 10 + 3 * 5))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 20352188,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not not (1903 is a leap year.)\nB. (The square root of 36 is 6.) and ((Christopher Columbus reached America occurred in 1492.) or (not ((3 - 0) >= (-10 * -14))))\nC. not not (not not ((-5 * 2) < (-9 + -10)))\nD. (not (((15 - -11) > (9 % 4)) and (Venus is the 2nd planet from the Sun.))) or ((The currency of European Union is the Peso.) or ((2 * 5) != (-20 + -7))) or ((((-3 * -2 * -6 * 1) == (5 - 15)) or (The chemical symbol for Sodium is S.)) or (not ((18 + -13) < (-1 * 10 + 3 * 5))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 20352188,
"true_count": 2
},
"seed": 20352188,
"task_id": 620352188,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (-7 * -8 * -2 * -6) <= (50 % 4) <= (3 % 7)
B. not (狗有4条腿。)
C. (not not ((-12 - -5) < (10 - -5))) or (1956年是闰年。)
D. 木星是距离太阳第5近的行星。
E. (not ((-5 - 4) != (1 ** 2))) or (((-2 + -9) > (-17 + 16)) or ((-15 * 10) <= (7 * -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": "C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 14973626,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. (-7 * -8 * -2 * -6) <= (50 % 4) <= (3 % 7)\nB. not (狗有4条腿。)\nC. (not not ((-12 - -5) < (10 - -5))) or (1956年是闰年。)\nD. 木星是距离太阳第5近的行星。\nE. (not ((-5 - 4) != (1 ** 2))) or (((-2 + -9) > (-17 + 16)) or ((-15 * 10) <= (7 * -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": 2,
"language": "cn",
"num_options": 5,
"seed": 14973626,
"true_count": 3
},
"seed": 14973626,
"task_id": 614973626,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not not ((not not ((3 ** 2) != (2 ** 1))) or ((人类有三个肺。) or (壁虎是鸟类。)))
B. (((墨西哥位于北美洲。) or (泰坦尼克号沉没发生在1914年。)) or ((1 ** 3) != (1 ** 3))) and ((((1 % 6) < (14 + 18)) or ((-5 * -17) >= (14 + -8))) or (钙的化学符号是Ca。))
C. (((4 ** 2) == (0 * 1 * -3 * 5)) or ((日本的首都是柏林。) and (1932年奥运会在洛杉矶举办。))) and ((29 % 8) < (1 * 3 * -4 * 6))
D. (金的化学符号是Ti。) or (not not (((11 + 7) <= (5 * -10 - 3 * 1) <= (-2 * 12)) or ((-4 * 10 * -9 * 4) != (5 ** 1))))
E. not ((((3 + 6) == (-3 - 4)) or (闪电不会两次击中同一个地方。)) or ((-11 + 6) < (3 ** 1) < (5 ** 1)))
F. not ((12 + 5) == (-10 * -1 + 3 * 9))
G. (not not ((酒精在常温下是液体。) and (25的平方根是5。))) and (not (not not (新西兰的首都是里斯本。)))
H. ((((-19 - 14) <= (-9 + -4) <= (-7 + -6)) and (1932年奥运会在墨西哥城举办。)) and ((钾的化学符号是K。) or (100小于等于28。))) or (((海王星是距离太阳第6近的行星。) or (火星是距离太阳最近的行星。)) and (((6 + -13) < (-19 + 16) < (5 * 10 - 7 * -8)) and ((-8 - -17) >= (1 ** 3))))
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,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 8759044,
"true_count": 5
},
"question": "给定以下布尔表达式：\n\nA. not not ((not not ((3 ** 2) != (2 ** 1))) or ((人类有三个肺。) or (壁虎是鸟类。)))\nB. (((墨西哥位于北美洲。) or (泰坦尼克号沉没发生在1914年。)) or ((1 ** 3) != (1 ** 3))) and ((((1 % 6) < (14 + 18)) or ((-5 * -17) >= (14 + -8))) or (钙的化学符号是Ca。))\nC. (((4 ** 2) == (0 * 1 * -3 * 5)) or ((日本的首都是柏林。) and (1932年奥运会在洛杉矶举办。))) and ((29 % 8) < (1 * 3 * -4 * 6))\nD. (金的化学符号是Ti。) or (not not (((11 + 7) <= (5 * -10 - 3 * 1) <= (-2 * 12)) or ((-4 * 10 * -9 * 4) != (5 ** 1))))\nE. not ((((3 + 6) == (-3 - 4)) or (闪电不会两次击中同一个地方。)) or ((-11 + 6) < (3 ** 1) < (5 ** 1)))\nF. not ((12 + 5) == (-10 * -1 + 3 * 9))\nG. (not not ((酒精在常温下是液体。) and (25的平方根是5。))) and (not (not not (新西兰的首都是里斯本。)))\nH. ((((-19 - 14) <= (-9 + -4) <= (-7 + -6)) and (1932年奥运会在墨西哥城举办。)) and ((钾的化学符号是K。) or (100小于等于28。))) or (((海王星是距离太阳第6近的行星。) or (火星是距离太阳最近的行星。)) and (((6 + -13) < (-19 + 16) < (5 * 10 - 7 * -8)) and ((-8 - -17) >= (1 ** 3))))\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": 8,
"seed": 8759044,
"true_count": 5
},
"seed": 8759044,
"task_id": 608759044,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (((-5 - 15) < (1 + 11)) and (((2058 is a leap year.) or (World War II ended occurred in 1945.)) and (not not ((6 * 8 - 1 * 5) == (1 ** 3))))) and (((((4 * 10 - -7 * 5) != (7 - 16)) and (A octopus has 8 legs.)) or (((5 ** 2) >= (1 ** 2)) or (The capital of Egypt is Ottawa.))) or ((not (The currency of Peru is the Sol.)) or ((2065 is a leap year.) and ((5 * -6 + 8 * -1) < (45 % 10)))))
B. not not (((((-11 * 5) == (11 - 7)) and (Helium is a liquid at room temperature.)) and (Bats are blind.)) and (There are 28 days in December.))
C. (((not not (The 1976 Olympics were held in Melbourne.)) or ((Diamonds are made of carbon.) and (Kenya is in Africa.))) or ((not ((-1 + -18) == (2 + 0))) or ((-4 - -2) != (12 - 14)))) or ((not not (The 1936 Olympics were held in Stockholm.)) and (not not ((-20 * 0) == (8 - -19)))) or ((A cow has 4 legs.) and (((16 % 1) >= (-12 * 5)) and (((-14 * -15) <= (11 - 6)) or ((-12 - -7) > (12 - -6)))))
D. ((((Peru is in South America.) or ((8 - -13) == (-17 * 8))) or ((The currency of Brazil is the Real.) and (The capital of Kenya is Singapore.))) or (not (Sharks are mammals.))) and (not not ((The capital of Italy is Rome.) or (World War I ended occurred in 1918.))) and (not not ((Gold is a liquid at room temperature.) and (not not ((7 - 10) < (13 * 5)))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 85501235,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. (((-5 - 15) < (1 + 11)) and (((2058 is a leap year.) or (World War II ended occurred in 1945.)) and (not not ((6 * 8 - 1 * 5) == (1 ** 3))))) and (((((4 * 10 - -7 * 5) != (7 - 16)) and (A octopus has 8 legs.)) or (((5 ** 2) >= (1 ** 2)) or (The capital of Egypt is Ottawa.))) or ((not (The currency of Peru is the Sol.)) or ((2065 is a leap year.) and ((5 * -6 + 8 * -1) < (45 % 10)))))\nB. not not (((((-11 * 5) == (11 - 7)) and (Helium is a liquid at room temperature.)) and (Bats are blind.)) and (There are 28 days in December.))\nC. (((not not (The 1976 Olympics were held in Melbourne.)) or ((Diamonds are made of carbon.) and (Kenya is in Africa.))) or ((not ((-1 + -18) == (2 + 0))) or ((-4 - -2) != (12 - 14)))) or ((not not (The 1936 Olympics were held in Stockholm.)) and (not not ((-20 * 0) == (8 - -19)))) or ((A cow has 4 legs.) and (((16 % 1) >= (-12 * 5)) and (((-14 * -15) <= (11 - 6)) or ((-12 - -7) > (12 - -6)))))\nD. ((((Peru is in South America.) or ((8 - -13) == (-17 * 8))) or ((The currency of Brazil is the Real.) and (The capital of Kenya is Singapore.))) or (not (Sharks are mammals.))) and (not not ((The capital of Italy is Rome.) or (World War I ended occurred in 1918.))) and (not not ((Gold is a liquid at room temperature.) and (not not ((7 - 10) < (13 * 5)))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 85501235,
"true_count": 1
},
"seed": 85501235,
"task_id": 685501235,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (-2 - -1) == (8 * 3 * -1 * -6)
B. ((17 - 6) == (9 * -2 * -5 * -2)) or ((巴西的货币是雷亚尔。) and (泰坦尼克号沉没发生在1912年。))
C. 闪电不会两次击中同一个地方。
D. (2 + -17) > (10 * -10)
E. (not not (铜的化学符号是N。)) and (not (泰坦尼克号沉没发生在1902年。))
F. (not (铂的化学符号是Pt。)) and (((3 ** 3) >= (2 - 15)) or ((5 ** 3) < (48 % 7)))
G. ((哥伦比亚位于南美洲。) or ((-15 + 12) != (-10 + -8))) or (1904年奥运会在莫斯科举办。)
H. ((4 ** 1) <= (-5 * -9 - -3 * 8)) or (not not ((-3 - 10) < (25 % 7)))
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,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 78751511,
"true_count": 4
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (-2 - -1) == (8 * 3 * -1 * -6)\nB. ((17 - 6) == (9 * -2 * -5 * -2)) or ((巴西的货币是雷亚尔。) and (泰坦尼克号沉没发生在1912年。))\nC. 闪电不会两次击中同一个地方。\nD. (2 + -17) > (10 * -10)\nE. (not not (铜的化学符号是N。)) and (not (泰坦尼克号沉没发生在1902年。))\nF. (not (铂的化学符号是Pt。)) and (((3 ** 3) >= (2 - 15)) or ((5 ** 3) < (48 % 7)))\nG. ((哥伦比亚位于南美洲。) or ((-15 + 12) != (-10 + -8))) or (1904年奥运会在莫斯科举办。)\nH. ((4 ** 1) <= (-5 * -9 - -3 * 8)) or (not not ((-3 - 10) < (25 % 7)))\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": 8,
"seed": 78751511,
"true_count": 4
},
"seed": 78751511,
"task_id": 678751511,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. ((not not ((十月有31天。) or ((15 + 0) <= (2 * 0)))) or ((not ((-20 + 19) <= (2 ** 2) <= (16 - 17))) and ((-5 * 20) <= (-7 + -10)))) and (((((-8 * 9 + -10 * 8) >= (17 * 15)) or (1970年是闰年。)) and ((新西兰位于大洋洲。) or (加拿大位于欧洲。))) and (莱特兄弟首次飞行发生在1903年。) and ((-10 * 7 * -6 * -2) != (-1 * -10 + 0 * 10)))
B. (not not (not not ((48能被6整除。) and (32是质数。)))) and (134是完全平方数。) and (not not ((-12 + -3) < (13 - 16)))
C. not (((-16 + 1) < (-8 + -2) < (-10 * 1 * -2 * -8)) and (1975年是闰年。) and (not not ((11 % 3) != (6 * 3))))
D. ((not (((11 - 18) >= (-19 - -7)) and ((1 * 5 * 6 * -7) > (-3 * 9 + -10 * 6)))) and (((1984年奥运会在斯德哥尔摩举办。) and (2008年奥运会在巴黎举办。)) or (not not ((-1 * 5) != (5 ** 3))))) and ((酒精在常温下是液体。) or (((10 + 6) <= (27 % 3)) or ((15 + 0) == (-9 * 0 + -7 * -10))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 69683171,
"true_count": 2
},
"question": "审视以下逻辑表达式：\n\nA. ((not not ((十月有31天。) or ((15 + 0) <= (2 * 0)))) or ((not ((-20 + 19) <= (2 ** 2) <= (16 - 17))) and ((-5 * 20) <= (-7 + -10)))) and (((((-8 * 9 + -10 * 8) >= (17 * 15)) or (1970年是闰年。)) and ((新西兰位于大洋洲。) or (加拿大位于欧洲。))) and (莱特兄弟首次飞行发生在1903年。) and ((-10 * 7 * -6 * -2) != (-1 * -10 + 0 * 10)))\nB. (not not (not not ((48能被6整除。) and (32是质数。)))) and (134是完全平方数。) and (not not ((-12 + -3) < (13 - 16)))\nC. not (((-16 + 1) < (-8 + -2) < (-10 * 1 * -2 * -8)) and (1975年是闰年。) and (not not ((11 % 3) != (6 * 3))))\nD. ((not (((11 - 18) >= (-19 - -7)) and ((1 * 5 * 6 * -7) > (-3 * 9 + -10 * 6)))) and (((1984年奥运会在斯德哥尔摩举办。) and (2008年奥运会在巴黎举办。)) or (not not ((-1 * 5) != (5 ** 3))))) and ((酒精在常温下是液体。) or (((10 + 6) <= (27 % 3)) or ((15 + 0) == (-9 * 0 + -7 * -10))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 69683171,
"true_count": 2
},
"seed": 69683171,
"task_id": 669683171,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not ((2 * -8 - -3 * -6) > (5 ** 2))
B. (((日本位于非洲。) and ((-4 + 2) == (14 + 1))) or ((澳大利亚位于南美洲。) or (1933年是闰年。))) or (not not (六月有30天。)) or (((铂的化学符号是P。) and ((-10 * -4 * -10 * -1) >= (14 - 19))) and ((7 * -5 + 3 * 3) != (12 * -9)))
C. (((氯的化学符号是K。) and (澳大利亚位于南美洲。)) or (not not (283是完全平方数。))) and ((((18 - 20) == (-2 * 3 * -10 * 6)) and ((14 - 17) <= (17 * -3) <= (7 * 6 + 9 * 7))) or (not not ((5 * 9 - 7 * 0) == (8 * -8 - 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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 30063806,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. not ((2 * -8 - -3 * -6) > (5 ** 2))\nB. (((日本位于非洲。) and ((-4 + 2) == (14 + 1))) or ((澳大利亚位于南美洲。) or (1933年是闰年。))) or (not not (六月有30天。)) or (((铂的化学符号是P。) and ((-10 * -4 * -10 * -1) >= (14 - 19))) and ((7 * -5 + 3 * 3) != (12 * -9)))\nC. (((氯的化学符号是K。) and (澳大利亚位于南美洲。)) or (not not (283是完全平方数。))) and ((((18 - 20) == (-2 * 3 * -10 * 6)) and ((14 - 17) <= (17 * -3) <= (7 * 6 + 9 * 7))) or (not not ((5 * 9 - 7 * 0) == (8 * -8 - 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": 3,
"seed": 30063806,
"true_count": 2
},
"seed": 30063806,
"task_id": 630063806,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((not not (((1 + 14) < (-10 + 7)) and (鲤鱼是鱼类。))) or (德国的首都是柏林。)) and ((((二月有28天。) or ((-16 - -18) >= (10 - 10))) or (巴西的货币是雷亚尔。)) and (not not (((15 % 9) <= (25 % 4)) and ((-12 * -11) >= (17 - 11)))))
B. (not ((not not (阿根廷的货币是里拉。)) or (not not (碳的化学符号是C。)))) and ((not (尼日利亚位于大洋洲。)) or ((1968年奥运会在墨西哥城举办。) and ((-1 * -7 - 9 * 7) <= (17 - -11))) or (not not (((4 * -18) > (-2 * 7 + 6 * -2)) or (1954年是闰年。))))
C. (not not (72大于20。)) or (not (not (哥伦布到达美洲发生在1492年。))) or (((not (地球是距离太阳第3近的行星。)) or ((34 % 10) <= (-6 * -3 - -2 * -6))) and (英国的货币是英镑。))
D. ((土耳其的货币是里拉。) or (not (钠的化学符号是Na。)) or ((not not (柏林墙倒塌发生在1988年。)) and (((3 ** 2) < (-15 - -7)) or (秘鲁的货币是雷亚尔。)))) or (not not ((not not (1928年奥运会在亚特兰大举办。)) or (not ((14 - -7) != (1 ** 3)))))
E. ((not (not ((14 + 11) <= (1 * -5 - -7 * -9)))) or ((7 - -18) < (1 ** 3)) or (not not (not (第一部iPhone发布发生在2017年。)))) and ((not (蝙蝠是哺乳动物。)) and (((17 * -1) >= (5 * 3 + -7 * -6)) and (巴西位于欧洲。))) and (not ((not not ((8 * -3 * 1 * -4) < (17 * 2))) or (((11 * -9) <= (5 ** 1)) and (锰的化学符号是N。))))
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,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 82579203,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. ((not not (((1 + 14) < (-10 + 7)) and (鲤鱼是鱼类。))) or (德国的首都是柏林。)) and ((((二月有28天。) or ((-16 - -18) >= (10 - 10))) or (巴西的货币是雷亚尔。)) and (not not (((15 % 9) <= (25 % 4)) and ((-12 * -11) >= (17 - 11)))))\nB. (not ((not not (阿根廷的货币是里拉。)) or (not not (碳的化学符号是C。)))) and ((not (尼日利亚位于大洋洲。)) or ((1968年奥运会在墨西哥城举办。) and ((-1 * -7 - 9 * 7) <= (17 - -11))) or (not not (((4 * -18) > (-2 * 7 + 6 * -2)) or (1954年是闰年。))))\nC. (not not (72大于20。)) or (not (not (哥伦布到达美洲发生在1492年。))) or (((not (地球是距离太阳第3近的行星。)) or ((34 % 10) <= (-6 * -3 - -2 * -6))) and (英国的货币是英镑。))\nD. ((土耳其的货币是里拉。) or (not (钠的化学符号是Na。)) or ((not not (柏林墙倒塌发生在1988年。)) and (((3 ** 2) < (-15 - -7)) or (秘鲁的货币是雷亚尔。)))) or (not not ((not not (1928年奥运会在亚特兰大举办。)) or (not ((14 - -7) != (1 ** 3)))))\nE. ((not (not ((14 + 11) <= (1 * -5 - -7 * -9)))) or ((7 - -18) < (1 ** 3)) or (not not (not (第一部iPhone发布发生在2017年。)))) and ((not (蝙蝠是哺乳动物。)) and (((17 * -1) >= (5 * 3 + -7 * -6)) and (巴西位于欧洲。))) and (not ((not not ((8 * -3 * 1 * -4) < (17 * 2))) or (((11 * -9) <= (5 ** 1)) and (锰的化学符号是N。))))\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": 5,
"seed": 82579203,
"true_count": 2
},
"seed": 82579203,
"task_id": 682579203,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (0 - -17) < (23 % 3)
B. The capital of Colombia is Bogota.
C. (not (Russia is in Europe.)) and (((5 - 13) < (-10 * 9 - 2 * -3)) and (India is in Asia.))
D. not not ((Mars is the closest planet to the Sun.) and (A bird has 2 legs.))
E. (The chemical symbol for Tin is Ca.) or (((28 % 4) == (50 % 7)) or (The capital of Saudi Arabia is Kyiv.))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 82557760,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. (0 - -17) < (23 % 3)\nB. The capital of Colombia is Bogota.\nC. (not (Russia is in Europe.)) and (((5 - 13) < (-10 * 9 - 2 * -3)) and (India is in Asia.))\nD. not not ((Mars is the closest planet to the Sun.) and (A bird has 2 legs.))\nE. (The chemical symbol for Tin is Ca.) or (((28 % 4) == (50 % 7)) or (The capital of Saudi Arabia is Kyiv.))\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": 82557760,
"true_count": 1
},
"seed": 82557760,
"task_id": 682557760,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((not not ((14 + -12) != (7 * 1))) and (not (钙的化学符号是Mn。))) or ((not (冰在常温下是液体。)) or ((7 * 16) <= (-8 * -2 - -4 * -3)))) and ((氦气在常温下是固体。) or ((((-2 * 8 * -10 * -7) > (7 - 17)) and (苏联解体发生在1991年。)) or ((澳大利亚的货币是澳元。) or ((1 * -5 + -8 * 4) < (-3 * -15)))))
B. ((86大于71。) or (((钛的化学符号是C。) or (钻石在常温下是固体。)) and (((15 + 7) >= (-20 * -19)) and ((-2 * 0 - 3 * 1) != (18 - -15))))) or ((油在常温下是气体。) and (((蝙蝠是瞎的。) and (木星是距离太阳第4近的行星。)) and (((5 ** 1) < (-18 - 2) < (3 * 4 - 4 * 3)) or ((14 - -8) <= (-9 * -3 - -4 * -9)))))
C. not not (not (第一次世界大战结束发生在1918年。))
D. ((氦的化学符号是He。) and ((1979年是闰年。) and (澳大利亚的货币是美元。)) and (((俄罗斯的货币是埃及镑。) and (摩洛哥位于非洲。)) and ((金的化学符号是Mg。) and ((6 * -10 + -7 * 5) < (7 * -3 - -4 * 3))))) or (not (2016年奥运会在亚特兰大举办。))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 56907580,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. (((not not ((14 + -12) != (7 * 1))) and (not (钙的化学符号是Mn。))) or ((not (冰在常温下是液体。)) or ((7 * 16) <= (-8 * -2 - -4 * -3)))) and ((氦气在常温下是固体。) or ((((-2 * 8 * -10 * -7) > (7 - 17)) and (苏联解体发生在1991年。)) or ((澳大利亚的货币是澳元。) or ((1 * -5 + -8 * 4) < (-3 * -15)))))\nB. ((86大于71。) or (((钛的化学符号是C。) or (钻石在常温下是固体。)) and (((15 + 7) >= (-20 * -19)) and ((-2 * 0 - 3 * 1) != (18 - -15))))) or ((油在常温下是气体。) and (((蝙蝠是瞎的。) and (木星是距离太阳第4近的行星。)) and (((5 ** 1) < (-18 - 2) < (3 * 4 - 4 * 3)) or ((14 - -8) <= (-9 * -3 - -4 * -9)))))\nC. not not (not (第一次世界大战结束发生在1918年。))\nD. ((氦的化学符号是He。) and ((1979年是闰年。) and (澳大利亚的货币是美元。)) and (((俄罗斯的货币是埃及镑。) and (摩洛哥位于非洲。)) and ((金的化学符号是Mg。) and ((6 * -10 + -7 * 5) < (7 * -3 - -4 * 3))))) or (not (2016年奥运会在亚特兰大举办。))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 56907580,
"true_count": 3
},
"seed": 56907580,
"task_id": 656907580,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((not ((-6 * -9 + 0 * -5) <= (3 + -4))) or (第二次世界大战开始发生在1939年。)) or ((2008年奥运会在北京举办。) and (((5 ** 1) == (13 + 19)) or ((0 - -15) > (-12 * 20)))) or (not ((((-4 - -11) == (34 % 2)) and (哥伦比亚的首都是堪培拉。)) or (((2 ** 1) <= (1 ** 3)) and (金鱼是鱼类。))))
B. ((((2020年奥运会在东京举办。) and (月球自己发光。)) or ((-19 + 1) != (16 * -15))) or (((-15 * -14) == (1 * -8 - -2 * 8)) and (天王星是距离太阳第4近的行星。)) or (水在海平面上的沸点是100摄氏度。)) or (not not (((2 * 1 - -1 * -10) > (6 + 1)) and (((14 + -6) <= (19 + 15) <= (-7 - -12)) and (铁的化学符号是N。))))
C. not (not not ((not ((-15 + -18) >= (-3 - 18))) or (((-11 * 3) >= (3 ** 3)) or ((-8 - -7) != (8 * -3 * 5 * 1)))))
D. ((((11 * 10) >= (7 - 18)) and (((19 - 20) < (-7 * 4 * -2 * 10)) and ((0 - 15) >= (-14 + 16)))) or ((((15 % 6) == (-9 * 5 - -1 * -7)) or (光速比声速快。)) or ((921是斐波那契数。) and (铜在常温下是液体。)))) or ((7 * -16) != (26 % 4)) or (((-5 * 0 - 1 * -10) != (15 + 1)) and ((闪电不会两次击中同一个地方。) and (油在常温下是固体。)) and (墨西哥位于亚洲。))
E. (((鸭子有10条腿。) and (((10 * -18) <= (3 * 6 - 10 * 2) <= (13 + 0)) or ((-8 * 7 + -9 * 3) == (-4 * -8 * 5 * 0)))) or (((6 + -13) >= (5 * 4 - 8 * -6)) and ((4 - -13) < (8 + 1))) or (火星是距离太阳第4近的行星。)) and (((-20 - 12) <= (1 ** 2)) and ((9的平方根是15。) or (((41 % 8) > (-17 * -10)) and (九月有28天。))))
F. not (not (not (not not (金的化学符号是Au。))))
G. ((not ((-17 + 14) > (18 - -17))) or ((人体有206块骨头。) or (钛的化学符号是Ti。)) or (not ((天王星是距离太阳第6近的行星。) and (铜在常温下是固体。)))) and ((((-17 * 1) != (18 + -11)) or (not (第一次世界大战开始发生在1914年。))) and (地球是距离太阳第3近的行星。) and (not not (not ((-14 * -15) <= (-15 * 5) <= (-18 - 16)))))
H. ((((30是质数。) and (越南的首都是波哥大。)) and (((-1 * -4 * -7 * 6) < (4 ** 3)) and (美国宣布独立发生在1781年。))) and (水在海平面上的沸点是100摄氏度。) and (not not ((12 + -19) <= (5 * 2 * -10 * -8)))) and (not (not not ((肯尼亚的首都是惠灵顿。) or (埃及位于非洲。))))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,B,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 8,
"seed": 45336702,
"true_count": 4
},
"question": "分析以下逻辑表达式：\n\nA. ((not ((-6 * -9 + 0 * -5) <= (3 + -4))) or (第二次世界大战开始发生在1939年。)) or ((2008年奥运会在北京举办。) and (((5 ** 1) == (13 + 19)) or ((0 - -15) > (-12 * 20)))) or (not ((((-4 - -11) == (34 % 2)) and (哥伦比亚的首都是堪培拉。)) or (((2 ** 1) <= (1 ** 3)) and (金鱼是鱼类。))))\nB. ((((2020年奥运会在东京举办。) and (月球自己发光。)) or ((-19 + 1) != (16 * -15))) or (((-15 * -14) == (1 * -8 - -2 * 8)) and (天王星是距离太阳第4近的行星。)) or (水在海平面上的沸点是100摄氏度。)) or (not not (((2 * 1 - -1 * -10) > (6 + 1)) and (((14 + -6) <= (19 + 15) <= (-7 - -12)) and (铁的化学符号是N。))))\nC. not (not not ((not ((-15 + -18) >= (-3 - 18))) or (((-11 * 3) >= (3 ** 3)) or ((-8 - -7) != (8 * -3 * 5 * 1)))))\nD. ((((11 * 10) >= (7 - 18)) and (((19 - 20) < (-7 * 4 * -2 * 10)) and ((0 - 15) >= (-14 + 16)))) or ((((15 % 6) == (-9 * 5 - -1 * -7)) or (光速比声速快。)) or ((921是斐波那契数。) and (铜在常温下是液体。)))) or ((7 * -16) != (26 % 4)) or (((-5 * 0 - 1 * -10) != (15 + 1)) and ((闪电不会两次击中同一个地方。) and (油在常温下是固体。)) and (墨西哥位于亚洲。))\nE. (((鸭子有10条腿。) and (((10 * -18) <= (3 * 6 - 10 * 2) <= (13 + 0)) or ((-8 * 7 + -9 * 3) == (-4 * -8 * 5 * 0)))) or (((6 + -13) >= (5 * 4 - 8 * -6)) and ((4 - -13) < (8 + 1))) or (火星是距离太阳第4近的行星。)) and (((-20 - 12) <= (1 ** 2)) and ((9的平方根是15。) or (((41 % 8) > (-17 * -10)) and (九月有28天。))))\nF. not (not (not (not not (金的化学符号是Au。))))\nG. ((not ((-17 + 14) > (18 - -17))) or ((人体有206块骨头。) or (钛的化学符号是Ti。)) or (not ((天王星是距离太阳第6近的行星。) and (铜在常温下是固体。)))) and ((((-17 * 1) != (18 + -11)) or (not (第一次世界大战开始发生在1914年。))) and (地球是距离太阳第3近的行星。) and (not not (not ((-14 * -15) <= (-15 * 5) <= (-18 - 16)))))\nH. ((((30是质数。) and (越南的首都是波哥大。)) and (((-1 * -4 * -7 * 6) < (4 ** 3)) and (美国宣布独立发生在1781年。))) and (水在海平面上的沸点是100摄氏度。) and (not not ((12 + -19) <= (5 * 2 * -10 * -8)))) and (not (not not ((肯尼亚的首都是惠灵顿。) or (埃及位于非洲。))))\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": 4,
"language": "cn",
"num_options": 8,
"seed": 45336702,
"true_count": 4
},
"seed": 45336702,
"task_id": 645336702,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (19 - -9) == (3 % 6)
B. (3 ** 2) > (3 % 6)
C. South Africa is in Oceania.
D. (((10 + -13) < (-20 + 10)) or ((-8 * 17) <= (-15 + 6))) or ((A sheep is a mammal.) and (The 2000 Olympics were held in Rome.))
E. ((-12 + -18) <= (-13 + 11) <= (-12 * -16)) and ((3 * 5 - -10 * 7) >= (3 * 8 - -1 * 8))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 3759845,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (19 - -9) == (3 % 6)\nB. (3 ** 2) > (3 % 6)\nC. South Africa is in Oceania.\nD. (((10 + -13) < (-20 + 10)) or ((-8 * 17) <= (-15 + 6))) or ((A sheep is a mammal.) and (The 2000 Olympics were held in Rome.))\nE. ((-12 + -18) <= (-13 + 11) <= (-12 * -16)) and ((3 * 5 - -10 * 7) >= (3 * 8 - -1 * 8))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 3759845,
"true_count": 3
},
"seed": 3759845,
"task_id": 603759845,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not (There are 30 days in July.)) or (((9 * -8 + 3 * -2) <= (19 % 2)) or (There are 31 days in January.))
B. (not (A snake has 8 legs.)) and (((9 * 16) == (13 * -14)) or ((-15 + -19) < (0 + -19)))
C. The chemical symbol for Uranium is U.
D. ((The currency of Switzerland is the Franc.) or (A butterfly has 6 legs.)) and ((A horse has 6 legs.) or (United States is in North America.))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 98985773,
"true_count": 4
},
"question": "Analyze these boolean expressions:\n\nA. (not (There are 30 days in July.)) or (((9 * -8 + 3 * -2) <= (19 % 2)) or (There are 31 days in January.))\nB. (not (A snake has 8 legs.)) and (((9 * 16) == (13 * -14)) or ((-15 + -19) < (0 + -19)))\nC. The chemical symbol for Uranium is U.\nD. ((The currency of Switzerland is the Franc.) or (A butterfly has 6 legs.)) and ((A horse has 6 legs.) or (United States is in North America.))\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": 98985773,
"true_count": 4
},
"seed": 98985773,
"task_id": 698985773,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not (not not (((The square root of 1 is 1.) and (A dragonfly is a mammal.)) and ((((-10 * 14) >= (-12 - 7)) or (Earth is the 2nd planet from the Sun.)) and (The chemical symbol for Platinum is Pt.)) and (not ((The capital of Sweden is Stockholm.) and ((The 1900 Olympics were held in Paris.) or (The capital of Cuba is Havana.))))))
B. not (not not ((((-6 * 16) >= (2 * 8 + 9 * -4)) and ((((-20 * 6) <= (-17 - 18) <= (20 * -7)) and (The capital of Saudi Arabia is Riyadh.)) or (Christopher Columbus reached America occurred in 1492.))) or (not (1943 is a leap year.))))
C. not (not not (not (not not ((4 * 0) >= (5 ** 3)))))
D. (((not not ((The capital of Canada is Prague.) or ((The 1972 Olympics were held in Munich.) and ((4 * 17) >= (-10 * 10 * -3 * -10))))) or (not not (not (((4 ** 2) == (23 % 7)) or ((8 * 2 * 2 * 9) < (28 % 6)))))) and (not (not (Peru is in Oceania.)))) or ((not (((4 ** 2) <= (-16 - 9) <= (7 * 6)) or ((-4 * 7 * -7 * 9) <= (-14 - -6)) or (not (The chemical symbol for Sulfur is S.)))) and (not not (not not (((-20 + 5) == (5 * 1)) or (((-20 + 4) >= (-5 * 2 * -5 * 4)) and (Germany is in Europe.))))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 22333382,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. not (not not (((The square root of 1 is 1.) and (A dragonfly is a mammal.)) and ((((-10 * 14) >= (-12 - 7)) or (Earth is the 2nd planet from the Sun.)) and (The chemical symbol for Platinum is Pt.)) and (not ((The capital of Sweden is Stockholm.) and ((The 1900 Olympics were held in Paris.) or (The capital of Cuba is Havana.))))))\nB. not (not not ((((-6 * 16) >= (2 * 8 + 9 * -4)) and ((((-20 * 6) <= (-17 - 18) <= (20 * -7)) and (The capital of Saudi Arabia is Riyadh.)) or (Christopher Columbus reached America occurred in 1492.))) or (not (1943 is a leap year.))))\nC. not (not not (not (not not ((4 * 0) >= (5 ** 3)))))\nD. (((not not ((The capital of Canada is Prague.) or ((The 1972 Olympics were held in Munich.) and ((4 * 17) >= (-10 * 10 * -3 * -10))))) or (not not (not (((4 ** 2) == (23 % 7)) or ((8 * 2 * 2 * 9) < (28 % 6)))))) and (not (not (Peru is in Oceania.)))) or ((not (((4 ** 2) <= (-16 - 9) <= (7 * 6)) or ((-4 * 7 * -7 * 9) <= (-14 - -6)) or (not (The chemical symbol for Sulfur is S.)))) and (not not (not not (((-20 + 5) == (5 * 1)) or (((-20 + 4) >= (-5 * 2 * -5 * 4)) and (Germany is in Europe.))))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 22333382,
"true_count": 1
},
"seed": 22333382,
"task_id": 622333382,
"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 not (木星是距离太阳第1近的行星。)) or (((4 + 5) < (22 % 3)) and ((17 - -14) >= (-3 * 0 - 7 * -6))))
B. (2092年是闰年。) or ((not ((5 * 13) <= (8 - -7))) or ((3 ** 3) > (-10 * 1 + -5 * 9)))
C. not (((铁的化学符号是Na。) or ((-2 * -3 + 7 * -7) <= (3 + -12))) or ((1982年是闰年。) and (地球上一天是24小时。)))
D. (((1 - 16) < (9 * -9 + 8 * 6) < (-11 - 0)) or (((-5 * -2 - 3 * -1) == (-10 * -8 - -1 * -3)) and ((-16 * 3) != (6 + 19)))) and ((1920年奥运会在雅典举办。) and ((68大于83。) and ((3 ** 2) <= (48 % 8))))
E. ((三月有29天。) or ((4 ** 2) == (28 % 2))) and ((泰坦尼克号沉没发生在1910年。) and ((18 * -13) <= (5 ** 2))) and ((6 - -18) != (10 * 3))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 36351730,
"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 not (木星是距离太阳第1近的行星。)) or (((4 + 5) < (22 % 3)) and ((17 - -14) >= (-3 * 0 - 7 * -6))))\nB. (2092年是闰年。) or ((not ((5 * 13) <= (8 - -7))) or ((3 ** 3) > (-10 * 1 + -5 * 9)))\nC. not (((铁的化学符号是Na。) or ((-2 * -3 + 7 * -7) <= (3 + -12))) or ((1982年是闰年。) and (地球上一天是24小时。)))\nD. (((1 - 16) < (9 * -9 + 8 * 6) < (-11 - 0)) or (((-5 * -2 - 3 * -1) == (-10 * -8 - -1 * -3)) and ((-16 * 3) != (6 + 19)))) and ((1920年奥运会在雅典举办。) and ((68大于83。) and ((3 ** 2) <= (48 % 8))))\nE. ((三月有29天。) or ((4 ** 2) == (28 % 2))) and ((泰坦尼克号沉没发生在1910年。) and ((18 * -13) <= (5 ** 2))) and ((6 - -18) != (10 * 3))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 36351730,
"true_count": 1
},
"seed": 36351730,
"task_id": 636351730,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (((not not (马是哺乳动物。)) and (((6 + -19) <= (-15 + 19)) or (阿根廷的首都是基辅。))) and (1912年奥运会在斯德哥尔摩举办。) and ((-20 * 20) != (20 - 14))) and ((not (新加坡的首都是开罗。)) or (not not (((6 - 4) < (39 % 4) < (0 * 8)) and (印度位于亚洲。))))
B. not not ((((12 * -6) >= (-7 - 1)) and (((-17 + 7) > (17 + -17)) and ((9 + -11) != (-7 - -5)))) or (not not (not not (加拿大位于北美洲。))))
C. (not ((not not ((1 ** 1) < (-15 * 19))) and (秘鲁的货币是英镑。))) or (((-2 + -10) >= (-5 * -8 + 2 * 6)) or (not not ((7 + 4) < (14 + 14) < (-13 - 19)))) or (not not (not (not (磷的化学符号是P。))))
D. (((not not (1979年是闰年。)) and (((-15 + -14) > (4 - -15)) and (韩国的首都是拉巴特。))) or (水星是距离太阳第1近的行星。)) or ((尼日利亚的首都是阿布贾。) or (not not ((2000年是闰年。) and ((9 * 4) == (16 + 18)))))
E. ((not (not not (土耳其的首都是安卡拉。))) or ((((1 * 2 + 1 * -6) != (-10 * -17)) and ((-17 * -20) <= (-20 - 8) <= (13 % 4))) or ((新西兰位于南极洲。) or (南非位于非洲。)))) and (not ((5 ** 2) == (-1 + 20)))
F. (not (比利时的首都是新德里。)) and ((3 ** 1) > (-15 * 15)) and ((1924年奥运会在巴黎举办。) or (钻石在常温下是固体。))
G. (not not (not (196的平方根是10。))) or ((((5 + 8) < (17 - 6)) or (not not (企鹅是鸟类。))) and (not not (氦的化学符号是Na。)) and ((not not ((1 * -8) >= (5 ** 3))) or (not not (4小于等于95。))))
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,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 70066651,
"true_count": 7
},
"question": "审视以下逻辑表达式：\n\nA. (((not not (马是哺乳动物。)) and (((6 + -19) <= (-15 + 19)) or (阿根廷的首都是基辅。))) and (1912年奥运会在斯德哥尔摩举办。) and ((-20 * 20) != (20 - 14))) and ((not (新加坡的首都是开罗。)) or (not not (((6 - 4) < (39 % 4) < (0 * 8)) and (印度位于亚洲。))))\nB. not not ((((12 * -6) >= (-7 - 1)) and (((-17 + 7) > (17 + -17)) and ((9 + -11) != (-7 - -5)))) or (not not (not not (加拿大位于北美洲。))))\nC. (not ((not not ((1 ** 1) < (-15 * 19))) and (秘鲁的货币是英镑。))) or (((-2 + -10) >= (-5 * -8 + 2 * 6)) or (not not ((7 + 4) < (14 + 14) < (-13 - 19)))) or (not not (not (not (磷的化学符号是P。))))\nD. (((not not (1979年是闰年。)) and (((-15 + -14) > (4 - -15)) and (韩国的首都是拉巴特。))) or (水星是距离太阳第1近的行星。)) or ((尼日利亚的首都是阿布贾。) or (not not ((2000年是闰年。) and ((9 * 4) == (16 + 18)))))\nE. ((not (not not (土耳其的首都是安卡拉。))) or ((((1 * 2 + 1 * -6) != (-10 * -17)) and ((-17 * -20) <= (-20 - 8) <= (13 % 4))) or ((新西兰位于南极洲。) or (南非位于非洲。)))) and (not ((5 ** 2) == (-1 + 20)))\nF. (not (比利时的首都是新德里。)) and ((3 ** 1) > (-15 * 15)) and ((1924年奥运会在巴黎举办。) or (钻石在常温下是固体。))\nG. (not not (not (196的平方根是10。))) or ((((5 + 8) < (17 - 6)) or (not not (企鹅是鸟类。))) and (not not (氦的化学符号是Na。)) and ((not not ((1 * -8) >= (5 ** 3))) or (not not (4小于等于95。))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 70066651,
"true_count": 7
},
"seed": 70066651,
"task_id": 670066651,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((-2 * -8 * 6 * -4) != (9 * -4 * 5 * 7)) or (((The 1964 Olympics were held in Tokyo.) or (The 1936 Olympics were held in Stockholm.)) and ((Saturn is the 6th planet from the Sun.) or (128 is an odd number.)))
B. not not (not not ((14 - -7) <= (4 * -13)))
C. not not (((210 is a perfect square.) or ((-3 * 5 * 5 * -7) == (27 % 3))) or (((-6 - -18) <= (4 ** 3) <= (2 ** 3)) and ((4 * 1 + 3 * -5) > (-14 * 14))))
D. ((((10 * -5 - 9 * 10) == (-15 + 1)) and ((-10 * -9 - -6 * -5) >= (-3 + -17))) or (not ((14 - -11) < (13 + 14)))) and (not not (The capital of Brazil is Brasilia.))
E. not ((-14 * -20) != (9 - 4))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 20850894,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. ((-2 * -8 * 6 * -4) != (9 * -4 * 5 * 7)) or (((The 1964 Olympics were held in Tokyo.) or (The 1936 Olympics were held in Stockholm.)) and ((Saturn is the 6th planet from the Sun.) or (128 is an odd number.)))\nB. not not (not not ((14 - -7) <= (4 * -13)))\nC. not not (((210 is a perfect square.) or ((-3 * 5 * 5 * -7) == (27 % 3))) or (((-6 - -18) <= (4 ** 3) <= (2 ** 3)) and ((4 * 1 + 3 * -5) > (-14 * 14))))\nD. ((((10 * -5 - 9 * 10) == (-15 + 1)) and ((-10 * -9 - -6 * -5) >= (-3 + -17))) or (not ((14 - -11) < (13 + 14)))) and (not not (The capital of Brazil is Brasilia.))\nE. not ((-14 * -20) != (9 - 4))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 20850894,
"true_count": 1
},
"seed": 20850894,
"task_id": 620850894,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((((尼日利亚位于非洲。) and ((-13 - 8) >= (-8 + 4))) and ((1936年奥运会在伦敦举办。) or (1948年奥运会在伦敦举办。))) or ((智利的货币是比索。) or ((钾的化学符号是Ag。) or (芬兰的首都是布加勒斯特。)))) or (((not ((48 % 2) != (-12 + -15))) or (((14 * -3) >= (12 + -18)) or (瑞士的货币是人民币。))) or ((10 % 1) <= (18 * 9)))
B. not not ((not not (埃及位于非洲。)) or (铬的化学符号是Cr。))
C. not not (not not ((5 ** 2) >= (6 + 6)))
D. not not (((not not (闪电不会两次击中同一个地方。)) or ((18 - 4) < (10 - -18) < (8 * 17))) and ((((-12 + 4) >= (6 - -6)) and (第二次世界大战结束发生在1945年。)) and (鳄鱼是昆虫。)))
E. ((((2 ** 3) >= (45 % 8)) or (美国宣布独立发生在1781年。)) and ((氧的化学符号是O。) and (1932年奥运会在雅典举办。))) or (not (蜜蜂是昆虫。))
F. (((-6 * -8 - 9 * -9) <= (0 * -8 - -2 * -5)) and (((4 * 7 * 1 * 9) > (-19 * -16)) and (not not ((0 + -2) >= (10 + 6))))) and ((冰的密度比液态水小。) or (((-8 + 17) > (15 - 20)) or (泰坦尼克号沉没发生在1913年。))) and ((美国位于大洋洲。) and ((((5 ** 3) > (0 * -9)) and ((18 * 10) != (5 ** 3))) and (((15 % 1) > (-8 * 9 - 9 * 5)) or (1928年奥运会在首尔举办。))))
G. not not ((((7 * -12) <= (14 + 6)) and (德国位于南极洲。)) or ((14 * 9) > (13 * 6)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B,C,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 47794496,
"true_count": 4
},
"question": "检验这些表达式：\n\nA. ((((尼日利亚位于非洲。) and ((-13 - 8) >= (-8 + 4))) and ((1936年奥运会在伦敦举办。) or (1948年奥运会在伦敦举办。))) or ((智利的货币是比索。) or ((钾的化学符号是Ag。) or (芬兰的首都是布加勒斯特。)))) or (((not ((48 % 2) != (-12 + -15))) or (((14 * -3) >= (12 + -18)) or (瑞士的货币是人民币。))) or ((10 % 1) <= (18 * 9)))\nB. not not ((not not (埃及位于非洲。)) or (铬的化学符号是Cr。))\nC. not not (not not ((5 ** 2) >= (6 + 6)))\nD. not not (((not not (闪电不会两次击中同一个地方。)) or ((18 - 4) < (10 - -18) < (8 * 17))) and ((((-12 + 4) >= (6 - -6)) and (第二次世界大战结束发生在1945年。)) and (鳄鱼是昆虫。)))\nE. ((((2 ** 3) >= (45 % 8)) or (美国宣布独立发生在1781年。)) and ((氧的化学符号是O。) and (1932年奥运会在雅典举办。))) or (not (蜜蜂是昆虫。))\nF. (((-6 * -8 - 9 * -9) <= (0 * -8 - -2 * -5)) and (((4 * 7 * 1 * 9) > (-19 * -16)) and (not not ((0 + -2) >= (10 + 6))))) and ((冰的密度比液态水小。) or (((-8 + 17) > (15 - 20)) or (泰坦尼克号沉没发生在1913年。))) and ((美国位于大洋洲。) and ((((5 ** 3) > (0 * -9)) and ((18 * 10) != (5 ** 3))) and (((15 % 1) > (-8 * 9 - 9 * 5)) or (1928年奥运会在首尔举办。))))\nG. not not ((((7 * -12) <= (14 + 6)) and (德国位于南极洲。)) or ((14 * 9) > (13 * 6)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 7,
"seed": 47794496,
"true_count": 4
},
"seed": 47794496,
"task_id": 647794496,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not (((The capital of Poland is Warsaw.) or (((A cat has 4 legs.) or ((8 * -12) == (-3 * 16))) and (Brazil is in South America.))) and (not not ((-19 * 9) > (9 - -17))))
B. not (not (not not (((Venus is the 1st planet from the Sun.) or (The currency of China is the Rupee.)) and (((14 - -14) <= (-7 + 7)) or (The currency of Egypt is the Baht.)))))
C. not ((((A snake has 0 legs.) or (not not (The currency of Argentina is the Peso.))) and (not (Light travels faster than sound.)) and ((not not ((19 + -12) <= (7 + -13))) or ((There are 31 days in April.) or ((19 % 2) != (3 ** 3))))) and ((Plants produce oxygen through photosynthesis.) and ((The chemical symbol for Chlorine is Zn.) and (((8 * -5 - 9 * 0) <= (5 ** 2) <= (5 ** 3)) and (A rabbit is a bird.)))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 65043845,
"true_count": 2
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not (((The capital of Poland is Warsaw.) or (((A cat has 4 legs.) or ((8 * -12) == (-3 * 16))) and (Brazil is in South America.))) and (not not ((-19 * 9) > (9 - -17))))\nB. not (not (not not (((Venus is the 1st planet from the Sun.) or (The currency of China is the Rupee.)) and (((14 - -14) <= (-7 + 7)) or (The currency of Egypt is the Baht.)))))\nC. not ((((A snake has 0 legs.) or (not not (The currency of Argentina is the Peso.))) and (not (Light travels faster than sound.)) and ((not not ((19 + -12) <= (7 + -13))) or ((There are 31 days in April.) or ((19 % 2) != (3 ** 3))))) and ((Plants produce oxygen through photosynthesis.) and ((The chemical symbol for Chlorine is Zn.) and (((8 * -5 - 9 * 0) <= (5 ** 2) <= (5 ** 3)) and (A rabbit is a bird.)))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 65043845,
"true_count": 2
},
"seed": 65043845,
"task_id": 665043845,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (not (((木星是距离太阳第5近的行星。) or (not not ((4 ** 2) != (-7 * 8 * -2 * 7)))) and ((((16 - -9) < (8 + -12) < (-2 - -7)) or ((8 * 0 - -2 * 1) < (-5 * -8 * -6 * -2))) and (not (279是完全平方数。))))) or ((((((6 * 0 * 3 * 5) > (-5 * 7 + -2 * -5)) and (第一次世界大战开始发生在1924年。)) or ((-13 - 16) != (7 - -4))) and (((铅的化学符号是Na。) or ((2 ** 3) >= (20 + -6))) or (柏林墙倒塌发生在1989年。))) or (((声音无法在真空中传播。) and (美国宣布独立发生在1774年。)) and (not not (乌鸦是鸟类。))) or (((13 + -3) != (19 * -11)) and (日本位于南美洲。)))
B. (((not not (((21 % 8) > (-3 * -5 + -10 * -2)) and ((13 % 8) == (10 + -4)))) or (2008年奥运会在雅典举办。)) and ((月球自己发光。) and (((九月有30天。) and ((-11 + 13) < (39 % 1))) or (not not ((27 % 9) == (-11 - 5)))))) or ((((not (145是奇数。)) and (((37 % 9) > (16 + 6)) and ((0 - -14) >= (2 - -8)))) and ((鲨鱼是鱼类。) and ((1 % 10) <= (8 % 6))) and (not (not (木头在常温下是固体。)))) or (not (not ((铅的化学符号是S。) and ((-17 + -3) < (8 - 4) < (-5 + 0))))))
C. (not not ((第二次世界大战开始发生在1929年。) and (not (((11 - 11) < (0 * 11) < (42 % 5)) or ((0 * 17) == (-2 * -9 + 5 * 8)))))) and ((not not (((-5 * -1 + -1 * 8) == (6 * 2 + 7 * 2)) and (1900年奥运会在伦敦举办。))) or (not (not ((三月有31天。) or ((-18 + 11) <= (-3 + 7))))))
D. not (not not ((not (((1 ** 3) > (20 - -7)) and ((14 % 10) <= (15 - -18)))) or ((日本的货币是日元。) or (not (1964年奥运会在东京举办。)))))
E. (((not not (1972年奥运会在慕尼黑举办。)) and ((27 % 9) > (-7 * -3 + 7 * 6))) or ((((泰坦尼克号沉没发生在1912年。) and (泰国位于南美洲。)) or (意大利位于南美洲。)) and ((-8 * -12) <= (-4 * 1 - -5 * 8)))) and ((not not (((-17 - -13) < (-6 - 4)) or (not not (十月有31天。)))) and ((((2 ** 2) <= (9 - -10) <= (2 - 7)) or (not not ((0 * 3) == (-13 - -16)))) or (二月有29天。)))
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": 5,
"language": "cn",
"num_options": 5,
"seed": 95447752,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. (not (((木星是距离太阳第5近的行星。) or (not not ((4 ** 2) != (-7 * 8 * -2 * 7)))) and ((((16 - -9) < (8 + -12) < (-2 - -7)) or ((8 * 0 - -2 * 1) < (-5 * -8 * -6 * -2))) and (not (279是完全平方数。))))) or ((((((6 * 0 * 3 * 5) > (-5 * 7 + -2 * -5)) and (第一次世界大战开始发生在1924年。)) or ((-13 - 16) != (7 - -4))) and (((铅的化学符号是Na。) or ((2 ** 3) >= (20 + -6))) or (柏林墙倒塌发生在1989年。))) or (((声音无法在真空中传播。) and (美国宣布独立发生在1774年。)) and (not not (乌鸦是鸟类。))) or (((13 + -3) != (19 * -11)) and (日本位于南美洲。)))\nB. (((not not (((21 % 8) > (-3 * -5 + -10 * -2)) and ((13 % 8) == (10 + -4)))) or (2008年奥运会在雅典举办。)) and ((月球自己发光。) and (((九月有30天。) and ((-11 + 13) < (39 % 1))) or (not not ((27 % 9) == (-11 - 5)))))) or ((((not (145是奇数。)) and (((37 % 9) > (16 + 6)) and ((0 - -14) >= (2 - -8)))) and ((鲨鱼是鱼类。) and ((1 % 10) <= (8 % 6))) and (not (not (木头在常温下是固体。)))) or (not (not ((铅的化学符号是S。) and ((-17 + -3) < (8 - 4) < (-5 + 0))))))\nC. (not not ((第二次世界大战开始发生在1929年。) and (not (((11 - 11) < (0 * 11) < (42 % 5)) or ((0 * 17) == (-2 * -9 + 5 * 8)))))) and ((not not (((-5 * -1 + -1 * 8) == (6 * 2 + 7 * 2)) and (1900年奥运会在伦敦举办。))) or (not (not ((三月有31天。) or ((-18 + 11) <= (-3 + 7))))))\nD. not (not not ((not (((1 ** 3) > (20 - -7)) and ((14 % 10) <= (15 - -18)))) or ((日本的货币是日元。) or (not (1964年奥运会在东京举办。)))))\nE. (((not not (1972年奥运会在慕尼黑举办。)) and ((27 % 9) > (-7 * -3 + 7 * 6))) or ((((泰坦尼克号沉没发生在1912年。) and (泰国位于南美洲。)) or (意大利位于南美洲。)) and ((-8 * -12) <= (-4 * 1 - -5 * 8)))) and ((not not (((-17 - -13) < (-6 - 4)) or (not not (十月有31天。)))) and ((((2 ** 2) <= (9 - -10) <= (2 - 7)) or (not not ((0 * 3) == (-13 - -16)))) or (二月有29天。)))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 95447752,
"true_count": 1
},
"seed": 95447752,
"task_id": 695447752,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (-1 * -9 * 1 * -6) <= (4 * -8 - -6 * 9)
B. not not (((18 + 13) == (13 + -18)) or ((4 - 1) >= (11 * 18)))
C. (0 * -6) >= (1 ** 1)
D. (not (现代奥运会首届举办发生在1898年。)) and ((7 - 18) <= (-9 * 7 * -7 * -6))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 15497131,
"true_count": 1
},
"question": "检验这些表达式：\n\nA. (-1 * -9 * 1 * -6) <= (4 * -8 - -6 * 9)\nB. not not (((18 + 13) == (13 + -18)) or ((4 - 1) >= (11 * 18)))\nC. (0 * -6) >= (1 ** 1)\nD. (not (现代奥运会首届举办发生在1898年。)) and ((7 - 18) <= (-9 * 7 * -7 * -6))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 15497131,
"true_count": 1
},
"seed": 15497131,
"task_id": 615497131,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (((((人类首次登月发生在1967年。) and (土星是距离太阳第6近的行星。)) and (((-16 + 18) > (-18 + -8)) or (1988年奥运会在首尔举办。))) or (((秘鲁的货币是索尔。) and ((-2 + 6) >= (6 - -7))) or ((1 ** 1) != (6 * 0)))) and (蜘蛛是昆虫。) and (not ((not not (大象有0条腿。)) or (铁在常温下是固体。)))) and (not not ((银在常温下是固体。) and ((-10 * -18) <= (-9 - -5))))
B. (((西班牙位于欧洲。) or ((not not (太阳绕地球运转。)) and (not not (2012年奥运会在伦敦举办。)))) and (not not (853是斐波那契数。))) and ((((((3 % 7) > (6 - -14)) or ((12 * 12) > (3 ** 2))) and (企鹅是鸟类。)) and ((((30 % 1) < (-7 * 2 - 5 * 3) < (12 + -6)) and (蟑螂是鱼类。)) and ((捷克的首都是墨西哥城。) or (2012年奥运会在伦敦举办。)))) or (not not (((西班牙的首都是马德里。) or ((-6 + 9) != (-14 * -7))) or ((20 * -16) >= (-3 - -7)))))
C. not ((not ((越南位于大洋洲。) and ((印度尼西亚的首都是首尔。) and ((-13 + -6) == (7 * 9 + -4 * 7))))) or ((金的化学符号是Au。) or (not (柏林墙倒塌发生在1989年。)) or ((((1 ** 2) < (3 ** 3)) or (人类有100条腿。)) or ((1952年奥运会在赫尔辛基举办。) and (日本的货币是日元。)))))
D. (((((加拿大位于大洋洲。) and ((1 ** 1) <= (-10 * 2 - -8 * 0))) or ((1908年是闰年。) or (第一部iPhone发布发生在2007年。))) or (((4 ** 3) <= (-2 - 14)) or (俄罗斯的货币是美元。)) or ((not not ((-16 * -7) <= (12 - 7))) or (伦敦大火发生在1666年。))) or ((中国位于亚洲。) or ((-15 * 18) >= (-5 * -4 + 1 * 1)))) or ((鳕鱼是鱼类。) or ((猫有4条腿。) or ((-9 + -13) == (-12 * 18)))) or (not (((印度位于亚洲。) and (((23 % 1) != (-1 + -4)) or (乌龟是哺乳动物。))) and (not not ((17 * -12) >= (-3 * 20)))))
E. ((((14 - 12) >= (-19 + 2)) and (((8 % 4) < (-8 * -3 * 5 * 8)) or (not not (1952年奥运会在赫尔辛基举办。)))) and (not (螃蟹有10条腿。))) or ((((not ((47 % 3) < (3 ** 3) < (14 * 13))) or (木头在常温下是固体。)) or ((13 * 12) <= (4 * 5 - -9 * -2) <= (0 - 16))) or (not (not ((铁在常温下是气体。) and (波兰的货币是兹罗提。)))))
F. not (not not (not (((韩国的首都是首尔。) and (金在常温下是固体。)) and (((4 + 18) < (15 * -11) < (-7 - -17)) and ((-4 + -1) != (-16 - -16))))))
G. not ((not not (not (一月有31天。))) or (((人类有10条腿。) or ((-6 * 8 + -2 * 7) > (-10 + 6))) and ((((-10 - 8) == (10 * 1 - -7 * 5)) or (尼日利亚的货币是奈拉。)) or ((1 * -6 * 3 * 1) >= (-7 * 7 - 5 * -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": "D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 84211843,
"true_count": 3
},
"question": "研究以下逻辑语句：\n\nA. (((((人类首次登月发生在1967年。) and (土星是距离太阳第6近的行星。)) and (((-16 + 18) > (-18 + -8)) or (1988年奥运会在首尔举办。))) or (((秘鲁的货币是索尔。) and ((-2 + 6) >= (6 - -7))) or ((1 ** 1) != (6 * 0)))) and (蜘蛛是昆虫。) and (not ((not not (大象有0条腿。)) or (铁在常温下是固体。)))) and (not not ((银在常温下是固体。) and ((-10 * -18) <= (-9 - -5))))\nB. (((西班牙位于欧洲。) or ((not not (太阳绕地球运转。)) and (not not (2012年奥运会在伦敦举办。)))) and (not not (853是斐波那契数。))) and ((((((3 % 7) > (6 - -14)) or ((12 * 12) > (3 ** 2))) and (企鹅是鸟类。)) and ((((30 % 1) < (-7 * 2 - 5 * 3) < (12 + -6)) and (蟑螂是鱼类。)) and ((捷克的首都是墨西哥城。) or (2012年奥运会在伦敦举办。)))) or (not not (((西班牙的首都是马德里。) or ((-6 + 9) != (-14 * -7))) or ((20 * -16) >= (-3 - -7)))))\nC. not ((not ((越南位于大洋洲。) and ((印度尼西亚的首都是首尔。) and ((-13 + -6) == (7 * 9 + -4 * 7))))) or ((金的化学符号是Au。) or (not (柏林墙倒塌发生在1989年。)) or ((((1 ** 2) < (3 ** 3)) or (人类有100条腿。)) or ((1952年奥运会在赫尔辛基举办。) and (日本的货币是日元。)))))\nD. (((((加拿大位于大洋洲。) and ((1 ** 1) <= (-10 * 2 - -8 * 0))) or ((1908年是闰年。) or (第一部iPhone发布发生在2007年。))) or (((4 ** 3) <= (-2 - 14)) or (俄罗斯的货币是美元。)) or ((not not ((-16 * -7) <= (12 - 7))) or (伦敦大火发生在1666年。))) or ((中国位于亚洲。) or ((-15 * 18) >= (-5 * -4 + 1 * 1)))) or ((鳕鱼是鱼类。) or ((猫有4条腿。) or ((-9 + -13) == (-12 * 18)))) or (not (((印度位于亚洲。) and (((23 % 1) != (-1 + -4)) or (乌龟是哺乳动物。))) and (not not ((17 * -12) >= (-3 * 20)))))\nE. ((((14 - 12) >= (-19 + 2)) and (((8 % 4) < (-8 * -3 * 5 * 8)) or (not not (1952年奥运会在赫尔辛基举办。)))) and (not (螃蟹有10条腿。))) or ((((not ((47 % 3) < (3 ** 3) < (14 * 13))) or (木头在常温下是固体。)) or ((13 * 12) <= (4 * 5 - -9 * -2) <= (0 - 16))) or (not (not ((铁在常温下是气体。) and (波兰的货币是兹罗提。)))))\nF. not (not not (not (((韩国的首都是首尔。) and (金在常温下是固体。)) and (((4 + 18) < (15 * -11) < (-7 - -17)) and ((-4 + -1) != (-16 - -16))))))\nG. not ((not not (not (一月有31天。))) or (((人类有10条腿。) or ((-6 * 8 + -2 * 7) > (-10 + 6))) and ((((-10 - 8) == (10 * 1 - -7 * 5)) or (尼日利亚的货币是奈拉。)) or ((1 * -6 * 3 * 1) >= (-7 * 7 - 5 * -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": 5,
"language": "cn",
"num_options": 7,
"seed": 84211843,
"true_count": 3
},
"seed": 84211843,
"task_id": 684211843,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not not (not not (63 is an odd number.)))
B. (not not ((The chemical symbol for Hydrogen is Cr.) and ((5 * 0) < (-3 * -5 * -4 * -7) < (-6 * 14)))) or ((Russia is in Europe.) or (2083 is a leap year.))
C. not not (((Steam is a liquid at room temperature.) or (The capital of Norway is Dublin.)) and ((Canada is in Africa.) or ((14 % 7) >= (-11 + 20))))
D. ((France is in Europe.) or (((3 * 8 * 7 * -4) > (-19 + -8)) and ((8 + 19) > (-3 * -9)))) and (not not (((-7 - -19) < (9 % 10)) and ((11 * -6) >= (1 ** 2))))
E. not not (not not ((The currency of Brazil is the Real.) or (Helium is a gas at room temperature.)))
F. ((((-7 - 2) <= (1 ** 3)) and ((13 - -6) > (15 - 4))) or (((3 ** 1) == (-4 * -5 * -1 * 1)) or ((-3 - -6) == (4 ** 3)))) or ((-15 - 0) == (-3 * 1 - 9 * 8))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "B,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 9024768,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not (not not (not not (63 is an odd number.)))\nB. (not not ((The chemical symbol for Hydrogen is Cr.) and ((5 * 0) < (-3 * -5 * -4 * -7) < (-6 * 14)))) or ((Russia is in Europe.) or (2083 is a leap year.))\nC. not not (((Steam is a liquid at room temperature.) or (The capital of Norway is Dublin.)) and ((Canada is in Africa.) or ((14 % 7) >= (-11 + 20))))\nD. ((France is in Europe.) or (((3 * 8 * 7 * -4) > (-19 + -8)) and ((8 + 19) > (-3 * -9)))) and (not not (((-7 - -19) < (9 % 10)) and ((11 * -6) >= (1 ** 2))))\nE. not not (not not ((The currency of Brazil is the Real.) or (Helium is a gas at room temperature.)))\nF. ((((-7 - 2) <= (1 ** 3)) and ((13 - -6) > (15 - 4))) or (((3 ** 1) == (-4 * -5 * -1 * 1)) or ((-3 - -6) == (4 ** 3)))) or ((-15 - 0) == (-3 * 1 - 9 * 8))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 9024768,
"true_count": 3
},
"seed": 9024768,
"task_id": 609024768,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not ((-14 - 20) == (3 * -3 * 5 * 5))
B. ((-4 * -11) < (5 * -10 - 7 * -2)) or ((-10 * 10 + 1 * 4) != (0 * -10 * 9 * 0))
C. (((12 + -4) == (-19 - -14)) or ((3 * 12) >= (18 % 4))) and ((The capital of Japan is Moscow.) or (2038 is a leap year.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 87542165,
"true_count": 1
},
"question": "Examine these expressions:\n\nA. not not ((-14 - 20) == (3 * -3 * 5 * 5))\nB. ((-4 * -11) < (5 * -10 - 7 * -2)) or ((-10 * 10 + 1 * 4) != (0 * -10 * 9 * 0))\nC. (((12 + -4) == (-19 - -14)) or ((3 * 12) >= (18 % 4))) and ((The capital of Japan is Moscow.) or (2038 is a leap year.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 87542165,
"true_count": 1
},
"seed": 87542165,
"task_id": 687542165,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. (not (The human body has 206 bones.)) or ((not not (not not (76 is less than or equal to 37.))) or (((-8 * 19) <= (10 * -4) <= (18 - 9)) or (((7 * -2 + 8 * -4) != (4 * -2 - 2 * 3)) and ((-9 * -18) < (-4 * 5 + 6 * -3)))))
B. ((not not (Silver is a liquid at room temperature.)) and ((20 % 1) > (-19 - 6))) or ((((-2 * -11) >= (7 + -12)) and ((-7 * 12) <= (-12 - 10))) or (The currency of Colombia is the Zloty.)) or (((not ((-15 - 10) != (1 ** 2))) or ((-15 - -17) < (-12 * 13))) or (((2 ** 3) >= (2 + -10)) or (((3 - -11) <= (-1 * -4 * 3 * 0) <= (4 ** 3)) or (Lightning never strikes the same place twice.))))
C. not not ((not ((The 1908 Olympics were held in Munich.) or ((24 % 4) <= (-6 + -17) <= (-20 + -15)))) or ((6 * -2 + -6 * 10) <= (50 % 10)))
D. (not (Christopher Columbus reached America occurred in 1492.)) and ((not not (15 is divisible by 4.)) or (((-5 - 2) != (-7 + -18)) and (Iron is a solid at room temperature.))) and (not not (not ((The chemical symbol for Zinc is N.) and (The chemical symbol for Uranium is U.))))
E. ((((18 + 10) != (-2 * 17)) or ((Helium is a gas at room temperature.) and (405 is a Fibonacci number.))) or (not (Spiders are insects.)) or ((The capital of Romania is Bucharest.) and (((29 % 2) <= (17 + 6)) or (A crab has 2 legs.)))) or (not ((4 ** 1) != (10 * 0 * 3 * -9)))
F. not not (((((17 * 14) > (12 % 10)) and ((4 ** 1) > (0 * 3 + -9 * -7))) or ((-15 - 10) == (3 - -9))) or ((The capital of Norway is Dublin.) or (A chicken is a bird.)) or (((-8 - 4) != (-20 * 20)) and ((The chemical symbol for Platinum is Pt.) or (The 1912 Olympics were held in Berlin.))))
G. not (not ((((6 * 4 - -4 * 10) > (8 * 7 - -4 * -5)) and ((11 + -17) <= (-8 + 6))) or (((-17 - -8) != (5 + 1)) and ((4 ** 3) >= (-2 + 3)))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 27565449,
"true_count": 6
},
"question": "Examine these expressions:\n\nA. (not (The human body has 206 bones.)) or ((not not (not not (76 is less than or equal to 37.))) or (((-8 * 19) <= (10 * -4) <= (18 - 9)) or (((7 * -2 + 8 * -4) != (4 * -2 - 2 * 3)) and ((-9 * -18) < (-4 * 5 + 6 * -3)))))\nB. ((not not (Silver is a liquid at room temperature.)) and ((20 % 1) > (-19 - 6))) or ((((-2 * -11) >= (7 + -12)) and ((-7 * 12) <= (-12 - 10))) or (The currency of Colombia is the Zloty.)) or (((not ((-15 - 10) != (1 ** 2))) or ((-15 - -17) < (-12 * 13))) or (((2 ** 3) >= (2 + -10)) or (((3 - -11) <= (-1 * -4 * 3 * 0) <= (4 ** 3)) or (Lightning never strikes the same place twice.))))\nC. not not ((not ((The 1908 Olympics were held in Munich.) or ((24 % 4) <= (-6 + -17) <= (-20 + -15)))) or ((6 * -2 + -6 * 10) <= (50 % 10)))\nD. (not (Christopher Columbus reached America occurred in 1492.)) and ((not not (15 is divisible by 4.)) or (((-5 - 2) != (-7 + -18)) and (Iron is a solid at room temperature.))) and (not not (not ((The chemical symbol for Zinc is N.) and (The chemical symbol for Uranium is U.))))\nE. ((((18 + 10) != (-2 * 17)) or ((Helium is a gas at room temperature.) and (405 is a Fibonacci number.))) or (not (Spiders are insects.)) or ((The capital of Romania is Bucharest.) and (((29 % 2) <= (17 + 6)) or (A crab has 2 legs.)))) or (not ((4 ** 1) != (10 * 0 * 3 * -9)))\nF. not not (((((17 * 14) > (12 % 10)) and ((4 ** 1) > (0 * 3 + -9 * -7))) or ((-15 - 10) == (3 - -9))) or ((The capital of Norway is Dublin.) or (A chicken is a bird.)) or (((-8 - 4) != (-20 * 20)) and ((The chemical symbol for Platinum is Pt.) or (The 1912 Olympics were held in Berlin.))))\nG. not (not ((((6 * 4 - -4 * 10) > (8 * 7 - -4 * -5)) and ((11 + -17) <= (-8 + 6))) or (((-17 - -8) != (5 + 1)) and ((4 ** 3) >= (-2 + 3)))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 27565449,
"true_count": 6
},
"seed": 27565449,
"task_id": 627565449,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((-9 * 10 * 0 * 3) < (-2 + 13) < (-3 * -8)) or (((19 + 16) != (-10 * 10)) and (Mars is the 4th planet from the Sun.)) or ((((-19 * -17) >= (-20 * -4)) and ((-17 - 8) >= (28 % 5))) or (((17 + 11) >= (18 - 15)) or ((-3 * 0 - 5 * 3) <= (5 * -5))))
B. ((((13 + -19) <= (17 * 18) <= (-20 + 11)) or (The 2012 Olympics were held in Paris.)) or (not (The chemical symbol for Sulfur is Cl.))) or (((2084 is a leap year.) and (Copper is a solid at room temperature.)) and (not ((9 * -8) != (-20 * 0))))
C. not ((((10 * -5 - -8 * -1) >= (4 * 4 - -9 * 6)) and (The currency of Malaysia is the Ringgit.)) and ((Diamond is a solid at room temperature.) or ((-3 * 2 * -10 * 8) <= (12 * -16) <= (-5 + 14))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 41989421,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. ((-9 * 10 * 0 * 3) < (-2 + 13) < (-3 * -8)) or (((19 + 16) != (-10 * 10)) and (Mars is the 4th planet from the Sun.)) or ((((-19 * -17) >= (-20 * -4)) and ((-17 - 8) >= (28 % 5))) or (((17 + 11) >= (18 - 15)) or ((-3 * 0 - 5 * 3) <= (5 * -5))))\nB. ((((13 + -19) <= (17 * 18) <= (-20 + 11)) or (The 2012 Olympics were held in Paris.)) or (not (The chemical symbol for Sulfur is Cl.))) or (((2084 is a leap year.) and (Copper is a solid at room temperature.)) and (not ((9 * -8) != (-20 * 0))))\nC. not ((((10 * -5 - -8 * -1) >= (4 * 4 - -9 * 6)) and (The currency of Malaysia is the Ringgit.)) and ((Diamond is a solid at room temperature.) or ((-3 * 2 * -10 * 8) <= (12 * -16) <= (-5 + 14))))\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": 41989421,
"true_count": 3
},
"seed": 41989421,
"task_id": 641989421,
"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. ((((((34 % 10) == (0 - 13)) and ((-1 * 18) <= (33 % 6))) or ((二月有30天。) or ((8 * 3 - 9 * 7) < (-8 * -4 + 1 * -8)))) and ((2 ** 2) != (2 * -8 - -9 * -9))) and (not not (((企鹅是鱼类。) and ((-8 * 17) <= (1 ** 2))) and (氮的化学符号是N。)))) and ((狮子是哺乳动物。) or (日本的货币是比索。)) and ((((((8 + -17) >= (7 * 14)) or ((-16 + -10) > (-15 * -18))) and (not (锌的化学符号是Cl。))) or (not ((18 + -6) < (20 * -13)))) or (((21 % 6) < (-11 - -2) < (1 * 4 * -10 * 9)) and ((9 * -5 - -3 * 7) != (-10 + 17))))
B. not (((鸭子有6条腿。) and (金鱼是鱼类。)) or (((1907年是闰年。) or ((-10 * 0 + -3 * -5) < (8 * 16))) and (一月有30天。) and ((((16 - 6) > (3 - -14)) and ((6 * -8) >= (13 + 10))) or ((空气在常温下是气体。) or ((-9 * 4) >= (19 - -20))))))
C. (not ((冰的密度比液态水小。) or ((意大利的首都是罗马。) and ((钻石由碳元素组成。) or ((38 % 5) >= (1 ** 3)))))) or ((((9 * -10 - -1 * 10) > (48 % 6)) and (((8 + 2) > (14 % 6)) or ((-4 * -14) < (-10 + 11) < (-19 + -8))) and (((铜的化学符号是Cu。) or (1984年奥运会在洛杉矶举办。)) and ((49的平方根是5。) and (苏联解体发生在1991年。)))) or (not ((13 % 1) <= (-18 + 12))))
D. ((not not ((2045年是闰年。) and (((18 - -14) <= (9 * -10 - 6 * -10) <= (8 + -10)) or (光速比声速快。)))) or ((20小于等于63。) or (((-7 * 10 * 4 * -4) < (16 - -13) < (-9 * 10 - -3 * -3)) and ((-7 * -7) < (-10 * -1 + 7 * 2))))) or (((not (367是完全平方数。)) or ((木星是距离太阳第5近的行星。) and ((12 + 15) != (7 * 16)))) and (not not ((((10 - -3) <= (-12 + 13)) and (电流比光速更快。)) or ((土星是距离太阳第6近的行星。) or (地球是距离太阳第6近的行星。)))))
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": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 25487766,
"true_count": 3
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. ((((((34 % 10) == (0 - 13)) and ((-1 * 18) <= (33 % 6))) or ((二月有30天。) or ((8 * 3 - 9 * 7) < (-8 * -4 + 1 * -8)))) and ((2 ** 2) != (2 * -8 - -9 * -9))) and (not not (((企鹅是鱼类。) and ((-8 * 17) <= (1 ** 2))) and (氮的化学符号是N。)))) and ((狮子是哺乳动物。) or (日本的货币是比索。)) and ((((((8 + -17) >= (7 * 14)) or ((-16 + -10) > (-15 * -18))) and (not (锌的化学符号是Cl。))) or (not ((18 + -6) < (20 * -13)))) or (((21 % 6) < (-11 - -2) < (1 * 4 * -10 * 9)) and ((9 * -5 - -3 * 7) != (-10 + 17))))\nB. not (((鸭子有6条腿。) and (金鱼是鱼类。)) or (((1907年是闰年。) or ((-10 * 0 + -3 * -5) < (8 * 16))) and (一月有30天。) and ((((16 - 6) > (3 - -14)) and ((6 * -8) >= (13 + 10))) or ((空气在常温下是气体。) or ((-9 * 4) >= (19 - -20))))))\nC. (not ((冰的密度比液态水小。) or ((意大利的首都是罗马。) and ((钻石由碳元素组成。) or ((38 % 5) >= (1 ** 3)))))) or ((((9 * -10 - -1 * 10) > (48 % 6)) and (((8 + 2) > (14 % 6)) or ((-4 * -14) < (-10 + 11) < (-19 + -8))) and (((铜的化学符号是Cu。) or (1984年奥运会在洛杉矶举办。)) and ((49的平方根是5。) and (苏联解体发生在1991年。)))) or (not ((13 % 1) <= (-18 + 12))))\nD. ((not not ((2045年是闰年。) and (((18 - -14) <= (9 * -10 - 6 * -10) <= (8 + -10)) or (光速比声速快。)))) or ((20小于等于63。) or (((-7 * 10 * 4 * -4) < (16 - -13) < (-9 * 10 - -3 * -3)) and ((-7 * -7) < (-10 * -1 + 7 * 2))))) or (((not (367是完全平方数。)) or ((木星是距离太阳第5近的行星。) and ((12 + 15) != (7 * 16)))) and (not not ((((10 - -3) <= (-12 + 13)) and (电流比光速更快。)) or ((土星是距离太阳第6近的行星。) or (地球是距离太阳第6近的行星。)))))\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": 5,
"language": "cn",
"num_options": 4,
"seed": 25487766,
"true_count": 3
},
"seed": 25487766,
"task_id": 625487766,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. ((17 * 8) <= (-4 * 2 - -5 * -4)) or (2017 is a leap year.)
B. not (Diamond is a solid at room temperature.)
C. ((-17 + 10) <= (-2 * -5 + 0 * -9)) and ((2 * 2) < (13 + 3)) and ((not ((5 ** 1) < (6 * 8 + -1 * -4))) or ((Mercury is the 1st planet from the Sun.) or ((11 % 10) != (-5 + -15))))
D. ((The capital of Belgium is Brussels.) and (Humans have five fingers on each hand.)) or ((((16 + 19) <= (5 ** 3) <= (-3 + 4)) and ((2 ** 2) == (10 * -5 + -3 * -10))) or (Venus is the 5th planet from the Sun.))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 94603336,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. ((17 * 8) <= (-4 * 2 - -5 * -4)) or (2017 is a leap year.)\nB. not (Diamond is a solid at room temperature.)\nC. ((-17 + 10) <= (-2 * -5 + 0 * -9)) and ((2 * 2) < (13 + 3)) and ((not ((5 ** 1) < (6 * 8 + -1 * -4))) or ((Mercury is the 1st planet from the Sun.) or ((11 % 10) != (-5 + -15))))\nD. ((The capital of Belgium is Brussels.) and (Humans have five fingers on each hand.)) or ((((16 + 19) <= (5 ** 3) <= (-3 + 4)) and ((2 ** 2) == (10 * -5 + -3 * -10))) or (Venus is the 5th planet from the Sun.))\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": 94603336,
"true_count": 2
},
"seed": 94603336,
"task_id": 694603336,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not (not not (not not ((-1 * 7 * 10 * -8) != (6 * -19))))
B. not ((((-3 * 9) < (-10 * 10 - -10 * 2)) and (哥伦比亚的首都是波哥大。)) and (氯的化学符号是Cl。))
C. ((((39 % 10) < (-4 * 10 - 7 * -5)) or ((5 * -1 * -10 * 5) < (4 ** 1))) and (not (闪电不会两次击中同一个地方。))) or (((222是完全平方数。) and (人类有2条腿。)) and (海王星是距离太阳第2近的行星。))
D. (((银在常温下是固体。) or ((15 + 7) != (3 * -7 - 0 * 3))) and (not not (水星是距离太阳第7近的行星。))) or (((鸡有2条腿。) and (墨西哥的货币是比索。)) and ((0 * 19) != (4 * -5 + 6 * 9)))
E. not not (not not (((-3 - 6) <= (3 + 3) <= (-13 * 17)) or ((3 * 7) >= (9 * -6))))
F. (冰在常温下是液体。) and (1977年是闰年。)
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": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 93689187,
"true_count": 3
},
"question": "给定以下布尔表达式：\n\nA. not (not not (not not ((-1 * 7 * 10 * -8) != (6 * -19))))\nB. not ((((-3 * 9) < (-10 * 10 - -10 * 2)) and (哥伦比亚的首都是波哥大。)) and (氯的化学符号是Cl。))\nC. ((((39 % 10) < (-4 * 10 - 7 * -5)) or ((5 * -1 * -10 * 5) < (4 ** 1))) and (not (闪电不会两次击中同一个地方。))) or (((222是完全平方数。) and (人类有2条腿。)) and (海王星是距离太阳第2近的行星。))\nD. (((银在常温下是固体。) or ((15 + 7) != (3 * -7 - 0 * 3))) and (not not (水星是距离太阳第7近的行星。))) or (((鸡有2条腿。) and (墨西哥的货币是比索。)) and ((0 * 19) != (4 * -5 + 6 * 9)))\nE. not not (not not (((-3 - 6) <= (3 + 3) <= (-13 * 17)) or ((3 * 7) >= (9 * -6))))\nF. (冰在常温下是液体。) and (1977年是闰年。)\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": 93689187,
"true_count": 3
},
"seed": 93689187,
"task_id": 693689187,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((not not ((海王星是距离太阳第8近的行星。) or (埃及的货币是泰铢。))) and ((1968年奥运会在墨西哥城举办。) or ((-4 * 18) == (-15 * -2))) and (((氢的化学符号是Sn。) or (银的化学符号是Hg。)) or ((2023年是闰年。) and ((15 + -8) <= (9 + 20))))) and (not (意大利的首都是拉巴特。)) and (not (银的化学符号是Ag。))) and (not (not not ((((17 * -14) > (-14 * -15)) and (硅的化学符号是Si。)) and (not (阿根廷位于南美洲。)))))
B. (((委内瑞拉的首都是新加坡。) and (not not (not not (俄罗斯位于欧洲。)))) or ((-14 - -7) <= (-8 + 19)) or ((水在常温下是液体。) and ((not (空气在常温下是气体。)) or (not not (植物通过光合作用产生氧气。))))) or (((not not (not not ((-15 - -12) < (-11 - -17) < (-20 - -9)))) or (not not ((-2 * -4 * 1 * 9) < (4 ** 3)))) or (not (锌的化学符号是Zn。)))
C. (((((-10 * 1 + -1 * -2) <= (-9 + 10)) or (((12 % 10) == (47 % 9)) or ((-2 * -4 * 8 * 1) != (-8 * -6 * 1 * 6)))) and ((((-2 - 19) > (-17 - 3)) or (193是偶数。)) or (((2 + 3) > (13 * -9)) or ((-16 + 5) != (-11 - -9))))) and (not ((加拿大的货币是欧元。) and ((285是完全平方数。) and ((-20 * 5) > (-6 * -6)))))) or (not (not not ((not not ((14 - 1) >= (0 + 7))) or ((32小于等于93。) or ((2 * 4 - -3 * -7) == (-10 * 2))))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 21821565,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. (((not not ((海王星是距离太阳第8近的行星。) or (埃及的货币是泰铢。))) and ((1968年奥运会在墨西哥城举办。) or ((-4 * 18) == (-15 * -2))) and (((氢的化学符号是Sn。) or (银的化学符号是Hg。)) or ((2023年是闰年。) and ((15 + -8) <= (9 + 20))))) and (not (意大利的首都是拉巴特。)) and (not (银的化学符号是Ag。))) and (not (not not ((((17 * -14) > (-14 * -15)) and (硅的化学符号是Si。)) and (not (阿根廷位于南美洲。)))))\nB. (((委内瑞拉的首都是新加坡。) and (not not (not not (俄罗斯位于欧洲。)))) or ((-14 - -7) <= (-8 + 19)) or ((水在常温下是液体。) and ((not (空气在常温下是气体。)) or (not not (植物通过光合作用产生氧气。))))) or (((not not (not not ((-15 - -12) < (-11 - -17) < (-20 - -9)))) or (not not ((-2 * -4 * 1 * 9) < (4 ** 3)))) or (not (锌的化学符号是Zn。)))\nC. (((((-10 * 1 + -1 * -2) <= (-9 + 10)) or (((12 % 10) == (47 % 9)) or ((-2 * -4 * 8 * 1) != (-8 * -6 * 1 * 6)))) and ((((-2 - 19) > (-17 - 3)) or (193是偶数。)) or (((2 + 3) > (13 * -9)) or ((-16 + 5) != (-11 - -9))))) and (not ((加拿大的货币是欧元。) and ((285是完全平方数。) and ((-20 * 5) > (-6 * -6)))))) or (not (not not ((not not ((14 - 1) >= (0 + 7))) or ((32小于等于93。) or ((2 * 4 - -3 * -7) == (-10 * 2))))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 21821565,
"true_count": 2
},
"seed": 21821565,
"task_id": 621821565,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not not (not not (((Ice is less dense than liquid water.) and (The first Olympic Games of modern era occurred in 1896.)) or (The United States declared independence occurred in 1776.)))
B. ((((The currency of Nigeria is the Real.) or (Humans only use 10% of their brain.)) and (((5 + -7) > (8 * -7)) and ((26 % 8) < (2 - -16) < (38 % 10)))) and ((((4 % 3) >= (15 % 4)) and ((10 + -17) >= (14 * 0))) and (2005 is a leap year.))) and ((not (((6 * -8 - -4 * 10) == (6 * -4 - -3 * 2)) and (The chemical symbol for Platinum is Pb.))) and ((41 % 8) > (1 * 8 * 2 * -7)))
C. (((Oxygen is a solid at room temperature.) or (not not ((6 * -5) != (8 - -14)))) or ((-4 * 14) < (0 * -13) < (-3 + -6)) or ((50 % 6) == (10 * 5 + -8 * -6))) and (not ((The chemical symbol for Iron is Fe.) and ((-6 + -16) < (5 * -1))))
D. (not (((Sharks are mammals.) or ((-4 * 8) < (4 ** 3) < (16 + 7))) and (((-14 + 11) >= (13 - -6)) and (The currency of Peru is the Peso.)))) and (((-7 * 1) == (1 * 2 * 3 * -9)) or ((There are 30 days in June.) and ((5 + 1) != (-3 * 1 - 1 * -10))) or (((Copper is a solid at room temperature.) or (The capital of Brazil is Lima.)) and (not not ((-4 * 6 * -10 * 4) >= (9 * 7 * 1 * 6)))))
E. not (not (not not (not ((5 ** 3) != (3 * -10 - -4 * 8)))))
F. (((not not (The currency of Hungary is the Naira.)) and ((Kenya is in Oceania.) or ((3 * 10 * -10 * 10) == (14 + 10)))) or (not ((Gold is a solid at room temperature.) or (There are 30 days in April.)))) and ((not not ((4 * -5) != (4 ** 1))) or (((319 is a perfect square.) or (The 1912 Olympics were held in Antwerp.)) and ((The chemical symbol for Gold is Au.) and (2072 is a leap year.))))
G. ((Indonesia is in Asia.) and (not ((11 * 12) <= (-13 + -10))) and ((679 is a Fibonacci number.) and ((-4 + -4) <= (-3 - 5) <= (2 + -20)))) or ((((19 * 10) != (16 - 2)) and ((-15 + 5) > (-9 * 11))) and ((1 * 11) < (-2 * -1 + 1 * -4))) or ((not (((-1 * 8 + 2 * 9) <= (20 * -18)) and ((9 % 10) < (12 + 20)))) and ((((-4 * -6 + -10 * -10) >= (5 + -18)) or ((-18 * -6) >= (1 * 9))) and (not not ((5 ** 1) <= (4 ** 3) <= (1 * -6 * 10 * 2)))))
H. not not (not not ((Oxygen is necessary for human survival.) and (not not (The capital of South Korea is Seoul.))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,D,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 41815404,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. not not (not not (((Ice is less dense than liquid water.) and (The first Olympic Games of modern era occurred in 1896.)) or (The United States declared independence occurred in 1776.)))\nB. ((((The currency of Nigeria is the Real.) or (Humans only use 10% of their brain.)) and (((5 + -7) > (8 * -7)) and ((26 % 8) < (2 - -16) < (38 % 10)))) and ((((4 % 3) >= (15 % 4)) and ((10 + -17) >= (14 * 0))) and (2005 is a leap year.))) and ((not (((6 * -8 - -4 * 10) == (6 * -4 - -3 * 2)) and (The chemical symbol for Platinum is Pb.))) and ((41 % 8) > (1 * 8 * 2 * -7)))\nC. (((Oxygen is a solid at room temperature.) or (not not ((6 * -5) != (8 - -14)))) or ((-4 * 14) < (0 * -13) < (-3 + -6)) or ((50 % 6) == (10 * 5 + -8 * -6))) and (not ((The chemical symbol for Iron is Fe.) and ((-6 + -16) < (5 * -1))))\nD. (not (((Sharks are mammals.) or ((-4 * 8) < (4 ** 3) < (16 + 7))) and (((-14 + 11) >= (13 - -6)) and (The currency of Peru is the Peso.)))) and (((-7 * 1) == (1 * 2 * 3 * -9)) or ((There are 30 days in June.) and ((5 + 1) != (-3 * 1 - 1 * -10))) or (((Copper is a solid at room temperature.) or (The capital of Brazil is Lima.)) and (not not ((-4 * 6 * -10 * 4) >= (9 * 7 * 1 * 6)))))\nE. not (not (not not (not ((5 ** 3) != (3 * -10 - -4 * 8)))))\nF. (((not not (The currency of Hungary is the Naira.)) and ((Kenya is in Oceania.) or ((3 * 10 * -10 * 10) == (14 + 10)))) or (not ((Gold is a solid at room temperature.) or (There are 30 days in April.)))) and ((not not ((4 * -5) != (4 ** 1))) or (((319 is a perfect square.) or (The 1912 Olympics were held in Antwerp.)) and ((The chemical symbol for Gold is Au.) and (2072 is a leap year.))))\nG. ((Indonesia is in Asia.) and (not ((11 * 12) <= (-13 + -10))) and ((679 is a Fibonacci number.) and ((-4 + -4) <= (-3 - 5) <= (2 + -20)))) or ((((19 * 10) != (16 - 2)) and ((-15 + 5) > (-9 * 11))) and ((1 * 11) < (-2 * -1 + 1 * -4))) or ((not (((-1 * 8 + 2 * 9) <= (20 * -18)) and ((9 % 10) < (12 + 20)))) and ((((-4 * -6 + -10 * -10) >= (5 + -18)) or ((-18 * -6) >= (1 * 9))) and (not not ((5 ** 1) <= (4 ** 3) <= (1 * -6 * 10 * 2)))))\nH. not not (not not ((Oxygen is necessary for human survival.) and (not not (The capital of South Korea is Seoul.))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 41815404,
"true_count": 3
},
"seed": 41815404,
"task_id": 641815404,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not (not (not not ((9 * 0) < (-17 - 1) < (3 * 7 + 0 * -6))))
B. ((not ((17 % 3) <= (1 ** 2))) or (Sharks are mammals.)) or ((3 - 18) > (-6 - 3)) or ((There are 30 days in April.) and (not not (346 is a perfect square.)))
C. (not (Spain is in Oceania.)) and (((41 % 3) < (-10 * 9 + 9 * -3) < (5 % 10)) or (((7 * -1) > (17 + -19)) and ((5 * -7 * -7 * -10) > (11 * 14))))
D. ((((-3 - -7) != (6 * 16)) and ((5 ** 3) <= (4 % 1) <= (4 * 7 - 3 * 9))) or ((The 2020 Olympics were held in Los Angeles.) and (Venus is the 6th planet from the Sun.))) and (((5 ** 1) >= (3 ** 1)) and ((2 ** 2) <= (15 - -10))) and (not not (not not (The currency of Canada is the Krona.)))
E. ((not not (Plants produce oxygen through photosynthesis.)) and ((A butterfly has 10 legs.) and (The capital of Belgium is Brussels.))) and ((not (Gold is a solid at room temperature.)) and ((Jupiter is the 2nd planet from the Sun.) or ((6 + -20) < (36 % 1) < (-3 * -3 + -4 * -9))))
F. ((not not (A crocodile is a fish.)) and (2024 is a leap year.)) or (not not (The chemical symbol for Chromium is Sn.)) or (There are 28 days in October.)
G. (not ((1 * -3 * -8 * 1) <= (2 % 7))) or (not (The currency of Indonesia is the Rupiah.)) or ((2097 is a leap year.) or (((19 - -18) != (-4 - 10)) and ((-9 - -8) > (-3 - 20))))
H. not not ((((4 ** 2) != (23 % 2)) or ((18 * 20) != (1 * 6))) or ((The first moon landing occurred in 1969.) and ((-7 - -6) > (-2 * -7 * 4 * -5))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 15756640,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. not (not (not not ((9 * 0) < (-17 - 1) < (3 * 7 + 0 * -6))))\nB. ((not ((17 % 3) <= (1 ** 2))) or (Sharks are mammals.)) or ((3 - 18) > (-6 - 3)) or ((There are 30 days in April.) and (not not (346 is a perfect square.)))\nC. (not (Spain is in Oceania.)) and (((41 % 3) < (-10 * 9 + 9 * -3) < (5 % 10)) or (((7 * -1) > (17 + -19)) and ((5 * -7 * -7 * -10) > (11 * 14))))\nD. ((((-3 - -7) != (6 * 16)) and ((5 ** 3) <= (4 % 1) <= (4 * 7 - 3 * 9))) or ((The 2020 Olympics were held in Los Angeles.) and (Venus is the 6th planet from the Sun.))) and (((5 ** 1) >= (3 ** 1)) and ((2 ** 2) <= (15 - -10))) and (not not (not not (The currency of Canada is the Krona.)))\nE. ((not not (Plants produce oxygen through photosynthesis.)) and ((A butterfly has 10 legs.) and (The capital of Belgium is Brussels.))) and ((not (Gold is a solid at room temperature.)) and ((Jupiter is the 2nd planet from the Sun.) or ((6 + -20) < (36 % 1) < (-3 * -3 + -4 * -9))))\nF. ((not not (A crocodile is a fish.)) and (2024 is a leap year.)) or (not not (The chemical symbol for Chromium is Sn.)) or (There are 28 days in October.)\nG. (not ((1 * -3 * -8 * 1) <= (2 % 7))) or (not (The currency of Indonesia is the Rupiah.)) or ((2097 is a leap year.) or (((19 - -18) != (-4 - 10)) and ((-9 - -8) > (-3 - 20))))\nH. not not ((((4 ** 2) != (23 % 2)) or ((18 * 20) != (1 * 6))) or ((The first moon landing occurred in 1969.) and ((-7 - -6) > (-2 * -7 * 4 * -5))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 15756640,
"true_count": 3
},
"seed": 15756640,
"task_id": 615756640,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. (not ((-18 + 2) != (-5 + 4))) or ((((7 % 3) <= (-4 * 14)) or (A spider has 8 legs.)) and (The 2012 Olympics were held in Rio de Janeiro.))
B. ((not not (There are 28 days in August.)) and (((40 % 7) < (-4 - -10) < (11 % 9)) and ((-6 * 2 - 7 * -6) == (19 + -7)))) or ((The Great Wall of China was built in one year.) and (World War II ended occurred in 1945.)) or (((Neptune is the 8th planet from the Sun.) or ((3 * -15) < (6 * -4 - 10 * -3))) or ((8 - 2) >= (31 % 8)))
C. ((-12 - 11) < (-8 * 7) < (-3 * 8 - -7 * -7)) or ((The capital of South Korea is Warsaw.) and (Carbon dioxide is a gas at room temperature.)) or (((1913 is a leap year.) or ((-1 * -6 - -9 * 10) <= (-20 + -14))) and (((-3 * 9 + -1 * 2) != (-14 * 6)) and (2013 is a leap year.)))
D. ((((32 % 9) < (6 * 3) < (2 ** 3)) and ((12 - -15) <= (10 - 1))) or ((1986 is a leap year.) or (The 1920 Olympics were held in Paris.))) or (((-12 - -10) >= (-10 * -5 + 10 * 10)) and (189 is an odd number.))
E. not ((not not (The currency of Hungary is the Ringgit.)) and (((-4 * -3 + -1 * 1) == (-14 * 7)) and (The 1952 Olympics were held in Helsinki.)))
F. not not (Saturn is the 1st planet from the Sun.)
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 6925711,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. (not ((-18 + 2) != (-5 + 4))) or ((((7 % 3) <= (-4 * 14)) or (A spider has 8 legs.)) and (The 2012 Olympics were held in Rio de Janeiro.))\nB. ((not not (There are 28 days in August.)) and (((40 % 7) < (-4 - -10) < (11 % 9)) and ((-6 * 2 - 7 * -6) == (19 + -7)))) or ((The Great Wall of China was built in one year.) and (World War II ended occurred in 1945.)) or (((Neptune is the 8th planet from the Sun.) or ((3 * -15) < (6 * -4 - 10 * -3))) or ((8 - 2) >= (31 % 8)))\nC. ((-12 - 11) < (-8 * 7) < (-3 * 8 - -7 * -7)) or ((The capital of South Korea is Warsaw.) and (Carbon dioxide is a gas at room temperature.)) or (((1913 is a leap year.) or ((-1 * -6 - -9 * 10) <= (-20 + -14))) and (((-3 * 9 + -1 * 2) != (-14 * 6)) and (2013 is a leap year.)))\nD. ((((32 % 9) < (6 * 3) < (2 ** 3)) and ((12 - -15) <= (10 - 1))) or ((1986 is a leap year.) or (The 1920 Olympics were held in Paris.))) or (((-12 - -10) >= (-10 * -5 + 10 * 10)) and (189 is an odd number.))\nE. not ((not not (The currency of Hungary is the Ringgit.)) and (((-4 * -3 + -1 * 1) == (-14 * 7)) and (The 1952 Olympics were held in Helsinki.)))\nF. not not (Saturn is the 1st planet from the Sun.)\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": 6925711,
"true_count": 2
},
"seed": 6925711,
"task_id": 606925711,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((((9 - 9) >= (-3 - 20)) and (((5 ** 1) >= (-16 - -9)) and (月球自己发光。))) or (((8 * 6 - -2 * -2) < (9 * 7 + 2 * -4)) or ((-20 - -15) >= (-19 + 9))) or (新西兰位于大洋洲。)) and (not not (4小于等于30。))
B. ((not not (not (挪威的首都是奥斯陆。))) or (((木头在常温下是气体。) or ((-4 * -6 * 4 * -5) < (3 ** 1))) and ((捷克的货币是克朗。) and (25的平方根是7。)))) or (not ((((7 * 4) >= (2 * -14)) and (三月有28天。)) or ((-1 + 4) <= (-10 * 5))))
C. ((六月有30天。) and (not (((10 * -9) >= (13 * 16)) or ((4 * -6 + -1 * 5) < (-3 * -7 * 6 * -4))))) or ((锰的化学符号是Cl。) or ((not not ((3 * -9 + 10 * 0) <= (-9 * 1 - 5 * -10))) or (21大于1。)))
D. not not (not not ((((-19 - 16) < (33 % 1)) and ((-15 + -15) < (5 ** 3))) and (not ((7 - -15) < (11 + -6) < (5 * -3)))))
E. ((水星是距离太阳第3近的行星。) or (2020年奥运会在东京举办。)) and ((not not (not ((7 * -6 - 1 * 1) > (-2 + -6)))) or ((not (埃及的首都是布拉格。)) and ((-16 + 20) <= (3 ** 3))))
F. ((((6 - 16) >= (-2 * 6 * -8 * -8)) and (以色列的货币是谢克尔。)) or ((地球绕太阳运转。) and (((6 * 3 + 7 * 4) <= (-7 + 1)) and ((7 * 3 - 8 * 2) <= (-1 * -9 + 9 * 10) <= (-11 * 2))))) and (not (木头在常温下是气体。))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,B,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 26785995,
"true_count": 6
},
"question": "下面是几个布尔表达式：\n\nA. ((((9 - 9) >= (-3 - 20)) and (((5 ** 1) >= (-16 - -9)) and (月球自己发光。))) or (((8 * 6 - -2 * -2) < (9 * 7 + 2 * -4)) or ((-20 - -15) >= (-19 + 9))) or (新西兰位于大洋洲。)) and (not not (4小于等于30。))\nB. ((not not (not (挪威的首都是奥斯陆。))) or (((木头在常温下是气体。) or ((-4 * -6 * 4 * -5) < (3 ** 1))) and ((捷克的货币是克朗。) and (25的平方根是7。)))) or (not ((((7 * 4) >= (2 * -14)) and (三月有28天。)) or ((-1 + 4) <= (-10 * 5))))\nC. ((六月有30天。) and (not (((10 * -9) >= (13 * 16)) or ((4 * -6 + -1 * 5) < (-3 * -7 * 6 * -4))))) or ((锰的化学符号是Cl。) or ((not not ((3 * -9 + 10 * 0) <= (-9 * 1 - 5 * -10))) or (21大于1。)))\nD. not not (not not ((((-19 - 16) < (33 % 1)) and ((-15 + -15) < (5 ** 3))) and (not ((7 - -15) < (11 + -6) < (5 * -3)))))\nE. ((水星是距离太阳第3近的行星。) or (2020年奥运会在东京举办。)) and ((not not (not ((7 * -6 - 1 * 1) > (-2 + -6)))) or ((not (埃及的首都是布拉格。)) and ((-16 + 20) <= (3 ** 3))))\nF. ((((6 - 16) >= (-2 * 6 * -8 * -8)) and (以色列的货币是谢克尔。)) or ((地球绕太阳运转。) and (((6 * 3 + 7 * 4) <= (-7 + 1)) and ((7 * 3 - 8 * 2) <= (-1 * -9 + 9 * 10) <= (-11 * 2))))) and (not (木头在常温下是气体。))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 26785995,
"true_count": 6
},
"seed": 26785995,
"task_id": 626785995,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not ((not (not not ((36 % 7) == (15 * -5)))) and ((-20 + 0) <= (-5 * -4 - 7 * 3)))
B. not (((40 % 2) < (1 + -11) < (14 * -14)) and (not not ((5 ** 1) > (-16 + 3))) and ((2 ** 2) > (-3 + 0)))
C. (((not not ((-6 - -14) < (-20 + -20))) and (((9 - -16) > (-1 * 3 * 2 * 6)) and ((-2 * 15) <= (10 * -1 * -9 * 4)))) or (Nitrogen is a gas at room temperature.)) and ((not (((-10 - 1) != (-2 - 19)) or ((7 - 8) < (17 - 12)))) and ((India is in Asia.) or (not not (Uranus is the 6th planet from the Sun.))))
D. ((Uranus is the 7th planet from the Sun.) and (A dolphin is a mammal.)) or (A trout is an insect.) or (not not ((29 % 1) != (-5 - -10)))
E. not not ((not (Diamond is a liquid at room temperature.)) or (not not ((-19 - -7) < (36 % 8))) or (not (not (South Korea is in Asia.))))
F. not (not not (((-16 + 7) >= (3 * -3)) or (The first moon landing occurred in 1969.)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 82352441,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. not ((not (not not ((36 % 7) == (15 * -5)))) and ((-20 + 0) <= (-5 * -4 - 7 * 3)))\nB. not (((40 % 2) < (1 + -11) < (14 * -14)) and (not not ((5 ** 1) > (-16 + 3))) and ((2 ** 2) > (-3 + 0)))\nC. (((not not ((-6 - -14) < (-20 + -20))) and (((9 - -16) > (-1 * 3 * 2 * 6)) and ((-2 * 15) <= (10 * -1 * -9 * 4)))) or (Nitrogen is a gas at room temperature.)) and ((not (((-10 - 1) != (-2 - 19)) or ((7 - 8) < (17 - 12)))) and ((India is in Asia.) or (not not (Uranus is the 6th planet from the Sun.))))\nD. ((Uranus is the 7th planet from the Sun.) and (A dolphin is a mammal.)) or (A trout is an insect.) or (not not ((29 % 1) != (-5 - -10)))\nE. not not ((not (Diamond is a liquid at room temperature.)) or (not not ((-19 - -7) < (36 % 8))) or (not (not (South Korea is in Asia.))))\nF. not (not not (((-16 + 7) >= (3 * -3)) or (The first moon landing occurred in 1969.)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 82352441,
"true_count": 3
},
"seed": 82352441,
"task_id": 682352441,
"task_type": "boolean_expressions"
} |
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