env stringclasses 1
value | prompt stringlengths 85 3.69k | extra dict |
|---|---|---|
logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. not (((-4 * -10 + -6 * -4) < (-11 - 14)) and ((日本的货币是日元。) or (丹麦的首都是奥斯陆。)))
B. (not ((2008年奥运会在北京举办。) and (氦的化学符号是Si。))) and (((2085年是闰年。) and ((8 * -12) < (9 * -2 * -4 * 10))) and ((太阳绕地球运转。) or ((19 + -14) <= (16 * -3) <= (5 * 9))))
C. (柏林墙倒塌发生在1989年。) and (((14 * 3) == (1 ** 1)) and (二氧化碳在常温下是气体。)) and (not not ((第二次世界大战开始发生在1939年。) or (1911年是闰年。)))
D. (not (((3 ** 2) != (16 + -5)) or (2024年奥运会在巴黎举办。))) or ((-12 + 20) < (18 + -2) < (-19 + -1))
E. not (((0 * -2 * -4 * 4) <= (-4 - 12)) or (not ((2 ** 3) >= (46 % 5))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 8623868,
"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 (((-4 * -10 + -6 * -4) < (-11 - 14)) and ((日本的货币是日元。) or (丹麦的首都是奥斯陆。)))\nB. (not ((2008年奥运会在北京举办。) and (氦的化学符号是Si。))) and (((2085年是闰年。) and ((8 * -12) < (9 * -2 * -4 * 10))) and ((太阳绕地球运转。) or ((19 + -14) <= (16 * -3) <= (5 * 9))))\nC. (柏林墙倒塌发生在1989年。) and (((14 * 3) == (1 ** 1)) and (二氧化碳在常温下是气体。)) and (not not ((第二次世界大战开始发生在1939年。) or (1911年是闰年。)))\nD. (not (((3 ** 2) != (16 + -5)) or (2024年奥运会在巴黎举办。))) or ((-12 + 20) < (18 + -2) < (-19 + -1))\nE. not (((0 * -2 * -4 * 4) <= (-4 - 12)) or (not ((2 ** 3) >= (46 % 5))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 8623868,
"true_count": 2
},
"seed": 8623868,
"task_id": 608623868,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not (not (not not ((((The human body has 206 bones.) and ((8 - 13) <= (-11 + 2))) and ((The currency of Australia is the Dollar.) or (Mercury is a liquid at room temperature.))) or (not not ((-16 * -8) < (-1 - 1))) or ((not (Diamond is a solid at room temperature.)) and ((1 ** 2) < (1 ** 1))))))
B. not (not (not ((((A dolphin is a mammal.) and (A snake has 0 legs.)) or (The chemical symbol for Chlorine is Cl.)) or ((The chemical symbol for Mercury is Hg.) and (64 is a prime number.)) or (not not (((18 + 16) > (-16 + 10)) and ((2 * 1 * 8 * 5) < (43 % 9)))))))
C. not not ((((not (not not (Steam is a gas at room temperature.))) or ((not (Oil is a liquid at room temperature.)) and (The capital of Italy is Brussels.))) and (not not (not (not ((12 * 19) <= (0 - -11) <= (4 + 20)))))) and ((not ((((19 * -17) > (-7 * -9 * -2 * -2)) or (A day on Earth is 24 hours.)) and (The chemical symbol for Lead is Pb.))) and (not (not not (Ice is a solid at room temperature.))) and (not ((4 * -5) <= (-5 - 20)))))
D. not ((not not ((not (((3 ** 1) < (-3 + 2)) and (A iguana is a reptile.))) or (((Mercury is the 1st planet from the Sun.) and (37 is a prime number.)) or (Plants produce oxygen through photosynthesis.)))) and (not not (not not (((-11 * 5) > (-4 * 5 + -5 * -1)) or ((4 * 4 - 2 * -9) < (17 * -6))))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 70123587,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. not not (not (not not ((((The human body has 206 bones.) and ((8 - 13) <= (-11 + 2))) and ((The currency of Australia is the Dollar.) or (Mercury is a liquid at room temperature.))) or (not not ((-16 * -8) < (-1 - 1))) or ((not (Diamond is a solid at room temperature.)) and ((1 ** 2) < (1 ** 1))))))\nB. not (not (not ((((A dolphin is a mammal.) and (A snake has 0 legs.)) or (The chemical symbol for Chlorine is Cl.)) or ((The chemical symbol for Mercury is Hg.) and (64 is a prime number.)) or (not not (((18 + 16) > (-16 + 10)) and ((2 * 1 * 8 * 5) < (43 % 9)))))))\nC. not not ((((not (not not (Steam is a gas at room temperature.))) or ((not (Oil is a liquid at room temperature.)) and (The capital of Italy is Brussels.))) and (not not (not (not ((12 * 19) <= (0 - -11) <= (4 + 20)))))) and ((not ((((19 * -17) > (-7 * -9 * -2 * -2)) or (A day on Earth is 24 hours.)) and (The chemical symbol for Lead is Pb.))) and (not (not not (Ice is a solid at room temperature.))) and (not ((4 * -5) <= (-5 - 20)))))\nD. not ((not not ((not (((3 ** 1) < (-3 + 2)) and (A iguana is a reptile.))) or (((Mercury is the 1st planet from the Sun.) and (37 is a prime number.)) or (Plants produce oxygen through photosynthesis.)))) and (not not (not not (((-11 * 5) > (-4 * 5 + -5 * -1)) or ((4 * 4 - 2 * -9) < (17 * -6))))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 70123587,
"true_count": 2
},
"seed": 70123587,
"task_id": 670123587,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not (not ((((5 * 7 * -6 * -1) < (3 ** 1)) or ((十二月有29天。) and ((-13 - 12) > (-4 * 12))) or (not (not ((3 ** 2) > (-20 * 0))))) and ((木星是距离太阳第5近的行星。) or (not ((36 % 7) <= (5 ** 1))))))
B. (not ((not (((氧气在常温下是气体。) and (中国位于非洲。)) or ((14 * 16) != (-2 * 10 * -10 * 7)))) and ((空气在常温下是气体。) and (金星是距离太阳第3近的行星。)))) or (not ((not not ((((10 * 12) == (-14 + 9)) or ((-15 + 17) >= (2 * 4))) and (((1 % 10) < (-11 + -2) < (-8 * -4)) and (第一部iPhone发布发生在2007年。)))) and (((澳大利亚位于北美洲。) or (((4 ** 2) <= (13 * 8)) and (水星是距离太阳第8近的行星。))) and (not (海王星是距离太阳第8近的行星。)))))
C. (not not (not not (not (not (((16 - 15) != (-13 * -1)) and ((5 - -12) < (-4 * 15))))))) or ((not (not (匈牙利的货币是克朗。))) or (((((-12 - -19) < (-4 * -4 + -1 * -5)) and ((3 ** 1) <= (-4 * -10 + 2 * -4) <= (-7 * -2 * 9 * -7))) or (((10 * 4 + -8 * 7) <= (1 ** 2)) or (85是质数。))) or ((((巴西位于南美洲。) or (1904年是闰年。)) or (((37 % 8) > (20 - -10)) or (熊是鱼类。))) and ((蟑螂是昆虫。) and (声音无法在真空中传播。)) and (not not ((地球是距离太阳第3近的行星。) and ((6 * 0 + 2 * 9) >= (0 - -17)))))))
D. not not (((not not ((not not (蛇是爬行动物。)) and (墨西哥的首都是墨西哥城。))) and (not ((not ((-18 * 8) < (3 * -7 * 6 * 4) < (-14 * 1))) and ((鲨鱼是鱼类。) and (钛的化学符号是Cl。))))) and ((not (not (((-18 * -5) >= (1 - -3)) and ((-16 + 5) >= (1 ** 3))))) or ((天王星是距离太阳第7近的行星。) and (马有4条腿。))))
E. (not not (((1980年奥运会在莫斯科举办。) or (钛的化学符号是Co。)) or (not (((20 - 18) < (3 + -7)) or ((50是奇数。) or ((7 * -1 - -8 * 6) >= (-7 * -4 + 7 * 4))))))) and (not not ((((12 - -19) == (5 ** 1)) and ((((43 % 10) > (4 * 3 + 1 * -1)) and ((-11 * -14) < (-19 - -12) < (10 - -14))) and ((海王星是距离太阳第3近的行星。) and (1972年奥运会在巴塞罗那举办。)))) or (not (智利位于南美洲。))))
F. not (((not (not ((-13 * 8) != (-3 + -7)))) or (((not not (银在常温下是固体。)) and (((18 - -1) > (16 * -17)) or ((15 - -12) <= (12 + 4)))) or ((1 - 13) == (-1 * -10)) or (((人类有三个肺。) or ((-14 - 2) < (19 * 17))) or (((-18 * 0) > (-17 - -15)) and ((5 ** 1) == (2 * 0 * 7 * 4)))))) or (not not (not (十一月有30天。))))
G. not ((((not (not not (沙特阿拉伯位于大洋洲。))) or (六月有30天。)) or (not ((((13 - -3) != (14 - 0)) or ((15 + -17) <= (5 ** 1) <= (2 + 5))) and (not not ((-18 + -10) < (-14 * -16)))))) and ((not not ((((-3 + -9) <= (-2 * -3 - 0 * -2) <= (-20 * 3)) and ((-13 + -15) > (-7 - -12))) or (((-16 * -15) == (5 * -20)) or (331是完全平方数。)))) or (not (((-2 - -13) <= (-13 + 13)) or ((-8 * 4 * 10 * -5) < (-12 * 16)))) or ((((92是质数。) or (1908年奥运会在里约热内卢举办。)) and (17小于等于77。)) or (not not (氮气在常温下是气体。)))))
H. not not ((not not (not not (((1 ** 1) != (37 % 10)) and (not not (人类每只手有五个手指。))))) and (not (((-9 + -14) <= (20 + -4)) and (蛇是爬行动物。))))
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": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 82408559,
"true_count": 4
},
"question": "检验这些表达式：\n\nA. not (not ((((5 * 7 * -6 * -1) < (3 ** 1)) or ((十二月有29天。) and ((-13 - 12) > (-4 * 12))) or (not (not ((3 ** 2) > (-20 * 0))))) and ((木星是距离太阳第5近的行星。) or (not ((36 % 7) <= (5 ** 1))))))\nB. (not ((not (((氧气在常温下是气体。) and (中国位于非洲。)) or ((14 * 16) != (-2 * 10 * -10 * 7)))) and ((空气在常温下是气体。) and (金星是距离太阳第3近的行星。)))) or (not ((not not ((((10 * 12) == (-14 + 9)) or ((-15 + 17) >= (2 * 4))) and (((1 % 10) < (-11 + -2) < (-8 * -4)) and (第一部iPhone发布发生在2007年。)))) and (((澳大利亚位于北美洲。) or (((4 ** 2) <= (13 * 8)) and (水星是距离太阳第8近的行星。))) and (not (海王星是距离太阳第8近的行星。)))))\nC. (not not (not not (not (not (((16 - 15) != (-13 * -1)) and ((5 - -12) < (-4 * 15))))))) or ((not (not (匈牙利的货币是克朗。))) or (((((-12 - -19) < (-4 * -4 + -1 * -5)) and ((3 ** 1) <= (-4 * -10 + 2 * -4) <= (-7 * -2 * 9 * -7))) or (((10 * 4 + -8 * 7) <= (1 ** 2)) or (85是质数。))) or ((((巴西位于南美洲。) or (1904年是闰年。)) or (((37 % 8) > (20 - -10)) or (熊是鱼类。))) and ((蟑螂是昆虫。) and (声音无法在真空中传播。)) and (not not ((地球是距离太阳第3近的行星。) and ((6 * 0 + 2 * 9) >= (0 - -17)))))))\nD. not not (((not not ((not not (蛇是爬行动物。)) and (墨西哥的首都是墨西哥城。))) and (not ((not ((-18 * 8) < (3 * -7 * 6 * 4) < (-14 * 1))) and ((鲨鱼是鱼类。) and (钛的化学符号是Cl。))))) and ((not (not (((-18 * -5) >= (1 - -3)) and ((-16 + 5) >= (1 ** 3))))) or ((天王星是距离太阳第7近的行星。) and (马有4条腿。))))\nE. (not not (((1980年奥运会在莫斯科举办。) or (钛的化学符号是Co。)) or (not (((20 - 18) < (3 + -7)) or ((50是奇数。) or ((7 * -1 - -8 * 6) >= (-7 * -4 + 7 * 4))))))) and (not not ((((12 - -19) == (5 ** 1)) and ((((43 % 10) > (4 * 3 + 1 * -1)) and ((-11 * -14) < (-19 - -12) < (10 - -14))) and ((海王星是距离太阳第3近的行星。) and (1972年奥运会在巴塞罗那举办。)))) or (not (智利位于南美洲。))))\nF. not (((not (not ((-13 * 8) != (-3 + -7)))) or (((not not (银在常温下是固体。)) and (((18 - -1) > (16 * -17)) or ((15 - -12) <= (12 + 4)))) or ((1 - 13) == (-1 * -10)) or (((人类有三个肺。) or ((-14 - 2) < (19 * 17))) or (((-18 * 0) > (-17 - -15)) and ((5 ** 1) == (2 * 0 * 7 * 4)))))) or (not not (not (十一月有30天。))))\nG. not ((((not (not not (沙特阿拉伯位于大洋洲。))) or (六月有30天。)) or (not ((((13 - -3) != (14 - 0)) or ((15 + -17) <= (5 ** 1) <= (2 + 5))) and (not not ((-18 + -10) < (-14 * -16)))))) and ((not not ((((-3 + -9) <= (-2 * -3 - 0 * -2) <= (-20 * 3)) and ((-13 + -15) > (-7 - -12))) or (((-16 * -15) == (5 * -20)) or (331是完全平方数。)))) or (not (((-2 - -13) <= (-13 + 13)) or ((-8 * 4 * 10 * -5) < (-12 * 16)))) or ((((92是质数。) or (1908年奥运会在里约热内卢举办。)) and (17小于等于77。)) or (not not (氮气在常温下是气体。)))))\nH. not not ((not not (not not (((1 ** 1) != (37 % 10)) and (not not (人类每只手有五个手指。))))) and (not (((-9 + -14) <= (20 + -4)) and (蛇是爬行动物。))))\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": 6,
"language": "cn",
"num_options": 8,
"seed": 82408559,
"true_count": 4
},
"seed": 82408559,
"task_id": 682408559,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not (not ((((9 + 15) != (-16 * -11)) or (There are 28 days in January.)) or (Uranus is the 7th planet from the Sun.)))) and (not ((((-19 * 5) != (0 + -20)) and ((14 + 14) == (35 % 4))) and (The Moon orbits the Earth.))) and ((not not (The 2024 Olympics were held in Paris.)) and (((((-12 - 13) == (-14 * -18)) or (The capital of Cuba is Seoul.)) and ((The 1924 Olympics were held in Los Angeles.) or ((-16 + -7) <= (33 % 9)))) or ((not (995 is a Fibonacci number.)) and (India is in Asia.))))
B. not not (((((Mars is the 6th planet from the Sun.) or ((1 + -2) < (3 - 19) < (-11 - 16))) or (((9 - 17) < (-6 * 3 - 4 * -8)) or (The square root of 16 is 4.))) or (not (Ice is a gas at room temperature.))) and ((not not ((11 + -12) >= (18 - 14))) or (((1934 is a leap year.) and ((-8 - 1) != (3 * 10 - -3 * -6))) and (not ((7 - 13) == (11 * 0))))))
C. not ((not not ((((36 % 5) == (5 ** 2)) and (The capital of Cuba is Havana.)) and (Ice is a solid at room temperature.))) or ((6 is a prime number.) or ((Alcohol is a liquid at room temperature.) or (The Great Fire of London occurred in 1666.)) or ((not not (Air is a gas at room temperature.)) and ((-18 - -5) < (-5 + 5)))))
D. not not (((not (Humans only use 10% of their brain.)) or (China is in Asia.) or ((((15 - 1) == (-8 * 4)) and (A turtle is a reptile.)) or ((Venus is the 2nd planet from the Sun.) and (Helium is a liquid at room temperature.)))) or (A chicken has 2 legs.) or (not (((The capital of Hungary is Budapest.) or (250 is a Fibonacci number.)) or (((-19 + 5) <= (-4 - 0)) or ((18 - -7) > (-14 + -16))))))
E. not not ((((5 ** 2) > (8 * -9 - 6 * 0)) and ((The capital of Mexico is Mexico City.) or (not not (The speed of light is approximately 300,000 km/s.)))) or (not not (The 2008 Olympics were held in Moscow.)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 35502909,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. (not (not ((((9 + 15) != (-16 * -11)) or (There are 28 days in January.)) or (Uranus is the 7th planet from the Sun.)))) and (not ((((-19 * 5) != (0 + -20)) and ((14 + 14) == (35 % 4))) and (The Moon orbits the Earth.))) and ((not not (The 2024 Olympics were held in Paris.)) and (((((-12 - 13) == (-14 * -18)) or (The capital of Cuba is Seoul.)) and ((The 1924 Olympics were held in Los Angeles.) or ((-16 + -7) <= (33 % 9)))) or ((not (995 is a Fibonacci number.)) and (India is in Asia.))))\nB. not not (((((Mars is the 6th planet from the Sun.) or ((1 + -2) < (3 - 19) < (-11 - 16))) or (((9 - 17) < (-6 * 3 - 4 * -8)) or (The square root of 16 is 4.))) or (not (Ice is a gas at room temperature.))) and ((not not ((11 + -12) >= (18 - 14))) or (((1934 is a leap year.) and ((-8 - 1) != (3 * 10 - -3 * -6))) and (not ((7 - 13) == (11 * 0))))))\nC. not ((not not ((((36 % 5) == (5 ** 2)) and (The capital of Cuba is Havana.)) and (Ice is a solid at room temperature.))) or ((6 is a prime number.) or ((Alcohol is a liquid at room temperature.) or (The Great Fire of London occurred in 1666.)) or ((not not (Air is a gas at room temperature.)) and ((-18 - -5) < (-5 + 5)))))\nD. not not (((not (Humans only use 10% of their brain.)) or (China is in Asia.) or ((((15 - 1) == (-8 * 4)) and (A turtle is a reptile.)) or ((Venus is the 2nd planet from the Sun.) and (Helium is a liquid at room temperature.)))) or (A chicken has 2 legs.) or (not (((The capital of Hungary is Budapest.) or (250 is a Fibonacci number.)) or (((-19 + 5) <= (-4 - 0)) or ((18 - -7) > (-14 + -16))))))\nE. not not ((((5 ** 2) > (8 * -9 - 6 * 0)) and ((The capital of Mexico is Mexico City.) or (not not (The speed of light is approximately 300,000 km/s.)))) or (not not (The 2008 Olympics were held in Moscow.)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 35502909,
"true_count": 3
},
"seed": 35502909,
"task_id": 635502909,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not not ((not (not ((The currency of Philippines is the Peso.) and ((The chemical symbol for Mercury is P.) and ((1 ** 3) <= (-8 * 9 - 9 * 2) <= (4 * -3 * 5 * 0)))))) or (not not (not not (not not ((5 + 4) > (-5 - 19))))))
B. not not ((not not ((not ((A bird has 2 legs.) and ((5 * 5) >= (-6 * -5 - 2 * -5)))) and (((-17 * -2) != (-7 * 6)) or (((6 * -4 + -2 * -6) <= (1 + 4) <= (-3 + 20)) or ((-11 * -18) > (-20 + -4)))))) and ((Uranus is the 7th planet from the Sun.) or (((1 * 1 * 0 * 2) > (-3 * -6 + -1 * 1)) or (Mercury is the 1st planet from the Sun.))) and (not (not not (not (Germany is in Europe.)))))
C. not (not not ((not (((The 1972 Olympics were held in Munich.) and (The square root of 25 is 14.)) and ((-16 - 12) == (0 * -5)))) or (((17 - -9) >= (13 % 8)) and ((((-17 + 14) == (20 - 0)) or (26 is a perfect square.)) and (The currency of Canada is the Dollar.)))))
D. not not (not not ((((4 ** 2) != (-4 + 17)) and (not not (((-10 + -20) <= (-7 + -9)) or (The capital of Saudi Arabia is Riyadh.)))) or ((192 is an odd number.) or (58 is a prime number.))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 32254846,
"true_count": 3
},
"question": "Review these logical expressions:\n\nA. not not ((not (not ((The currency of Philippines is the Peso.) and ((The chemical symbol for Mercury is P.) and ((1 ** 3) <= (-8 * 9 - 9 * 2) <= (4 * -3 * 5 * 0)))))) or (not not (not not (not not ((5 + 4) > (-5 - 19))))))\nB. not not ((not not ((not ((A bird has 2 legs.) and ((5 * 5) >= (-6 * -5 - 2 * -5)))) and (((-17 * -2) != (-7 * 6)) or (((6 * -4 + -2 * -6) <= (1 + 4) <= (-3 + 20)) or ((-11 * -18) > (-20 + -4)))))) and ((Uranus is the 7th planet from the Sun.) or (((1 * 1 * 0 * 2) > (-3 * -6 + -1 * 1)) or (Mercury is the 1st planet from the Sun.))) and (not (not not (not (Germany is in Europe.)))))\nC. not (not not ((not (((The 1972 Olympics were held in Munich.) and (The square root of 25 is 14.)) and ((-16 - 12) == (0 * -5)))) or (((17 - -9) >= (13 % 8)) and ((((-17 + 14) == (20 - 0)) or (26 is a perfect square.)) and (The currency of Canada is the Dollar.)))))\nD. not not (not not ((((4 ** 2) != (-4 + 17)) and (not not (((-10 + -20) <= (-7 + -9)) or (The capital of Saudi Arabia is Riyadh.)))) or ((192 is an odd number.) or (58 is a prime number.))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 32254846,
"true_count": 3
},
"seed": 32254846,
"task_id": 632254846,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((not not ((1952年奥运会在赫尔辛基举办。) and ((1 * -5 + 1 * -3) != (16 * 13)))) or ((-6 * -5 * 10 * 2) > (1 - 8)) or (not ((((6 * -8 + -6 * -6) <= (-1 + 10) <= (-1 - -4)) and (肯尼亚位于非洲。)) or (海王星是距离太阳第8近的行星。)))) or (((捷克的首都是马尼拉。) or ((第一次世界大战结束发生在1918年。) and (蝙蝠是瞎的。))) or ((-5 * -5 + 6 * -10) > (-3 * 5 + -1 * -10))) or ((not ((8 * 10) <= (30 % 9) <= (-4 * -15))) or ((美国宣布独立发生在1776年。) or ((((13 * 5) < (8 - -13)) and (80小于等于37。)) or (not not ((7 * 2 - -3 * -3) <= (-15 + -7) <= (-5 - -11))))))
B. ((not not (金在常温下是固体。)) or (not not ((人类有2条腿。) or (俄罗斯的货币是欧元。)))) and (not (((57能被9整除。) or (银的化学符号是Ag。)) and (not not (苍蝇是鸟类。)))) and (not (not not ((尼日利亚位于南极洲。) and ((氦气在常温下是气体。) or ((14 % 8) == (5 * -3 - 2 * -5))))))
C. not (not not ((not not (not (新西兰的货币是新西兰元。))) and (2008年奥运会在北京举办。) and ((not (一月有29天。)) and (((6 * 2 * 0 * -10) < (-7 - -7)) and (81是质数。)))))
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",
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"gpt_response": "",
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"language": "cn",
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"true_count": 3
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"question": "检验这些表达式：\n\nA. ((not not ((1952年奥运会在赫尔辛基举办。) and ((1 * -5 + 1 * -3) != (16 * 13)))) or ((-6 * -5 * 10 * 2) > (1 - 8)) or (not ((((6 * -8 + -6 * -6) <= (-1 + 10) <= (-1 - -4)) and (肯尼亚位于非洲。)) or (海王星是距离太阳第8近的行星。)))) or (((捷克的首都是马尼拉。) or ((第一次世界大战结束发生在1918年。) and (蝙蝠是瞎的。))) or ((-5 * -5 + 6 * -10) > (-3 * 5 + -1 * -10))) or ((not ((8 * 10) <= (30 % 9) <= (-4 * -15))) or ((美国宣布独立发生在1776年。) or ((((13 * 5) < (8 - -13)) and (80小于等于37。)) or (not not ((7 * 2 - -3 * -3) <= (-15 + -7) <= (-5 - -11))))))\nB. ((not not (金在常温下是固体。)) or (not not ((人类有2条腿。) or (俄罗斯的货币是欧元。)))) and (not (((57能被9整除。) or (银的化学符号是Ag。)) and (not not (苍蝇是鸟类。)))) and (not (not not ((尼日利亚位于南极洲。) and ((氦气在常温下是气体。) or ((14 % 8) == (5 * -3 - 2 * -5))))))\nC. not (not not ((not not (not (新西兰的货币是新西兰元。))) and (2008年奥运会在北京举办。) and ((not (一月有29天。)) and (((6 * 2 * 0 * -10) < (-7 - -7)) and (81是质数。)))))\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": 9532333,
"true_count": 3
},
"seed": 9532333,
"task_id": 609532333,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not not ((((not ((2063年是闰年。) and ((18 % 5) == (4 * -9 * 7 * 6)))) or ((not not ((1 ** 3) != (-10 + 19))) or ((摩洛哥的首都是拉巴特。) and (钙的化学符号是Ca。)))) or ((not ((-12 - -20) <= (9 * -2 * -9 * -1))) or (not ((12 - -6) >= (-15 * -8)))) or (not (((-18 + 11) <= (2 * -8 * 4 * 9)) or ((52大于76。) and ((-12 - 19) <= (-8 * -2 + -8 * 5)))))) or (not ((((南非的货币是兰特。) or ((24 % 3) <= (5 ** 2))) or (((14 - 8) >= (-13 - -6)) and (泰国的首都是曼谷。))) and (not not (not (火星是距离太阳第1近的行星。))))))
B. not not (((((3 * 0 + -7 * 6) < (-7 * -12)) and (((17 * -12) > (47 % 9)) and (电流比光速更快。)) and ((115是奇数。) or (鲱鱼是昆虫。))) and ((((水星是距离太阳第5近的行星。) or (水在常温下是气体。)) and (not not ((17 + -7) < (45 % 5) < (34 % 7)))) or ((4 - -15) < (5 ** 3)))) or (not ((not ((智利位于南极洲。) or (美国的货币是美元。))) or ((((11 * 12) != (-1 * 0 * -5 * -7)) or (波兰的首都是赫尔辛基。)) or ((64的平方根是5。) and ((32 % 10) <= (-1 + -16)))))))
C. not (((not not (((银在常温下是液体。) or ((-9 * 7 * 5 * -7) < (2 * -10))) and (((10 + 10) == (5 ** 3)) and (铂的化学符号是Pb。)))) and (((3 * 19) < (-19 - 3)) and (not ((11 * 11) <= (-10 + 9))))) and (((印度的货币是卢比。) or ((1 % 9) > (12 + 5))) or (not not (not not ((镍的化学符号是Ni。) and (100的平方根是13。))))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
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"true_count": 2
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"question": "评估以下每个表达式：\n\nA. not not ((((not ((2063年是闰年。) and ((18 % 5) == (4 * -9 * 7 * 6)))) or ((not not ((1 ** 3) != (-10 + 19))) or ((摩洛哥的首都是拉巴特。) and (钙的化学符号是Ca。)))) or ((not ((-12 - -20) <= (9 * -2 * -9 * -1))) or (not ((12 - -6) >= (-15 * -8)))) or (not (((-18 + 11) <= (2 * -8 * 4 * 9)) or ((52大于76。) and ((-12 - 19) <= (-8 * -2 + -8 * 5)))))) or (not ((((南非的货币是兰特。) or ((24 % 3) <= (5 ** 2))) or (((14 - 8) >= (-13 - -6)) and (泰国的首都是曼谷。))) and (not not (not (火星是距离太阳第1近的行星。))))))\nB. not not (((((3 * 0 + -7 * 6) < (-7 * -12)) and (((17 * -12) > (47 % 9)) and (电流比光速更快。)) and ((115是奇数。) or (鲱鱼是昆虫。))) and ((((水星是距离太阳第5近的行星。) or (水在常温下是气体。)) and (not not ((17 + -7) < (45 % 5) < (34 % 7)))) or ((4 - -15) < (5 ** 3)))) or (not ((not ((智利位于南极洲。) or (美国的货币是美元。))) or ((((11 * 12) != (-1 * 0 * -5 * -7)) or (波兰的首都是赫尔辛基。)) or ((64的平方根是5。) and ((32 % 10) <= (-1 + -16)))))))\nC. not (((not not (((银在常温下是液体。) or ((-9 * 7 * 5 * -7) < (2 * -10))) and (((10 + 10) == (5 ** 3)) and (铂的化学符号是Pb。)))) and (((3 * 19) < (-19 - 3)) and (not ((11 * 11) <= (-10 + 9))))) and (((印度的货币是卢比。) or ((1 % 9) > (12 + 5))) or (not not (not not ((镍的化学符号是Ni。) and (100的平方根是13。))))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 11353533,
"true_count": 2
},
"seed": 11353533,
"task_id": 611353533,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (not not (not ((((鸡有2条腿。) and (人类只使用了大脑的10%。)) and (((1 * -6 * 8 * 5) >= (0 + 18)) or (水星是距离太阳第1近的行星。))) or (火星是距离太阳最近的行星。) or (((3 ** 1) < (7 * -9 + -5 * -2)) and (not not (1960年奥运会在伦敦举办。)))))) and (not (((not not (中国位于大洋洲。)) and (not not (((0 + 7) < (-7 * 7 * 2 * 6)) or (章鱼有0条腿。)))) and (((-15 * -3) < (7 * 2 + 8 * 5)) and (not (((2 ** 2) == (0 * -10 - 2 * -5)) and ((3 * 2 - 6 * 9) != (-10 * 8 - -8 * -8)))))))
B. not ((not (((-13 - 19) > (-11 * 0)) and (not (2061年是闰年。)) and ((not ((16 - 18) <= (-16 + 12))) and (not (蝙蝠是瞎的。))))) and ((not not (((7 - 11) != (-4 - -12)) and ((6 - -19) != (-7 - 8)))) and (not not (not not (希腊的首都是阿布贾。)))) and ((not (((10 * -20) <= (-9 * 17)) or ((-4 + 17) != (5 * 8)))) or (not ((-11 - 15) <= (2 + 2)))))
C. not (not ((not (((瓢虫是昆虫。) and (65小于等于44。)) or (not not (南非位于非洲。)))) and (((12 + 0) != (7 * -8 * -7 * 8)) and (((4 * 0 * -10 * -5) < (-4 - -17)) and (哥伦布到达美洲发生在1482年。))) and ((((鹰是昆虫。) or (瓢虫是昆虫。)) or ((八月有30天。) or (氧气在常温下是气体。))) and (1968年奥运会在墨西哥城举办。))))
D. not not (not (not (((((36 % 6) >= (10 * 0)) and (海王星是距离太阳第8近的行星。)) or (not ((9 * 13) != (-5 - -9)))) and ((氢的化学符号是H。) or ((-14 + -15) != (12 * 1))) and ((not not ((19 - -13) <= (-1 + 14))) and ((木星是距离太阳第1近的行星。) or ((-20 * 20) >= (16 + 12)))))))
E. not (((not ((not ((7 * 8) >= (-16 - -18))) or (not ((7 * 0 + 9 * -5) <= (-9 + -7) <= (13 % 8))))) or ((电流比光速更快。) or (not not ((0 + 5) < (19 - -11)))) or ((not not ((木头在常温下是固体。) or ((-4 + 11) == (-18 * 20)))) or (韩国位于南美洲。) or ((not not ((-13 * -19) < (-12 - -16))) or (not (十一月有30天。))))) and (not not ((((人体有206块骨头。) or ((-8 * -10 - 5 * -4) != (-9 + 7))) or (not not (大象有2条腿。))) and (not not (匈牙利的首都是布达佩斯。)))))
F. (not not (not not ((莱特兄弟首次飞行发生在1903年。) or (not not (葡萄牙的首都是布宜诺斯艾利斯。))))) or (not ((((-16 - 18) >= (-15 - -14)) or (((1976年奥运会在蒙特利尔举办。) or (六月有31天。)) and ((海王星是距离太阳第8近的行星。) or (土耳其的首都是安卡拉。)))) or (((not not (金星是距离太阳第8近的行星。)) and ((第一次世界大战开始发生在1924年。) and (木头在常温下是气体。))) or ((埃及的首都是开罗。) and (人类有2条腿。)) or (not not (((-13 * 10) < (9 * -10 - 10 * -5)) and ((-2 * 16) <= (6 * -1) <= (2 ** 1)))))))
G. not (not not ((not not (鸭子有10条腿。)) or ((not not (锰的化学符号是Ni。)) and (水在海平面上的沸点是100摄氏度。)) or (((not not (苏联解体发生在1996年。)) and (((-9 - 12) >= (-2 - 2)) and ((-3 - 16) != (3 ** 1)))) or (水蒸气在常温下是固体。))))
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,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"seed": 2228302,
"true_count": 4
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"question": "检验这些表达式：\n\nA. (not not (not ((((鸡有2条腿。) and (人类只使用了大脑的10%。)) and (((1 * -6 * 8 * 5) >= (0 + 18)) or (水星是距离太阳第1近的行星。))) or (火星是距离太阳最近的行星。) or (((3 ** 1) < (7 * -9 + -5 * -2)) and (not not (1960年奥运会在伦敦举办。)))))) and (not (((not not (中国位于大洋洲。)) and (not not (((0 + 7) < (-7 * 7 * 2 * 6)) or (章鱼有0条腿。)))) and (((-15 * -3) < (7 * 2 + 8 * 5)) and (not (((2 ** 2) == (0 * -10 - 2 * -5)) and ((3 * 2 - 6 * 9) != (-10 * 8 - -8 * -8)))))))\nB. not ((not (((-13 - 19) > (-11 * 0)) and (not (2061年是闰年。)) and ((not ((16 - 18) <= (-16 + 12))) and (not (蝙蝠是瞎的。))))) and ((not not (((7 - 11) != (-4 - -12)) and ((6 - -19) != (-7 - 8)))) and (not not (not not (希腊的首都是阿布贾。)))) and ((not (((10 * -20) <= (-9 * 17)) or ((-4 + 17) != (5 * 8)))) or (not ((-11 - 15) <= (2 + 2)))))\nC. not (not ((not (((瓢虫是昆虫。) and (65小于等于44。)) or (not not (南非位于非洲。)))) and (((12 + 0) != (7 * -8 * -7 * 8)) and (((4 * 0 * -10 * -5) < (-4 - -17)) and (哥伦布到达美洲发生在1482年。))) and ((((鹰是昆虫。) or (瓢虫是昆虫。)) or ((八月有30天。) or (氧气在常温下是气体。))) and (1968年奥运会在墨西哥城举办。))))\nD. not not (not (not (((((36 % 6) >= (10 * 0)) and (海王星是距离太阳第8近的行星。)) or (not ((9 * 13) != (-5 - -9)))) and ((氢的化学符号是H。) or ((-14 + -15) != (12 * 1))) and ((not not ((19 - -13) <= (-1 + 14))) and ((木星是距离太阳第1近的行星。) or ((-20 * 20) >= (16 + 12)))))))\nE. not (((not ((not ((7 * 8) >= (-16 - -18))) or (not ((7 * 0 + 9 * -5) <= (-9 + -7) <= (13 % 8))))) or ((电流比光速更快。) or (not not ((0 + 5) < (19 - -11)))) or ((not not ((木头在常温下是固体。) or ((-4 + 11) == (-18 * 20)))) or (韩国位于南美洲。) or ((not not ((-13 * -19) < (-12 - -16))) or (not (十一月有30天。))))) and (not not ((((人体有206块骨头。) or ((-8 * -10 - 5 * -4) != (-9 + 7))) or (not not (大象有2条腿。))) and (not not (匈牙利的首都是布达佩斯。)))))\nF. (not not (not not ((莱特兄弟首次飞行发生在1903年。) or (not not (葡萄牙的首都是布宜诺斯艾利斯。))))) or (not ((((-16 - 18) >= (-15 - -14)) or (((1976年奥运会在蒙特利尔举办。) or (六月有31天。)) and ((海王星是距离太阳第8近的行星。) or (土耳其的首都是安卡拉。)))) or (((not not (金星是距离太阳第8近的行星。)) and ((第一次世界大战开始发生在1924年。) and (木头在常温下是气体。))) or ((埃及的首都是开罗。) and (人类有2条腿。)) or (not not (((-13 * 10) < (9 * -10 - 10 * -5)) and ((-2 * 16) <= (6 * -1) <= (2 ** 1)))))))\nG. not (not not ((not not (鸭子有10条腿。)) or ((not not (锰的化学符号是Ni。)) and (水在海平面上的沸点是100摄氏度。)) or (((not not (苏联解体发生在1996年。)) and (((-9 - 12) >= (-2 - 2)) and ((-3 - 16) != (3 ** 1)))) or (水蒸气在常温下是固体。))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
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"language": "cn",
"num_options": 7,
"seed": 2228302,
"true_count": 4
},
"seed": 2228302,
"task_id": 602228302,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (not ((not ((-3 * 2) <= (23 % 8))) and ((8 * 7 - 8 * -10) > (0 * -3 - 5 * 0)) and ((not ((芬兰的首都是赫尔辛基。) and (龙虾有10条腿。))) or (not ((1 ** 1) <= (16 * 16)))))) or (not ((not (十一月有31天。)) and (not not (not (((-2 * -8 * 5 * 7) != (5 ** 2)) and (第一部iPhone发布发生在2006年。))))))
B. not not (((not not ((not (肯尼亚的首都是布拉格。)) and ((1996年奥运会在亚特兰大举办。) and (人类有三个肺。)))) and (not ((六月有30天。) and (蚂蚁有0条腿。))) and (((not not (2024年奥运会在巴黎举办。)) and (((6 + -18) >= (7 * 12)) and ((-18 + -12) >= (5 ** 2)))) or ((((17 * -15) == (-9 * -4 * 9 * -10)) or ((-10 - 6) == (-17 * 0))) and (not (加拿大位于非洲。))))) or ((not (镁的化学符号是Mg。)) and ((((4 ** 1) != (-15 + -2)) or ((人类只使用了大脑的10%。) or ((-12 - 3) == (-14 + 6)))) and ((11是奇数。) and (not not (1932年奥运会在慕尼黑举办。))))))
C. ((not (not (火星是距离太阳最近的行星。))) or ((not (油在常温下是气体。)) or (not not (((43大于43。) or ((3 + 20) != (-10 * 1 + -5 * -9))) or ((5 * 15) == (-18 - -3)))))) and (not (not not (((not (蝙蝠是瞎的。)) or (((8 + -10) > (9 % 2)) or (金的化学符号是Au。))) and ((((10 * 10 + 4 * 2) <= (-20 * 20)) or (人类每只手有五个手指。)) and (((-6 * 4 + -1 * 6) == (11 + -5)) and ((12 + -18) >= (-7 - -14)))))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
"num_options": 3,
"seed": 99819143,
"true_count": 2
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"question": "研究以下逻辑语句：\n\nA. (not ((not ((-3 * 2) <= (23 % 8))) and ((8 * 7 - 8 * -10) > (0 * -3 - 5 * 0)) and ((not ((芬兰的首都是赫尔辛基。) and (龙虾有10条腿。))) or (not ((1 ** 1) <= (16 * 16)))))) or (not ((not (十一月有31天。)) and (not not (not (((-2 * -8 * 5 * 7) != (5 ** 2)) and (第一部iPhone发布发生在2006年。))))))\nB. not not (((not not ((not (肯尼亚的首都是布拉格。)) and ((1996年奥运会在亚特兰大举办。) and (人类有三个肺。)))) and (not ((六月有30天。) and (蚂蚁有0条腿。))) and (((not not (2024年奥运会在巴黎举办。)) and (((6 + -18) >= (7 * 12)) and ((-18 + -12) >= (5 ** 2)))) or ((((17 * -15) == (-9 * -4 * 9 * -10)) or ((-10 - 6) == (-17 * 0))) and (not (加拿大位于非洲。))))) or ((not (镁的化学符号是Mg。)) and ((((4 ** 1) != (-15 + -2)) or ((人类只使用了大脑的10%。) or ((-12 - 3) == (-14 + 6)))) and ((11是奇数。) and (not not (1932年奥运会在慕尼黑举办。))))))\nC. ((not (not (火星是距离太阳最近的行星。))) or ((not (油在常温下是气体。)) or (not not (((43大于43。) or ((3 + 20) != (-10 * 1 + -5 * -9))) or ((5 * 15) == (-18 - -3)))))) and (not (not not (((not (蝙蝠是瞎的。)) or (((8 + -10) > (9 % 2)) or (金的化学符号是Au。))) and ((((10 * 10 + 4 * 2) <= (-20 * 20)) or (人类每只手有五个手指。)) and (((-6 * 4 + -1 * 6) == (11 + -5)) and ((12 + -18) >= (-7 - -14)))))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
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"language": "cn",
"num_options": 3,
"seed": 99819143,
"true_count": 2
},
"seed": 99819143,
"task_id": 699819143,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (not (not ((光速比声速快。) and (((7 * 10) > (-2 * 3 - -6 * 2)) or (((5 ** 3) >= (-14 + -18)) or (牛有0条腿。)))))) or ((not (not not ((not not ((-13 + -20) > (-15 + 17))) or (1994年是闰年。)))) or (not (((巴西的货币是瑞士法郎。) and (西班牙位于欧洲。)) and ((17 + 14) != (12 + 9)))) or (((not not (not (菲律宾的货币是比索。))) or (not (天王星是距离太阳第3近的行星。)) or ((((-7 * 7 * -6 * -9) < (-4 * 1) < (-17 * -6)) or ((4 ** 2) == (4 - -11))) and (not ((-14 + -15) >= (10 - -10))))) or (not not (哥伦比亚位于亚洲。))))
B. not not (not ((not not ((50 % 10) > (9 * 1 + -8 * -4))) and (not not (((19 + 12) <= (-16 - -15) <= (17 + -15)) or ((16 - 1) != (-15 - 0)))) and (((-11 + 0) > (5 ** 2)) or (俄罗斯位于欧洲。))))
C. not not ((not not ((45是偶数。) and ((-2 * -2) == (10 * -10 * -6 * 4)) and (not (((17 % 10) >= (-6 + 0)) or ((15 + -13) >= (-17 - 11)))))) and (((((1932年奥运会在洛杉矶举办。) or (锰的化学符号是Mg。)) and ((-7 * 18) <= (2 * 10 * -6 * -6))) or (秘鲁的货币是索尔。)) or (not not ((((20 % 1) == (13 - -5)) and (短吻鳄是爬行动物。)) or (地球上一天是24小时。)))))
D. not (not not (((not not ((第二次世界大战结束发生在1946年。) or ((9 * -8 + -8 * -1) != (1 ** 1)))) and (1932年奥运会在洛杉矶举办。)) and ((((鲨鱼是哺乳动物。) and (银在常温下是固体。)) and ((土星是距离太阳第8近的行星。) and (印度尼西亚的货币是日元。))) or ((not not (1904年奥运会在圣路易斯举办。)) and (((6 - -13) <= (3 * 6 * -2 * -1) <= (3 ** 1)) and (泰坦尼克号沉没发生在1922年。))))))
E. not ((((((秘鲁的首都是利马。) and (汞在常温下是固体。)) and ((5 * -8 * -6 * -2) <= (1 ** 1))) and ((((13 - -2) < (2 % 5) < (6 + 5)) and (猫有4条腿。)) or ((2 * -13) > (42 % 5)))) or (((-15 + -17) < (10 + -11)) or (((15 * 17) == (19 + -14)) or ((哥伦比亚位于亚洲。) and (氧气对人类生存是必需的。))))) and (not (not (新西兰位于大洋洲。))))
F. not (not not (((((-12 * -7) <= (5 * 4 * -5 * 9) <= (-1 - 2)) or (((-11 * 6) == (-6 * -4 - 0 * 1)) and (印度的货币是克朗。))) or ((not ((-11 * -1) < (-8 + -17) < (0 * -5 - 7 * -3))) or ((太平洋是最大的海洋。) and (第二次世界大战结束发生在1945年。)))) and ((美国的货币是日元。) and ((14 - -19) > (-15 - -14)))))
G. not (not not ((((40 % 7) < (11 + 15)) and ((not not (第一部iPhone发布发生在2007年。)) or ((-19 - -9) != (5 * 6)))) and ((not (印度尼西亚的首都是利雅得。)) and ((not not (中国长城是在一年内建成的。)) or (((-1 - 3) != (-15 + 5)) and ((7 - 12) > (4 ** 3)))))))
H. not ((((((6 * -5 + -10 * -6) != (47 % 4)) or (((12 * -6) > (-6 - -11)) or ((-5 * 16) >= (1 * 19)))) and (not ((1的平方根是9。) or (冰的密度比液态水小。)))) and ((水星是距离太阳第2近的行星。) or ((柏林墙倒塌发生在1989年。) or (铜在常温下是固体。)) or (((挪威的首都是都柏林。) or (光速约为每秒30万公里。)) and ((20 % 1) == (34 % 6))))) and (not (not not (((1 % 8) < (-18 - 19) < (14 + 18)) or ((9 - 16) == (17 * 13))))))
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": {
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"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
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"seed": 13122775,
"true_count": 6
},
"question": "给定以下布尔表达式：\n\nA. (not (not ((光速比声速快。) and (((7 * 10) > (-2 * 3 - -6 * 2)) or (((5 ** 3) >= (-14 + -18)) or (牛有0条腿。)))))) or ((not (not not ((not not ((-13 + -20) > (-15 + 17))) or (1994年是闰年。)))) or (not (((巴西的货币是瑞士法郎。) and (西班牙位于欧洲。)) and ((17 + 14) != (12 + 9)))) or (((not not (not (菲律宾的货币是比索。))) or (not (天王星是距离太阳第3近的行星。)) or ((((-7 * 7 * -6 * -9) < (-4 * 1) < (-17 * -6)) or ((4 ** 2) == (4 - -11))) and (not ((-14 + -15) >= (10 - -10))))) or (not not (哥伦比亚位于亚洲。))))\nB. not not (not ((not not ((50 % 10) > (9 * 1 + -8 * -4))) and (not not (((19 + 12) <= (-16 - -15) <= (17 + -15)) or ((16 - 1) != (-15 - 0)))) and (((-11 + 0) > (5 ** 2)) or (俄罗斯位于欧洲。))))\nC. not not ((not not ((45是偶数。) and ((-2 * -2) == (10 * -10 * -6 * 4)) and (not (((17 % 10) >= (-6 + 0)) or ((15 + -13) >= (-17 - 11)))))) and (((((1932年奥运会在洛杉矶举办。) or (锰的化学符号是Mg。)) and ((-7 * 18) <= (2 * 10 * -6 * -6))) or (秘鲁的货币是索尔。)) or (not not ((((20 % 1) == (13 - -5)) and (短吻鳄是爬行动物。)) or (地球上一天是24小时。)))))\nD. not (not not (((not not ((第二次世界大战结束发生在1946年。) or ((9 * -8 + -8 * -1) != (1 ** 1)))) and (1932年奥运会在洛杉矶举办。)) and ((((鲨鱼是哺乳动物。) and (银在常温下是固体。)) and ((土星是距离太阳第8近的行星。) and (印度尼西亚的货币是日元。))) or ((not not (1904年奥运会在圣路易斯举办。)) and (((6 - -13) <= (3 * 6 * -2 * -1) <= (3 ** 1)) and (泰坦尼克号沉没发生在1922年。))))))\nE. not ((((((秘鲁的首都是利马。) and (汞在常温下是固体。)) and ((5 * -8 * -6 * -2) <= (1 ** 1))) and ((((13 - -2) < (2 % 5) < (6 + 5)) and (猫有4条腿。)) or ((2 * -13) > (42 % 5)))) or (((-15 + -17) < (10 + -11)) or (((15 * 17) == (19 + -14)) or ((哥伦比亚位于亚洲。) and (氧气对人类生存是必需的。))))) and (not (not (新西兰位于大洋洲。))))\nF. not (not not (((((-12 * -7) <= (5 * 4 * -5 * 9) <= (-1 - 2)) or (((-11 * 6) == (-6 * -4 - 0 * 1)) and (印度的货币是克朗。))) or ((not ((-11 * -1) < (-8 + -17) < (0 * -5 - 7 * -3))) or ((太平洋是最大的海洋。) and (第二次世界大战结束发生在1945年。)))) and ((美国的货币是日元。) and ((14 - -19) > (-15 - -14)))))\nG. not (not not ((((40 % 7) < (11 + 15)) and ((not not (第一部iPhone发布发生在2007年。)) or ((-19 - -9) != (5 * 6)))) and ((not (印度尼西亚的首都是利雅得。)) and ((not not (中国长城是在一年内建成的。)) or (((-1 - 3) != (-15 + 5)) and ((7 - 12) > (4 ** 3)))))))\nH. not ((((((6 * -5 + -10 * -6) != (47 % 4)) or (((12 * -6) > (-6 - -11)) or ((-5 * 16) >= (1 * 19)))) and (not ((1的平方根是9。) or (冰的密度比液态水小。)))) and ((水星是距离太阳第2近的行星。) or ((柏林墙倒塌发生在1989年。) or (铜在常温下是固体。)) or (((挪威的首都是都柏林。) or (光速约为每秒30万公里。)) and ((20 % 1) == (34 % 6))))) and (not (not not (((1 % 8) < (-18 - 19) < (14 + 18)) or ((9 - 16) == (17 * 13))))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 13122775,
"true_count": 6
},
"seed": 13122775,
"task_id": 613122775,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. not ((((not not ((美国宣布独立发生在1776年。) and (地球上一天是24小时。))) or (((蝙蝠是瞎的。) or (氧气对人类生存是必需的。)) and (not (银在常温下是气体。)))) or (not not (not ((鲸鱼是鱼类。) and ((-11 * -10) >= (12 + -5)))))) and ((((not not (委内瑞拉的首都是巴黎。)) and (龙虾有10条腿。)) or (not not ((10大于54。) or (金星是距离太阳第5近的行星。)))) or ((-4 - 5) == (-1 - 7)) or ((((12 * 2) >= (-6 - -14)) or (((2 * 1 * -4 * -2) <= (4 % 4)) or ((9 % 6) <= (-5 * 2 * -6 * -9)))) and (((-12 * 18) <= (42 % 9)) and (not ((12 + -7) != (-14 - -11)))))))
B. not ((not ((氧气在常温下是固体。) or (not (美国宣布独立发生在1775年。)) or ((8 % 6) != (28 % 9)))) and (not not (((((-8 * 4 + -10 * 7) != (-8 * 4 * -5 * -1)) and ((6 - 20) <= (-6 - -10))) or (not not ((14 + -8) <= (16 + 3) <= (1 * 7 - 6 * -7)))) or (not (第二次世界大战结束发生在1945年。)) or (not not (哥伦比亚位于北美洲。)))))
C. not not (not ((not not (not ((9 * 5 * -3 * 8) > (15 * -17)))) or ((土星是距离太阳第6近的行星。) and (二氧化碳在常温下是气体。)) or (not not (not ((意大利的首都是罗马。) and ((2 % 2) == (12 % 2)))))))
D. ((((地球是距离太阳第3近的行星。) and ((((1 ** 2) <= (6 * 19)) or ((-13 * 16) != (35 % 4))) and (((7 + -1) != (-9 * -16)) or (钙的化学符号是Ca。)))) or (((-4 * -5) > (-18 - 5)) or (蜘蛛有8条腿。))) and (not (not not (((4 * 4 - -9 * -8) >= (7 % 10)) and ((12 * 8) > (44 % 1))))) and (not not ((not (((5 - 0) != (-17 + -14)) and (南极洲是最冷的大陆。))) or ((兔子是哺乳动物。) or (not (泰坦尼克号沉没发生在1922年。)))))) and (not ((not (空气在常温下是固体。)) or (not not (((海王星是距离太阳第8近的行星。) and (天王星是距离太阳第2近的行星。)) and ((2072年是闰年。) and ((18 + -8) == (35 % 2)))))))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 57918296,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. not ((((not not ((美国宣布独立发生在1776年。) and (地球上一天是24小时。))) or (((蝙蝠是瞎的。) or (氧气对人类生存是必需的。)) and (not (银在常温下是气体。)))) or (not not (not ((鲸鱼是鱼类。) and ((-11 * -10) >= (12 + -5)))))) and ((((not not (委内瑞拉的首都是巴黎。)) and (龙虾有10条腿。)) or (not not ((10大于54。) or (金星是距离太阳第5近的行星。)))) or ((-4 - 5) == (-1 - 7)) or ((((12 * 2) >= (-6 - -14)) or (((2 * 1 * -4 * -2) <= (4 % 4)) or ((9 % 6) <= (-5 * 2 * -6 * -9)))) and (((-12 * 18) <= (42 % 9)) and (not ((12 + -7) != (-14 - -11)))))))\nB. not ((not ((氧气在常温下是固体。) or (not (美国宣布独立发生在1775年。)) or ((8 % 6) != (28 % 9)))) and (not not (((((-8 * 4 + -10 * 7) != (-8 * 4 * -5 * -1)) and ((6 - 20) <= (-6 - -10))) or (not not ((14 + -8) <= (16 + 3) <= (1 * 7 - 6 * -7)))) or (not (第二次世界大战结束发生在1945年。)) or (not not (哥伦比亚位于北美洲。)))))\nC. not not (not ((not not (not ((9 * 5 * -3 * 8) > (15 * -17)))) or ((土星是距离太阳第6近的行星。) and (二氧化碳在常温下是气体。)) or (not not (not ((意大利的首都是罗马。) and ((2 % 2) == (12 % 2)))))))\nD. ((((地球是距离太阳第3近的行星。) and ((((1 ** 2) <= (6 * 19)) or ((-13 * 16) != (35 % 4))) and (((7 + -1) != (-9 * -16)) or (钙的化学符号是Ca。)))) or (((-4 * -5) > (-18 - 5)) or (蜘蛛有8条腿。))) and (not (not not (((4 * 4 - -9 * -8) >= (7 % 10)) and ((12 * 8) > (44 % 1))))) and (not not ((not (((5 - 0) != (-17 + -14)) and (南极洲是最冷的大陆。))) or ((兔子是哺乳动物。) or (not (泰坦尼克号沉没发生在1922年。)))))) and (not ((not (空气在常温下是固体。)) or (not not (((海王星是距离太阳第8近的行星。) and (天王星是距离太阳第2近的行星。)) and ((2072年是闰年。) and ((18 + -8) == (35 % 2)))))))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 57918296,
"true_count": 2
},
"seed": 57918296,
"task_id": 657918296,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (not (not ((A crocodile is a bird.) and (The currency of Israel is the Shekel.))))
B. not not (not ((((-9 * 10) >= (45 % 2)) and (The chemical symbol for Uranium is U.)) and ((1 ** 2) == (-17 + -19))))
C. not not (not not ((not (31 is divisible by 7.)) and (not (The chemical symbol for Aluminum is Al.))))
D. (((15 - 14) == (3 * 5 - 8 * -6)) or (Christopher Columbus reached America occurred in 1492.)) and (not not ((((-1 * -4 - -3 * 7) > (-1 * 3 + 10 * -10)) or ((3 * -3) > (-2 * -9 - 3 * -4))) and (((-9 + -11) <= (-1 * 5 - 9 * 0) <= (37 % 10)) and ((-12 * 17) > (14 + 17)))))
E. ((88 is a perfect square.) or (((5 ** 3) < (-18 + -4)) or (Ice is a liquid at room temperature.)) or (not ((The currency of Colombia is the Dollar.) and (28 is greater than 98.)))) or (not (((The chemical symbol for Chlorine is Cl.) or (The chemical symbol for Nitrogen is N.)) and (The currency of Indonesia is the Yen.)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 63243149,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (not (not ((A crocodile is a bird.) and (The currency of Israel is the Shekel.))))\nB. not not (not ((((-9 * 10) >= (45 % 2)) and (The chemical symbol for Uranium is U.)) and ((1 ** 2) == (-17 + -19))))\nC. not not (not not ((not (31 is divisible by 7.)) and (not (The chemical symbol for Aluminum is Al.))))\nD. (((15 - 14) == (3 * 5 - 8 * -6)) or (Christopher Columbus reached America occurred in 1492.)) and (not not ((((-1 * -4 - -3 * 7) > (-1 * 3 + 10 * -10)) or ((3 * -3) > (-2 * -9 - 3 * -4))) and (((-9 + -11) <= (-1 * 5 - 9 * 0) <= (37 % 10)) and ((-12 * 17) > (14 + 17)))))\nE. ((88 is a perfect square.) or (((5 ** 3) < (-18 + -4)) or (Ice is a liquid at room temperature.)) or (not ((The currency of Colombia is the Dollar.) and (28 is greater than 98.)))) or (not (((The chemical symbol for Chlorine is Cl.) or (The chemical symbol for Nitrogen is N.)) and (The currency of Indonesia is the Yen.)))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 63243149,
"true_count": 2
},
"seed": 63243149,
"task_id": 663243149,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not ((((3 ** 2) == (-14 + 2)) and (Mercury is a liquid at room temperature.)) or (not (Neptune is the 3rd planet from the Sun.)))
B. not not (not not ((-10 * -3) <= (-20 + -7)))
C. ((-10 - -12) < (-20 * 5) < (-5 * -6 + -9 * 8)) or (1935 is a leap year.)
D. (not not (((15 + 12) < (1 * 3 * 10 * -6)) and ((5 ** 2) < (8 * 7 * 7 * -1)))) or ((The chemical symbol for Zinc is Zn.) or ((1 * -3 + 6 * -3) >= (15 - -4))) or (Venus is the 2nd planet from the Sun.)
E. not (not not (((19 + -18) < (9 - 18)) or ((-3 * -3 * 2 * 8) <= (5 * 3) <= (-14 * -15))))
F. not ((((8 + -1) < (-17 - -3)) or (Saturn is the 6th planet from the Sun.)) and ((2021 is a leap year.) or (The 1900 Olympics were held in Paris.)))
G. (34 is a prime number.) and ((-13 + -14) < (6 + -11))
H. ((The 1960 Olympics were held in Berlin.) or (not not ((0 - 13) == (-2 * -5)))) and (Antarctica is the coldest continent.) and (Jupiter is the 7th planet from the Sun.)
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 40630310,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not ((((3 ** 2) == (-14 + 2)) and (Mercury is a liquid at room temperature.)) or (not (Neptune is the 3rd planet from the Sun.)))\nB. not not (not not ((-10 * -3) <= (-20 + -7)))\nC. ((-10 - -12) < (-20 * 5) < (-5 * -6 + -9 * 8)) or (1935 is a leap year.)\nD. (not not (((15 + 12) < (1 * 3 * 10 * -6)) and ((5 ** 2) < (8 * 7 * 7 * -1)))) or ((The chemical symbol for Zinc is Zn.) or ((1 * -3 + 6 * -3) >= (15 - -4))) or (Venus is the 2nd planet from the Sun.)\nE. not (not not (((19 + -18) < (9 - 18)) or ((-3 * -3 * 2 * 8) <= (5 * 3) <= (-14 * -15))))\nF. not ((((8 + -1) < (-17 - -3)) or (Saturn is the 6th planet from the Sun.)) and ((2021 is a leap year.) or (The 1900 Olympics were held in Paris.)))\nG. (34 is a prime number.) and ((-13 + -14) < (6 + -11))\nH. ((The 1960 Olympics were held in Berlin.) or (not not ((0 - 13) == (-2 * -5)))) and (Antarctica is the coldest continent.) and (Jupiter is the 7th 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": 8,
"seed": 40630310,
"true_count": 2
},
"seed": 40630310,
"task_id": 640630310,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (((The currency of Mexico is the Peso.) or (Nitrogen is a gas at room temperature.)) or ((The 1952 Olympics were held in Mexico City.) or ((24 % 10) > (10 + 9)))) and (((There are 30 days in November.) or ((10 * 2 + 6 * 2) > (46 % 7))) and (The chemical symbol for Oxygen is Au.))
B. not ((-5 - -3) <= (-18 - 20))
C. ((19 * 12) <= (5 - 19)) and ((((18 + -10) > (3 - 13)) and (Water boils at 100 degrees Celsius at sea level.)) and (((-7 + 9) < (-16 - 1)) and (A mosquito is an insect.)))
D. not (not (Mars is the closest planet to the Sun.))
E. not not (Saturn is the 3rd planet from the Sun.)
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 48269138,
"true_count": 1
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (((The currency of Mexico is the Peso.) or (Nitrogen is a gas at room temperature.)) or ((The 1952 Olympics were held in Mexico City.) or ((24 % 10) > (10 + 9)))) and (((There are 30 days in November.) or ((10 * 2 + 6 * 2) > (46 % 7))) and (The chemical symbol for Oxygen is Au.))\nB. not ((-5 - -3) <= (-18 - 20))\nC. ((19 * 12) <= (5 - 19)) and ((((18 + -10) > (3 - 13)) and (Water boils at 100 degrees Celsius at sea level.)) and (((-7 + 9) < (-16 - 1)) and (A mosquito is an insect.)))\nD. not (not (Mars is the closest planet to the Sun.))\nE. not not (Saturn is the 3rd planet from the Sun.)\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 48269138,
"true_count": 1
},
"seed": 48269138,
"task_id": 648269138,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not (not (not not (There are 31 days in March.)))
B. (not (not ((not not ((-6 - 5) <= (-5 + -6))) or (Copper is a liquid at room temperature.)))) and (not (not (not not (not not ((0 + -12) > (-17 * -5))))))
C. not not (not ((Brazil is in Asia.) or (((-4 * 8 + 1 * -3) >= (10 * -5 - 1 * -9)) and ((614 is a Fibonacci number.) and (40 is less than or equal to 62.)))))
D. not (not not (not not (not not ((The 1956 Olympics were held in Tokyo.) and (The human body has 150 bones.)))))
E. not (((((45 is less than or equal to 56.) or (Spiders are insects.)) or (((6 + 5) < (-8 * 2 + 8 * 6)) or ((-11 + -6) > (-3 * 7 - 9 * 6)))) or (((3 * 2 - 6 * 6) == (5 ** 3)) and ((2 * -10 + 6 * -4) <= (9 + -12))) or ((-6 * -11) >= (-2 * 5 - -1 * 6))) and (not ((14 + -13) <= (-8 + -12) <= (7 + -3))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 28358040,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. not not (not (not not (There are 31 days in March.)))\nB. (not (not ((not not ((-6 - 5) <= (-5 + -6))) or (Copper is a liquid at room temperature.)))) and (not (not (not not (not not ((0 + -12) > (-17 * -5))))))\nC. not not (not ((Brazil is in Asia.) or (((-4 * 8 + 1 * -3) >= (10 * -5 - 1 * -9)) and ((614 is a Fibonacci number.) and (40 is less than or equal to 62.)))))\nD. not (not not (not not (not not ((The 1956 Olympics were held in Tokyo.) and (The human body has 150 bones.)))))\nE. not (((((45 is less than or equal to 56.) or (Spiders are insects.)) or (((6 + 5) < (-8 * 2 + 8 * 6)) or ((-11 + -6) > (-3 * 7 - 9 * 6)))) or (((3 * 2 - 6 * 6) == (5 ** 3)) and ((2 * -10 + 6 * -4) <= (9 + -12))) or ((-6 * -11) >= (-2 * 5 - -1 * 6))) and (not ((14 + -13) <= (-8 + -12) <= (7 + -3))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 28358040,
"true_count": 2
},
"seed": 28358040,
"task_id": 628358040,
"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 ((3 ** 1) >= (9 * 8 * 3 * 5))) or (not not ((-4 * -6) <= (-10 * 10 - 7 * -6))))
B. not ((0 * -16) != (-3 + -18))
C. (not not (金在常温下是固体。)) or (not not (750是斐波那契数。)) or ((-7 + -1) != (16 * -8))
D. ((20 - -13) > (2 * 10 - 3 * 7)) and ((-14 - 18) < (-2 + 18)) and (((铜在常温下是液体。) and ((-4 * 2) <= (9 * -12) <= (6 - -6))) and (((6 * 10) < (-10 + 17)) or (沙特阿拉伯位于欧洲。)))
E. ((24 % 2) >= (19 + 11)) or (九月有30天。)
F. not not (((人类每只手有五个手指。) and (人体有150块骨头。)) and ((14是奇数。) or (氮的化学符号是Fe。)))
G. (((-4 * 2) != (-9 - 0)) and (not (第一部iPhone发布发生在2007年。))) and (1976年奥运会在柏林举办。) and ((-20 + 0) > (9 * 4 + 4 * -9))
H. (乌龟是爬行动物。) and (not not (氧的化学符号是O。)) and (((372是完全平方数。) and (巴西位于南美洲。)) or ((2 ** 2) == (0 * 4 * -8 * 8)))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 60600009,
"true_count": 3
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not ((not not ((3 ** 1) >= (9 * 8 * 3 * 5))) or (not not ((-4 * -6) <= (-10 * 10 - 7 * -6))))\nB. not ((0 * -16) != (-3 + -18))\nC. (not not (金在常温下是固体。)) or (not not (750是斐波那契数。)) or ((-7 + -1) != (16 * -8))\nD. ((20 - -13) > (2 * 10 - 3 * 7)) and ((-14 - 18) < (-2 + 18)) and (((铜在常温下是液体。) and ((-4 * 2) <= (9 * -12) <= (6 - -6))) and (((6 * 10) < (-10 + 17)) or (沙特阿拉伯位于欧洲。)))\nE. ((24 % 2) >= (19 + 11)) or (九月有30天。)\nF. not not (((人类每只手有五个手指。) and (人体有150块骨头。)) and ((14是奇数。) or (氮的化学符号是Fe。)))\nG. (((-4 * 2) != (-9 - 0)) and (not (第一部iPhone发布发生在2007年。))) and (1976年奥运会在柏林举办。) and ((-20 + 0) > (9 * 4 + 4 * -9))\nH. (乌龟是爬行动物。) and (not not (氧的化学符号是O。)) and (((372是完全平方数。) and (巴西位于南美洲。)) or ((2 ** 2) == (0 * 4 * -8 * 8)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 60600009,
"true_count": 3
},
"seed": 60600009,
"task_id": 660600009,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not (英国的货币是埃及镑。)
B. (((海王星是距离太阳第8近的行星。) and (锌的化学符号是Ne。)) and ((14 - -19) >= (13 % 4))) and ((8 * 17) < (19 * 8)) and (声音无法在真空中传播。)
C. ((10 - 6) < (17 - 15)) and ((((3 - 19) < (12 + 12)) or (人类只使用了大脑的10%。)) or ((阿根廷的货币是日元。) and ((-4 * 10 + -10 * -7) <= (2 * -3 - 1 * -5))))
D. ((((5 ** 2) > (9 * -9 * -4 * 7)) or (钻石由碳元素组成。)) or ((2016年奥运会在里约热内卢举办。) and ((-16 + 12) < (-1 * -2 - -1 * 10)))) and ((((-15 - 6) == (3 * -3)) and ((-4 * 1 + 8 * 5) == (4 ** 2))) and (木星是距离太阳第3近的行星。))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 77404057,
"true_count": 1
},
"question": "下面是几个布尔表达式：\n\nA. not (英国的货币是埃及镑。)\nB. (((海王星是距离太阳第8近的行星。) and (锌的化学符号是Ne。)) and ((14 - -19) >= (13 % 4))) and ((8 * 17) < (19 * 8)) and (声音无法在真空中传播。)\nC. ((10 - 6) < (17 - 15)) and ((((3 - 19) < (12 + 12)) or (人类只使用了大脑的10%。)) or ((阿根廷的货币是日元。) and ((-4 * 10 + -10 * -7) <= (2 * -3 - 1 * -5))))\nD. ((((5 ** 2) > (9 * -9 * -4 * 7)) or (钻石由碳元素组成。)) or ((2016年奥运会在里约热内卢举办。) and ((-16 + 12) < (-1 * -2 - -1 * 10)))) and ((((-15 - 6) == (3 * -3)) and ((-4 * 1 + 8 * 5) == (4 ** 2))) and (木星是距离太阳第3近的行星。))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 77404057,
"true_count": 1
},
"seed": 77404057,
"task_id": 677404057,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not (not not (not not (2030 is a leap year.)))
B. not not (not ((19 is a prime number.) and ((3 ** 3) < (2 ** 2))))
C. not not ((South Korea is in Africa.) and (((Oil is a liquid at room temperature.) and (Venus is the 8th planet from the Sun.)) or ((3 ** 2) != (-18 + -1))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 80400554,
"true_count": 2
},
"question": "Given the following boolean expressions:\n\nA. not (not not (not not (2030 is a leap year.)))\nB. not not (not ((19 is a prime number.) and ((3 ** 3) < (2 ** 2))))\nC. not not ((South Korea is in Africa.) and (((Oil is a liquid at room temperature.) and (Venus is the 8th planet from the Sun.)) or ((3 ** 2) != (-18 + -1))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 80400554,
"true_count": 2
},
"seed": 80400554,
"task_id": 680400554,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not (((金星是距离太阳第2近的行星。) and (光速约为每秒30万公里。)) or (((14 - 2) != (9 * 0 * -5 * -10)) and (1984年奥运会在巴塞罗那举办。)))
B. (not ((猫头鹰是鸟类。) or ((25 % 6) == (-19 - -13)))) and ((铜在常温下是固体。) and (669是斐波那契数。)) and ((3 - 4) > (-2 * 9))
C. ((((-5 * -7 * -7 * -6) <= (-4 + 6)) and (企鹅能飞翔。)) or (not not (中国位于亚洲。))) or ((290是斐波那契数。) and ((44 % 2) != (3 * -4 * -9 * -5)))
D. (((10 * -10) >= (10 + -5)) and ((3 * -10 + -7 * -2) != (-2 * -6 + -6 * 10))) or ((((-19 + 11) != (16 - -18)) and ((1 * 9 + 3 * -9) >= (17 * -2))) and ((钛的化学符号是Ti。) or (瑞士的货币是瑞士法郎。)))
E. ((19 + 14) < (3 * -10 + 0 * 4)) and (((16 + 9) < (12 * -3)) or (1972年奥运会在莫斯科举办。)) and (变色龙是爬行动物。)
F. (金的化学符号是C。) and (not not (((5 ** 1) <= (-10 * -6 + 5 * -5)) or (第一次世界大战结束发生在1917年。)))
G. ((((1 % 5) <= (5 * 5 * 8 * 3) <= (-8 + 3)) and (木头在常温下是固体。)) or (植物通过光合作用产生氧气。)) or (伦敦大火发生在1666年。)
H. not not ((墨西哥的首都是墨西哥城。) or (地球是距离太阳第3近的行星。))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "C,D,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 88247394,
"true_count": 4
},
"question": "评估以下每个表达式：\n\nA. not (((金星是距离太阳第2近的行星。) and (光速约为每秒30万公里。)) or (((14 - 2) != (9 * 0 * -5 * -10)) and (1984年奥运会在巴塞罗那举办。)))\nB. (not ((猫头鹰是鸟类。) or ((25 % 6) == (-19 - -13)))) and ((铜在常温下是固体。) and (669是斐波那契数。)) and ((3 - 4) > (-2 * 9))\nC. ((((-5 * -7 * -7 * -6) <= (-4 + 6)) and (企鹅能飞翔。)) or (not not (中国位于亚洲。))) or ((290是斐波那契数。) and ((44 % 2) != (3 * -4 * -9 * -5)))\nD. (((10 * -10) >= (10 + -5)) and ((3 * -10 + -7 * -2) != (-2 * -6 + -6 * 10))) or ((((-19 + 11) != (16 - -18)) and ((1 * 9 + 3 * -9) >= (17 * -2))) and ((钛的化学符号是Ti。) or (瑞士的货币是瑞士法郎。)))\nE. ((19 + 14) < (3 * -10 + 0 * 4)) and (((16 + 9) < (12 * -3)) or (1972年奥运会在莫斯科举办。)) and (变色龙是爬行动物。)\nF. (金的化学符号是C。) and (not not (((5 ** 1) <= (-10 * -6 + 5 * -5)) or (第一次世界大战结束发生在1917年。)))\nG. ((((1 % 5) <= (5 * 5 * 8 * 3) <= (-8 + 3)) and (木头在常温下是固体。)) or (植物通过光合作用产生氧气。)) or (伦敦大火发生在1666年。)\nH. not not ((墨西哥的首都是墨西哥城。) or (地球是距离太阳第3近的行星。))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 88247394,
"true_count": 4
},
"seed": 88247394,
"task_id": 688247394,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (((A rabbit is a mammal.) or (The 1992 Olympics were held in Barcelona.)) or ((3 * -2 - 8 * 6) > (-11 + -7)))
B. not not ((((Saturn is the 6th planet from the Sun.) and (Iron is a solid at room temperature.)) or (not not (The 1896 Olympics were held in Athens.))) and (The capital of Denmark is Hanoi.))
C. not (not (not not ((The currency of China is the Krona.) and ((14 + 0) != (-10 - -10)))))
D. (((10 * 2 * -7 * 1) <= (10 - -1)) or ((-6 * -10 - 1 * 0) >= (15 + 20))) and (((34 % 9) <= (-3 * 4) <= (-20 * 9)) or (97 is greater than 37.) or ((not not ((28 % 4) >= (1 + -9))) and ((The chemical symbol for Potassium is K.) and (Helium is a solid at room temperature.))))
E. (((The currency of Canada is the Yuan.) and ((-15 + -20) != (16 % 6))) or (not not (((49 % 7) > (-8 * 7)) and (The capital of India is New Delhi.)))) or (not not ((27 % 8) <= (0 - -4) <= (5 ** 2)))
F. (not not (((2020 is a leap year.) or (Saturn is the 2nd planet from the Sun.)) or (South Africa is in Africa.))) or ((not not ((1 % 3) <= (13 + 6))) and (((Oxygen is a solid at room temperature.) and ((-18 + 6) <= (-15 - -8) <= (-19 * -20))) and ((Mars is the 4th planet from the Sun.) or ((26 % 2) >= (2 - 2)))))
G. (not not ((-1 * 9 + 3 * -9) <= (7 * 4 - 9 * 1))) and (not ((3 + 4) >= (5 * 5 + 5 * -10))) and (not (not not (((1 ** 2) < (-20 * -18)) and (The capital of Belgium is Stockholm.))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 38744878,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not (((A rabbit is a mammal.) or (The 1992 Olympics were held in Barcelona.)) or ((3 * -2 - 8 * 6) > (-11 + -7)))\nB. not not ((((Saturn is the 6th planet from the Sun.) and (Iron is a solid at room temperature.)) or (not not (The 1896 Olympics were held in Athens.))) and (The capital of Denmark is Hanoi.))\nC. not (not (not not ((The currency of China is the Krona.) and ((14 + 0) != (-10 - -10)))))\nD. (((10 * 2 * -7 * 1) <= (10 - -1)) or ((-6 * -10 - 1 * 0) >= (15 + 20))) and (((34 % 9) <= (-3 * 4) <= (-20 * 9)) or (97 is greater than 37.) or ((not not ((28 % 4) >= (1 + -9))) and ((The chemical symbol for Potassium is K.) and (Helium is a solid at room temperature.))))\nE. (((The currency of Canada is the Yuan.) and ((-15 + -20) != (16 % 6))) or (not not (((49 % 7) > (-8 * 7)) and (The capital of India is New Delhi.)))) or (not not ((27 % 8) <= (0 - -4) <= (5 ** 2)))\nF. (not not (((2020 is a leap year.) or (Saturn is the 2nd planet from the Sun.)) or (South Africa is in Africa.))) or ((not not ((1 % 3) <= (13 + 6))) and (((Oxygen is a solid at room temperature.) and ((-18 + 6) <= (-15 - -8) <= (-19 * -20))) and ((Mars is the 4th planet from the Sun.) or ((26 % 2) >= (2 - 2)))))\nG. (not not ((-1 * 9 + 3 * -9) <= (7 * 4 - 9 * 1))) and (not ((3 + 4) >= (5 * 5 + 5 * -10))) and (not (not not (((1 ** 2) < (-20 * -18)) and (The capital of Belgium is Stockholm.))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 38744878,
"true_count": 3
},
"seed": 38744878,
"task_id": 638744878,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not not (法国大革命开始发生在1787年。)
B. 冰的密度比液态水小。
C. (氖的化学符号是Ne。) and ((6 * -4 * -3 * -4) < (-17 + -12) < (5 ** 2)) and (((-8 * 2 + 0 * -7) == (-10 + -10)) and (not ((10 - -18) > (2 ** 3))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 24095766,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. not not (法国大革命开始发生在1787年。)\nB. 冰的密度比液态水小。\nC. (氖的化学符号是Ne。) and ((6 * -4 * -3 * -4) < (-17 + -12) < (5 ** 2)) and (((-8 * 2 + 0 * -7) == (-10 + -10)) and (not ((10 - -18) > (2 ** 3))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 24095766,
"true_count": 1
},
"seed": 24095766,
"task_id": 624095766,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not not (((The human body has 150 bones.) and (((15 % 9) == (-9 - 5)) and (A pig has 8 legs.))) and (not not (((-8 * 6) >= (4 ** 1)) and (not not (Water is a liquid at room temperature.)))))
B. (not (((13 % 10) != (-8 * 5 - -8 * 1)) or (The first Olympic Games of modern era occurred in 1896.) or ((((15 * -8) <= (-1 * -3 * 0 * 3)) and (There are 28 days in November.)) or ((-3 + 4) >= (3 - -2))))) or (not ((The currency of Malaysia is the Ringgit.) or ((The capital of Belgium is Amsterdam.) or ((16 + 15) >= (-6 - -10))) or (((1966 is a leap year.) or (A elephant has 8 legs.)) and ((A turtle is a fish.) and (121 is an odd number.)))))
C. (((((11 * -8) != (3 ** 3)) and (The Soviet Union dissolved occurred in 1991.)) or (World War I began occurred in 1914.)) and ((((The capital of Czech Republic is Berlin.) or (There are 29 days in December.)) or ((70 is less than or equal to 48.) or ((-16 - 6) >= (-15 + 7)))) or (not not ((33 is greater than 72.) and ((10 + -20) < (-3 * 9 - -6 * -1) < (-3 + -7)))))) and (not (not ((-13 + 18) <= (20 + -2) <= (-7 * 0))))
D. not not (((((8 * 10 + 10 * -10) != (5 ** 3)) and (((16 - -3) < (4 * -1 * 3 * 2)) and ((9 * 16) <= (10 * 8 - 0 * -8)))) or (The currency of Singapore is the Dollar.)) and ((8 % 5) != (-5 * 7 + -1 * -5)) and (((7 + -17) == (-3 * 6 - -5 * 3)) or (not (The capital of China is Hanoi.))))
E. (not (not not ((not ((1 * -11) == (-5 + 2))) or (not not ((-18 - -2) <= (-12 * 20)))))) and ((Saturn is the 6th planet from the Sun.) and (not not ((The 1992 Olympics were held in Paris.) or ((1 * 4 - -10 * -9) < (-15 * -19))))) and (not not ((not ((Earth is the 1st planet from the Sun.) or ((2 ** 3) == (1 + -2)))) and ((There are 30 days in October.) and (not not (Carbon dioxide is a solid at room temperature.)))))
F. not (not (((4 ** 3) > (19 - -4)) and ((Spiders are insects.) or (There are 28 days in July.))))
G. not ((((not (Jupiter is the 5th planet from the Sun.)) and ((The capital of Romania is Oslo.) and (The capital of Chile is Santiago.))) or ((1 * 8 * -4 * 6) != (15 + 8))) or (not not ((((5 ** 3) <= (2 % 6)) or ((1 ** 3) <= (13 - 7))) and (not (82 is divisible by 6.)))))
H. not (((The currency of Argentina is the Peso.) or ((France is in Europe.) or (88 is divisible by 7.)) or (((-2 * 3) == (1 * 9 - 5 * 9)) and ((15 * 13) == (9 * -16)))) or (((The currency of European Union is the Peso.) or ((3 * 1) <= (-3 + -2))) and (The 1964 Olympics were held in Stockholm.)) or ((The capital of Thailand is Bangkok.) and ((not (The 1992 Olympics were held in Barcelona.)) and ((Nigeria is in Africa.) and ((18 * -13) >= (-5 * 16))))))
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": 5,
"language": "en",
"num_options": 8,
"seed": 73745621,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. not not (((The human body has 150 bones.) and (((15 % 9) == (-9 - 5)) and (A pig has 8 legs.))) and (not not (((-8 * 6) >= (4 ** 1)) and (not not (Water is a liquid at room temperature.)))))\nB. (not (((13 % 10) != (-8 * 5 - -8 * 1)) or (The first Olympic Games of modern era occurred in 1896.) or ((((15 * -8) <= (-1 * -3 * 0 * 3)) and (There are 28 days in November.)) or ((-3 + 4) >= (3 - -2))))) or (not ((The currency of Malaysia is the Ringgit.) or ((The capital of Belgium is Amsterdam.) or ((16 + 15) >= (-6 - -10))) or (((1966 is a leap year.) or (A elephant has 8 legs.)) and ((A turtle is a fish.) and (121 is an odd number.)))))\nC. (((((11 * -8) != (3 ** 3)) and (The Soviet Union dissolved occurred in 1991.)) or (World War I began occurred in 1914.)) and ((((The capital of Czech Republic is Berlin.) or (There are 29 days in December.)) or ((70 is less than or equal to 48.) or ((-16 - 6) >= (-15 + 7)))) or (not not ((33 is greater than 72.) and ((10 + -20) < (-3 * 9 - -6 * -1) < (-3 + -7)))))) and (not (not ((-13 + 18) <= (20 + -2) <= (-7 * 0))))\nD. not not (((((8 * 10 + 10 * -10) != (5 ** 3)) and (((16 - -3) < (4 * -1 * 3 * 2)) and ((9 * 16) <= (10 * 8 - 0 * -8)))) or (The currency of Singapore is the Dollar.)) and ((8 % 5) != (-5 * 7 + -1 * -5)) and (((7 + -17) == (-3 * 6 - -5 * 3)) or (not (The capital of China is Hanoi.))))\nE. (not (not not ((not ((1 * -11) == (-5 + 2))) or (not not ((-18 - -2) <= (-12 * 20)))))) and ((Saturn is the 6th planet from the Sun.) and (not not ((The 1992 Olympics were held in Paris.) or ((1 * 4 - -10 * -9) < (-15 * -19))))) and (not not ((not ((Earth is the 1st planet from the Sun.) or ((2 ** 3) == (1 + -2)))) and ((There are 30 days in October.) and (not not (Carbon dioxide is a solid at room temperature.)))))\nF. not (not (((4 ** 3) > (19 - -4)) and ((Spiders are insects.) or (There are 28 days in July.))))\nG. not ((((not (Jupiter is the 5th planet from the Sun.)) and ((The capital of Romania is Oslo.) and (The capital of Chile is Santiago.))) or ((1 * 8 * -4 * 6) != (15 + 8))) or (not not ((((5 ** 3) <= (2 % 6)) or ((1 ** 3) <= (13 - 7))) and (not (82 is divisible by 6.)))))\nH. not (((The currency of Argentina is the Peso.) or ((France is in Europe.) or (88 is divisible by 7.)) or (((-2 * 3) == (1 * 9 - 5 * 9)) and ((15 * 13) == (9 * -16)))) or (((The currency of European Union is the Peso.) or ((3 * 1) <= (-3 + -2))) and (The 1964 Olympics were held in Stockholm.)) or ((The capital of Thailand is Bangkok.) and ((not (The 1992 Olympics were held in Barcelona.)) and ((Nigeria is in Africa.) and ((18 * -13) >= (-5 * 16))))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 73745621,
"true_count": 1
},
"seed": 73745621,
"task_id": 673745621,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((((1988年奥运会在斯德哥尔摩举办。) and (丹麦的货币是克朗。)) and (柏林墙倒塌发生在1989年。)) and (((((-11 - 9) < (-3 * -2 + -9 * -10)) or (瑞士的货币是比索。)) or (((1 % 10) <= (5 - 5)) or ((0 + -10) < (41 % 3)))) and (not not (2024年奥运会在亚特兰大举办。)))) and ((((水星是距离太阳第1近的行星。) or ((-10 - 10) != (46 % 3))) or (((5 % 5) != (8 * 12)) or ((4 * 0 * 9 * -9) == (6 * -2)))) and (21能被3整除。)) and ((not not (not not (1976年奥运会在巴塞罗那举办。))) or (not (((19 * 9) < (19 + 15) < (3 * -2 + 0 * -1)) and (2029年是闰年。))))
B. (not not ((((-18 - -14) == (-2 * 8 - -6 * -6)) and ((日本位于北美洲。) or ((19 + 1) > (-1 * 6 - -5 * 1)))) and (((氦气在常温下是液体。) and ((-12 + -12) <= (9 % 1))) or (((4 + -8) < (3 * 3 + 6 * -9)) or (二氧化碳在常温下是液体。))))) and (not ((马是昆虫。) or (((2 ** 3) <= (3 ** 2)) or ((1 * -3 - -8 * 5) >= (15 + -11))) or (((11 + -13) <= (20 + -5) <= (10 + -16)) or (not (1927年是闰年。)))))
C. (not not (((-1 + 19) >= (10 + 5)) and ((伦敦大火发生在1666年。) and ((4 ** 2) == (-17 - 5))))) and (((not (2000年奥运会在北京举办。)) and ((44 % 6) > (11 - -18))) and (not not ((15 + -18) == (-10 * -17)))) and (not not ((((-1 * 6 * 0 * -6) == (1 ** 1)) and ((加拿大位于大洋洲。) and ((5 ** 3) <= (10 * -7 - -6 * 5) <= (-10 * -3 + -5 * -4)))) and ((七月有31天。) or ((-18 + -14) > (0 + -16))) and (not not (not ((12 * 12) >= (4 * -2 * 9 * -3))))))
D. ((not not (not not ((0 * -1) != (-9 * 16)))) and (not not ((not not (印度尼西亚位于非洲。)) and (((-11 * -13) < (34 % 8) < (2 - 5)) or ((-19 - -1) >= (-10 * 3 - -1 * -3)))))) or ((not (变色龙是爬行动物。)) or (((狗是哺乳动物。) or (摩洛哥的首都是拉巴特。)) and (not not (44大于26。))) or (not ((-12 * -16) < (20 - -11))))
E. (not not (not not (not ((5 + -5) == (4 ** 1))))) and ((not ((((12 * 11) <= (13 - 20)) and ((9 * -2 + 4 * 0) != (-4 + 7))) or (((0 - 8) <= (32 % 10) <= (11 - 6)) or (20是质数。)))) and ((天王星是距离太阳第2近的行星。) and (((60大于92。) and (日本位于亚洲。)) or (((30 % 7) >= (-17 - -12)) and ((2 ** 2) == (-16 * -10))))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 4000719,
"true_count": 1
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. ((((1988年奥运会在斯德哥尔摩举办。) and (丹麦的货币是克朗。)) and (柏林墙倒塌发生在1989年。)) and (((((-11 - 9) < (-3 * -2 + -9 * -10)) or (瑞士的货币是比索。)) or (((1 % 10) <= (5 - 5)) or ((0 + -10) < (41 % 3)))) and (not not (2024年奥运会在亚特兰大举办。)))) and ((((水星是距离太阳第1近的行星。) or ((-10 - 10) != (46 % 3))) or (((5 % 5) != (8 * 12)) or ((4 * 0 * 9 * -9) == (6 * -2)))) and (21能被3整除。)) and ((not not (not not (1976年奥运会在巴塞罗那举办。))) or (not (((19 * 9) < (19 + 15) < (3 * -2 + 0 * -1)) and (2029年是闰年。))))\nB. (not not ((((-18 - -14) == (-2 * 8 - -6 * -6)) and ((日本位于北美洲。) or ((19 + 1) > (-1 * 6 - -5 * 1)))) and (((氦气在常温下是液体。) and ((-12 + -12) <= (9 % 1))) or (((4 + -8) < (3 * 3 + 6 * -9)) or (二氧化碳在常温下是液体。))))) and (not ((马是昆虫。) or (((2 ** 3) <= (3 ** 2)) or ((1 * -3 - -8 * 5) >= (15 + -11))) or (((11 + -13) <= (20 + -5) <= (10 + -16)) or (not (1927年是闰年。)))))\nC. (not not (((-1 + 19) >= (10 + 5)) and ((伦敦大火发生在1666年。) and ((4 ** 2) == (-17 - 5))))) and (((not (2000年奥运会在北京举办。)) and ((44 % 6) > (11 - -18))) and (not not ((15 + -18) == (-10 * -17)))) and (not not ((((-1 * 6 * 0 * -6) == (1 ** 1)) and ((加拿大位于大洋洲。) and ((5 ** 3) <= (10 * -7 - -6 * 5) <= (-10 * -3 + -5 * -4)))) and ((七月有31天。) or ((-18 + -14) > (0 + -16))) and (not not (not ((12 * 12) >= (4 * -2 * 9 * -3))))))\nD. ((not not (not not ((0 * -1) != (-9 * 16)))) and (not not ((not not (印度尼西亚位于非洲。)) and (((-11 * -13) < (34 % 8) < (2 - 5)) or ((-19 - -1) >= (-10 * 3 - -1 * -3)))))) or ((not (变色龙是爬行动物。)) or (((狗是哺乳动物。) or (摩洛哥的首都是拉巴特。)) and (not not (44大于26。))) or (not ((-12 * -16) < (20 - -11))))\nE. (not not (not not (not ((5 + -5) == (4 ** 1))))) and ((not ((((12 * 11) <= (13 - 20)) and ((9 * -2 + 4 * 0) != (-4 + 7))) or (((0 - 8) <= (32 % 10) <= (11 - 6)) or (20是质数。)))) and ((天王星是距离太阳第2近的行星。) and (((60大于92。) and (日本位于亚洲。)) or (((30 % 7) >= (-17 - -12)) and ((2 ** 2) == (-16 * -10))))))\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": 5,
"seed": 4000719,
"true_count": 1
},
"seed": 4000719,
"task_id": 604000719,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((not not ((35 % 2) < (17 * -3) < (33 % 5))) and (not not (not (((15 % 9) >= (50 % 2)) or (1980年奥运会在东京举办。))))) or (not (not (((-9 * -11) > (7 * -1 - 4 * -10)) and (1908年奥运会在亚特兰大举办。)))) or (((水在常温下是液体。) and ((4 - 12) >= (18 - -11))) and (not ((-13 * -14) >= (25 % 5))) and ((not not (挪威的货币是克朗。)) or ((日本的首都是东京。) or (1968年奥运会在雅典举办。))))
B. (not (((-2 + 4) <= (-18 - 8) <= (-9 * 1 - -6 * 9)) or ((((13 * -19) == (-2 * 6 - -5 * -8)) and (2000年奥运会在首尔举办。)) and ((4 * -19) >= (14 + -16))))) and (not not ((铀的化学符号是U。) and (新西兰的货币是谢克尔。)))
C. not not (((((钴的化学符号是He。) and ((9 * -2 * 0 * -9) == (-14 * -15))) or (not not ((42 % 10) == (-13 + 13)))) or (((火星是距离太阳第4近的行星。) or ((11 * -1) <= (36 % 10))) or (人类有0条腿。))) or (((14 * 20) == (9 * -10 * 7 * 7)) and ((哥伦比亚的货币是比索。) and ((20 - 15) >= (15 - -4)))) or (((-6 - 16) >= (8 % 8)) and (((金星是距离太阳第2近的行星。) or (沙特阿拉伯位于亚洲。)) or (not not (比利时的首都是布鲁塞尔。)))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 88478093,
"true_count": 1
},
"question": "下面是几个布尔表达式：\n\nA. ((not not ((35 % 2) < (17 * -3) < (33 % 5))) and (not not (not (((15 % 9) >= (50 % 2)) or (1980年奥运会在东京举办。))))) or (not (not (((-9 * -11) > (7 * -1 - 4 * -10)) and (1908年奥运会在亚特兰大举办。)))) or (((水在常温下是液体。) and ((4 - 12) >= (18 - -11))) and (not ((-13 * -14) >= (25 % 5))) and ((not not (挪威的货币是克朗。)) or ((日本的首都是东京。) or (1968年奥运会在雅典举办。))))\nB. (not (((-2 + 4) <= (-18 - 8) <= (-9 * 1 - -6 * 9)) or ((((13 * -19) == (-2 * 6 - -5 * -8)) and (2000年奥运会在首尔举办。)) and ((4 * -19) >= (14 + -16))))) and (not not ((铀的化学符号是U。) and (新西兰的货币是谢克尔。)))\nC. not not (((((钴的化学符号是He。) and ((9 * -2 * 0 * -9) == (-14 * -15))) or (not not ((42 % 10) == (-13 + 13)))) or (((火星是距离太阳第4近的行星。) or ((11 * -1) <= (36 % 10))) or (人类有0条腿。))) or (((14 * 20) == (9 * -10 * 7 * 7)) and ((哥伦比亚的货币是比索。) and ((20 - 15) >= (15 - -4)))) or (((-6 - 16) >= (8 % 8)) and (((金星是距离太阳第2近的行星。) or (沙特阿拉伯位于亚洲。)) or (not not (比利时的首都是布鲁塞尔。)))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 88478093,
"true_count": 1
},
"seed": 88478093,
"task_id": 688478093,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (not not ((not ((not (22是偶数。)) and (硅的化学符号是Al。))) and (not not ((not ((3 ** 2) <= (-12 - -7) <= (-4 * -3 * 2 * 1))) or ((铜的化学符号是Na。) or ((-8 + 11) < (-10 * -4 + 10 * 1))))))) and ((not (not not (not (((-13 * 19) <= (3 ** 3) <= (8 * 7 + 2 * -6)) or (1932年奥运会在墨西哥城举办。))))) or ((not not (俄罗斯位于欧洲。)) and (not not (铀的化学符号是U。))))
B. ((not not (not (not not (not ((-6 * -9) <= (8 - 6) <= (-4 + -4)))))) or ((not not (((银的化学符号是Ag。) and ((12 * 20) == (19 + 1))) and ((三文鱼是鱼类。) or (菲律宾的首都是马尼拉。)))) and (not not (泰坦尼克号沉没发生在1912年。)))) and (not (not not ((((第二次世界大战结束发生在1945年。) and (天王星是距离太阳第2近的行星。)) and (2086年是闰年。)) and (5小于等于19。))))
C. not (not (not not (((7 * -2) < (-7 * -8 + 5 * 1)) and ((2 ** 1) == (-9 * -14)) and (((鳕鱼是鱼类。) and (法国位于欧洲。)) and ((马有4条腿。) or (南非位于非洲。))))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 49057825,
"true_count": 1
},
"question": "给定以下布尔表达式：\n\nA. (not not ((not ((not (22是偶数。)) and (硅的化学符号是Al。))) and (not not ((not ((3 ** 2) <= (-12 - -7) <= (-4 * -3 * 2 * 1))) or ((铜的化学符号是Na。) or ((-8 + 11) < (-10 * -4 + 10 * 1))))))) and ((not (not not (not (((-13 * 19) <= (3 ** 3) <= (8 * 7 + 2 * -6)) or (1932年奥运会在墨西哥城举办。))))) or ((not not (俄罗斯位于欧洲。)) and (not not (铀的化学符号是U。))))\nB. ((not not (not (not not (not ((-6 * -9) <= (8 - 6) <= (-4 + -4)))))) or ((not not (((银的化学符号是Ag。) and ((12 * 20) == (19 + 1))) and ((三文鱼是鱼类。) or (菲律宾的首都是马尼拉。)))) and (not not (泰坦尼克号沉没发生在1912年。)))) and (not (not not ((((第二次世界大战结束发生在1945年。) and (天王星是距离太阳第2近的行星。)) and (2086年是闰年。)) and (5小于等于19。))))\nC. not (not (not not (((7 * -2) < (-7 * -8 + 5 * 1)) and ((2 ** 1) == (-9 * -14)) and (((鳕鱼是鱼类。) and (法国位于欧洲。)) and ((马有4条腿。) or (南非位于非洲。))))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 49057825,
"true_count": 1
},
"seed": 49057825,
"task_id": 649057825,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. ((((铜的化学符号是Fe。) or ((-8 * -6) < (0 * 20))) or (西班牙位于欧洲。)) or (not (土星是距离太阳第2近的行星。))) or (((-4 - 18) >= (2 ** 3)) or ((not not (铝的化学符号是Al。)) and (((10 * -8) == (0 - -8)) or (30是奇数。))))
B. (((32是偶数。) or ((1964年奥运会在东京举办。) and (声音在真空中传播更快。))) and (((-16 - -8) <= (-2 + -18)) or (埃及位于非洲。)) and ((((2 + -19) != (9 + 11)) or ((-7 * 3) != (-7 * 6 + -7 * 3))) and ((酒精在常温下是液体。) and ((-10 + -9) == (-16 * 14))))) and ((钙的化学符号是Ag。) or ((((5 ** 2) != (4 - -20)) or (2091年是闰年。)) and ((美国位于欧洲。) or ((-17 * 19) > (-10 * 9 + 5 * 9)))))
C. (((澳大利亚的首都是阿布贾。) or ((5 ** 1) >= (-12 - -20))) or ((0 * 10 + -7 * -9) == (5 * -6 + 7 * 5))) and ((((93是质数。) or (145是完全平方数。)) or (not (76能被3整除。))) or (((哥伦布到达美洲发生在1482年。) and (1996年奥运会在北京举办。)) or (((-20 + 2) == (-4 * -8 - 10 * -1)) and (秘鲁的首都是哥本哈根。))))
D. (((15 - -20) > (-11 - 0)) and (not not (氧的化学符号是U。))) and (((((6 - 9) <= (-2 * 10 * -10 * -7)) and ((-8 * 10 - 0 * 6) <= (3 * -8 - 2 * -4))) or (铜在常温下是固体。)) or ((81是质数。) and (俄罗斯的首都是莫斯科。)) or (not (油在常温下是液体。)))
E. not not ((not not (not not ((1 * 0) >= (9 + -17)))) and (not ((印度尼西亚位于北美洲。) or (24是质数。))))
F. (not ((not (1976年奥运会在蒙特利尔举办。)) or (not ((9 * -8) > (8 * 9 - 4 * -3))))) and (not not (not ((埃及的首都是开罗。) and ((44 % 10) < (3 * -12)))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 23570722,
"true_count": 2
},
"question": "审视以下逻辑表达式：\n\nA. ((((铜的化学符号是Fe。) or ((-8 * -6) < (0 * 20))) or (西班牙位于欧洲。)) or (not (土星是距离太阳第2近的行星。))) or (((-4 - 18) >= (2 ** 3)) or ((not not (铝的化学符号是Al。)) and (((10 * -8) == (0 - -8)) or (30是奇数。))))\nB. (((32是偶数。) or ((1964年奥运会在东京举办。) and (声音在真空中传播更快。))) and (((-16 - -8) <= (-2 + -18)) or (埃及位于非洲。)) and ((((2 + -19) != (9 + 11)) or ((-7 * 3) != (-7 * 6 + -7 * 3))) and ((酒精在常温下是液体。) and ((-10 + -9) == (-16 * 14))))) and ((钙的化学符号是Ag。) or ((((5 ** 2) != (4 - -20)) or (2091年是闰年。)) and ((美国位于欧洲。) or ((-17 * 19) > (-10 * 9 + 5 * 9)))))\nC. (((澳大利亚的首都是阿布贾。) or ((5 ** 1) >= (-12 - -20))) or ((0 * 10 + -7 * -9) == (5 * -6 + 7 * 5))) and ((((93是质数。) or (145是完全平方数。)) or (not (76能被3整除。))) or (((哥伦布到达美洲发生在1482年。) and (1996年奥运会在北京举办。)) or (((-20 + 2) == (-4 * -8 - 10 * -1)) and (秘鲁的首都是哥本哈根。))))\nD. (((15 - -20) > (-11 - 0)) and (not not (氧的化学符号是U。))) and (((((6 - 9) <= (-2 * 10 * -10 * -7)) and ((-8 * 10 - 0 * 6) <= (3 * -8 - 2 * -4))) or (铜在常温下是固体。)) or ((81是质数。) and (俄罗斯的首都是莫斯科。)) or (not (油在常温下是液体。)))\nE. not not ((not not (not not ((1 * 0) >= (9 + -17)))) and (not ((印度尼西亚位于北美洲。) or (24是质数。))))\nF. (not ((not (1976年奥运会在蒙特利尔举办。)) or (not ((9 * -8) > (8 * 9 - 4 * -3))))) and (not not (not ((埃及的首都是开罗。) and ((44 % 10) < (3 * -12)))))\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": 23570722,
"true_count": 2
},
"seed": 23570722,
"task_id": 623570722,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((not (not ((1977年是闰年。) or (1988年奥运会在赫尔辛基举办。)))) and (((1908年奥运会在伦敦举办。) or (第一次世界大战开始发生在1916年。)) or (not not ((0 + -18) < (-10 * -9) < (7 * 9 - -10 * 9))) or (not ((1932年奥运会在悉尼举办。) or (南极洲是最冷的大陆。))))) and (not (not (南极洲是最冷的大陆。)))
B. not (not (((not not (62是质数。)) or (三月有31天。)) or (十二月有31天。)))
C. (not not (not not (not ((20小于等于51。) and ((6 % 7) < (-5 * -5)))))) or ((((31 % 3) <= (6 + -20) <= (-18 + -3)) and ((19 % 9) <= (32 % 6) <= (10 * 7 - -6 * 9)) and (not not ((狗有4条腿。) or (海王星是距离太阳第3近的行星。)))) or (not not (((德国位于欧洲。) and ((4 ** 2) >= (-6 * -8 - 6 * 10))) or (not (捷克的首都是阿姆斯特丹。)))))
D. not ((not not ((((-6 * 0 * -8 * -2) != (5 ** 3)) or (硫的化学符号是S。)) or (not (鸡有2条腿。)))) and (not ((not not (176是奇数。)) or (2000年奥运会在悉尼举办。))))
E. (not (not not (not (not ((1 * 5 - 0 * -9) != (6 * -10 - 3 * 6)))))) or (not ((48 % 9) <= (-8 * -17) <= (25 % 8))) or ((not (((氧气对人类生存是必需的。) or ((7 * -8) != (-9 - 4))) or (((-6 + 6) == (4 ** 2)) and (第一次世界大战结束发生在1918年。)))) and (((企鹅能飞翔。) and (木头在常温下是固体。)) or (((4 ** 1) == (4 + -16)) or ((9 + -7) != (20 + 9)))) and (not (((柏林墙倒塌发生在1989年。) or ((-19 - -18) != (4 * 3 - 5 * -5))) or ((钻石由碳元素组成。) or (168是偶数。)))))
F. (((镁的化学符号是Ne。) or (not (日本位于北美洲。)) or (印度尼西亚的货币是印尼盾。)) and ((not (not (铀的化学符号是Ne。))) or (((熊是昆虫。) or (现代奥运会首届举办发生在1901年。)) and (((4 ** 3) >= (9 + 17)) and ((11 - -4) < (3 * 17)))))) and ((not not (古巴的首都是哈瓦那。)) and ((((苏联解体发生在1991年。) and (十一月有28天。)) and ((秘鲁的货币是索尔。) or (太平洋是最大的海洋。))) and (土星是距离太阳第6近的行星。)))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"seed": 73149166,
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"question": "下面是几个布尔表达式：\n\nA. ((not (not ((1977年是闰年。) or (1988年奥运会在赫尔辛基举办。)))) and (((1908年奥运会在伦敦举办。) or (第一次世界大战开始发生在1916年。)) or (not not ((0 + -18) < (-10 * -9) < (7 * 9 - -10 * 9))) or (not ((1932年奥运会在悉尼举办。) or (南极洲是最冷的大陆。))))) and (not (not (南极洲是最冷的大陆。)))\nB. not (not (((not not (62是质数。)) or (三月有31天。)) or (十二月有31天。)))\nC. (not not (not not (not ((20小于等于51。) and ((6 % 7) < (-5 * -5)))))) or ((((31 % 3) <= (6 + -20) <= (-18 + -3)) and ((19 % 9) <= (32 % 6) <= (10 * 7 - -6 * 9)) and (not not ((狗有4条腿。) or (海王星是距离太阳第3近的行星。)))) or (not not (((德国位于欧洲。) and ((4 ** 2) >= (-6 * -8 - 6 * 10))) or (not (捷克的首都是阿姆斯特丹。)))))\nD. not ((not not ((((-6 * 0 * -8 * -2) != (5 ** 3)) or (硫的化学符号是S。)) or (not (鸡有2条腿。)))) and (not ((not not (176是奇数。)) or (2000年奥运会在悉尼举办。))))\nE. (not (not not (not (not ((1 * 5 - 0 * -9) != (6 * -10 - 3 * 6)))))) or (not ((48 % 9) <= (-8 * -17) <= (25 % 8))) or ((not (((氧气对人类生存是必需的。) or ((7 * -8) != (-9 - 4))) or (((-6 + 6) == (4 ** 2)) and (第一次世界大战结束发生在1918年。)))) and (((企鹅能飞翔。) and (木头在常温下是固体。)) or (((4 ** 1) == (4 + -16)) or ((9 + -7) != (20 + 9)))) and (not (((柏林墙倒塌发生在1989年。) or ((-19 - -18) != (4 * 3 - 5 * -5))) or ((钻石由碳元素组成。) or (168是偶数。)))))\nF. (((镁的化学符号是Ne。) or (not (日本位于北美洲。)) or (印度尼西亚的货币是印尼盾。)) and ((not (not (铀的化学符号是Ne。))) or (((熊是昆虫。) or (现代奥运会首届举办发生在1901年。)) and (((4 ** 3) >= (9 + 17)) and ((11 - -4) < (3 * 17)))))) and ((not not (古巴的首都是哈瓦那。)) and ((((苏联解体发生在1991年。) and (十一月有28天。)) and ((秘鲁的货币是索尔。) or (太平洋是最大的海洋。))) and (土星是距离太阳第6近的行星。)))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
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"language": "cn",
"num_options": 6,
"seed": 73149166,
"true_count": 4
},
"seed": 73149166,
"task_id": 673149166,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. ((not ((5 - -9) > (4 ** 3))) and ((19 - 1) != (-12 + 0)) and ((Japan is in Asia.) and ((2060 is a leap year.) and (Mars is the 1st planet from the Sun.)))) or (1984 is a leap year.) or ((not (not not ((12 * 9) < (2 + 17)))) and ((3 * -3 * 0 * -7) == (3 * -9 + -10 * -4)))
B. (((7 * 4 * 4 * -6) >= (17 * -4)) or (not ((The 2012 Olympics were held in London.) or (United Kingdom is in Europe.)))) or ((((Earth is the 3rd planet from the Sun.) or (A salmon is a mammal.)) and ((The capital of India is Brasilia.) and (Australia is in Africa.))) and (not (The capital of Denmark is Warsaw.)) and (The first Olympic Games of modern era occurred in 1896.))
C. (((The chemical symbol for Platinum is P.) or (not ((-14 + -7) > (-20 + 2)))) and ((2 - -18) > (34 % 8))) or (not (((The currency of Australia is the Dollar.) or ((33 % 4) < (-18 + -6))) or ((19 + 9) <= (-12 + 19) <= (17 * 12))))
D. ((Water boils at 100 degrees Celsius at sea level.) or (((8 * 0 - 5 * 1) <= (23 % 8)) and (((-1 * 6 + -9 * 3) >= (19 + -17)) and (The currency of Mexico is the Baht.)))) and (((((-15 - 15) < (7 + 7)) or ((16 * -8) < (19 * -6))) and (The chemical symbol for Helium is Ca.)) and ((The currency of Denmark is the Krone.) or (A lion is a mammal.)) and (not (not not (There are 30 days in April.))))
E. ((((Argentina is in South America.) and (The currency of Japan is the Won.)) and ((The 2000 Olympics were held in Sydney.) and ((9 * 14) <= (-7 + 9) <= (10 * 5 - 7 * 8)))) and ((Steam is a gas at room temperature.) and ((The 1896 Olympics were held in Moscow.) or (143 is an even number.)))) and (((-9 * -7 * -4 * 4) <= (-12 * -1)) and (Saturn is the 1st planet from the Sun.))
F. (not not (not (((43 % 7) <= (8 % 6)) or (Mars is the 5th planet from the Sun.)))) or ((15 + -7) >= (-16 * 1)) or (((10 + -1) < (6 * -17)) and (((Bats are blind.) and ((-6 * -6 - 1 * 5) >= (2 + -20))) and (not not (Sound travels faster in a vacuum.))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "en",
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"question": "Consider the following logical expressions:\n\nA. ((not ((5 - -9) > (4 ** 3))) and ((19 - 1) != (-12 + 0)) and ((Japan is in Asia.) and ((2060 is a leap year.) and (Mars is the 1st planet from the Sun.)))) or (1984 is a leap year.) or ((not (not not ((12 * 9) < (2 + 17)))) and ((3 * -3 * 0 * -7) == (3 * -9 + -10 * -4)))\nB. (((7 * 4 * 4 * -6) >= (17 * -4)) or (not ((The 2012 Olympics were held in London.) or (United Kingdom is in Europe.)))) or ((((Earth is the 3rd planet from the Sun.) or (A salmon is a mammal.)) and ((The capital of India is Brasilia.) and (Australia is in Africa.))) and (not (The capital of Denmark is Warsaw.)) and (The first Olympic Games of modern era occurred in 1896.))\nC. (((The chemical symbol for Platinum is P.) or (not ((-14 + -7) > (-20 + 2)))) and ((2 - -18) > (34 % 8))) or (not (((The currency of Australia is the Dollar.) or ((33 % 4) < (-18 + -6))) or ((19 + 9) <= (-12 + 19) <= (17 * 12))))\nD. ((Water boils at 100 degrees Celsius at sea level.) or (((8 * 0 - 5 * 1) <= (23 % 8)) and (((-1 * 6 + -9 * 3) >= (19 + -17)) and (The currency of Mexico is the Baht.)))) and (((((-15 - 15) < (7 + 7)) or ((16 * -8) < (19 * -6))) and (The chemical symbol for Helium is Ca.)) and ((The currency of Denmark is the Krone.) or (A lion is a mammal.)) and (not (not not (There are 30 days in April.))))\nE. ((((Argentina is in South America.) and (The currency of Japan is the Won.)) and ((The 2000 Olympics were held in Sydney.) and ((9 * 14) <= (-7 + 9) <= (10 * 5 - 7 * 8)))) and ((Steam is a gas at room temperature.) and ((The 1896 Olympics were held in Moscow.) or (143 is an even number.)))) and (((-9 * -7 * -4 * 4) <= (-12 * -1)) and (Saturn is the 1st planet from the Sun.))\nF. (not not (not (((43 % 7) <= (8 % 6)) or (Mars is the 5th planet from the Sun.)))) or ((15 + -7) >= (-16 * 1)) or (((10 + -1) < (6 * -17)) and (((Bats are blind.) and ((-6 * -6 - 1 * 5) >= (2 + -20))) and (not not (Sound travels faster in a vacuum.))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
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"language": "en",
"num_options": 6,
"seed": 54844454,
"true_count": 3
},
"seed": 54844454,
"task_id": 654844454,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (not not (not not (The chemical symbol for Silver is Ag.)))
B. (not not (not not ((-17 + 5) != (-6 + 15)))) and (World War I ended occurred in 1918.)
C. not ((1 ** 3) >= (6 % 6))
D. (not (((-1 * 14) == (17 - -19)) and ((-6 * -13) <= (7 % 9) <= (-9 * 3 + -5 * 5)))) and (((-15 - -9) != (20 + -3)) and (((2 ** 1) <= (-7 * -7) <= (5 + 5)) or ((-12 - 6) < (5 % 6))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 44528623,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (not not (not not (The chemical symbol for Silver is Ag.)))\nB. (not not (not not ((-17 + 5) != (-6 + 15)))) and (World War I ended occurred in 1918.)\nC. not ((1 ** 3) >= (6 % 6))\nD. (not (((-1 * 14) == (17 - -19)) and ((-6 * -13) <= (7 % 9) <= (-9 * 3 + -5 * 5)))) and (((-15 - -9) != (20 + -3)) and (((2 ** 1) <= (-7 * -7) <= (5 + 5)) or ((-12 - 6) < (5 % 6))))\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": 44528623,
"true_count": 3
},
"seed": 44528623,
"task_id": 644528623,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (not not ((((-6 + 20) <= (2 ** 3)) or ((氧气在常温下是液体。) and (变色龙是昆虫。))) and ((木星是距离太阳第5近的行星。) or ((-4 * -4) < (5 ** 3))) and (not ((印度位于亚洲。) or ((2 ** 1) >= (1 * -7 - 7 * 6)))))) or ((not (1936年奥运会在柏林举办。)) or (not (伦敦大火发生在1666年。)))
B. 钻石由碳元素组成。
C. not not (((((5 % 1) < (6 * -10 - 9 * -6) < (7 - 2)) or (not ((3 ** 3) >= (-1 - 2)))) or ((((41 % 3) <= (-9 * -7)) or ((7 * -9 * -10 * 10) < (10 - -6))) and (not not ((-20 - 15) < (17 * -14))))) or ((蝴蝶有2条腿。) and (not ((16 + -17) < (16 - -16) < (7 + -20)))) or (not not (((月球绕地球运转。) and ((17 - -11) < (15 + 1))) and (太平洋是最大的海洋。))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 8599992,
"true_count": 1
},
"question": "给定以下布尔表达式：\n\nA. (not not ((((-6 + 20) <= (2 ** 3)) or ((氧气在常温下是液体。) and (变色龙是昆虫。))) and ((木星是距离太阳第5近的行星。) or ((-4 * -4) < (5 ** 3))) and (not ((印度位于亚洲。) or ((2 ** 1) >= (1 * -7 - 7 * 6)))))) or ((not (1936年奥运会在柏林举办。)) or (not (伦敦大火发生在1666年。)))\nB. 钻石由碳元素组成。\nC. not not (((((5 % 1) < (6 * -10 - 9 * -6) < (7 - 2)) or (not ((3 ** 3) >= (-1 - 2)))) or ((((41 % 3) <= (-9 * -7)) or ((7 * -9 * -10 * 10) < (10 - -6))) and (not not ((-20 - 15) < (17 * -14))))) or ((蝴蝶有2条腿。) and (not ((16 + -17) < (16 - -16) < (7 + -20)))) or (not not (((月球绕地球运转。) and ((17 - -11) < (15 + 1))) and (太平洋是最大的海洋。))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 8599992,
"true_count": 1
},
"seed": 8599992,
"task_id": 608599992,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (The capital of China is Beijing.) or (not ((3 * -3 - -9 * -6) < (18 - 19))) or (A bear is a bird.)
B. (not ((The currency of Hungary is the Dollar.) and (The capital of Italy is Rome.))) and (((-6 + 20) != (4 * 17)) or (The square root of 49 is 7.))
C. ((10 * 19) <= (17 + -3)) and (The currency of South Korea is the Ruble.)
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 98769688,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (The capital of China is Beijing.) or (not ((3 * -3 - -9 * -6) < (18 - 19))) or (A bear is a bird.)\nB. (not ((The currency of Hungary is the Dollar.) and (The capital of Italy is Rome.))) and (((-6 + 20) != (4 * 17)) or (The square root of 49 is 7.))\nC. ((10 * 19) <= (17 + -3)) and (The currency of South Korea is the Ruble.)\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": 98769688,
"true_count": 2
},
"seed": 98769688,
"task_id": 698769688,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not (not not ((南非位于非洲。) or (地球上一天是24小时。)))
B. not (荷兰的首都是安卡拉。)
C. (not not (((-8 * -5 + 0 * -10) != (-6 * -2 + -3 * 2)) and (氧气对人类生存是必需的。))) and (((人类有三个肺。) and ((-1 * -10 * -1 * 2) < (31 % 10))) or (1904年奥运会在圣路易斯举办。))
D. (not ((-6 - 3) >= (-14 * 10))) or (not not ((-10 - -3) < (8 + -5)))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 83267049,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. not (not not ((南非位于非洲。) or (地球上一天是24小时。)))\nB. not (荷兰的首都是安卡拉。)\nC. (not not (((-8 * -5 + 0 * -10) != (-6 * -2 + -3 * 2)) and (氧气对人类生存是必需的。))) and (((人类有三个肺。) and ((-1 * -10 * -1 * 2) < (31 % 10))) or (1904年奥运会在圣路易斯举办。))\nD. (not ((-6 - 3) >= (-14 * 10))) or (not not ((-10 - -3) < (8 + -5)))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 83267049,
"true_count": 3
},
"seed": 83267049,
"task_id": 683267049,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not ((18 * -12) >= (-18 + -18))
B. (not not ((The chemical symbol for Cobalt is Co.) and ((1 + 3) != (5 ** 3)))) and (((8 * -1 * 2 * 6) == (20 * -14)) and ((The capital of Indonesia is Jakarta.) or ((-10 - 16) < (-10 + 7))))
C. (((132 is a perfect square.) and ((1 * 7 + 0 * 4) >= (-8 * -8 + 8 * -7))) and ((A beetle is an insect.) or ((5 ** 1) <= (8 * 2 - 3 * 1)))) and ((The currency of Brazil is the Peso.) and (The capital of South Korea is Seoul.)) and (((The chemical symbol for Zinc is Mg.) or ((-13 + -4) == (5 + 17))) and ((The capital of Poland is Warsaw.) and ((1 * -8) != (4 ** 1))))
D. ((not not ((5 + 6) == (-12 * 2))) and ((A eagle is a mammal.) and ((-20 + 1) > (-9 - -16)))) or ((not ((-11 * 20) == (-4 + 17))) and ((The chemical symbol for Titanium is Ti.) and (9 is an even number.)))
E. ((32 % 1) != (5 * -7)) and ((Venus is the 2nd planet from the Sun.) or ((13 + -20) <= (3 - -15) <= (6 * 0))) and ((13 % 10) == (-10 * -3 - 1 * 2))
F. (not not ((There are 30 days in June.) and (Uranus is the 1st planet from the Sun.))) and ((not ((0 * 9 - -6 * -3) <= (-2 * -3 * -9 * 6) <= (-15 - 6))) and ((-20 + -14) < (-1 + -9)))
G. not not (The capital of Cuba is Dublin.)
H. ((The capital of Austria is Hanoi.) or (not not ((15 % 2) <= (-1 * 3 + 7 * 5)))) and (Mars is the 4th planet from the Sun.) and (Copper is a solid at room temperature.)
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 64207353,
"true_count": 2
},
"question": "Below are several boolean expressions:\n\nA. not ((18 * -12) >= (-18 + -18))\nB. (not not ((The chemical symbol for Cobalt is Co.) and ((1 + 3) != (5 ** 3)))) and (((8 * -1 * 2 * 6) == (20 * -14)) and ((The capital of Indonesia is Jakarta.) or ((-10 - 16) < (-10 + 7))))\nC. (((132 is a perfect square.) and ((1 * 7 + 0 * 4) >= (-8 * -8 + 8 * -7))) and ((A beetle is an insect.) or ((5 ** 1) <= (8 * 2 - 3 * 1)))) and ((The currency of Brazil is the Peso.) and (The capital of South Korea is Seoul.)) and (((The chemical symbol for Zinc is Mg.) or ((-13 + -4) == (5 + 17))) and ((The capital of Poland is Warsaw.) and ((1 * -8) != (4 ** 1))))\nD. ((not not ((5 + 6) == (-12 * 2))) and ((A eagle is a mammal.) and ((-20 + 1) > (-9 - -16)))) or ((not ((-11 * 20) == (-4 + 17))) and ((The chemical symbol for Titanium is Ti.) and (9 is an even number.)))\nE. ((32 % 1) != (5 * -7)) and ((Venus is the 2nd planet from the Sun.) or ((13 + -20) <= (3 - -15) <= (6 * 0))) and ((13 % 10) == (-10 * -3 - 1 * 2))\nF. (not not ((There are 30 days in June.) and (Uranus is the 1st planet from the Sun.))) and ((not ((0 * 9 - -6 * -3) <= (-2 * -3 * -9 * 6) <= (-15 - 6))) and ((-20 + -14) < (-1 + -9)))\nG. not not (The capital of Cuba is Dublin.)\nH. ((The capital of Austria is Hanoi.) or (not not ((15 % 2) <= (-1 * 3 + 7 * 5)))) and (Mars is the 4th planet from the Sun.) and (Copper is a solid at room temperature.)\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 64207353,
"true_count": 2
},
"seed": 64207353,
"task_id": 664207353,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not (((((34 % 9) < (2 ** 2)) or (1936年奥运会在柏林举办。)) and ((-3 * -4) > (42 % 8))) and (((-18 - -16) > (-2 * -5 + 2 * 1)) or ((伦敦大火发生在1671年。) and (泰国的首都是曼谷。))))
B. not (not not (not not ((2006年是闰年。) or ((2 ** 2) < (9 * -12)))))
C. (((not ((-2 * -9) != (6 * 0 + -2 * 0))) and (月球绕地球运转。)) or ((1960年奥运会在巴黎举办。) or ((34 % 1) >= (-10 * -3 * -7 * 2))) or (not not (((17 % 8) != (-17 * 6)) or (土耳其的货币是里拉。)))) or ((((-7 * 6 * -7 * -10) < (7 * -13)) or (2057年是闰年。)) and (not ((-10 * -9 * -1 * 1) >= (-17 * 12)))) or (((18 % 9) > (4 ** 1)) or (((沙特阿拉伯的货币是比索。) or ((-6 - -5) > (-17 - 12))) or ((蜥蜴是爬行动物。) and ((-18 + -1) < (-15 * -7)))))
D. not (not not (not (((4 * -4 * 6 * -2) < (1 - 11) < (8 * -7 - 2 * -9)) or (秘鲁位于北美洲。))))
E. ((人体有150块骨头。) and (((莱特兄弟首次飞行发生在1904年。) or (空气在常温下是液体。)) or (((-6 * 5 + -9 * -8) < (5 ** 2)) or ((-10 + 9) > (38 % 8))))) and (((-3 + 13) <= (-14 * 14)) or (((-9 * -1 - -3 * -4) < (-7 * 3 + 5 * 6)) and (第一次世界大战结束发生在1923年。)) or (柏林墙倒塌发生在1979年。))
F. not not (not not (((14 - -14) >= (-12 - -10)) and (((-17 + -5) < (-10 * -1 * -8 * 5)) or ((7 + -20) > (-10 + -20)))))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 38531584,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. not (((((34 % 9) < (2 ** 2)) or (1936年奥运会在柏林举办。)) and ((-3 * -4) > (42 % 8))) and (((-18 - -16) > (-2 * -5 + 2 * 1)) or ((伦敦大火发生在1671年。) and (泰国的首都是曼谷。))))\nB. not (not not (not not ((2006年是闰年。) or ((2 ** 2) < (9 * -12)))))\nC. (((not ((-2 * -9) != (6 * 0 + -2 * 0))) and (月球绕地球运转。)) or ((1960年奥运会在巴黎举办。) or ((34 % 1) >= (-10 * -3 * -7 * 2))) or (not not (((17 % 8) != (-17 * 6)) or (土耳其的货币是里拉。)))) or ((((-7 * 6 * -7 * -10) < (7 * -13)) or (2057年是闰年。)) and (not ((-10 * -9 * -1 * 1) >= (-17 * 12)))) or (((18 % 9) > (4 ** 1)) or (((沙特阿拉伯的货币是比索。) or ((-6 - -5) > (-17 - 12))) or ((蜥蜴是爬行动物。) and ((-18 + -1) < (-15 * -7)))))\nD. not (not not (not (((4 * -4 * 6 * -2) < (1 - 11) < (8 * -7 - 2 * -9)) or (秘鲁位于北美洲。))))\nE. ((人体有150块骨头。) and (((莱特兄弟首次飞行发生在1904年。) or (空气在常温下是液体。)) or (((-6 * 5 + -9 * -8) < (5 ** 2)) or ((-10 + 9) > (38 % 8))))) and (((-3 + 13) <= (-14 * 14)) or (((-9 * -1 - -3 * -4) < (-7 * 3 + 5 * 6)) and (第一次世界大战结束发生在1923年。)) or (柏林墙倒塌发生在1979年。))\nF. not not (not not (((14 - -14) >= (-12 - -10)) and (((-17 + -5) < (-10 * -1 * -8 * 5)) or ((7 + -20) > (-10 + -20)))))\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": 38531584,
"true_count": 4
},
"seed": 38531584,
"task_id": 638531584,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (1 * -9 - 2 * -6) > (-6 * -17)
B. not not ((The Moon orbits the Earth.) or (Mercury is the 6th planet from the Sun.))
C. ((The 1984 Olympics were held in Mexico City.) and ((16 + -19) <= (-19 * -6))) or (373 is a perfect square.)
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 64404645,
"true_count": 1
},
"question": "Review these logical expressions:\n\nA. (1 * -9 - 2 * -6) > (-6 * -17)\nB. not not ((The Moon orbits the Earth.) or (Mercury is the 6th planet from the Sun.))\nC. ((The 1984 Olympics were held in Mexico City.) and ((16 + -19) <= (-19 * -6))) or (373 is a perfect square.)\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 64404645,
"true_count": 1
},
"seed": 64404645,
"task_id": 664404645,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((not not (((19 + 13) < (-1 * -9 * -9 * 7) < (-7 * -6 * 5 * -9)) or (蝙蝠是瞎的。))) or (((2 ** 2) != (12 - -9)) and (not ((17 * -11) >= (-7 - 13))))) or (not (铁在常温下是液体。)) or ((((1 ** 2) <= (-16 * 12)) or (((9 * 0 * 8 * -8) > (13 + 7)) and (第一次世界大战开始发生在1914年。))) or (((泰坦尼克号沉没发生在1907年。) or (氦气在常温下是气体。)) and (((2 + 8) >= (46 % 7)) and ((19 - -4) != (15 + -16)))))
B. not not (((not ((3 ** 1) < (5 + -8) < (12 - -1))) or (not ((6 + 0) <= (-12 - 6) <= (-9 + -13)))) and (((南非位于北美洲。) and ((-5 * 6 - 9 * 10) != (2 ** 3))) and ((新西兰的货币是英镑。) or ((-1 * -2 * 7 * -6) == (-5 * 9)))))
C. ((not ((火星是距离太阳最近的行星。) or (水在海平面上的沸点是100摄氏度。))) or ((not ((-10 + 13) <= (1 * 15))) and (((-6 * 7 * 4 * 6) == (4 * -8 * 6 * 10)) and (第二次世界大战结束发生在1935年。)))) and ((not not (((-16 + 9) > (-2 + 4)) and (俄罗斯的首都是莫斯科。))) and ((((5 * 8) != (-3 - 11)) or (菲律宾的首都是马尼拉。)) and (((-11 - -6) == (3 * -3)) and ((0 + -14) == (7 * 6 * -8 * 0)))))
D. (not not (((兔子是哺乳动物。) or (青蛙有8条腿。)) or (not not (天王星是距离太阳第5近的行星。)))) or (((十二月有31天。) or ((-19 * -5) != (14 - -11))) or (((-20 + -19) != (3 * 3 + -9 * -10)) and (第一部iPhone发布发生在2017年。))) or (not not (企鹅能飞翔。))
E. not not (not ((not not (英国的货币是泰铢。)) and (((-1 * -8 - -7 * 3) <= (-1 + 7)) or (空气在常温下是气体。))))
F. not (((((6 + 13) > (5 ** 3)) or ((4 * 2) == (0 * -6 + 3 * 6))) and (79小于等于60。)) or (((德国的首都是柏林。) and (火星是距离太阳最近的行星。)) or ((丹麦的货币是新西兰元。) and ((7 - 20) == (-2 * -9 * 7 * -1)))))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 67834403,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. ((not not (((19 + 13) < (-1 * -9 * -9 * 7) < (-7 * -6 * 5 * -9)) or (蝙蝠是瞎的。))) or (((2 ** 2) != (12 - -9)) and (not ((17 * -11) >= (-7 - 13))))) or (not (铁在常温下是液体。)) or ((((1 ** 2) <= (-16 * 12)) or (((9 * 0 * 8 * -8) > (13 + 7)) and (第一次世界大战开始发生在1914年。))) or (((泰坦尼克号沉没发生在1907年。) or (氦气在常温下是气体。)) and (((2 + 8) >= (46 % 7)) and ((19 - -4) != (15 + -16)))))\nB. not not (((not ((3 ** 1) < (5 + -8) < (12 - -1))) or (not ((6 + 0) <= (-12 - 6) <= (-9 + -13)))) and (((南非位于北美洲。) and ((-5 * 6 - 9 * 10) != (2 ** 3))) and ((新西兰的货币是英镑。) or ((-1 * -2 * 7 * -6) == (-5 * 9)))))\nC. ((not ((火星是距离太阳最近的行星。) or (水在海平面上的沸点是100摄氏度。))) or ((not ((-10 + 13) <= (1 * 15))) and (((-6 * 7 * 4 * 6) == (4 * -8 * 6 * 10)) and (第二次世界大战结束发生在1935年。)))) and ((not not (((-16 + 9) > (-2 + 4)) and (俄罗斯的首都是莫斯科。))) and ((((5 * 8) != (-3 - 11)) or (菲律宾的首都是马尼拉。)) and (((-11 - -6) == (3 * -3)) and ((0 + -14) == (7 * 6 * -8 * 0)))))\nD. (not not (((兔子是哺乳动物。) or (青蛙有8条腿。)) or (not not (天王星是距离太阳第5近的行星。)))) or (((十二月有31天。) or ((-19 * -5) != (14 - -11))) or (((-20 + -19) != (3 * 3 + -9 * -10)) and (第一部iPhone发布发生在2017年。))) or (not not (企鹅能飞翔。))\nE. not not (not ((not not (英国的货币是泰铢。)) and (((-1 * -8 - -7 * 3) <= (-1 + 7)) or (空气在常温下是气体。))))\nF. not (((((6 + 13) > (5 ** 3)) or ((4 * 2) == (0 * -6 + 3 * 6))) and (79小于等于60。)) or (((德国的首都是柏林。) and (火星是距离太阳最近的行星。)) or ((丹麦的货币是新西兰元。) and ((7 - 20) == (-2 * -9 * 7 * -1)))))\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": 67834403,
"true_count": 4
},
"seed": 67834403,
"task_id": 667834403,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (((-5 * 10 + 3 * -9) < (-14 * 3) < (-8 * 2)) or (((2098 is a leap year.) or ((6 * 8 * 3 * 5) == (-12 - -6))) and (The capital of Belgium is Brussels.))) or ((Earth is the 3rd planet from the Sun.) and (not (((1 * -2) <= (4 * 6)) or (There are 31 days in May.))))
B. not not ((not not ((The square root of 9 is 3.) and ((6 * -7 + 0 * -10) != (3 ** 1)))) and ((11 - 19) < (-14 - -11)))
C. not (not not ((1 ** 1) <= (-8 * 3 - 3 * 7)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 46235396,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (((-5 * 10 + 3 * -9) < (-14 * 3) < (-8 * 2)) or (((2098 is a leap year.) or ((6 * 8 * 3 * 5) == (-12 - -6))) and (The capital of Belgium is Brussels.))) or ((Earth is the 3rd planet from the Sun.) and (not (((1 * -2) <= (4 * 6)) or (There are 31 days in May.))))\nB. not not ((not not ((The square root of 9 is 3.) and ((6 * -7 + 0 * -10) != (3 ** 1)))) and ((11 - 19) < (-14 - -11)))\nC. not (not not ((1 ** 1) <= (-8 * 3 - 3 * 7)))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 46235396,
"true_count": 3
},
"seed": 46235396,
"task_id": 646235396,
"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. 人体有150块骨头。
B. ((27 % 5) >= (-9 * -8 - 3 * 2)) and (水蒸气在常温下是气体。)
C. (not (1924年奥运会在巴黎举办。)) and (not not (钛的化学符号是Ti。))
D. not (not not (2020年奥运会在雅典举办。))
E. (铝的化学符号是Al。) and (((17 - -8) <= (-16 * -11)) or ((1 % 2) == (4 * -5 + -6 * -7)))
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": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 84582349,
"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. 人体有150块骨头。\nB. ((27 % 5) >= (-9 * -8 - 3 * 2)) and (水蒸气在常温下是气体。)\nC. (not (1924年奥运会在巴黎举办。)) and (not not (钛的化学符号是Ti。))\nD. not (not not (2020年奥运会在雅典举办。))\nE. (铝的化学符号是Al。) and (((17 - -8) <= (-16 * -11)) or ((1 % 2) == (4 * -5 + -6 * -7)))\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": 5,
"seed": 84582349,
"true_count": 2
},
"seed": 84582349,
"task_id": 684582349,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. ((not (((-4 * -4 - 3 * -9) != (10 + -6)) and (94能被12整除。))) and (((11 * 20) < (-8 + 6) < (-2 * 3 - -3 * 3)) and (not (肯尼亚位于非洲。)))) or ((-12 - 18) >= (0 + 16)) or ((((15 * -14) != (3 ** 3)) or (((-9 - -2) < (10 % 1) < (-5 * -3 - -8 * -2)) or (天王星是距离太阳第7近的行星。))) and (铅的化学符号是Pb。))
B. (not not ((not ((2 * -7 * 9 * 6) == (5 * 1 * 2 * -3))) and (((-6 + -5) >= (-1 * -6 * 10 * 1)) or (海王星是距离太阳第8近的行星。)))) or (not not (以色列的货币是谢克尔。))
C. ((六月有30天。) and (((-18 * 6) == (1 ** 1)) or (氧气在常温下是气体。)) and ((南极洲是最冷的大陆。) or (((5 + 2) > (-10 * 8 * 1 * -9)) or ((-13 + -13) > (11 * -15))))) and (((比利时的首都是河内。) and (鸡有100条腿。)) and (((47 % 9) <= (12 + -10)) or (印度的首都是新德里。)) and (((铬的化学符号是Sn。) or (74小于等于34。)) and (((-7 * -10 - 5 * -7) > (-5 * 7)) and (1947年是闰年。))))
D. (((-15 - 13) < (20 * 1)) and (not (((17 - -10) <= (-1 * 4) <= (3 ** 2)) and (1968年奥运会在柏林举办。)))) and (((44 % 1) != (3 % 9)) and (((0 * 4 - -2 * -7) >= (0 + 17)) and (((-4 * -4 - -2 * 6) <= (13 + -6)) or ((-7 + 16) < (-2 * -14)))))
E. not ((铁的化学符号是Fe。) or (not not ((-12 * -7) <= (1 * -15))) or ((((6 * 8 + 2 * 8) == (20 - -1)) or (第一部iPhone发布发生在2007年。)) or (not (哥伦布到达美洲发生在1491年。))))
F. (not (((-17 - -11) >= (4 ** 1)) or ((-5 * -4 - 9 * 10) >= (17 - 7)))) or ((not ((十二月有29天。) or (氮的化学符号是N。))) and ((((-5 * 16) == (5 % 2)) and (人类有三个肺。)) or (((2 * -9) > (5 ** 3)) and ((1 * 9 * 10 * 8) != (7 * 9 + 7 * -3)))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 27357926,
"true_count": 3
},
"question": "研究以下逻辑语句：\n\nA. ((not (((-4 * -4 - 3 * -9) != (10 + -6)) and (94能被12整除。))) and (((11 * 20) < (-8 + 6) < (-2 * 3 - -3 * 3)) and (not (肯尼亚位于非洲。)))) or ((-12 - 18) >= (0 + 16)) or ((((15 * -14) != (3 ** 3)) or (((-9 - -2) < (10 % 1) < (-5 * -3 - -8 * -2)) or (天王星是距离太阳第7近的行星。))) and (铅的化学符号是Pb。))\nB. (not not ((not ((2 * -7 * 9 * 6) == (5 * 1 * 2 * -3))) and (((-6 + -5) >= (-1 * -6 * 10 * 1)) or (海王星是距离太阳第8近的行星。)))) or (not not (以色列的货币是谢克尔。))\nC. ((六月有30天。) and (((-18 * 6) == (1 ** 1)) or (氧气在常温下是气体。)) and ((南极洲是最冷的大陆。) or (((5 + 2) > (-10 * 8 * 1 * -9)) or ((-13 + -13) > (11 * -15))))) and (((比利时的首都是河内。) and (鸡有100条腿。)) and (((47 % 9) <= (12 + -10)) or (印度的首都是新德里。)) and (((铬的化学符号是Sn。) or (74小于等于34。)) and (((-7 * -10 - 5 * -7) > (-5 * 7)) and (1947年是闰年。))))\nD. (((-15 - 13) < (20 * 1)) and (not (((17 - -10) <= (-1 * 4) <= (3 ** 2)) and (1968年奥运会在柏林举办。)))) and (((44 % 1) != (3 % 9)) and (((0 * 4 - -2 * -7) >= (0 + 17)) and (((-4 * -4 - -2 * 6) <= (13 + -6)) or ((-7 + 16) < (-2 * -14)))))\nE. not ((铁的化学符号是Fe。) or (not not ((-12 * -7) <= (1 * -15))) or ((((6 * 8 + 2 * 8) == (20 - -1)) or (第一部iPhone发布发生在2007年。)) or (not (哥伦布到达美洲发生在1491年。))))\nF. (not (((-17 - -11) >= (4 ** 1)) or ((-5 * -4 - 9 * 10) >= (17 - 7)))) or ((not ((十二月有29天。) or (氮的化学符号是N。))) and ((((-5 * 16) == (5 % 2)) and (人类有三个肺。)) or (((2 * -9) > (5 ** 3)) and ((1 * 9 * 10 * 8) != (7 * 9 + 7 * -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": 4,
"language": "cn",
"num_options": 6,
"seed": 27357926,
"true_count": 3
},
"seed": 27357926,
"task_id": 627357926,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not ((((not not (The currency of Malaysia is the Ringgit.)) or ((-20 * 3) > (12 % 10))) and ((not not (The currency of Mexico is the Peso.)) and ((1 - 7) < (5 * -2 * -9 * 9) < (-7 * 2 * 1 * -7)))) or ((not (((-17 + -9) >= (10 * -3)) or ((6 * 9 + 2 * 1) >= (13 + 9)))) or (not not ((47 is greater than 49.) and (Egypt is in Africa.)))))
B. not (not (((not ((1 ** 2) > (-18 - -16))) or (((1 + 12) == (-6 * -2 + -3 * 0)) and (The human body has 206 bones.))) or ((A kangaroo has 100 legs.) and (not not (The 1952 Olympics were held in London.)))))
C. (not (not ((((-16 * -9) < (-14 + -19)) or ((19 + -9) < (2 ** 1))) and ((-2 - -12) != (4 - -6))))) or (not not ((((The Great Wall of China was built in one year.) or ((15 * -18) > (7 * 12))) or (((-6 + -8) <= (1 * -1)) or (There are 29 days in April.))) or ((((-4 * 10 - -2 * 8) > (7 * -9)) or (A bird has 2 legs.)) or ((A frog has 2 legs.) or (53 is a prime number.)))))
D. ((not not ((not (Spain is in Asia.)) or (((-2 * 4 + 8 * -4) < (16 * 14) < (-4 * -5 + -3 * 5)) and (78 is greater than 18.)))) or ((18 % 5) <= (20 * -5)) or (not not (not ((A shark is a fish.) and ((20 - 4) > (4 * 1 - 2 * -4)))))) and (not not ((not not ((A kangaroo has 2 legs.) or ((-14 + 11) != (-7 + 0)))) and ((The chemical symbol for Calcium is Ca.) or (Helium is a gas at room temperature.)) and (Wood is a solid at room temperature.)))
E. not (not ((not ((-15 - 8) >= (13 % 9))) and (((There are 31 days in March.) and ((5 ** 2) <= (-2 + 11) <= (-12 + 3))) and (not not (A horse has 100 legs.)))))
F. (not (not (not not ((11 * 5) < (6 - -18) < (-11 + -18))))) or (((not (A sheep is a mammal.)) and (((There are 30 days in August.) or ((9 - -4) > (13 - -8))) or (((-2 + 0) <= (20 + -11)) and (Light travels faster than sound.)))) or ((4 - 11) >= (-6 * -2)) or (((not not (The capital of France is Prague.)) or ((The capital of Italy is Rome.) or ((-9 * 7 * 4 * -2) < (9 * 10 + 10 * 6)))) or (not (A penguin is an insect.))))
G. not (((((18 + 7) > (11 % 9)) and (((-10 + -13) < (15 + -16)) and (The currency of Colombia is the Euro.))) and ((8 * -8 - -9 * -3) < (-1 + 4))) or ((not not (((-13 * -12) != (-19 + 16)) and (The currency of Egypt is the Pound.))) or ((-2 * 3) <= (10 * -3))))
H. (not (not not (not ((The 1988 Olympics were held in Seoul.) and (Bats are blind.))))) and (((90 is an even number.) and ((2 * 9 * -1 * -6) <= (-2 * -5 + -4 * 7))) or (((-3 * -9 * 0 * -1) != (-11 - 7)) and (The 2016 Olympics were held in Stockholm.)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 30093133,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not ((((not not (The currency of Malaysia is the Ringgit.)) or ((-20 * 3) > (12 % 10))) and ((not not (The currency of Mexico is the Peso.)) and ((1 - 7) < (5 * -2 * -9 * 9) < (-7 * 2 * 1 * -7)))) or ((not (((-17 + -9) >= (10 * -3)) or ((6 * 9 + 2 * 1) >= (13 + 9)))) or (not not ((47 is greater than 49.) and (Egypt is in Africa.)))))\nB. not (not (((not ((1 ** 2) > (-18 - -16))) or (((1 + 12) == (-6 * -2 + -3 * 0)) and (The human body has 206 bones.))) or ((A kangaroo has 100 legs.) and (not not (The 1952 Olympics were held in London.)))))\nC. (not (not ((((-16 * -9) < (-14 + -19)) or ((19 + -9) < (2 ** 1))) and ((-2 - -12) != (4 - -6))))) or (not not ((((The Great Wall of China was built in one year.) or ((15 * -18) > (7 * 12))) or (((-6 + -8) <= (1 * -1)) or (There are 29 days in April.))) or ((((-4 * 10 - -2 * 8) > (7 * -9)) or (A bird has 2 legs.)) or ((A frog has 2 legs.) or (53 is a prime number.)))))\nD. ((not not ((not (Spain is in Asia.)) or (((-2 * 4 + 8 * -4) < (16 * 14) < (-4 * -5 + -3 * 5)) and (78 is greater than 18.)))) or ((18 % 5) <= (20 * -5)) or (not not (not ((A shark is a fish.) and ((20 - 4) > (4 * 1 - 2 * -4)))))) and (not not ((not not ((A kangaroo has 2 legs.) or ((-14 + 11) != (-7 + 0)))) and ((The chemical symbol for Calcium is Ca.) or (Helium is a gas at room temperature.)) and (Wood is a solid at room temperature.)))\nE. not (not ((not ((-15 - 8) >= (13 % 9))) and (((There are 31 days in March.) and ((5 ** 2) <= (-2 + 11) <= (-12 + 3))) and (not not (A horse has 100 legs.)))))\nF. (not (not (not not ((11 * 5) < (6 - -18) < (-11 + -18))))) or (((not (A sheep is a mammal.)) and (((There are 30 days in August.) or ((9 - -4) > (13 - -8))) or (((-2 + 0) <= (20 + -11)) and (Light travels faster than sound.)))) or ((4 - 11) >= (-6 * -2)) or (((not not (The capital of France is Prague.)) or ((The capital of Italy is Rome.) or ((-9 * 7 * 4 * -2) < (9 * 10 + 10 * 6)))) or (not (A penguin is an insect.))))\nG. not (((((18 + 7) > (11 % 9)) and (((-10 + -13) < (15 + -16)) and (The currency of Colombia is the Euro.))) and ((8 * -8 - -9 * -3) < (-1 + 4))) or ((not not (((-13 * -12) != (-19 + 16)) and (The currency of Egypt is the Pound.))) or ((-2 * 3) <= (10 * -3))))\nH. (not (not not (not ((The 1988 Olympics were held in Seoul.) and (Bats are blind.))))) and (((90 is an even number.) and ((2 * 9 * -1 * -6) <= (-2 * -5 + -4 * 7))) or (((-3 * -9 * 0 * -1) != (-11 - 7)) and (The 2016 Olympics were held in Stockholm.)))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 30093133,
"true_count": 4
},
"seed": 30093133,
"task_id": 630093133,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (((((-9 + -16) != (-10 - -17)) or (木星是距离太阳第8近的行星。)) and ((金鱼是爬行动物。) or (法国大革命开始发生在1787年。))) and ((巴西的货币是克朗。) and ((硫的化学符号是S。) or (现代奥运会首届举办发生在1894年。)))) or ((((美国宣布独立发生在1778年。) or (鱼有0条腿。)) and (((-10 * 11) >= (28 % 6)) and ((3 ** 2) >= (-15 + -14)))) and (not not ((-8 * 9 - 1 * 9) < (-9 * 10 * -3 * 0))) and ((not not ((8 - -17) < (-2 + 10))) or (((4 ** 3) < (3 ** 1)) or (1988年奥运会在首尔举办。))))
B. ((((植物通过光合作用产生氧气。) and (智利位于北美洲。)) or ((汞的化学符号是Hg。) or (哥伦比亚位于大洋洲。))) or (二月有28天。) or (((三月有31天。) or ((4 ** 2) > (-13 * -7))) and (((10 * -3 * -2 * 9) > (10 * 8 * -10 * -5)) or ((19 * 3) <= (23 % 3))))) and (袋鼠有6条腿。) and (not not (水蒸气在常温下是固体。))
C. not not (((法国大革命开始发生在1784年。) and ((98小于等于87。) or ((35 % 9) < (20 * 6)))) or ((2 ** 3) == (3 ** 1)) or (not not (天王星是距离太阳第1近的行星。)))
D. ((火星是距离太阳第4近的行星。) or (沙特阿拉伯的货币是比索。) or ((5 ** 1) > (1 * -8 - 3 * 7))) or ((((水星是距离太阳第4近的行星。) or (火星是距离太阳第3近的行星。)) and (not not ((-20 + -10) <= (2 + -9)))) and (埃及的货币是埃及镑。))
E. (((13 * -6) <= (10 * 10 * -3 * -5) <= (0 + 14)) and (((汞的化学符号是Hg。) or ((10 * 7 + -4 * -7) >= (-8 * -9 - 10 * -8))) or (((8 * 9 - -3 * 0) < (8 + -13)) or (乌克兰的首都是基辅。)))) or (((1 * 0 * 6 * 9) <= (-12 - -5) <= (4 ** 1)) or (新加坡的首都是布拉格。))
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": 4,
"language": "cn",
"num_options": 5,
"seed": 1925005,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. (((((-9 + -16) != (-10 - -17)) or (木星是距离太阳第8近的行星。)) and ((金鱼是爬行动物。) or (法国大革命开始发生在1787年。))) and ((巴西的货币是克朗。) and ((硫的化学符号是S。) or (现代奥运会首届举办发生在1894年。)))) or ((((美国宣布独立发生在1778年。) or (鱼有0条腿。)) and (((-10 * 11) >= (28 % 6)) and ((3 ** 2) >= (-15 + -14)))) and (not not ((-8 * 9 - 1 * 9) < (-9 * 10 * -3 * 0))) and ((not not ((8 - -17) < (-2 + 10))) or (((4 ** 3) < (3 ** 1)) or (1988年奥运会在首尔举办。))))\nB. ((((植物通过光合作用产生氧气。) and (智利位于北美洲。)) or ((汞的化学符号是Hg。) or (哥伦比亚位于大洋洲。))) or (二月有28天。) or (((三月有31天。) or ((4 ** 2) > (-13 * -7))) and (((10 * -3 * -2 * 9) > (10 * 8 * -10 * -5)) or ((19 * 3) <= (23 % 3))))) and (袋鼠有6条腿。) and (not not (水蒸气在常温下是固体。))\nC. not not (((法国大革命开始发生在1784年。) and ((98小于等于87。) or ((35 % 9) < (20 * 6)))) or ((2 ** 3) == (3 ** 1)) or (not not (天王星是距离太阳第1近的行星。)))\nD. ((火星是距离太阳第4近的行星。) or (沙特阿拉伯的货币是比索。) or ((5 ** 1) > (1 * -8 - 3 * 7))) or ((((水星是距离太阳第4近的行星。) or (火星是距离太阳第3近的行星。)) and (not not ((-20 + -10) <= (2 + -9)))) and (埃及的货币是埃及镑。))\nE. (((13 * -6) <= (10 * 10 * -3 * -5) <= (0 + 14)) and (((汞的化学符号是Hg。) or ((10 * 7 + -4 * -7) >= (-8 * -9 - 10 * -8))) or (((8 * 9 - -3 * 0) < (8 + -13)) or (乌克兰的首都是基辅。)))) or (((1 * 0 * 6 * 9) <= (-12 - -5) <= (4 ** 1)) or (新加坡的首都是布拉格。))\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": 5,
"seed": 1925005,
"true_count": 1
},
"seed": 1925005,
"task_id": 601925005,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((((0 * -12) == (15 + -7)) and (菲律宾的货币是里拉。)) and (锌的化学符号是Al。)) or ((柏林墙倒塌发生在1989年。) or ((二月有28天。) and ((8 * -1) >= (-4 * 5 - -1 * 5))))) and ((((俄罗斯位于欧洲。) and (银在常温下是固体。)) or ((天王星是距离太阳第7近的行星。) and (1908年奥运会在伦敦举办。))) and (not ((19 + -20) == (-5 * 10))) and (((55小于等于99。) or (墨西哥的首都是开罗。)) or ((1 % 8) == (9 * 9 * 4 * 6))))
B. not ((((尼日利亚的首都是阿布贾。) and (蜻蜓是昆虫。)) or (铁的化学符号是Fe。)) and (not (鲨鱼是鱼类。)) and (猪有0条腿。))
C. ((((氦气在常温下是固体。) and (碳的化学符号是C。)) and (((20 + -17) <= (-14 + -12)) or ((14 + 12) < (-1 * -8 + 0 * 6)))) or ((((16 * -7) < (8 % 4)) or (铜在常温下是气体。)) or (not not (四月有30天。)))) and ((光速比声速快。) or (not (韩国位于亚洲。))) and (not not ((not not ((-16 - -13) < (-6 * -6))) and (((-11 * 0) <= (1 - 5)) or ((34 % 9) == (3 * 4 - -9 * -8)))))
D. not not (not not (铅的化学符号是Si。))
E. not (((苏联解体发生在2001年。) and ((铝的化学符号是He。) and (二氧化碳在常温下是气体。))) or (((8 % 3) <= (10 - -16)) or (((17 + 7) == (2 ** 2)) or (加拿大位于北美洲。))))
F. (not (海王星是距离太阳第6近的行星。)) and (((not not (瓢虫是昆虫。)) or ((银的化学符号是Ag。) and ((2 * 4 - 6 * 3) <= (-7 * -1 - -5 * 4)))) and (乌克兰的首都是渥太华。) and ((8 - -9) <= (17 + -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": 4,
"language": "cn",
"num_options": 6,
"seed": 74263244,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. (((((0 * -12) == (15 + -7)) and (菲律宾的货币是里拉。)) and (锌的化学符号是Al。)) or ((柏林墙倒塌发生在1989年。) or ((二月有28天。) and ((8 * -1) >= (-4 * 5 - -1 * 5))))) and ((((俄罗斯位于欧洲。) and (银在常温下是固体。)) or ((天王星是距离太阳第7近的行星。) and (1908年奥运会在伦敦举办。))) and (not ((19 + -20) == (-5 * 10))) and (((55小于等于99。) or (墨西哥的首都是开罗。)) or ((1 % 8) == (9 * 9 * 4 * 6))))\nB. not ((((尼日利亚的首都是阿布贾。) and (蜻蜓是昆虫。)) or (铁的化学符号是Fe。)) and (not (鲨鱼是鱼类。)) and (猪有0条腿。))\nC. ((((氦气在常温下是固体。) and (碳的化学符号是C。)) and (((20 + -17) <= (-14 + -12)) or ((14 + 12) < (-1 * -8 + 0 * 6)))) or ((((16 * -7) < (8 % 4)) or (铜在常温下是气体。)) or (not not (四月有30天。)))) and ((光速比声速快。) or (not (韩国位于亚洲。))) and (not not ((not not ((-16 - -13) < (-6 * -6))) and (((-11 * 0) <= (1 - 5)) or ((34 % 9) == (3 * 4 - -9 * -8)))))\nD. not not (not not (铅的化学符号是Si。))\nE. not (((苏联解体发生在2001年。) and ((铝的化学符号是He。) and (二氧化碳在常温下是气体。))) or (((8 % 3) <= (10 - -16)) or (((17 + 7) == (2 ** 2)) or (加拿大位于北美洲。))))\nF. (not (海王星是距离太阳第6近的行星。)) and (((not not (瓢虫是昆虫。)) or ((银的化学符号是Ag。) and ((2 * 4 - 6 * 3) <= (-7 * -1 - -5 * 4)))) and (乌克兰的首都是渥太华。) and ((8 - -9) <= (17 + -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": 4,
"language": "cn",
"num_options": 6,
"seed": 74263244,
"true_count": 2
},
"seed": 74263244,
"task_id": 674263244,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not ((((2 ** 2) >= (-10 * -8 + -6 * 8)) and (捷克的货币是克朗。)) or (((8 + -1) >= (-6 * -4)) and (人体有150块骨头。)))
B. not not ((墨西哥的首都是墨西哥城。) and (((8 * -7 - -1 * 1) < (7 + -7)) and (磷的化学符号是P。)))
C. not not ((((7 - 4) != (13 + -18)) and (铜在常温下是气体。)) or (铜的化学符号是Cu。))
D. (((380是完全平方数。) and (美国宣布独立发生在1778年。)) and ((金星是距离太阳第8近的行星。) or (2055年是闰年。))) and ((-2 + 5) < (2 * 11))
E. ((越南的首都是河内。) or (not not (鲨鱼是鸟类。))) or (not not (not ((-14 * 13) == (19 % 5))))
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,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 74612716,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. not ((((2 ** 2) >= (-10 * -8 + -6 * 8)) and (捷克的货币是克朗。)) or (((8 + -1) >= (-6 * -4)) and (人体有150块骨头。)))\nB. not not ((墨西哥的首都是墨西哥城。) and (((8 * -7 - -1 * 1) < (7 + -7)) and (磷的化学符号是P。)))\nC. not not ((((7 - 4) != (13 + -18)) and (铜在常温下是气体。)) or (铜的化学符号是Cu。))\nD. (((380是完全平方数。) and (美国宣布独立发生在1778年。)) and ((金星是距离太阳第8近的行星。) or (2055年是闰年。))) and ((-2 + 5) < (2 * 11))\nE. ((越南的首都是河内。) or (not not (鲨鱼是鸟类。))) or (not not (not ((-14 * 13) == (19 % 5))))\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": 5,
"seed": 74612716,
"true_count": 4
},
"seed": 74612716,
"task_id": 674612716,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((中国长城是在一年内建成的。) or (俄罗斯位于欧洲。) or (金星是距离太阳第8近的行星。)) and (((((0 * 5 * 1 * 5) >= (11 % 2)) and ((3 ** 3) != (-12 + -10))) and (泰坦尼克号沉没发生在1912年。)) and (not not (伦敦大火发生在1671年。)))
B. (((19 + 18) > (1 ** 3)) and (巴西位于南美洲。)) and ((-10 + -5) == (5 ** 2)) and ((((泰坦尼克号沉没发生在1912年。) or ((1 ** 2) >= (3 % 8))) and ((2004年奥运会在雅典举办。) or (鲤鱼是鱼类。))) and (铬的化学符号是Al。) and ((((-3 - -4) > (4 * 8 - -9 * 10)) and (火星是距离太阳第2近的行星。)) or (芬兰的首都是赫尔辛基。)))
C. 月球绕地球运转。
D. ((((金的化学符号是Pb。) and ((0 * -7 - 8 * -8) < (13 - -7))) or (not not ((-11 * -1) >= (7 - -9)))) and (波兰的货币是越南盾。)) and ((-11 * -20) <= (-11 - -3)) and ((((钻石由碳元素组成。) and ((-6 * -6 - -9 * -2) < (5 * -14))) and (190是斐波那契数。)) or (not ((铅的化学符号是Mg。) and (以色列的货币是谢克尔。))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 72888894,
"true_count": 1
},
"question": "下面是几个布尔表达式：\n\nA. ((中国长城是在一年内建成的。) or (俄罗斯位于欧洲。) or (金星是距离太阳第8近的行星。)) and (((((0 * 5 * 1 * 5) >= (11 % 2)) and ((3 ** 3) != (-12 + -10))) and (泰坦尼克号沉没发生在1912年。)) and (not not (伦敦大火发生在1671年。)))\nB. (((19 + 18) > (1 ** 3)) and (巴西位于南美洲。)) and ((-10 + -5) == (5 ** 2)) and ((((泰坦尼克号沉没发生在1912年。) or ((1 ** 2) >= (3 % 8))) and ((2004年奥运会在雅典举办。) or (鲤鱼是鱼类。))) and (铬的化学符号是Al。) and ((((-3 - -4) > (4 * 8 - -9 * 10)) and (火星是距离太阳第2近的行星。)) or (芬兰的首都是赫尔辛基。)))\nC. 月球绕地球运转。\nD. ((((金的化学符号是Pb。) and ((0 * -7 - 8 * -8) < (13 - -7))) or (not not ((-11 * -1) >= (7 - -9)))) and (波兰的货币是越南盾。)) and ((-11 * -20) <= (-11 - -3)) and ((((钻石由碳元素组成。) and ((-6 * -6 - -9 * -2) < (5 * -14))) and (190是斐波那契数。)) or (not ((铅的化学符号是Mg。) and (以色列的货币是谢克尔。))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 72888894,
"true_count": 1
},
"seed": 72888894,
"task_id": 672888894,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not not (not not ((The capital of Italy is Bucharest.) and (The capital of New Zealand is Jakarta.)))
B. (((((-6 + -1) == (-19 + 18)) or ((-6 * 4 - 2 * -2) < (-9 * -11))) and ((-13 * 7) <= (-16 - -1))) and (not ((The currency of Japan is the Franc.) and (Earth is the 7th planet from the Sun.)))) or (((The currency of Czech Republic is the Euro.) and ((The capital of Portugal is Lisbon.) and ((13 + -16) >= (19 + -14)))) or ((((3 ** 3) < (14 * -13)) and ((-10 + 11) == (20 + -6))) and (((-3 * -7) <= (-9 * -3 - 10 * -6)) or (Carbon dioxide is a gas at room temperature.))))
C. not not (((31 is less than or equal to 78.) or (The capital of Sweden is Stockholm.)) and (The chemical symbol for Helium is Ti.))
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": 4,
"language": "en",
"num_options": 3,
"seed": 20596006,
"true_count": 1
},
"question": "Analyze these boolean expressions:\n\nA. not not (not not ((The capital of Italy is Bucharest.) and (The capital of New Zealand is Jakarta.)))\nB. (((((-6 + -1) == (-19 + 18)) or ((-6 * 4 - 2 * -2) < (-9 * -11))) and ((-13 * 7) <= (-16 - -1))) and (not ((The currency of Japan is the Franc.) and (Earth is the 7th planet from the Sun.)))) or (((The currency of Czech Republic is the Euro.) and ((The capital of Portugal is Lisbon.) and ((13 + -16) >= (19 + -14)))) or ((((3 ** 3) < (14 * -13)) and ((-10 + 11) == (20 + -6))) and (((-3 * -7) <= (-9 * -3 - 10 * -6)) or (Carbon dioxide is a gas at room temperature.))))\nC. not not (((31 is less than or equal to 78.) or (The capital of Sweden is Stockholm.)) and (The chemical symbol for Helium is Ti.))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 20596006,
"true_count": 1
},
"seed": 20596006,
"task_id": 620596006,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (((not not (not not (摩洛哥位于非洲。))) and (智利的首都是东京。)) and (((-7 * 0) < (6 * -6)) and (((-10 - 15) == (16 % 9)) and (智利位于南美洲。))) and (not ((6 % 10) < (-2 * 1)))) and ((not not (人类有三个肺。)) or (not not (not not ((巴西位于南美洲。) and ((17 - 18) == (20 - -16))))))
B. not (not (((not not ((-1 * -4 + -7 * 8) < (-6 * 2 + -8 * 2) < (-17 + -19))) and (((20 * 15) > (30 % 8)) and ((7 * -7 * 0 * 1) > (-2 * -2 * 3 * 4)))) or (墨西哥的货币是比索。)))
C. (((((1 ** 2) > (4 * -2 + 6 * -3)) or (((-6 - -2) <= (2 ** 3)) or (1904年是闰年。))) and ((not not ((7 * 5 * 9 * -8) <= (16 + -3))) or (1920年奥运会在安特卫普举办。))) or (not not (not not (not ((2 ** 1) < (-17 - 14) < (2 - 20)))))) and (not not (not (not (60大于78。))))
D. not not ((((not not ((6 % 9) == (17 + -1))) or (((-8 + 5) >= (-3 * 2 + 7 * -10)) or (现代奥运会首届举办发生在1895年。))) or (油在常温下是液体。)) or ((八月有28天。) and (((1952年奥运会在墨西哥城举办。) or (人类首次登月发生在1970年。)) and (not not ((-9 * -6) < (-2 * -3 * -2 * -1))))))
E. not ((((((0 * 2 + 3 * -3) < (13 - -18)) and ((-7 - -19) != (-20 * -14))) and ((希腊的首都是利马。) and (1936年奥运会在柏林举办。))) or (((3 ** 1) < (3 + -2) < (7 * -3 + -3 * -9)) and (1933年是闰年。))) and (((地球是距离太阳第3近的行星。) and (俄罗斯的首都是维也纳。)) and ((1948年奥运会在伦敦举办。) or (1908年奥运会在伦敦举办。))) and (not (木头在常温下是气体。)))
F. (((印度位于南美洲。) and ((((-1 + -10) <= (1 ** 1)) and (美国位于北美洲。)) or (((-16 * 14) >= (2 ** 3)) or (法国大革命开始发生在1789年。)))) or ((尼日利亚位于亚洲。) or ((5 * 7 - 10 * 4) < (8 - -20) < (10 * 10 * -8 * -9)))) or ((not (((-8 * -2 * -6 * -2) == (5 + 18)) and (((-8 - 0) == (5 * 9 - -5 * -3)) and ((-7 * -8 * 1 * -4) <= (8 * 18))))) or (not (not not ((-1 * 0 - -3 * -3) >= (-11 + -11)))) or ((墨西哥位于北美洲。) and ((-2 - 13) != (5 + 20)) and (以色列的货币是欧元。)))
G. (((not not ((-17 - -14) == (-4 * -5))) or ((鱼有2条腿。) and (氮气在常温下是气体。)) or (not not ((芬兰的首都是赫尔辛基。) or (鲸鱼是鱼类。)))) or (((not not (54是质数。)) and (not not ((1 ** 3) < (-2 * -9 + -3 * 0) < (5 - 12)))) and (罗马尼亚的首都是布加勒斯特。))) and (not ((((六月有28天。) or ((-13 - 2) <= (17 * -5))) and (钛的化学符号是Mn。)) and (((钙的化学符号是Ca。) or (76能被7整除。)) or (((18 + 11) < (-4 * 0 * 3 * 8)) or ((20 + -18) < (15 * -18))))))
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,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 53251350,
"true_count": 5
},
"question": "审视以下逻辑表达式：\n\nA. (((not not (not not (摩洛哥位于非洲。))) and (智利的首都是东京。)) and (((-7 * 0) < (6 * -6)) and (((-10 - 15) == (16 % 9)) and (智利位于南美洲。))) and (not ((6 % 10) < (-2 * 1)))) and ((not not (人类有三个肺。)) or (not not (not not ((巴西位于南美洲。) and ((17 - 18) == (20 - -16))))))\nB. not (not (((not not ((-1 * -4 + -7 * 8) < (-6 * 2 + -8 * 2) < (-17 + -19))) and (((20 * 15) > (30 % 8)) and ((7 * -7 * 0 * 1) > (-2 * -2 * 3 * 4)))) or (墨西哥的货币是比索。)))\nC. (((((1 ** 2) > (4 * -2 + 6 * -3)) or (((-6 - -2) <= (2 ** 3)) or (1904年是闰年。))) and ((not not ((7 * 5 * 9 * -8) <= (16 + -3))) or (1920年奥运会在安特卫普举办。))) or (not not (not not (not ((2 ** 1) < (-17 - 14) < (2 - 20)))))) and (not not (not (not (60大于78。))))\nD. not not ((((not not ((6 % 9) == (17 + -1))) or (((-8 + 5) >= (-3 * 2 + 7 * -10)) or (现代奥运会首届举办发生在1895年。))) or (油在常温下是液体。)) or ((八月有28天。) and (((1952年奥运会在墨西哥城举办。) or (人类首次登月发生在1970年。)) and (not not ((-9 * -6) < (-2 * -3 * -2 * -1))))))\nE. not ((((((0 * 2 + 3 * -3) < (13 - -18)) and ((-7 - -19) != (-20 * -14))) and ((希腊的首都是利马。) and (1936年奥运会在柏林举办。))) or (((3 ** 1) < (3 + -2) < (7 * -3 + -3 * -9)) and (1933年是闰年。))) and (((地球是距离太阳第3近的行星。) and (俄罗斯的首都是维也纳。)) and ((1948年奥运会在伦敦举办。) or (1908年奥运会在伦敦举办。))) and (not (木头在常温下是气体。)))\nF. (((印度位于南美洲。) and ((((-1 + -10) <= (1 ** 1)) and (美国位于北美洲。)) or (((-16 * 14) >= (2 ** 3)) or (法国大革命开始发生在1789年。)))) or ((尼日利亚位于亚洲。) or ((5 * 7 - 10 * 4) < (8 - -20) < (10 * 10 * -8 * -9)))) or ((not (((-8 * -2 * -6 * -2) == (5 + 18)) and (((-8 - 0) == (5 * 9 - -5 * -3)) and ((-7 * -8 * 1 * -4) <= (8 * 18))))) or (not (not not ((-1 * 0 - -3 * -3) >= (-11 + -11)))) or ((墨西哥位于北美洲。) and ((-2 - 13) != (5 + 20)) and (以色列的货币是欧元。)))\nG. (((not not ((-17 - -14) == (-4 * -5))) or ((鱼有2条腿。) and (氮气在常温下是气体。)) or (not not ((芬兰的首都是赫尔辛基。) or (鲸鱼是鱼类。)))) or (((not not (54是质数。)) and (not not ((1 ** 3) < (-2 * -9 + -3 * 0) < (5 - 12)))) and (罗马尼亚的首都是布加勒斯特。))) and (not ((((六月有28天。) or ((-13 - 2) <= (17 * -5))) and (钛的化学符号是Mn。)) and (((钙的化学符号是Ca。) or (76能被7整除。)) or (((18 + 11) < (-4 * 0 * 3 * 8)) or ((20 + -18) < (15 * -18))))))\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": 7,
"seed": 53251350,
"true_count": 5
},
"seed": 53251350,
"task_id": 653251350,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not ((钻石在常温下是固体。) and ((not not (氧气在常温下是气体。)) or (not ((2 * -2 - 7 * -4) <= (-18 + -13) <= (3 * 0 - -8 * 8)))))
B. not (not ((not (阿根廷的货币是比索。)) and ((海王星是距离太阳第8近的行星。) and (100小于等于35。))))
C. ((匈牙利的货币是福林。) and ((4 * 2 + -2 * -7) < (16 * 8))) and ((not ((4 ** 3) == (11 + -1))) or (((-19 + 8) < (-10 - 16)) and (月球绕地球运转。))) and (((((28 % 9) == (7 * -8 + 7 * 10)) and ((4 + -14) != (-7 + -11))) and (((2 * -8 - 2 * 6) < (41 % 1)) or (2016年奥运会在蒙特利尔举办。))) or (not not (新西兰的货币是比索。)))
D. ((鬣蜥是爬行动物。) and (天王星是距离太阳第7近的行星。) and (not (not not ((3 * 3 * 3 * 1) != (2 * -10 - 1 * 5))))) or (not ((人体有150块骨头。) or (碳的化学符号是Na。))) or (not not (((20 - 6) <= (-17 * -3) <= (-6 * 0 * -7 * -4)) and (((1 + 9) >= (7 - 8)) and ((8 % 10) <= (9 * -17)))))
E. not (not (钛的化学符号是He。))
F. (((-7 + 9) == (-17 - -9)) and (not not (鲸鱼是鱼类。)) and (蚱蜢是昆虫。)) or (((((5 * -6 + 7 * 3) > (4 + -6)) or ((9 * 1) < (-6 - 18) < (29 % 1))) or ((哥伦布到达美洲发生在1493年。) or ((-9 + -11) != (12 + 4)))) and ((2 * -3 + 0 * -9) <= (5 - 9)))
G. (not not (2012年奥运会在伦敦举办。)) or (not ((not (甲虫是昆虫。)) and ((50 % 10) != (32 % 2))))
H. ((五月有29天。) or (not (1932年奥运会在洛杉矶举办。)) or (鸭子有10条腿。)) or ((not (美国宣布独立发生在1775年。)) or (1952年奥运会在伦敦举办。)) or ((((1 % 8) > (14 - 19)) and (not not (韩国的货币是韩元。))) and (((智利的货币是里拉。) and (冰的密度比液态水小。)) or ((芬兰的首都是利马。) and (日本的首都是开罗。))))
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": "D,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 8,
"seed": 68745689,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. not ((钻石在常温下是固体。) and ((not not (氧气在常温下是气体。)) or (not ((2 * -2 - 7 * -4) <= (-18 + -13) <= (3 * 0 - -8 * 8)))))\nB. not (not ((not (阿根廷的货币是比索。)) and ((海王星是距离太阳第8近的行星。) and (100小于等于35。))))\nC. ((匈牙利的货币是福林。) and ((4 * 2 + -2 * -7) < (16 * 8))) and ((not ((4 ** 3) == (11 + -1))) or (((-19 + 8) < (-10 - 16)) and (月球绕地球运转。))) and (((((28 % 9) == (7 * -8 + 7 * 10)) and ((4 + -14) != (-7 + -11))) and (((2 * -8 - 2 * 6) < (41 % 1)) or (2016年奥运会在蒙特利尔举办。))) or (not not (新西兰的货币是比索。)))\nD. ((鬣蜥是爬行动物。) and (天王星是距离太阳第7近的行星。) and (not (not not ((3 * 3 * 3 * 1) != (2 * -10 - 1 * 5))))) or (not ((人体有150块骨头。) or (碳的化学符号是Na。))) or (not not (((20 - 6) <= (-17 * -3) <= (-6 * 0 * -7 * -4)) and (((1 + 9) >= (7 - 8)) and ((8 % 10) <= (9 * -17)))))\nE. not (not (钛的化学符号是He。))\nF. (((-7 + 9) == (-17 - -9)) and (not not (鲸鱼是鱼类。)) and (蚱蜢是昆虫。)) or (((((5 * -6 + 7 * 3) > (4 + -6)) or ((9 * 1) < (-6 - 18) < (29 % 1))) or ((哥伦布到达美洲发生在1493年。) or ((-9 + -11) != (12 + 4)))) and ((2 * -3 + 0 * -9) <= (5 - 9)))\nG. (not not (2012年奥运会在伦敦举办。)) or (not ((not (甲虫是昆虫。)) and ((50 % 10) != (32 % 2))))\nH. ((五月有29天。) or (not (1932年奥运会在洛杉矶举办。)) or (鸭子有10条腿。)) or ((not (美国宣布独立发生在1775年。)) or (1952年奥运会在伦敦举办。)) or ((((1 % 8) > (14 - 19)) and (not not (韩国的货币是韩元。))) and (((智利的货币是里拉。) and (冰的密度比液态水小。)) or ((芬兰的首都是利马。) and (日本的首都是开罗。))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 8,
"seed": 68745689,
"true_count": 4
},
"seed": 68745689,
"task_id": 668745689,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (not ((not (not ((埃及位于大洋洲。) and (氢的化学符号是H。)))) or ((-15 * 13) < (-6 + -16)) or (((46 % 8) < (10 + 5)) and (not ((16 - 16) <= (19 - -13) <= (5 * -6 - 4 * 6))) and ((-3 * 0 - -10 * -9) > (18 % 10))))) and (not (not not (not not ((-6 + 1) <= (-4 * -6 + 1 * 10) <= (12 * -11)))))
B. not ((not (((not (瓢虫是昆虫。)) or ((十二月有31天。) or ((20 - 0) < (-16 * 5)))) and (not not ((牛是鱼类。) and (爱尔兰的首都是都柏林。))))) and (not ((((-10 * 10) >= (-10 * -3)) and (((6 + 6) <= (3 ** 3)) or (鲨鱼是鱼类。))) or (声音在真空中传播更快。))))
C. ((not ((((595是斐波那契数。) and (柏林墙倒塌发生在1991年。)) and (锡的化学符号是Sn。)) or (((6 * -18) < (13 - 2)) and ((30 % 9) < (18 - 3))) or (41是质数。))) or (((((硅的化学符号是Si。) or ((-11 * -19) != (-18 - -15))) and ((大象有4条腿。) or (1912年奥运会在斯德哥尔摩举办。))) or (not not (not (海王星是距离太阳第8近的行星。)))) or ((not ((1959年是闰年。) or (澳大利亚位于大洋洲。))) and ((7 * -5 - -6 * -3) <= (10 * -7 * -7 * 4))))) and (not (not not ((2006年是闰年。) or ((not ((3 + -9) <= (11 - -5))) and ((法国大革命开始发生在1789年。) and (铬的化学符号是N。))))))
D. (not not (not not ((1988年奥运会在首尔举办。) and (((-20 + -19) == (-8 * -8 * 4 * 2)) or ((1970年是闰年。) and ((0 * 8 * -9 * 5) > (-1 + -13))))))) and (not ((((((-17 + -10) < (7 % 6)) or (81的平方根是9。)) and (((1 ** 2) > (23 % 7)) or (汞的化学符号是Hg。))) and ((16 + -20) != (14 - 18))) or ((not not ((1 - -7) == (-6 + 1))) or (柏林墙倒塌发生在1989年。)) or (((((5 ** 1) > (-3 * 12)) or ((33 % 5) == (-11 * 12))) or (((5 ** 1) > (17 + -6)) and (捷克的首都是奥斯陆。))) or (not not (not not (三文鱼是鱼类。))))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 96228419,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. (not ((not (not ((埃及位于大洋洲。) and (氢的化学符号是H。)))) or ((-15 * 13) < (-6 + -16)) or (((46 % 8) < (10 + 5)) and (not ((16 - 16) <= (19 - -13) <= (5 * -6 - 4 * 6))) and ((-3 * 0 - -10 * -9) > (18 % 10))))) and (not (not not (not not ((-6 + 1) <= (-4 * -6 + 1 * 10) <= (12 * -11)))))\nB. not ((not (((not (瓢虫是昆虫。)) or ((十二月有31天。) or ((20 - 0) < (-16 * 5)))) and (not not ((牛是鱼类。) and (爱尔兰的首都是都柏林。))))) and (not ((((-10 * 10) >= (-10 * -3)) and (((6 + 6) <= (3 ** 3)) or (鲨鱼是鱼类。))) or (声音在真空中传播更快。))))\nC. ((not ((((595是斐波那契数。) and (柏林墙倒塌发生在1991年。)) and (锡的化学符号是Sn。)) or (((6 * -18) < (13 - 2)) and ((30 % 9) < (18 - 3))) or (41是质数。))) or (((((硅的化学符号是Si。) or ((-11 * -19) != (-18 - -15))) and ((大象有4条腿。) or (1912年奥运会在斯德哥尔摩举办。))) or (not not (not (海王星是距离太阳第8近的行星。)))) or ((not ((1959年是闰年。) or (澳大利亚位于大洋洲。))) and ((7 * -5 - -6 * -3) <= (10 * -7 * -7 * 4))))) and (not (not not ((2006年是闰年。) or ((not ((3 + -9) <= (11 - -5))) and ((法国大革命开始发生在1789年。) and (铬的化学符号是N。))))))\nD. (not not (not not ((1988年奥运会在首尔举办。) and (((-20 + -19) == (-8 * -8 * 4 * 2)) or ((1970年是闰年。) and ((0 * 8 * -9 * 5) > (-1 + -13))))))) and (not ((((((-17 + -10) < (7 % 6)) or (81的平方根是9。)) and (((1 ** 2) > (23 % 7)) or (汞的化学符号是Hg。))) and ((16 + -20) != (14 - 18))) or ((not not ((1 - -7) == (-6 + 1))) or (柏林墙倒塌发生在1989年。)) or (((((5 ** 1) > (-3 * 12)) or ((33 % 5) == (-11 * 12))) or (((5 ** 1) > (17 + -6)) and (捷克的首都是奥斯陆。))) or (not not (not not (三文鱼是鱼类。))))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 96228419,
"true_count": 1
},
"seed": 96228419,
"task_id": 696228419,
"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 ((氦的化学符号是He。) or (哥伦布到达美洲发生在1502年。))) or ((-8 - 0) <= (-17 - 17))) and ((not (((7 * -8 * 1 * 3) <= (5 * -3 + -8 * 1) <= (-4 * -10 - -3 * 5)) and ((4 + -16) != (45 % 3)))) and ((not not ((-13 + -7) >= (11 * -8))) or (not not (油在常温下是液体。))))
B. not ((((八月有31天。) and (银在常温下是固体。)) and ((81的平方根是7。) or (木星是距离太阳第5近的行星。))) and (冰的密度比液态水小。))
C. 南极洲是最冷的大陆。
D. not not (((not (鹰是鸟类。)) and (((-9 * 8 * 4 * 3) < (15 - -3)) and ((-10 + -3) < (-2 + 18)))) or (地球是距离太阳第8近的行星。))
E. ((not (((-17 * -7) != (5 ** 1)) or (植物通过光合作用产生氧气。))) or ((英国的货币是克朗。) or ((苏联解体发生在1992年。) and (碳的化学符号是C。)))) and (((银在常温下是固体。) and (第二次世界大战结束发生在1944年。)) and (铜在常温下是液体。)) and (((2008年奥运会在北京举办。) and ((土星是距离太阳第7近的行星。) or (2008年是闰年。))) and (((氮气在常温下是气体。) and ((1 + 8) != (-5 * -6 - 2 * 0))) or ((蜻蜓是爬行动物。) or ((20 - 3) > (16 * 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": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
"num_options": 5,
"seed": 90463155,
"true_count": 1
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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 ((氦的化学符号是He。) or (哥伦布到达美洲发生在1502年。))) or ((-8 - 0) <= (-17 - 17))) and ((not (((7 * -8 * 1 * 3) <= (5 * -3 + -8 * 1) <= (-4 * -10 - -3 * 5)) and ((4 + -16) != (45 % 3)))) and ((not not ((-13 + -7) >= (11 * -8))) or (not not (油在常温下是液体。))))\nB. not ((((八月有31天。) and (银在常温下是固体。)) and ((81的平方根是7。) or (木星是距离太阳第5近的行星。))) and (冰的密度比液态水小。))\nC. 南极洲是最冷的大陆。\nD. not not (((not (鹰是鸟类。)) and (((-9 * 8 * 4 * 3) < (15 - -3)) and ((-10 + -3) < (-2 + 18)))) or (地球是距离太阳第8近的行星。))\nE. ((not (((-17 * -7) != (5 ** 1)) or (植物通过光合作用产生氧气。))) or ((英国的货币是克朗。) or ((苏联解体发生在1992年。) and (碳的化学符号是C。)))) and (((银在常温下是固体。) and (第二次世界大战结束发生在1944年。)) and (铜在常温下是液体。)) and (((2008年奥运会在北京举办。) and ((土星是距离太阳第7近的行星。) or (2008年是闰年。))) and (((氮气在常温下是气体。) and ((1 + 8) != (-5 * -6 - 2 * 0))) or ((蜻蜓是爬行动物。) or ((20 - 3) > (16 * 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。"
},
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logic-v2 | 分析以下逻辑表达式：
A. (16 - 14) != (-18 * -9)
B. not (not not (企鹅能飞翔。))
C. not ((-8 + -6) < (10 * -1 - 2 * -8) < (44 % 8))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
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"question": "分析以下逻辑表达式：\n\nA. (16 - 14) != (-18 * -9)\nB. not (not not (企鹅能飞翔。))\nC. not ((-8 + -6) < (10 * -1 - 2 * -8) < (44 % 8))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 65749196,
"true_count": 3
},
"seed": 65749196,
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"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. ((((1924年奥运会在柏林举办。) and (苏联解体发生在1991年。)) or (比利时的首都是布鲁塞尔。)) or ((氖的化学符号是Cr。) or (not not (钻石在常温下是固体。)))) or (not (not (六月有29天。))) or ((((土星是距离太阳第4近的行星。) and ((37 % 2) <= (10 + 19) <= (-1 * 9 + -9 * -10))) or (((-15 * -14) != (-8 * -2 * 0 * 8)) or (硫的化学符号是S。))) or ((not not (美国位于北美洲。)) or (not (摩洛哥位于非洲。))))
B. (not ((not not (73能被4整除。)) and (not ((4 - 20) >= (17 - 17))))) or (not (not not ((3 ** 3) < (9 - -19) < (-17 - -18))))
C. (not (((16 + 9) < (-3 * -2 + 0 * 4) < (20 - -13)) or ((镁的化学符号是Fe。) or (匈牙利的首都是巴黎。)))) or (((((-15 - 1) <= (-1 * 10 - -7 * -8)) and ((-20 + 6) < (44 % 7) < (2 * 6))) and (not not ((-9 * 5) != (5 ** 1)))) and (not (not not (美国位于北美洲。))))
D. (not not (1936年奥运会在柏林举办。)) and ((二氧化碳在常温下是气体。) or ((not not ((2 * 9 - -6 * -6) <= (32 % 8) <= (14 - -7))) or (not (龙虾有10条腿。))))
E. not (((5 ** 3) <= (4 ** 2)) or (((-8 * 12) <= (-20 - 18)) or (日本的首都是圣地亚哥。)) or ((not ((17 * 4) < (8 * 10 * 6 * -5))) or (1905年是闰年。)))
F. not not (not ((4 - -11) < (-16 * -19)))
G. ((not not ((-6 * 4 + 2 * 0) == (12 + 7))) and ((((19 + -5) != (15 * 11)) or (氮气在常温下是固体。)) and (1923年是闰年。))) and (((人类是哺乳动物。) or ((50 % 8) > (23 % 7))) and (not (1984年奥运会在洛杉矶举办。))) and (((光速约为每秒30万公里。) or (((-10 - 6) == (-10 + -12)) and (铝的化学符号是Al。))) or (((-11 + -15) <= (-19 - 10)) or ((32 % 5) < (-6 * 9) < (13 + -15))) or (((第一次世界大战结束发生在1923年。) and (钻石在常温下是气体。)) and ((第二次世界大战开始发生在1949年。) and (水在常温下是液体。))))
H. not (not (not ((17 + 7) >= (3 * -8 - -9 * 9))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"question": "给定以下布尔表达式：\n\nA. ((((1924年奥运会在柏林举办。) and (苏联解体发生在1991年。)) or (比利时的首都是布鲁塞尔。)) or ((氖的化学符号是Cr。) or (not not (钻石在常温下是固体。)))) or (not (not (六月有29天。))) or ((((土星是距离太阳第4近的行星。) and ((37 % 2) <= (10 + 19) <= (-1 * 9 + -9 * -10))) or (((-15 * -14) != (-8 * -2 * 0 * 8)) or (硫的化学符号是S。))) or ((not not (美国位于北美洲。)) or (not (摩洛哥位于非洲。))))\nB. (not ((not not (73能被4整除。)) and (not ((4 - 20) >= (17 - 17))))) or (not (not not ((3 ** 3) < (9 - -19) < (-17 - -18))))\nC. (not (((16 + 9) < (-3 * -2 + 0 * 4) < (20 - -13)) or ((镁的化学符号是Fe。) or (匈牙利的首都是巴黎。)))) or (((((-15 - 1) <= (-1 * 10 - -7 * -8)) and ((-20 + 6) < (44 % 7) < (2 * 6))) and (not not ((-9 * 5) != (5 ** 1)))) and (not (not not (美国位于北美洲。))))\nD. (not not (1936年奥运会在柏林举办。)) and ((二氧化碳在常温下是气体。) or ((not not ((2 * 9 - -6 * -6) <= (32 % 8) <= (14 - -7))) or (not (龙虾有10条腿。))))\nE. not (((5 ** 3) <= (4 ** 2)) or (((-8 * 12) <= (-20 - 18)) or (日本的首都是圣地亚哥。)) or ((not ((17 * 4) < (8 * 10 * 6 * -5))) or (1905年是闰年。)))\nF. not not (not ((4 - -11) < (-16 * -19)))\nG. ((not not ((-6 * 4 + 2 * 0) == (12 + 7))) and ((((19 + -5) != (15 * 11)) or (氮气在常温下是固体。)) and (1923年是闰年。))) and (((人类是哺乳动物。) or ((50 % 8) > (23 % 7))) and (not (1984年奥运会在洛杉矶举办。))) and (((光速约为每秒30万公里。) or (((-10 - 6) == (-10 + -12)) and (铝的化学符号是Al。))) or (((-11 + -15) <= (-19 - 10)) or ((32 % 5) < (-6 * 9) < (13 + -15))) or (((第一次世界大战结束发生在1923年。) and (钻石在常温下是气体。)) and ((第二次世界大战开始发生在1949年。) and (水在常温下是液体。))))\nH. not (not (not ((17 + 7) >= (3 * -8 - -9 * 9))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
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"language": "cn",
"num_options": 8,
"seed": 42912006,
"true_count": 5
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"seed": 42912006,
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"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. 木星是距离太阳第1近的行星。
B. ((十二月有30天。) and (二氧化碳在常温下是气体。)) and ((三月有31天。) or (金星是距离太阳第2近的行星。))
C. not (not not (人类只使用了大脑的10%。))
D. (not (牛有10条腿。)) and (((1 * -14) < (-14 * 14) < (-14 + -18)) or ((-17 - -8) < (0 - -3)))
E. not not (((19 + -2) >= (-17 - -11)) and (钛的化学符号是Ti。))
F. (天王星是距离太阳第6近的行星。) or (((7 + 17) <= (9 - 19) <= (-19 - 14)) or (金在常温下是固体。))
G. (not not ((-10 + -15) == (9 * 6 * 0 * 1))) and (人体有206块骨头。)
H. not (not ((4 * 8 - 7 * -5) < (-6 * 8 + 9 * 3)))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
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"difficulty": 1,
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"question": "评估以下每个表达式：\n\nA. 木星是距离太阳第1近的行星。\nB. ((十二月有30天。) and (二氧化碳在常温下是气体。)) and ((三月有31天。) or (金星是距离太阳第2近的行星。))\nC. not (not not (人类只使用了大脑的10%。))\nD. (not (牛有10条腿。)) and (((1 * -14) < (-14 * 14) < (-14 + -18)) or ((-17 - -8) < (0 - -3)))\nE. not not (((19 + -2) >= (-17 - -11)) and (钛的化学符号是Ti。))\nF. (天王星是距离太阳第6近的行星。) or (((7 + 17) <= (9 - 19) <= (-19 - 14)) or (金在常温下是固体。))\nG. (not not ((-10 + -15) == (9 * 6 * 0 * 1))) and (人体有206块骨头。)\nH. not (not ((4 * 8 - 7 * -5) < (-6 * 8 + 9 * 3)))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
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"language": "cn",
"num_options": 8,
"seed": 53337319,
"true_count": 4
},
"seed": 53337319,
"task_id": 653337319,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (not (not (越南位于亚洲。))) and (((((沙特阿拉伯位于亚洲。) and (地球是距离太阳第3近的行星。)) and (希腊的首都是雅典。)) or (2000年奥运会在北京举办。)) and ((not not ((2053年是闰年。) or (海王星是距离太阳第8近的行星。))) and (((泰坦尼克号沉没发生在1913年。) or ((2 ** 2) <= (5 ** 2))) or (not (月球绕地球运转。)))))
B. not (not (((not not ((9 * 9 + -1 * -9) == (4 * 18))) or (铜在常温下是气体。)) and (((中国位于亚洲。) or (墨西哥的货币是韩元。)) and (not ((0 * 17) != (14 + -8))))))
C. not ((((((-2 * 9 * -3 * 2) > (4 ** 1)) or ((4 ** 3) > (-16 * 17))) and (not not ((-8 * -4 + -2 * -5) < (-2 + 3) < (32 % 10)))) and ((2 ** 3) < (19 + -3) < (9 * 5 + -10 * -9))) or ((not (((8 - 6) > (17 % 9)) and (1900年奥运会在巴黎举办。))) or (not (2078年是闰年。)) or ((not not (爱尔兰的首都是都柏林。)) or (((-5 * -2 * 2 * 4) <= (-13 * -7)) and ((5 * 5 - 6 * 10) == (-20 - 5))))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
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"question": "下面是几个布尔表达式：\n\nA. (not (not (越南位于亚洲。))) and (((((沙特阿拉伯位于亚洲。) and (地球是距离太阳第3近的行星。)) and (希腊的首都是雅典。)) or (2000年奥运会在北京举办。)) and ((not not ((2053年是闰年。) or (海王星是距离太阳第8近的行星。))) and (((泰坦尼克号沉没发生在1913年。) or ((2 ** 2) <= (5 ** 2))) or (not (月球绕地球运转。)))))\nB. not (not (((not not ((9 * 9 + -1 * -9) == (4 * 18))) or (铜在常温下是气体。)) and (((中国位于亚洲。) or (墨西哥的货币是韩元。)) and (not ((0 * 17) != (14 + -8))))))\nC. not ((((((-2 * 9 * -3 * 2) > (4 ** 1)) or ((4 ** 3) > (-16 * 17))) and (not not ((-8 * -4 + -2 * -5) < (-2 + 3) < (32 % 10)))) and ((2 ** 3) < (19 + -3) < (9 * 5 + -10 * -9))) or ((not (((8 - 6) > (17 % 9)) and (1900年奥运会在巴黎举办。))) or (not (2078年是闰年。)) or ((not not (爱尔兰的首都是都柏林。)) or (((-5 * -2 * 2 * 4) <= (-13 * -7)) and ((5 * 5 - 6 * 10) == (-20 - 5))))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
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"language": "cn",
"num_options": 3,
"seed": 68377427,
"true_count": 1
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"seed": 68377427,
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"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not not ((not not (((14 * 20) != (4 + 14)) and (((Iron is a solid at room temperature.) or ((-8 + 20) != (8 * -3 * 8 * 0))) and (World War I began occurred in 1914.)))) and ((not not (not not (Mercury is the 5th planet from the Sun.))) or ((((1959 is a leap year.) or (The 1896 Olympics were held in Seoul.)) or (163 is a Fibonacci number.)) or (Mercury is the 1st planet from the Sun.))))
B. not not (((not not (The chemical symbol for Sodium is Na.)) or ((not not (Japan is in Europe.)) and (not ((3 ** 2) < (14 + 16))))) and ((The chemical symbol for Chromium is Pb.) or (The 1936 Olympics were held in Berlin.) or ((not ((16 * -1) < (3 ** 3) < (-12 * 13))) or ((The capital of Norway is Ottawa.) and (Humans only use 10% of their brain.)))) and (not not (not ((3 - 5) < (-7 * -1 + 0 * 4)))))
C. not not ((not (not ((16 + 8) < (13 - 16)))) and (not (((((6 - 20) == (4 * 3 * 5 * -6)) or (Uranus is the 2nd planet from the Sun.)) or (((-5 * 1 * -2 * -5) < (-1 * 7 + 5 * 10)) or ((-5 * -10 - 1 * -3) < (7 - 14) < (-13 + -2)))) or (not (not ((12 * -19) >= (23 % 10)))))))
D. not not ((not not ((The chemical symbol for Uranium is U.) or (not not (The chemical symbol for Tin is Pb.)))) or (not ((not not (((34 % 3) <= (14 + 6)) or ((1 - 6) < (31 % 1) < (8 - 16)))) or (not not (not ((-7 * 5) >= (14 * 7)))))))
E. not (not not (not (((((-7 * -8 * 10 * -9) != (7 * -6 * -9 * 3)) or ((-7 * 19) != (2 * 7))) or (((40 % 6) >= (17 * -2)) and (A tuna is a fish.))) or ((36 is a perfect square.) and (Colombia is in South America.)))))
F. not ((not not (not not (((A pig has 4 legs.) and ((10 % 6) >= (-4 * -2 - -4 * 7))) or ((Water is a liquid at room temperature.) or (A sheep is a mammal.))))) or (not not (((((5 * -8 + 3 * -8) >= (2 ** 2)) and ((-8 * -9 + 1 * 3) == (12 % 3))) or (not not ((11 - -7) < (5 * 6 + -5 * -3) < (-17 * 18)))) and ((33 is divisible by 4.) and ((The currency of Philippines is the Peso.) and ((20 + 19) != (3 ** 3)))))))
G. not (not ((not ((0 * -4) < (5 ** 1))) or ((not not ((-3 * 7 * 6 * 3) >= (2 - 17))) and ((11 + -5) < (-3 * -6 + -9 * -10)) and ((Nitrogen is a gas at room temperature.) or ((A snake has 0 legs.) and (There are 31 days in July.))))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"question": "Review these logical expressions:\n\nA. not not ((not not (((14 * 20) != (4 + 14)) and (((Iron is a solid at room temperature.) or ((-8 + 20) != (8 * -3 * 8 * 0))) and (World War I began occurred in 1914.)))) and ((not not (not not (Mercury is the 5th planet from the Sun.))) or ((((1959 is a leap year.) or (The 1896 Olympics were held in Seoul.)) or (163 is a Fibonacci number.)) or (Mercury is the 1st planet from the Sun.))))\nB. not not (((not not (The chemical symbol for Sodium is Na.)) or ((not not (Japan is in Europe.)) and (not ((3 ** 2) < (14 + 16))))) and ((The chemical symbol for Chromium is Pb.) or (The 1936 Olympics were held in Berlin.) or ((not ((16 * -1) < (3 ** 3) < (-12 * 13))) or ((The capital of Norway is Ottawa.) and (Humans only use 10% of their brain.)))) and (not not (not ((3 - 5) < (-7 * -1 + 0 * 4)))))\nC. not not ((not (not ((16 + 8) < (13 - 16)))) and (not (((((6 - 20) == (4 * 3 * 5 * -6)) or (Uranus is the 2nd planet from the Sun.)) or (((-5 * 1 * -2 * -5) < (-1 * 7 + 5 * 10)) or ((-5 * -10 - 1 * -3) < (7 - 14) < (-13 + -2)))) or (not (not ((12 * -19) >= (23 % 10)))))))\nD. not not ((not not ((The chemical symbol for Uranium is U.) or (not not (The chemical symbol for Tin is Pb.)))) or (not ((not not (((34 % 3) <= (14 + 6)) or ((1 - 6) < (31 % 1) < (8 - 16)))) or (not not (not ((-7 * 5) >= (14 * 7)))))))\nE. not (not not (not (((((-7 * -8 * 10 * -9) != (7 * -6 * -9 * 3)) or ((-7 * 19) != (2 * 7))) or (((40 % 6) >= (17 * -2)) and (A tuna is a fish.))) or ((36 is a perfect square.) and (Colombia is in South America.)))))\nF. not ((not not (not not (((A pig has 4 legs.) and ((10 % 6) >= (-4 * -2 - -4 * 7))) or ((Water is a liquid at room temperature.) or (A sheep is a mammal.))))) or (not not (((((5 * -8 + 3 * -8) >= (2 ** 2)) and ((-8 * -9 + 1 * 3) == (12 % 3))) or (not not ((11 - -7) < (5 * 6 + -5 * -3) < (-17 * 18)))) and ((33 is divisible by 4.) and ((The currency of Philippines is the Peso.) and ((20 + 19) != (3 ** 3)))))))\nG. not (not ((not ((0 * -4) < (5 ** 1))) or ((not not ((-3 * 7 * 6 * 3) >= (2 - 17))) and ((11 + -5) < (-3 * -6 + -9 * -10)) and ((Nitrogen is a gas at room temperature.) or ((A snake has 0 legs.) and (There are 31 days in July.))))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
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logic-v2 | Analyze these boolean expressions:
A. not (not not (((((The 2024 Olympics were held in Paris.) or (The 2024 Olympics were held in Antwerp.)) and (The currency of Canada is the Naira.)) and ((-10 * 2 - -5 * -8) == (-19 - 6))) or (not (not (((9 - -20) != (2 + -15)) and ((-9 * -4) <= (1 * 1)))))))
B. not (not not (not not ((Penguins can fly.) or (((0 + 14) <= (0 * 16) <= (3 ** 3)) and (((34 % 5) >= (-16 * -16)) or ((11 % 2) <= (3 * -15)))))))
C. not (not ((((-17 - -3) > (20 * -10)) and ((not (The 1960 Olympics were held in Rome.)) and ((12 * 15) >= (17 * 19)))) or (not not ((Jupiter is the 1st planet from the Sun.) and ((-14 - -6) > (-15 - -18))))))
D. ((not not (((-14 * -9) < (-3 - -13) < (-3 * -8 + -7 * 2)) or ((9 - 6) <= (6 - -3)))) and ((not not (((A mouse is a mammal.) and (1958 is a leap year.)) or (not ((1 ** 2) >= (17 - 6))))) or (not (The 1964 Olympics were held in Tokyo.)))) and (not not ((not not (The 1896 Olympics were held in Athens.)) or ((not not (Brazil is in Europe.)) and (not not ((18 + 11) == (1 ** 1)))) or (not (((13 - 20) == (6 * -2)) or ((11 + -20) == (2 ** 1))))))
E. not not (not not (((((Nitrogen is a liquid at room temperature.) or (The 1928 Olympics were held in Amsterdam.)) or ((The capital of Kenya is Nairobi.) or ((10 + -1) <= (3 * 11) <= (-4 * 14)))) or (((-7 - 14) != (17 + -11)) or (Spain is in Europe.)) or (((Canada is in Europe.) and ((5 ** 1) >= (19 - 3))) and ((The 1948 Olympics were held in London.) and ((20 * 11) <= (19 * 12) <= (-7 + 7))))) and (not (not (((15 - 10) < (4 ** 2)) or (Alcohol is a liquid at room temperature.))))))
F. not not (not (not (not ((not not (A penguin is a bird.)) or (not ((-11 + -15) > (5 + 10)))))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
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"true_count": 4
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"question": "Analyze these boolean expressions:\n\nA. not (not not (((((The 2024 Olympics were held in Paris.) or (The 2024 Olympics were held in Antwerp.)) and (The currency of Canada is the Naira.)) and ((-10 * 2 - -5 * -8) == (-19 - 6))) or (not (not (((9 - -20) != (2 + -15)) and ((-9 * -4) <= (1 * 1)))))))\nB. not (not not (not not ((Penguins can fly.) or (((0 + 14) <= (0 * 16) <= (3 ** 3)) and (((34 % 5) >= (-16 * -16)) or ((11 % 2) <= (3 * -15)))))))\nC. not (not ((((-17 - -3) > (20 * -10)) and ((not (The 1960 Olympics were held in Rome.)) and ((12 * 15) >= (17 * 19)))) or (not not ((Jupiter is the 1st planet from the Sun.) and ((-14 - -6) > (-15 - -18))))))\nD. ((not not (((-14 * -9) < (-3 - -13) < (-3 * -8 + -7 * 2)) or ((9 - 6) <= (6 - -3)))) and ((not not (((A mouse is a mammal.) and (1958 is a leap year.)) or (not ((1 ** 2) >= (17 - 6))))) or (not (The 1964 Olympics were held in Tokyo.)))) and (not not ((not not (The 1896 Olympics were held in Athens.)) or ((not not (Brazil is in Europe.)) and (not not ((18 + 11) == (1 ** 1)))) or (not (((13 - 20) == (6 * -2)) or ((11 + -20) == (2 ** 1))))))\nE. not not (not not (((((Nitrogen is a liquid at room temperature.) or (The 1928 Olympics were held in Amsterdam.)) or ((The capital of Kenya is Nairobi.) or ((10 + -1) <= (3 * 11) <= (-4 * 14)))) or (((-7 - 14) != (17 + -11)) or (Spain is in Europe.)) or (((Canada is in Europe.) and ((5 ** 1) >= (19 - 3))) and ((The 1948 Olympics were held in London.) and ((20 * 11) <= (19 * 12) <= (-7 + 7))))) and (not (not (((15 - 10) < (4 ** 2)) or (Alcohol is a liquid at room temperature.))))))\nF. not not (not (not (not ((not not (A penguin is a bird.)) or (not ((-11 + -15) > (5 + 10)))))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
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"seed": 68674653,
"true_count": 4
},
"seed": 68674653,
"task_id": 668674653,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (not (not not ((Diamonds are made of carbon.) and ((not (Mercury is the 6th planet from the Sun.)) and (((-5 * -3) != (-14 + -5)) or (Australia is in Oceania.)))))) and (not not (not (((not ((-14 * 6) <= (-8 * -8 * 7 * -7))) and (not ((-9 * -9 * -7 * 8) <= (7 + 15)))) or (The currency of South Korea is the Franc.))))
B. not ((((The 1972 Olympics were held in Munich.) or (((Brazil is in South America.) or ((-11 + 9) <= (17 * -3))) or (((45 % 9) <= (8 * -5 - 4 * -2)) or ((5 ** 3) == (-16 - -12))))) or (not ((-8 * 10 + -8 * -5) <= (13 - -14) <= (3 % 2)))) and (not (((((0 * 8) >= (-7 - 11)) and (Carbon dioxide is a gas at room temperature.)) and ((36 % 3) == (13 + -8))) or (((The currency of Mexico is the Yen.) or ((-15 + 8) > (-14 + 14))) and (59 is a perfect square.)))))
C. not not ((not (not not (The 1984 Olympics were held in Los Angeles.))) or (not (not not (((4 + -7) < (-11 + -11)) and (not not ((20 * 3) > (11 - 11)))))))
D. not (((((not not ((3 ** 3) > (2 - 18))) or ((The currency of Mexico is the Peso.) or ((-8 - 14) <= (17 * -2) <= (1 ** 3)))) and (The capital of Saudi Arabia is Riyadh.) and (((-19 * 0) <= (19 + 10) <= (-19 - -3)) or ((Sound cannot travel through a vacuum.) or (A cat has 2 legs.)))) and (not (not (Saturn is the 6th planet from the Sun.)))) and (not not ((not not ((-16 + 14) != (6 * -9 - 3 * -6))) or (30 is a prime number.))))
E. not (not not ((not (((Nitrogen is a solid at room temperature.) or ((19 % 9) == (2 + 5))) and (((11 - -18) == (4 * 8 * -6 * -3)) or (A bird has 10 legs.)))) and (not not (((The currency of Singapore is the Dollar.) and (The currency of Turkey is the Pound.)) or ((Humans have three lungs.) or (There are 30 days in September.))))))
F. not not (not (not ((Russia is in Oceania.) or ((not (Germany is in Europe.)) and ((2012 is a leap year.) or (The capital of Philippines is Manila.))))))
G. not (not (((not not (((-19 + -10) <= (1 * 1) <= (9 - 6)) and ((3 ** 2) != (3 - -14)))) or ((((12 * 10) <= (-4 * -10) <= (2 - -14)) and (The capital of Sweden is Madrid.)) and (There are 28 days in February.))) or (((19 * -8) != (12 - -3)) or ((Peru is in Antarctica.) or (A cow has 4 legs.)))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
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"answer": "C,G",
"difficulty": 1,
"gpt_response": "",
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"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (not (not not ((Diamonds are made of carbon.) and ((not (Mercury is the 6th planet from the Sun.)) and (((-5 * -3) != (-14 + -5)) or (Australia is in Oceania.)))))) and (not not (not (((not ((-14 * 6) <= (-8 * -8 * 7 * -7))) and (not ((-9 * -9 * -7 * 8) <= (7 + 15)))) or (The currency of South Korea is the Franc.))))\nB. not ((((The 1972 Olympics were held in Munich.) or (((Brazil is in South America.) or ((-11 + 9) <= (17 * -3))) or (((45 % 9) <= (8 * -5 - 4 * -2)) or ((5 ** 3) == (-16 - -12))))) or (not ((-8 * 10 + -8 * -5) <= (13 - -14) <= (3 % 2)))) and (not (((((0 * 8) >= (-7 - 11)) and (Carbon dioxide is a gas at room temperature.)) and ((36 % 3) == (13 + -8))) or (((The currency of Mexico is the Yen.) or ((-15 + 8) > (-14 + 14))) and (59 is a perfect square.)))))\nC. not not ((not (not not (The 1984 Olympics were held in Los Angeles.))) or (not (not not (((4 + -7) < (-11 + -11)) and (not not ((20 * 3) > (11 - 11)))))))\nD. not (((((not not ((3 ** 3) > (2 - 18))) or ((The currency of Mexico is the Peso.) or ((-8 - 14) <= (17 * -2) <= (1 ** 3)))) and (The capital of Saudi Arabia is Riyadh.) and (((-19 * 0) <= (19 + 10) <= (-19 - -3)) or ((Sound cannot travel through a vacuum.) or (A cat has 2 legs.)))) and (not (not (Saturn is the 6th planet from the Sun.)))) and (not not ((not not ((-16 + 14) != (6 * -9 - 3 * -6))) or (30 is a prime number.))))\nE. not (not not ((not (((Nitrogen is a solid at room temperature.) or ((19 % 9) == (2 + 5))) and (((11 - -18) == (4 * 8 * -6 * -3)) or (A bird has 10 legs.)))) and (not not (((The currency of Singapore is the Dollar.) and (The currency of Turkey is the Pound.)) or ((Humans have three lungs.) or (There are 30 days in September.))))))\nF. not not (not (not ((Russia is in Oceania.) or ((not (Germany is in Europe.)) and ((2012 is a leap year.) or (The capital of Philippines is Manila.))))))\nG. not (not (((not not (((-19 + -10) <= (1 * 1) <= (9 - 6)) and ((3 ** 2) != (3 - -14)))) or ((((12 * 10) <= (-4 * -10) <= (2 - -14)) and (The capital of Sweden is Madrid.)) and (There are 28 days in February.))) or (((19 * -8) != (12 - -3)) or ((Peru is in Antarctica.) or (A cow has 4 legs.)))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
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"seed": 5692413,
"true_count": 2
},
"seed": 5692413,
"task_id": 605692413,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not (not not (not (((-12 * -10) <= (-1 * 5 * 0 * -7) <= (-19 - -11)) or (((19 - 14) < (22 % 6)) or (((10 * 3) < (-8 - -17) < (-10 * 7)) and (Saturn is the 6th planet from the Sun.))))))
B. not (not (((not ((Copper is a solid at room temperature.) or (Mars is the 2nd planet from the Sun.))) or ((47 % 8) <= (1 * -2 - 7 * 6))) or ((Earth is the 3rd planet from the Sun.) and (not (The currency of New Zealand is the Dollar.))) or (((not (1 is an even number.)) or ((The currency of Thailand is the Euro.) and (World War I began occurred in 1914.))) and (not not ((350 is a perfect square.) or ((3 * -4 + 5 * 2) != (-8 + -5)))))))
C. (not (not ((not not ((1 * 6 + 10 * -2) == (-7 - 8))) or ((The capital of Greece is Ottawa.) or ((42 % 5) == (23 % 8))) or (((The Berlin Wall fell occurred in 1989.) and (World War II ended occurred in 1945.)) or ((The currency of Turkey is the Lira.) and ((10 + 13) <= (-16 + -4))))))) and (not ((not ((10 + -20) >= (1 ** 3))) and ((((World War I began occurred in 1914.) or ((17 % 4) == (1 % 8))) or ((3 * -16) < (14 - -12))) or (not not ((28 % 2) == (-1 * -8))) or ((4 ** 1) <= (-7 + 2)))))
D. (not (not (not not ((12 % 10) != (-13 + -10))))) and (((not ((Uranus is the 4th planet from the Sun.) and ((The currency of Vietnam is the Dong.) or (The 1904 Olympics were held in Rio de Janeiro.)))) or (not (A cow has 4 legs.))) and (((not (not (24 is a Fibonacci number.))) and (((20 * 1) == (7 - 4)) or ((12 + -18) > (46 % 6))) and ((4 - 8) >= (5 ** 3))) and ((The currency of China is the Yuan.) and (not (The chemical symbol for Titanium is Ti.)) and (A snake has 0 legs.))))
E. not (not not (((not (((-2 * -2 - -2 * 0) > (-6 + 10)) and ((-4 * 3 * -10 * -5) >= (-3 - -11)))) and ((not (A butterfly has 6 legs.)) and (((6 * 8 * -8 * 1) > (-14 + 1)) or ((7 * 7 * 6 * -9) != (4 * 20))))) and (not ((not not ((1 ** 1) > (-10 * -1 - -7 * 5))) and (Venus is the 2nd planet from the Sun.)))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"question": "Review these logical expressions:\n\nA. not (not not (not (((-12 * -10) <= (-1 * 5 * 0 * -7) <= (-19 - -11)) or (((19 - 14) < (22 % 6)) or (((10 * 3) < (-8 - -17) < (-10 * 7)) and (Saturn is the 6th planet from the Sun.))))))\nB. not (not (((not ((Copper is a solid at room temperature.) or (Mars is the 2nd planet from the Sun.))) or ((47 % 8) <= (1 * -2 - 7 * 6))) or ((Earth is the 3rd planet from the Sun.) and (not (The currency of New Zealand is the Dollar.))) or (((not (1 is an even number.)) or ((The currency of Thailand is the Euro.) and (World War I began occurred in 1914.))) and (not not ((350 is a perfect square.) or ((3 * -4 + 5 * 2) != (-8 + -5)))))))\nC. (not (not ((not not ((1 * 6 + 10 * -2) == (-7 - 8))) or ((The capital of Greece is Ottawa.) or ((42 % 5) == (23 % 8))) or (((The Berlin Wall fell occurred in 1989.) and (World War II ended occurred in 1945.)) or ((The currency of Turkey is the Lira.) and ((10 + 13) <= (-16 + -4))))))) and (not ((not ((10 + -20) >= (1 ** 3))) and ((((World War I began occurred in 1914.) or ((17 % 4) == (1 % 8))) or ((3 * -16) < (14 - -12))) or (not not ((28 % 2) == (-1 * -8))) or ((4 ** 1) <= (-7 + 2)))))\nD. (not (not (not not ((12 % 10) != (-13 + -10))))) and (((not ((Uranus is the 4th planet from the Sun.) and ((The currency of Vietnam is the Dong.) or (The 1904 Olympics were held in Rio de Janeiro.)))) or (not (A cow has 4 legs.))) and (((not (not (24 is a Fibonacci number.))) and (((20 * 1) == (7 - 4)) or ((12 + -18) > (46 % 6))) and ((4 - 8) >= (5 ** 3))) and ((The currency of China is the Yuan.) and (not (The chemical symbol for Titanium is Ti.)) and (A snake has 0 legs.))))\nE. not (not not (((not (((-2 * -2 - -2 * 0) > (-6 + 10)) and ((-4 * 3 * -10 * -5) >= (-3 - -11)))) and ((not (A butterfly has 6 legs.)) and (((6 * 8 * -8 * 1) > (-14 + 1)) or ((7 * 7 * 6 * -9) != (4 * 20))))) and (not ((not not ((1 ** 1) > (-10 * -1 - -7 * 5))) and (Venus is the 2nd planet from the Sun.)))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
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"seed": 57545484,
"true_count": 2
},
"seed": 57545484,
"task_id": 657545484,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not not ((not ((not (Earth is the 1st planet from the Sun.)) or (not ((Mercury is a liquid at room temperature.) or (There are 28 days in November.))))) and (not (((14 - 14) >= (19 % 2)) and ((not not (A human has 2 legs.)) or (not (The currency of Switzerland is the Yen.))))))
B. not not (((not not (The 1984 Olympics were held in Mexico City.)) or (The chemical symbol for Cobalt is Zn.) or (not not ((((4 ** 1) >= (-4 * -9 - 0 * -8)) and ((-1 * -6 + -9 * -10) == (-19 + 19))) or ((Jupiter is the 5th planet from the Sun.) and ((19 * 19) == (-11 * -2)))))) and (not not ((not (not (A trout is a mammal.))) and ((-19 + 14) == (1 - 18)))))
C. not not ((not (not ((not not (The capital of Italy is Budapest.)) and ((12 * 10) <= (18 - -15))))) or (((not not ((The capital of Saudi Arabia is Berlin.) and ((4 - -18) > (15 + -14)))) or (not not ((-20 * -20) == (1 % 9))) or (not (not (Uranus is the 4th planet from the Sun.)))) and ((A fish has 0 legs.) and (((The chemical symbol for Carbon is U.) or ((29 % 5) != (-6 + 20))) or (Neptune is the 3rd planet from the Sun.)))))
D. not ((not not (((((4 * -8) == (0 * 3 + 5 * 10)) or ((-20 + 5) <= (1 ** 1) <= (6 - 15))) and ((-14 + -4) == (1 * -14))) or ((6 - 12) <= (20 - -20)))) or (((((Neptune is the 8th planet from the Sun.) and (The currency of Malaysia is the Ringgit.)) and (Electricity flows faster than light.)) and ((20 - 8) >= (2 ** 2)) and (not (not (The human body has 150 bones.)))) or (not (((-8 - -10) <= (4 * 4 + -2 * -5)) and (not not (A cod is a fish.))))))
E. not (not not (not not (not not (A kangaroo is a mammal.))))
F. not not ((not not (not (The 1976 Olympics were held in Munich.))) or ((((8 * 2 + 5 * 8) >= (-12 * -17)) or ((not (A whale is a mammal.)) and (not ((-17 + 6) < (5 - -8))))) and ((not (The 1952 Olympics were held in Munich.)) and ((((2 ** 3) < (8 * 7 * -8 * -3)) or ((12 % 9) != (-18 * 0))) and (((-5 * 8 + -4 * 9) <= (20 - -3)) or ((1 ** 2) < (16 * -18)))))))
G. not ((not not ((((Jupiter is the 5th planet from the Sun.) and (The capital of Sweden is Mexico City.)) and ((438 is a Fibonacci number.) and (World War I began occurred in 1914.))) or (There are 31 days in August.) or (Plants produce oxygen through photosynthesis.))) and (not (((((20 * 3) >= (1 - 9)) and (2055 is a leap year.)) or (Sharks are mammals.)) and ((((-11 * 5) != (-9 + -10)) or (The capital of India is Budapest.)) or (not not (Silver is a solid at room temperature.))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 48381074,
"true_count": 1
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"question": "Given the following boolean expressions:\n\nA. not not ((not ((not (Earth is the 1st planet from the Sun.)) or (not ((Mercury is a liquid at room temperature.) or (There are 28 days in November.))))) and (not (((14 - 14) >= (19 % 2)) and ((not not (A human has 2 legs.)) or (not (The currency of Switzerland is the Yen.))))))\nB. not not (((not not (The 1984 Olympics were held in Mexico City.)) or (The chemical symbol for Cobalt is Zn.) or (not not ((((4 ** 1) >= (-4 * -9 - 0 * -8)) and ((-1 * -6 + -9 * -10) == (-19 + 19))) or ((Jupiter is the 5th planet from the Sun.) and ((19 * 19) == (-11 * -2)))))) and (not not ((not (not (A trout is a mammal.))) and ((-19 + 14) == (1 - 18)))))\nC. not not ((not (not ((not not (The capital of Italy is Budapest.)) and ((12 * 10) <= (18 - -15))))) or (((not not ((The capital of Saudi Arabia is Berlin.) and ((4 - -18) > (15 + -14)))) or (not not ((-20 * -20) == (1 % 9))) or (not (not (Uranus is the 4th planet from the Sun.)))) and ((A fish has 0 legs.) and (((The chemical symbol for Carbon is U.) or ((29 % 5) != (-6 + 20))) or (Neptune is the 3rd planet from the Sun.)))))\nD. not ((not not (((((4 * -8) == (0 * 3 + 5 * 10)) or ((-20 + 5) <= (1 ** 1) <= (6 - 15))) and ((-14 + -4) == (1 * -14))) or ((6 - 12) <= (20 - -20)))) or (((((Neptune is the 8th planet from the Sun.) and (The currency of Malaysia is the Ringgit.)) and (Electricity flows faster than light.)) and ((20 - 8) >= (2 ** 2)) and (not (not (The human body has 150 bones.)))) or (not (((-8 - -10) <= (4 * 4 + -2 * -5)) and (not not (A cod is a fish.))))))\nE. not (not not (not not (not not (A kangaroo is a mammal.))))\nF. not not ((not not (not (The 1976 Olympics were held in Munich.))) or ((((8 * 2 + 5 * 8) >= (-12 * -17)) or ((not (A whale is a mammal.)) and (not ((-17 + 6) < (5 - -8))))) and ((not (The 1952 Olympics were held in Munich.)) and ((((2 ** 3) < (8 * 7 * -8 * -3)) or ((12 % 9) != (-18 * 0))) and (((-5 * 8 + -4 * 9) <= (20 - -3)) or ((1 ** 2) < (16 * -18)))))))\nG. not ((not not ((((Jupiter is the 5th planet from the Sun.) and (The capital of Sweden is Mexico City.)) and ((438 is a Fibonacci number.) and (World War I began occurred in 1914.))) or (There are 31 days in August.) or (Plants produce oxygen through photosynthesis.))) and (not (((((20 * 3) >= (1 - 9)) and (2055 is a leap year.)) or (Sharks are mammals.)) and ((((-11 * 5) != (-9 + -10)) or (The capital of India is Budapest.)) or (not not (Silver is a solid at room temperature.))))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
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"language": "en",
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"seed": 48381074,
"true_count": 1
},
"seed": 48381074,
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"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not not (not not ((not ((((-4 + -6) <= (1 % 6)) or ((-7 * -17) < (7 * -2 * 9 * -1))) or (not (The currency of South Korea is the Dong.)))) or ((A lobster has 2 legs.) and (not not (not not (A mosquito is a bird.))))))
B. not not ((not not ((not not ((Spain is in Europe.) and (Jupiter is the 5th planet from the Sun.))) and ((-4 * -8) > (10 * 1 + -7 * -9)))) and (not ((((A herring is a bird.) and (Thailand is in Asia.)) or ((Light travels faster than sound.) or ((9 % 9) > (4 ** 3)))) and (not not ((The currency of Colombia is the Dollar.) and ((-14 - -7) == (43 % 3)))))))
C. (not not (not not (((The capital of Canada is Ottawa.) or ((The chemical symbol for Sulfur is S.) and (A herring is a fish.))) or ((not not ((10 * 0 - 6 * -9) > (6 * 5 - -1 * -9))) and (not (114 is an even number.)))))) and (not not (not not ((((Earth is the 7th planet from the Sun.) and (The currency of Russia is the Sol.)) or (The capital of Italy is Lisbon.)) or (A whale is an insect.))))
D. (not not (not (not not ((((-10 * 0 + -6 * -5) != (23 % 3)) and ((-7 * -6) != (-9 + -15))) and ((Earth is the 3rd planet from the Sun.) and (The currency of Saudi Arabia is the Shekel.)))))) or (not ((not not (There are 31 days in February.)) and (not not (((5 - -20) == (-12 - -5)) or (not ((6 * 4 - -3 * 1) >= (-17 - 15)))))))
E. (not (not not (not ((The capital of Morocco is Rabat.) or ((Saudi Arabia is in Asia.) and (The capital of Venezuela is Warsaw.)))))) or ((not (((-10 * -20) != (2 ** 1)) or (not not ((35 % 7) <= (17 * -8))))) or ((((-7 * 4 * 9 * 0) == (13 - 10)) and ((A koala is a mammal.) and ((5 ** 3) >= (4 ** 2)))) or (246 is a perfect square.))) or (not not (not not (not ((((1 - 0) == (16 * 13)) or (The capital of Netherlands is Amsterdam.)) and (not not (The chemical symbol for Platinum is Pt.))))))
F. not ((not (not (not not (A whale is a fish.)))) or (((not (((14 - -11) != (17 + -9)) and ((-9 + 3) != (2 ** 3)))) and ((-12 - -4) == (12 + 9))) and ((Wood is a solid at room temperature.) or (((-1 * 7 - -7 * -5) <= (-5 - -5) <= (11 + 6)) and (Air is a gas at room temperature.)) or (not ((A goldfish is a fish.) and (Russia is in Antarctica.))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
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"answer": "D,E,F",
"difficulty": 1,
"gpt_response": "",
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"question": "Given the following boolean expressions:\n\nA. not not (not not ((not ((((-4 + -6) <= (1 % 6)) or ((-7 * -17) < (7 * -2 * 9 * -1))) or (not (The currency of South Korea is the Dong.)))) or ((A lobster has 2 legs.) and (not not (not not (A mosquito is a bird.))))))\nB. not not ((not not ((not not ((Spain is in Europe.) and (Jupiter is the 5th planet from the Sun.))) and ((-4 * -8) > (10 * 1 + -7 * -9)))) and (not ((((A herring is a bird.) and (Thailand is in Asia.)) or ((Light travels faster than sound.) or ((9 % 9) > (4 ** 3)))) and (not not ((The currency of Colombia is the Dollar.) and ((-14 - -7) == (43 % 3)))))))\nC. (not not (not not (((The capital of Canada is Ottawa.) or ((The chemical symbol for Sulfur is S.) and (A herring is a fish.))) or ((not not ((10 * 0 - 6 * -9) > (6 * 5 - -1 * -9))) and (not (114 is an even number.)))))) and (not not (not not ((((Earth is the 7th planet from the Sun.) and (The currency of Russia is the Sol.)) or (The capital of Italy is Lisbon.)) or (A whale is an insect.))))\nD. (not not (not (not not ((((-10 * 0 + -6 * -5) != (23 % 3)) and ((-7 * -6) != (-9 + -15))) and ((Earth is the 3rd planet from the Sun.) and (The currency of Saudi Arabia is the Shekel.)))))) or (not ((not not (There are 31 days in February.)) and (not not (((5 - -20) == (-12 - -5)) or (not ((6 * 4 - -3 * 1) >= (-17 - 15)))))))\nE. (not (not not (not ((The capital of Morocco is Rabat.) or ((Saudi Arabia is in Asia.) and (The capital of Venezuela is Warsaw.)))))) or ((not (((-10 * -20) != (2 ** 1)) or (not not ((35 % 7) <= (17 * -8))))) or ((((-7 * 4 * 9 * 0) == (13 - 10)) and ((A koala is a mammal.) and ((5 ** 3) >= (4 ** 2)))) or (246 is a perfect square.))) or (not not (not not (not ((((1 - 0) == (16 * 13)) or (The capital of Netherlands is Amsterdam.)) and (not not (The chemical symbol for Platinum is Pt.))))))\nF. not ((not (not (not not (A whale is a fish.)))) or (((not (((14 - -11) != (17 + -9)) and ((-9 + 3) != (2 ** 3)))) and ((-12 - -4) == (12 + 9))) and ((Wood is a solid at room temperature.) or (((-1 * 7 - -7 * -5) <= (-5 - -5) <= (11 + 6)) and (Air is a gas at room temperature.)) or (not ((A goldfish is a fish.) and (Russia is in Antarctica.))))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
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"seed": 68408443,
"true_count": 3
},
"seed": 68408443,
"task_id": 668408443,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not not ((((((巴西位于南极洲。) and ((2 ** 1) > (12 + -15))) or (36是质数。)) and (not (not not (1918年是闰年。)))) and ((not not (第二次世界大战开始发生在1934年。)) or ((中国位于欧洲。) or (泰坦尼克号沉没发生在1912年。))) and (((1964年奥运会在雅典举办。) and ((-2 * -5 - -1 * -7) >= (-1 * 0 - 3 * -10))) and ((-14 + -1) < (-3 * 6 * 1 * 4)))) and (((芬兰的首都是华沙。) or ((((-4 - 12) >= (-13 - -13)) and ((37 % 10) != (-16 + 9))) and ((1920年奥运会在北京举办。) or ((14 + 6) != (5 * -19))))) and ((not (((2 ** 2) >= (4 - -12)) and ((-12 * -20) == (2 ** 1)))) or (空气在常温下是气体。))))
B. not not (not not ((((not (冰在常温下是固体。)) or (二氧化碳在常温下是液体。)) and (not not (铜在常温下是固体。))) and (not not (印度的货币是卢比。))))
C. (not (((not not ((新加坡的首都是都柏林。) or ((-15 - 18) == (1 % 7)))) and ((not not ((-9 - 9) <= (-19 * 13))) or ((1 ** 3) < (15 * 11)))) or ((人类首次登月发生在1979年。) or (not not (智利的首都是莫斯科。))) or ((五月有31天。) or (not (not not ((26 % 6) < (0 * 5 + 4 * -10))))))) and (not (((((1992年奥运会在巴塞罗那举办。) and ((-8 - -15) <= (5 ** 3))) or (声音无法在真空中传播。)) or ((-20 - -1) >= (1 + -4))) and ((93是奇数。) or ((not not (冰在常温下是固体。)) and ((35是质数。) and (39是质数。))))))
D. not (((not not ((-5 * -7 * -7 * -5) <= (42 % 3))) or (((8 * 12) > (-18 * 3)) and ((100是奇数。) and ((木头在常温下是固体。) and (欧盟的货币是比索。))))) and (((十二月有28天。) or ((16 - 0) == (-14 * 1))) and ((1980年奥运会在里约热内卢举办。) or ((not (121的平方根是8。)) and ((32 % 4) < (12 - 6) < (8 * 3 * -7 * 8))))))
E. not ((not (((33 % 10) > (3 * 4 * -7 * 8)) or (not not (巴西位于北美洲。)) or ((((15 % 4) < (10 * -10 * -6 * 4)) and (罗马尼亚的首都是布拉格。)) and ((龙虾有10条腿。) or ((50 % 1) > (11 - 4)))))) or (not not (((((19 - -8) >= (0 + -4)) or ((19 * 11) <= (1 ** 3))) and ((火星是距离太阳第6近的行星。) and ((-4 * -1) <= (-10 * 5 + 3 * 10)))) or ((-4 - 4) == (6 * 4)))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
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"question": "下面是几个布尔表达式：\n\nA. not not ((((((巴西位于南极洲。) and ((2 ** 1) > (12 + -15))) or (36是质数。)) and (not (not not (1918年是闰年。)))) and ((not not (第二次世界大战开始发生在1934年。)) or ((中国位于欧洲。) or (泰坦尼克号沉没发生在1912年。))) and (((1964年奥运会在雅典举办。) and ((-2 * -5 - -1 * -7) >= (-1 * 0 - 3 * -10))) and ((-14 + -1) < (-3 * 6 * 1 * 4)))) and (((芬兰的首都是华沙。) or ((((-4 - 12) >= (-13 - -13)) and ((37 % 10) != (-16 + 9))) and ((1920年奥运会在北京举办。) or ((14 + 6) != (5 * -19))))) and ((not (((2 ** 2) >= (4 - -12)) and ((-12 * -20) == (2 ** 1)))) or (空气在常温下是气体。))))\nB. not not (not not ((((not (冰在常温下是固体。)) or (二氧化碳在常温下是液体。)) and (not not (铜在常温下是固体。))) and (not not (印度的货币是卢比。))))\nC. (not (((not not ((新加坡的首都是都柏林。) or ((-15 - 18) == (1 % 7)))) and ((not not ((-9 - 9) <= (-19 * 13))) or ((1 ** 3) < (15 * 11)))) or ((人类首次登月发生在1979年。) or (not not (智利的首都是莫斯科。))) or ((五月有31天。) or (not (not not ((26 % 6) < (0 * 5 + 4 * -10))))))) and (not (((((1992年奥运会在巴塞罗那举办。) and ((-8 - -15) <= (5 ** 3))) or (声音无法在真空中传播。)) or ((-20 - -1) >= (1 + -4))) and ((93是奇数。) or ((not not (冰在常温下是固体。)) and ((35是质数。) and (39是质数。))))))\nD. not (((not not ((-5 * -7 * -7 * -5) <= (42 % 3))) or (((8 * 12) > (-18 * 3)) and ((100是奇数。) and ((木头在常温下是固体。) and (欧盟的货币是比索。))))) and (((十二月有28天。) or ((16 - 0) == (-14 * 1))) and ((1980年奥运会在里约热内卢举办。) or ((not (121的平方根是8。)) and ((32 % 4) < (12 - 6) < (8 * 3 * -7 * 8))))))\nE. not ((not (((33 % 10) > (3 * 4 * -7 * 8)) or (not not (巴西位于北美洲。)) or ((((15 % 4) < (10 * -10 * -6 * 4)) and (罗马尼亚的首都是布拉格。)) and ((龙虾有10条腿。) or ((50 % 1) > (11 - 4)))))) or (not not (((((19 - -8) >= (0 + -4)) or ((19 * 11) <= (1 ** 3))) and ((火星是距离太阳第6近的行星。) and ((-4 * -1) <= (-10 * 5 + 3 * 10)))) or ((-4 - 4) == (6 * 4)))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
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logic-v2 | 给定以下布尔表达式：
A. (((1981年是闰年。) or (not not (锰的化学符号是U。)) or ((硅的化学符号是Si。) and (((21 % 7) == (-9 * -3 - -5 * 8)) and ((4 * -20) < (-17 * -1))))) or ((not (肯尼亚的首都是内罗毕。)) and (南极洲是最冷的大陆。) and ((-3 + -16) <= (-4 - 13) <= (2 * 6 * 0 * -4)))) and ((not ((((2 + -1) < (4 ** 1)) or ((-16 - 10) != (2 * -6 + -10 * 8))) and (279是斐波那契数。))) or ((((3 * 17) == (14 % 6)) or ((1 * 2 + -8 * -4) != (4 ** 2))) or ((not not (俄罗斯的货币是卢布。)) and (((13 + 2) <= (17 - 19)) or ((1 * -2 * 4 * -2) <= (6 * -11))))))
B. ((not (not ((42 % 4) < (4 ** 2)))) or (((汞在常温下是液体。) or ((3 ** 2) <= (-9 * -2) <= (-19 - -12))) or (((12 + 14) <= (-9 * 8 + -1 * 7)) or (蝴蝶有100条腿。)) or ((海王星是距离太阳第5近的行星。) and ((土星是距离太阳第8近的行星。) and ((20 - -16) < (7 - -4)))))) or ((((2 + -10) != (10 + 13)) or (((德国位于非洲。) or (南非位于南极洲。)) and (土星是距离太阳第7近的行星。))) and ((1912年奥运会在巴黎举办。) and ((not not (地球绕太阳运转。)) and (not (鲱鱼是爬行动物。)))))
C. (not not ((((澳大利亚的首都是维也纳。) or (1908年奥运会在伦敦举办。)) and ((地球是距离太阳第3近的行星。) or (水星是距离太阳第3近的行星。))) and ((哥伦布到达美洲发生在1490年。) or (四月有30天。)) and (((2 * -4 - 4 * -9) >= (7 * 4)) and (((5 ** 2) > (-5 * 0)) or (水在常温下是液体。))))) or (not not (((1 + 10) > (19 - 18)) and ((铅的化学符号是He。) and (柏林墙倒塌发生在1999年。)) and ((((-11 - 2) != (-4 + 18)) or ((44 % 1) < (18 + 7))) or ((第一次世界大战结束发生在1918年。) or (地球是距离太阳第3近的行星。)))))
D. ((not not (1961年是闰年。)) and (巴西的首都是圣地亚哥。) and (((((-17 + 7) < (-20 - 15)) or (奥地利的首都是维也纳。)) or ((3 * 10 * -10 * 10) >= (10 % 10))) and (not not (not not (火星是距离太阳第1近的行星。))))) and (((菲律宾的首都是利马。) and ((8 * -8 * -3 * 4) == (-1 * -17))) or ((铁的化学符号是Fe。) and (not (not not (水在常温下是液体。)))))
E. (not not (((6 * -10 - 6 * 0) == (-13 - -20)) or (((地球是距离太阳第8近的行星。) or ((-5 * 0 + 4 * -9) != (1 * 2 - 4 * -10))) and (((-1 * -9 + -5 * -4) > (13 * -8)) and (乌龟是鸟类。))))) and (((not not ((1 * 5 + -5 * 9) < (-9 + -17))) or (not (澳大利亚位于北美洲。))) and ((-12 * 0) > (8 - 16))) and (not not ((比利时的首都是布鲁塞尔。) or (not (爱尔兰的首都是都柏林。)) or (((8 - 9) >= (-4 * -17)) and ((钾的化学符号是Pb。) and ((50 % 2) <= (7 % 3) <= (9 % 8))))))
F. not (((澳大利亚的货币是澳元。) and (not (((-3 * 4 - -6 * -6) <= (11 - 16)) and (蜘蛛有8条腿。)))) and (((not ((-8 * 15) <= (-19 - 4) <= (1 % 5))) and (not not (哥伦比亚位于非洲。))) or ((not not (2084年是闰年。)) and ((现代奥运会首届举办发生在1886年。) and (三月有31天。)))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"question": "给定以下布尔表达式：\n\nA. (((1981年是闰年。) or (not not (锰的化学符号是U。)) or ((硅的化学符号是Si。) and (((21 % 7) == (-9 * -3 - -5 * 8)) and ((4 * -20) < (-17 * -1))))) or ((not (肯尼亚的首都是内罗毕。)) and (南极洲是最冷的大陆。) and ((-3 + -16) <= (-4 - 13) <= (2 * 6 * 0 * -4)))) and ((not ((((2 + -1) < (4 ** 1)) or ((-16 - 10) != (2 * -6 + -10 * 8))) and (279是斐波那契数。))) or ((((3 * 17) == (14 % 6)) or ((1 * 2 + -8 * -4) != (4 ** 2))) or ((not not (俄罗斯的货币是卢布。)) and (((13 + 2) <= (17 - 19)) or ((1 * -2 * 4 * -2) <= (6 * -11))))))\nB. ((not (not ((42 % 4) < (4 ** 2)))) or (((汞在常温下是液体。) or ((3 ** 2) <= (-9 * -2) <= (-19 - -12))) or (((12 + 14) <= (-9 * 8 + -1 * 7)) or (蝴蝶有100条腿。)) or ((海王星是距离太阳第5近的行星。) and ((土星是距离太阳第8近的行星。) and ((20 - -16) < (7 - -4)))))) or ((((2 + -10) != (10 + 13)) or (((德国位于非洲。) or (南非位于南极洲。)) and (土星是距离太阳第7近的行星。))) and ((1912年奥运会在巴黎举办。) and ((not not (地球绕太阳运转。)) and (not (鲱鱼是爬行动物。)))))\nC. (not not ((((澳大利亚的首都是维也纳。) or (1908年奥运会在伦敦举办。)) and ((地球是距离太阳第3近的行星。) or (水星是距离太阳第3近的行星。))) and ((哥伦布到达美洲发生在1490年。) or (四月有30天。)) and (((2 * -4 - 4 * -9) >= (7 * 4)) and (((5 ** 2) > (-5 * 0)) or (水在常温下是液体。))))) or (not not (((1 + 10) > (19 - 18)) and ((铅的化学符号是He。) and (柏林墙倒塌发生在1999年。)) and ((((-11 - 2) != (-4 + 18)) or ((44 % 1) < (18 + 7))) or ((第一次世界大战结束发生在1918年。) or (地球是距离太阳第3近的行星。)))))\nD. ((not not (1961年是闰年。)) and (巴西的首都是圣地亚哥。) and (((((-17 + 7) < (-20 - 15)) or (奥地利的首都是维也纳。)) or ((3 * 10 * -10 * 10) >= (10 % 10))) and (not not (not not (火星是距离太阳第1近的行星。))))) and (((菲律宾的首都是利马。) and ((8 * -8 * -3 * 4) == (-1 * -17))) or ((铁的化学符号是Fe。) and (not (not not (水在常温下是液体。)))))\nE. (not not (((6 * -10 - 6 * 0) == (-13 - -20)) or (((地球是距离太阳第8近的行星。) or ((-5 * 0 + 4 * -9) != (1 * 2 - 4 * -10))) and (((-1 * -9 + -5 * -4) > (13 * -8)) and (乌龟是鸟类。))))) and (((not not ((1 * 5 + -5 * 9) < (-9 + -17))) or (not (澳大利亚位于北美洲。))) and ((-12 * 0) > (8 - 16))) and (not not ((比利时的首都是布鲁塞尔。) or (not (爱尔兰的首都是都柏林。)) or (((8 - 9) >= (-4 * -17)) and ((钾的化学符号是Pb。) and ((50 % 2) <= (7 % 3) <= (9 % 8))))))\nF. not (((澳大利亚的货币是澳元。) and (not (((-3 * 4 - -6 * -6) <= (11 - 16)) and (蜘蛛有8条腿。)))) and (((not ((-8 * 15) <= (-19 - 4) <= (1 % 5))) and (not not (哥伦比亚位于非洲。))) or ((not not (2084年是闰年。)) and ((现代奥运会首届举办发生在1886年。) and (三月有31天。)))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
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logic-v2 | Given the following boolean expressions:
A. ((((197 is an even number.) and ((-3 * 7 * 9 * 3) <= (9 * -8 - 2 * 4) <= (7 % 1))) and (((The chemical symbol for Silver is Ag.) or (not not (The chemical symbol for Potassium is K.))) or (((17 * -9) < (-20 + -13)) and (((-6 + -19) == (-2 - 8)) or ((4 + 10) == (-12 * -15)))))) or (not (((-19 + -1) <= (4 * 7 + -5 * 2)) and (Chile is in South America.)))) and (not not ((not not (not not (((-1 * 0 * -10 * 10) >= (5 * -9 + 4 * 4)) and ((-10 * 2) < (10 * -8))))) and (not not ((3 ** 3) > (-8 - 14)))))
B. not (not not (not (not ((((11 + 6) <= (9 * 9 + -3 * 2)) or (The capital of Singapore is Singapore.)) or ((Saturn is the 6th planet from the Sun.) or (United States is in Antarctica.))))))
C. not not (not (((Indonesia is in Africa.) and ((The currency of United Kingdom is the Krona.) and (Alcohol is a liquid at room temperature.)) and (((-20 * 8) != (17 % 6)) and (not ((20 + 8) > (-6 * -1 + 4 * 10))))) and ((((Saudi Arabia is in Europe.) and (The chemical symbol for Silicon is Cu.)) and ((-7 * 3 - -9 * -9) < (5 ** 3))) or ((((-2 * 3 * 4 * -10) <= (19 + -13) <= (5 * -6 * 7 * -3)) and (618 is a Fibonacci number.)) or (not (Spain is in Europe.))))))
D. not (((not (not ((-20 * 14) <= (8 - 5)))) or ((((3 - 11) != (7 - -11)) and (((14 + -15) != (4 ** 3)) or ((9 + 0) > (17 + -8)))) and ((2 ** 1) <= (14 - -5) <= (18 + 8)))) or (not not (not ((not not ((12 + 11) >= (16 + 18))) or ((The chemical symbol for Sulfur is S.) or (A owl is a reptile.))))))
E. not not (not not (not not (not not ((14 + 20) > (-3 * -9 * -10 * 7)))))
F. not ((not ((((-10 * -11) <= (2 - 1)) and ((The square root of 25 is 5.) and (Germany is in Europe.))) or (not (((-5 - 20) == (2 ** 1)) and ((5 ** 1) >= (-15 + -13)))))) or (not (((5 ** 1) <= (-19 + 4) <= (2 ** 1)) and (((3 * 9 * 1 * 6) <= (0 - 14) <= (-10 - -7)) or (The Great Wall of China was built in one year.)))) or ((not not (not not ((1 ** 1) >= (17 - -15)))) or ((Mercury is the 2nd planet from the Sun.) or ((-7 + 0) != (12 * 19)))))
G. not (not (not (not (Russia is in Europe.))))
H. not not (not not (((not (The currency of China is the Yuan.)) and (Saturn is the 6th planet from the Sun.)) or ((((-12 - 16) <= (-10 * 6 - 3 * -8)) and ((1908 is a leap year.) or ((10 + -17) == (39 % 8)))) and ((((2 ** 1) <= (10 * -17) <= (7 * 2 * -3 * -5)) or (1919 is a leap year.)) or (((2 ** 2) != (5 - -5)) or (The Pacific Ocean is the largest ocean.))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
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"question": "Given the following boolean expressions:\n\nA. ((((197 is an even number.) and ((-3 * 7 * 9 * 3) <= (9 * -8 - 2 * 4) <= (7 % 1))) and (((The chemical symbol for Silver is Ag.) or (not not (The chemical symbol for Potassium is K.))) or (((17 * -9) < (-20 + -13)) and (((-6 + -19) == (-2 - 8)) or ((4 + 10) == (-12 * -15)))))) or (not (((-19 + -1) <= (4 * 7 + -5 * 2)) and (Chile is in South America.)))) and (not not ((not not (not not (((-1 * 0 * -10 * 10) >= (5 * -9 + 4 * 4)) and ((-10 * 2) < (10 * -8))))) and (not not ((3 ** 3) > (-8 - 14)))))\nB. not (not not (not (not ((((11 + 6) <= (9 * 9 + -3 * 2)) or (The capital of Singapore is Singapore.)) or ((Saturn is the 6th planet from the Sun.) or (United States is in Antarctica.))))))\nC. not not (not (((Indonesia is in Africa.) and ((The currency of United Kingdom is the Krona.) and (Alcohol is a liquid at room temperature.)) and (((-20 * 8) != (17 % 6)) and (not ((20 + 8) > (-6 * -1 + 4 * 10))))) and ((((Saudi Arabia is in Europe.) and (The chemical symbol for Silicon is Cu.)) and ((-7 * 3 - -9 * -9) < (5 ** 3))) or ((((-2 * 3 * 4 * -10) <= (19 + -13) <= (5 * -6 * 7 * -3)) and (618 is a Fibonacci number.)) or (not (Spain is in Europe.))))))\nD. not (((not (not ((-20 * 14) <= (8 - 5)))) or ((((3 - 11) != (7 - -11)) and (((14 + -15) != (4 ** 3)) or ((9 + 0) > (17 + -8)))) and ((2 ** 1) <= (14 - -5) <= (18 + 8)))) or (not not (not ((not not ((12 + 11) >= (16 + 18))) or ((The chemical symbol for Sulfur is S.) or (A owl is a reptile.))))))\nE. not not (not not (not not (not not ((14 + 20) > (-3 * -9 * -10 * 7)))))\nF. not ((not ((((-10 * -11) <= (2 - 1)) and ((The square root of 25 is 5.) and (Germany is in Europe.))) or (not (((-5 - 20) == (2 ** 1)) and ((5 ** 1) >= (-15 + -13)))))) or (not (((5 ** 1) <= (-19 + 4) <= (2 ** 1)) and (((3 * 9 * 1 * 6) <= (0 - 14) <= (-10 - -7)) or (The Great Wall of China was built in one year.)))) or ((not not (not not ((1 ** 1) >= (17 - -15)))) or ((Mercury is the 2nd planet from the Sun.) or ((-7 + 0) != (12 * 19)))))\nG. not (not (not (not (Russia is in Europe.))))\nH. not not (not not (((not (The currency of China is the Yuan.)) and (Saturn is the 6th planet from the Sun.)) or ((((-12 - 16) <= (-10 * 6 - 3 * -8)) and ((1908 is a leap year.) or ((10 + -17) == (39 % 8)))) and ((((2 ** 1) <= (10 * -17) <= (7 * 2 * -3 * -5)) or (1919 is a leap year.)) or (((2 ** 2) != (5 - -5)) or (The Pacific Ocean is the largest ocean.))))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
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logic-v2 | 给定以下布尔表达式：
A. not not (not not (((蜻蜓是哺乳动物。) and (not not ((23 % 7) >= (-1 * 11))) and (((2012年奥运会在伦敦举办。) or ((2 ** 3) <= (-1 + 19))) and (not not ((16 - 6) < (-14 * -10) < (13 + 13))))) and (not (not ((氧气在常温下是气体。) and ((15 - -15) < (-19 * -16) < (-3 * 2)))))))
B. not (not not (((((章鱼有2条腿。) or (1928年奥运会在阿姆斯特丹举办。)) or (not not (德国位于南极洲。))) and ((((3 ** 1) <= (-4 * -6 + -5 * 5)) or (企鹅能飞翔。)) and ((鲨鱼是哺乳动物。) and (1896年奥运会在墨尔本举办。)))) and (not (氯的化学符号是Sn。))))
C. not not ((((俄罗斯的货币是谢克尔。) and ((((-16 - -3) > (0 - -19)) and ((21 % 1) != (1 + 13))) and (((16 - -15) != (3 - 2)) and (泰国位于亚洲。)))) or ((1 * -3) == (37 % 5)) or (not ((((-2 * 8 * 7 * 0) == (-9 * -9)) and ((-20 * -1) <= (-11 - -14) <= (4 * 8 * -10 * -7))) and (not ((1 * -4) != (4 ** 2)))))) and (not ((1988年奥运会在首尔举办。) or (not ((-20 - -6) != (-3 - 12))) or ((not not ((9 * 11) <= (4 - -4))) or (印度尼西亚的首都是莫斯科。)))))
D. not not (not not ((((((5 ** 2) < (7 * 8)) and (木星是距离太阳第5近的行星。)) and (not ((11 * 18) < (5 * 6)))) or ((1 ** 2) <= (-3 + 14) <= (-5 - 3))) or (not not ((爱尔兰的首都是内罗毕。) or (not not ((-6 - 9) <= (-1 - 1)))))))
E. (not (((((-2 - 15) != (12 - 18)) and (人类有三个肺。)) or ((氧气对人类生存是必需的。) or ((-7 * 1 - 8 * 1) == (-17 + 6))) or ((1936年奥运会在柏林举办。) and (氮气在常温下是气体。))) and (not (not not ((626是斐波那契数。) and (海王星是距离太阳第8近的行星。)))))) or (not ((not not ((((2 + -17) != (14 + 0)) or (169的平方根是13。)) or (沙特阿拉伯的首都是阿布贾。))) or (not (((葡萄牙的首都是布加勒斯特。) and (金星是距离太阳第6近的行星。)) and ((苏联解体发生在1981年。) or ((-7 * 7 - 9 * 2) > (-2 + -10)))))))
F. (not not (((阿根廷位于亚洲。) or ((((-8 * -20) >= (-2 - -13)) and (空气在常温下是固体。)) or (not not (阿根廷的首都是马德里。)))) or (((14 + 10) == (13 + -3)) and (美国宣布独立发生在1776年。)) or ((not ((猪有4条腿。) and (加拿大位于大洋洲。))) and ((1908年奥运会在慕尼黑举办。) or (马来西亚的首都是吉隆坡。))))) or (not not (not (((not ((8 * -17) < (5 ** 1))) or (声音无法在真空中传播。)) and (not (((-20 - -16) != (-3 * 7 * 9 * 3)) and (蜘蛛是昆虫。))))))
G. not (((((墨西哥的货币是比索。) or (油在常温下是液体。)) or (第二次世界大战结束发生在1946年。)) or (not not (((-20 - -3) > (19 - 9)) or (1975年是闰年。))) or ((((-1 * -3 - 4 * 8) < (2 - -2)) and (((1 ** 3) != (-13 * -11)) or ((-3 + -6) > (10 + -19)))) or (短吻鳄是爬行动物。) or (电流比光速更快。))) and (((((铝的化学符号是U。) or (电流比光速更快。)) or (not not (2008年奥运会在巴塞罗那举办。))) and (not ((光速比声速快。) or ((4 * 18) != (-5 * -9 * -1 * -7))))) or (not (钻石由碳元素组成。))))
H. not not (((not not (not (((2 ** 1) < (5 * 2 + 2 * -9) < (-9 * 5)) or ((2 ** 3) != (-14 + 6))))) and (((-2 * 9 * 6 * -9) <= (1 ** 2) <= (10 * 9 - -9 * -4)) or (铅的化学符号是Cu。))) or (((17 % 9) <= (39 % 4)) and ((-20 + 7) != (-2 * -7))) or ((((1914年是闰年。) and (1908年奥运会在伦敦举办。)) and ((not ((-4 * -3 + -9 * -10) == (6 % 10))) and (not not ((11 % 5) != (-20 * 17))))) or (((9 * -4 * -8 * 4) == (15 - 11)) or (not not ((-4 * 5 + -3 * 3) >= (5 ** 1))) or (not (((6 + -18) >= (-16 + -2)) or (木星是距离太阳第4近的行星。))))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"question": "给定以下布尔表达式：\n\nA. not not (not not (((蜻蜓是哺乳动物。) and (not not ((23 % 7) >= (-1 * 11))) and (((2012年奥运会在伦敦举办。) or ((2 ** 3) <= (-1 + 19))) and (not not ((16 - 6) < (-14 * -10) < (13 + 13))))) and (not (not ((氧气在常温下是气体。) and ((15 - -15) < (-19 * -16) < (-3 * 2)))))))\nB. not (not not (((((章鱼有2条腿。) or (1928年奥运会在阿姆斯特丹举办。)) or (not not (德国位于南极洲。))) and ((((3 ** 1) <= (-4 * -6 + -5 * 5)) or (企鹅能飞翔。)) and ((鲨鱼是哺乳动物。) and (1896年奥运会在墨尔本举办。)))) and (not (氯的化学符号是Sn。))))\nC. not not ((((俄罗斯的货币是谢克尔。) and ((((-16 - -3) > (0 - -19)) and ((21 % 1) != (1 + 13))) and (((16 - -15) != (3 - 2)) and (泰国位于亚洲。)))) or ((1 * -3) == (37 % 5)) or (not ((((-2 * 8 * 7 * 0) == (-9 * -9)) and ((-20 * -1) <= (-11 - -14) <= (4 * 8 * -10 * -7))) and (not ((1 * -4) != (4 ** 2)))))) and (not ((1988年奥运会在首尔举办。) or (not ((-20 - -6) != (-3 - 12))) or ((not not ((9 * 11) <= (4 - -4))) or (印度尼西亚的首都是莫斯科。)))))\nD. not not (not not ((((((5 ** 2) < (7 * 8)) and (木星是距离太阳第5近的行星。)) and (not ((11 * 18) < (5 * 6)))) or ((1 ** 2) <= (-3 + 14) <= (-5 - 3))) or (not not ((爱尔兰的首都是内罗毕。) or (not not ((-6 - 9) <= (-1 - 1)))))))\nE. (not (((((-2 - 15) != (12 - 18)) and (人类有三个肺。)) or ((氧气对人类生存是必需的。) or ((-7 * 1 - 8 * 1) == (-17 + 6))) or ((1936年奥运会在柏林举办。) and (氮气在常温下是气体。))) and (not (not not ((626是斐波那契数。) and (海王星是距离太阳第8近的行星。)))))) or (not ((not not ((((2 + -17) != (14 + 0)) or (169的平方根是13。)) or (沙特阿拉伯的首都是阿布贾。))) or (not (((葡萄牙的首都是布加勒斯特。) and (金星是距离太阳第6近的行星。)) and ((苏联解体发生在1981年。) or ((-7 * 7 - 9 * 2) > (-2 + -10)))))))\nF. (not not (((阿根廷位于亚洲。) or ((((-8 * -20) >= (-2 - -13)) and (空气在常温下是固体。)) or (not not (阿根廷的首都是马德里。)))) or (((14 + 10) == (13 + -3)) and (美国宣布独立发生在1776年。)) or ((not ((猪有4条腿。) and (加拿大位于大洋洲。))) and ((1908年奥运会在慕尼黑举办。) or (马来西亚的首都是吉隆坡。))))) or (not not (not (((not ((8 * -17) < (5 ** 1))) or (声音无法在真空中传播。)) and (not (((-20 - -16) != (-3 * 7 * 9 * 3)) and (蜘蛛是昆虫。))))))\nG. not (((((墨西哥的货币是比索。) or (油在常温下是液体。)) or (第二次世界大战结束发生在1946年。)) or (not not (((-20 - -3) > (19 - 9)) or (1975年是闰年。))) or ((((-1 * -3 - 4 * 8) < (2 - -2)) and (((1 ** 3) != (-13 * -11)) or ((-3 + -6) > (10 + -19)))) or (短吻鳄是爬行动物。) or (电流比光速更快。))) and (((((铝的化学符号是U。) or (电流比光速更快。)) or (not not (2008年奥运会在巴塞罗那举办。))) and (not ((光速比声速快。) or ((4 * 18) != (-5 * -9 * -1 * -7))))) or (not (钻石由碳元素组成。))))\nH. not not (((not not (not (((2 ** 1) < (5 * 2 + 2 * -9) < (-9 * 5)) or ((2 ** 3) != (-14 + 6))))) and (((-2 * 9 * 6 * -9) <= (1 ** 2) <= (10 * 9 - -9 * -4)) or (铅的化学符号是Cu。))) or (((17 % 9) <= (39 % 4)) and ((-20 + 7) != (-2 * -7))) or ((((1914年是闰年。) and (1908年奥运会在伦敦举办。)) and ((not ((-4 * -3 + -9 * -10) == (6 % 10))) and (not not ((11 % 5) != (-20 * 17))))) or (((9 * -4 * -8 * 4) == (15 - 11)) or (not not ((-4 * 5 + -3 * 3) >= (5 ** 1))) or (not (((6 + -18) >= (-16 + -2)) or (木星是距离太阳第4近的行星。))))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
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logic-v2 | Consider the following logical expressions:
A. not not ((not not (not (The 1952 Olympics were held in Helsinki.))) and (((Iron is a solid at room temperature.) and ((((11 * 11) < (0 + 19)) or (The currency of Egypt is the Krone.)) and ((8 - 18) < (35 % 4)))) and (((The currency of South Korea is the Won.) and ((12 + 17) < (19 - -3) < (-1 * -8 * -5 * -1))) or (The currency of Saudi Arabia is the Riyal.)) and (not (not ((The 1980 Olympics were held in Moscow.) or (A octopus has 8 legs.))))))
B. ((not (not not (not not (((9 - 20) != (0 + -10)) or ((7 * 8 * -4 * 1) > (4 ** 2)))))) or (not (not (not not ((1967 is a leap year.) or (The chemical symbol for Sulfur is S.)))))) or (not (not not (not not ((((-7 * -8 + 10 * 9) > (7 * 6 + -2 * -8)) and (Jupiter is the 8th planet from the Sun.)) and (((2 ** 3) <= (49 % 6) <= (-14 - 9)) and ((-11 * -13) > (2 ** 3)))))))
C. not not (not ((not not (not (((10 - -7) > (2 ** 2)) and (The chemical symbol for Calcium is Co.)))) or ((not not (not not ((-4 * -17) <= (-7 + -5)))) or ((-3 - 10) <= (-6 + -20)))))
D. not not (not not (((The Pacific Ocean is the largest ocean.) or (not (not ((-18 * -20) != (-10 + -8))))) or ((A butterfly has 6 legs.) and ((-20 * 9) < (-7 + 4)))))
E. not ((not not ((not not (((4 % 10) <= (-4 * 9 * 0 * 10)) or ((15 + -7) >= (41 % 6)))) and (The first airplane flight by the Wright Brothers occurred in 1903.))) and (not not (((257 is a Fibonacci number.) or ((-18 + -10) == (28 % 6))) or ((2 ** 2) >= (4 ** 3)))))
F. not not (not not (not ((((The chemical symbol for Chlorine is Cl.) or (The 1952 Olympics were held in Helsinki.)) and (not ((-10 - 7) != (-4 * 3 + -9 * 4)))) or (The 1908 Olympics were held in London.))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
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"difficulty": 1,
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"question": "Consider the following logical expressions:\n\nA. not not ((not not (not (The 1952 Olympics were held in Helsinki.))) and (((Iron is a solid at room temperature.) and ((((11 * 11) < (0 + 19)) or (The currency of Egypt is the Krone.)) and ((8 - 18) < (35 % 4)))) and (((The currency of South Korea is the Won.) and ((12 + 17) < (19 - -3) < (-1 * -8 * -5 * -1))) or (The currency of Saudi Arabia is the Riyal.)) and (not (not ((The 1980 Olympics were held in Moscow.) or (A octopus has 8 legs.))))))\nB. ((not (not not (not not (((9 - 20) != (0 + -10)) or ((7 * 8 * -4 * 1) > (4 ** 2)))))) or (not (not (not not ((1967 is a leap year.) or (The chemical symbol for Sulfur is S.)))))) or (not (not not (not not ((((-7 * -8 + 10 * 9) > (7 * 6 + -2 * -8)) and (Jupiter is the 8th planet from the Sun.)) and (((2 ** 3) <= (49 % 6) <= (-14 - 9)) and ((-11 * -13) > (2 ** 3)))))))\nC. not not (not ((not not (not (((10 - -7) > (2 ** 2)) and (The chemical symbol for Calcium is Co.)))) or ((not not (not not ((-4 * -17) <= (-7 + -5)))) or ((-3 - 10) <= (-6 + -20)))))\nD. not not (not not (((The Pacific Ocean is the largest ocean.) or (not (not ((-18 * -20) != (-10 + -8))))) or ((A butterfly has 6 legs.) and ((-20 * 9) < (-7 + 4)))))\nE. not ((not not ((not not (((4 % 10) <= (-4 * 9 * 0 * 10)) or ((15 + -7) >= (41 % 6)))) and (The first airplane flight by the Wright Brothers occurred in 1903.))) and (not not (((257 is a Fibonacci number.) or ((-18 + -10) == (28 % 6))) or ((2 ** 2) >= (4 ** 3)))))\nF. not not (not not (not ((((The chemical symbol for Chlorine is Cl.) or (The 1952 Olympics were held in Helsinki.)) and (not ((-10 - 7) != (-4 * 3 + -9 * 4)))) or (The 1908 Olympics were held in London.))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
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"language": "en",
"num_options": 6,
"seed": 66547591,
"true_count": 3
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"seed": 66547591,
"task_id": 666547591,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. ((((铅的化学符号是Pb。) and (42大于77。)) and ((13 + -11) < (-20 * -4) < (-6 + 3))) and (((1 * -7) == (19 + -16)) and (欧盟的货币是欧元。)) and ((-3 + 14) != (5 ** 2))) and (not ((越南位于非洲。) or ((45 % 2) < (24 % 9)))) and (not not (not (not not (地球是距离太阳第3近的行星。))))
B. not not (not not ((美国位于北美洲。) and (((-18 * 17) <= (4 - -18)) and (沙特阿拉伯位于亚洲。))))
C. (((埃及的货币是新加坡元。) or (汞在常温下是气体。)) or ((((8 * -6 + 6 * -1) <= (-8 * 0 + -10 * 4) <= (0 - -14)) and (冰在常温下是固体。)) or (((3 - -13) <= (-1 * -10 - -3 * 5)) or (地球上一天是24小时。)))) or ((1 + 19) > (-8 * 6 + -6 * -3)) or (((氮气在常温下是气体。) and ((-1 - -4) < (-9 * -5 + 10 * -5) < (-9 * 1))) or ((4 ** 3) >= (-1 + 1)))
D. not (not not (((44 % 3) < (5 * -10 + 2 * 5)) or (not not (冰在常温下是气体。))))
E. (not not ((碳的化学符号是C。) and ((-3 * -8 * 5 * 4) < (-7 * 5 - 3 * 5) < (6 * 5 * 10 * 7)))) or ((空气在常温下是气体。) and (not not ((1976年奥运会在蒙特利尔举办。) and (94是质数。))))
F. not not (((((12 * -17) > (-3 * -9)) and ((4 * 10 + -6 * -9) >= (0 + 19))) and (((18 + -13) != (-1 * -4 * 10 * -1)) or (第二次世界大战结束发生在1945年。))) and (((-9 * 2 + -4 * 4) >= (-13 + -15)) or ((17 + 11) > (-3 * 20))) and (not not ((8 + 6) < (3 + 13) < (-11 * -20))))
G. not not ((not ((63能被8整除。) and ((-3 - 7) < (16 * -7) < (16 - 15)))) or (not not ((2 ** 3) > (42 % 1))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"answer": "B,C,D,G",
"difficulty": 1,
"gpt_response": "",
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"language": "cn",
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"seed": 51719231,
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"question": "给定以下布尔表达式：\n\nA. ((((铅的化学符号是Pb。) and (42大于77。)) and ((13 + -11) < (-20 * -4) < (-6 + 3))) and (((1 * -7) == (19 + -16)) and (欧盟的货币是欧元。)) and ((-3 + 14) != (5 ** 2))) and (not ((越南位于非洲。) or ((45 % 2) < (24 % 9)))) and (not not (not (not not (地球是距离太阳第3近的行星。))))\nB. not not (not not ((美国位于北美洲。) and (((-18 * 17) <= (4 - -18)) and (沙特阿拉伯位于亚洲。))))\nC. (((埃及的货币是新加坡元。) or (汞在常温下是气体。)) or ((((8 * -6 + 6 * -1) <= (-8 * 0 + -10 * 4) <= (0 - -14)) and (冰在常温下是固体。)) or (((3 - -13) <= (-1 * -10 - -3 * 5)) or (地球上一天是24小时。)))) or ((1 + 19) > (-8 * 6 + -6 * -3)) or (((氮气在常温下是气体。) and ((-1 - -4) < (-9 * -5 + 10 * -5) < (-9 * 1))) or ((4 ** 3) >= (-1 + 1)))\nD. not (not not (((44 % 3) < (5 * -10 + 2 * 5)) or (not not (冰在常温下是气体。))))\nE. (not not ((碳的化学符号是C。) and ((-3 * -8 * 5 * 4) < (-7 * 5 - 3 * 5) < (6 * 5 * 10 * 7)))) or ((空气在常温下是气体。) and (not not ((1976年奥运会在蒙特利尔举办。) and (94是质数。))))\nF. not not (((((12 * -17) > (-3 * -9)) and ((4 * 10 + -6 * -9) >= (0 + 19))) and (((18 + -13) != (-1 * -4 * 10 * -1)) or (第二次世界大战结束发生在1945年。))) and (((-9 * 2 + -4 * 4) >= (-13 + -15)) or ((17 + 11) > (-3 * 20))) and (not not ((8 + 6) < (3 + 13) < (-11 * -20))))\nG. not not ((not ((63能被8整除。) and ((-3 - 7) < (16 * -7) < (16 - 15)))) or (not not ((2 ** 3) > (42 % 1))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
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"language": "cn",
"num_options": 7,
"seed": 51719231,
"true_count": 4
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"seed": 51719231,
"task_id": 651719231,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. ((((1958年是闰年。) and ((-10 + 0) >= (3 * -2 * 9 * -3))) or ((肯尼亚位于非洲。) or (1948年奥运会在巴塞罗那举办。))) and (加拿大的货币是美元。)) and ((((1980年奥运会在亚特兰大举办。) and (匈牙利的首都是布达佩斯。)) or (not not (第一次世界大战结束发生在1918年。))) or (((印度位于亚洲。) and (鸭子有6条腿。)) and ((6 * 8 - -7 * 5) >= (-11 + -18))))
B. ((((德国的首都是柏林。) and ((11 - -16) >= (4 % 7))) or (not not ((-12 - 11) >= (-20 - 3)))) and (美国宣布独立发生在1776年。)) or (not not (not not ((-2 * -5 * 1 * 9) == (-15 - -1))))
C. (not not (not (not not ((-2 * 11) >= (3 ** 2))))) or (((5 ** 3) <= (-14 - -5)) or ((柏林墙倒塌发生在1991年。) or ((11 * 17) < (-10 * -8) < (-8 - -16))) or ((not not ((25 % 2) != (11 + -18))) or ((智利位于南美洲。) or (意大利的首都是罗马。))))
D. (not (地球是距离太阳第1近的行星。)) or ((水蒸气在常温下是气体。) or ((五月有31天。) or ((鹰是鱼类。) and ((-1 - -5) < (3 + 16)))))
E. ((((冰在常温下是固体。) or ((-12 - -6) < (-19 + -19))) or ((人类只使用了大脑的10%。) and ((-1 * -18) >= (-6 * -10)))) and ((11 - 12) <= (45 % 8))) or (((((9 * -7 - -4 * 3) != (17 + -8)) or (1984年奥运会在洛杉矶举办。)) or (((7 * -5) >= (2 - 9)) and ((-13 * 20) != (-7 * -8 + 2 * -7)))) or (not ((印度尼西亚位于亚洲。) and ((-13 + 13) > (7 * -4 + -10 * -9)))))
F. (((not ((14 + -2) == (-14 * 1))) and (not not (1924年奥运会在巴黎举办。))) and (氦的化学符号是Si。)) and ((苏联解体发生在1991年。) or ((-3 * 3 * -4 * -1) > (18 * -11)))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
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"difficulty": 1,
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"true_count": 4
},
"question": "研究以下逻辑语句：\n\nA. ((((1958年是闰年。) and ((-10 + 0) >= (3 * -2 * 9 * -3))) or ((肯尼亚位于非洲。) or (1948年奥运会在巴塞罗那举办。))) and (加拿大的货币是美元。)) and ((((1980年奥运会在亚特兰大举办。) and (匈牙利的首都是布达佩斯。)) or (not not (第一次世界大战结束发生在1918年。))) or (((印度位于亚洲。) and (鸭子有6条腿。)) and ((6 * 8 - -7 * 5) >= (-11 + -18))))\nB. ((((德国的首都是柏林。) and ((11 - -16) >= (4 % 7))) or (not not ((-12 - 11) >= (-20 - 3)))) and (美国宣布独立发生在1776年。)) or (not not (not not ((-2 * -5 * 1 * 9) == (-15 - -1))))\nC. (not not (not (not not ((-2 * 11) >= (3 ** 2))))) or (((5 ** 3) <= (-14 - -5)) or ((柏林墙倒塌发生在1991年。) or ((11 * 17) < (-10 * -8) < (-8 - -16))) or ((not not ((25 % 2) != (11 + -18))) or ((智利位于南美洲。) or (意大利的首都是罗马。))))\nD. (not (地球是距离太阳第1近的行星。)) or ((水蒸气在常温下是气体。) or ((五月有31天。) or ((鹰是鱼类。) and ((-1 - -5) < (3 + 16)))))\nE. ((((冰在常温下是固体。) or ((-12 - -6) < (-19 + -19))) or ((人类只使用了大脑的10%。) and ((-1 * -18) >= (-6 * -10)))) and ((11 - 12) <= (45 % 8))) or (((((9 * -7 - -4 * 3) != (17 + -8)) or (1984年奥运会在洛杉矶举办。)) or (((7 * -5) >= (2 - 9)) and ((-13 * 20) != (-7 * -8 + 2 * -7)))) or (not ((印度尼西亚位于亚洲。) and ((-13 + 13) > (7 * -4 + -10 * -9)))))\nF. (((not ((14 + -2) == (-14 * 1))) and (not not (1924年奥运会在巴黎举办。))) and (氦的化学符号是Si。)) and ((苏联解体发生在1991年。) or ((-3 * 3 * -4 * -1) > (18 * -11)))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 70668101,
"true_count": 4
},
"seed": 70668101,
"task_id": 670668101,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not ((((A frog has 4 legs.) or ((not ((-4 * -7) < (-8 + 11) < (1 ** 1))) or (((9 * -6 + -8 * 7) <= (-2 * -18)) or ((9 - 9) > (5 ** 3))))) or ((4 * 8) == (-2 * -5)) or (((0 * -7 + -3 * 5) > (6 * 0 * -8 * 7)) and (not (not (Mercury is the 1st planet from the Sun.))))) and (not (not not (Oxygen is a solid at room temperature.))))
B. not not (not not (not (not (727 is a Fibonacci number.))))
C. not not (not not ((not not ((Morocco is in Africa.) and ((-6 * -1) > (4 - -13)))) and (((not not ((13 + 13) != (10 * 1 * -10 * 10))) or ((1 * 10 + 8 * -7) != (18 + 15))) and ((The capital of Philippines is Manila.) or (Wood is a solid at room temperature.)) and ((not (Australia is in Oceania.)) and (((11 * 20) == (6 * -7 - -9 * 8)) and (The chemical symbol for Oxygen is O.))))))
D. not ((not ((((The chemical symbol for Iron is Fe.) or ((-1 * 0) == (13 + -13))) and (not (Neptune is the 8th planet from the Sun.))) and ((-9 * -5) <= (0 * 0 * 6 * 0) <= (38 % 9)))) or ((not ((The chemical symbol for Silver is K.) and (not (Neptune is the 6th planet from the Sun.)))) and (not ((-20 + 20) <= (-14 - -14)))))
E. not (((not not (not not ((A ladybug is a reptile.) and ((11 % 4) != (-2 * -3 * -1 * -10))))) and (((((19 * -9) != (3 - 15)) or ((-20 - -19) > (31 % 3))) or (A turtle is a reptile.)) and ((19 * 15) > (-2 * 0 * 0 * -8)) and (Iron is a solid at room temperature.))) and (not (((1958 is a leap year.) and ((Saturn is the 8th planet from the Sun.) or ((8 * -6 - -1 * 3) < (-4 * -2 * 1 * 8) < (-17 + -9)))) or ((4 + -6) < (13 * -8)))))
F. (not not (not (not not (The first iPhone was released occurred in 2007.)))) and (not not (not not ((((The square root of 9 is 1.) and (Thailand is in Asia.)) and (Earth is the 4th planet from the Sun.)) or (not (A human has 2 legs.)))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 6,
"seed": 66952487,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. not ((((A frog has 4 legs.) or ((not ((-4 * -7) < (-8 + 11) < (1 ** 1))) or (((9 * -6 + -8 * 7) <= (-2 * -18)) or ((9 - 9) > (5 ** 3))))) or ((4 * 8) == (-2 * -5)) or (((0 * -7 + -3 * 5) > (6 * 0 * -8 * 7)) and (not (not (Mercury is the 1st planet from the Sun.))))) and (not (not not (Oxygen is a solid at room temperature.))))\nB. not not (not not (not (not (727 is a Fibonacci number.))))\nC. not not (not not ((not not ((Morocco is in Africa.) and ((-6 * -1) > (4 - -13)))) and (((not not ((13 + 13) != (10 * 1 * -10 * 10))) or ((1 * 10 + 8 * -7) != (18 + 15))) and ((The capital of Philippines is Manila.) or (Wood is a solid at room temperature.)) and ((not (Australia is in Oceania.)) and (((11 * 20) == (6 * -7 - -9 * 8)) and (The chemical symbol for Oxygen is O.))))))\nD. not ((not ((((The chemical symbol for Iron is Fe.) or ((-1 * 0) == (13 + -13))) and (not (Neptune is the 8th planet from the Sun.))) and ((-9 * -5) <= (0 * 0 * 6 * 0) <= (38 % 9)))) or ((not ((The chemical symbol for Silver is K.) and (not (Neptune is the 6th planet from the Sun.)))) and (not ((-20 + 20) <= (-14 - -14)))))\nE. not (((not not (not not ((A ladybug is a reptile.) and ((11 % 4) != (-2 * -3 * -1 * -10))))) and (((((19 * -9) != (3 - 15)) or ((-20 - -19) > (31 % 3))) or (A turtle is a reptile.)) and ((19 * 15) > (-2 * 0 * 0 * -8)) and (Iron is a solid at room temperature.))) and (not (((1958 is a leap year.) and ((Saturn is the 8th planet from the Sun.) or ((8 * -6 - -1 * 3) < (-4 * -2 * 1 * 8) < (-17 + -9)))) or ((4 + -6) < (13 * -8)))))\nF. (not not (not (not not (The first iPhone was released occurred in 2007.)))) and (not not (not not ((((The square root of 9 is 1.) and (Thailand is in Asia.)) and (Earth is the 4th planet from the Sun.)) or (not (A human has 2 legs.)))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 6,
"seed": 66952487,
"true_count": 1
},
"seed": 66952487,
"task_id": 666952487,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not (not (((not not (not (Water is a liquid at room temperature.))) or (not (The 1948 Olympics were held in Tokyo.)) or ((((-6 * 10 + -9 * -10) < (-6 * -8) < (-7 * 1 - -9 * 2)) and ((2 ** 2) <= (10 * -15))) or ((The chemical symbol for Magnesium is Pb.) or ((2 * -7 - -4 * -4) == (11 - 2))))) or (not ((not not ((4 * 5) == (15 + 20))) and (54 is an even number.)))))
B. not (((((not ((-12 + 15) < (2 * 1 - 5 * -7))) or ((10 + 8) <= (8 * 6 + -6 * -6))) and (The 1932 Olympics were held in Rome.)) or (not ((not not (Venus is the 2nd planet from the Sun.)) or (((-12 + 4) > (15 + -19)) or ((1 - -20) <= (-17 - 16) <= (9 + -18)))))) and (not not ((not (Spain is in Africa.)) or (Lightning never strikes the same place twice.))) and (not ((not not (The capital of Saudi Arabia is Mexico City.)) or (not ((A cod is a fish.) or (A spider has 100 legs.))))))
C. not (not not (not not ((((1997 is a leap year.) or ((4 ** 2) >= (-5 - -9))) or (((2 ** 1) <= (10 - 2)) or ((19 - 20) == (5 ** 2)))) and (((-10 * -9 + 4 * 0) < (20 * 18)) and ((3 ** 3) >= (-14 - 5))) and ((((-14 * 10) < (-19 * 16) < (5 * 5 - 6 * -2)) and (The currency of Thailand is the Baht.)) or ((A lobster has 4 legs.) and ((15 * 6) >= (2 + -8)))))))
D. (not not (not not (not ((A eagle is a bird.) or ((11 is a perfect square.) or (A pig has 10 legs.)))))) and (not not ((((10 + 15) < (-6 * -5 * 6 * 5)) or (not not (not not (The chemical symbol for Nitrogen is C.)))) and (((The Pacific Ocean is the largest ocean.) and (The 1960 Olympics were held in Tokyo.)) or ((4 * -7 - 5 * 1) <= (7 - -14)) or (not not ((-6 - -2) <= (-5 - 16) <= (-5 * 10 - -1 * 3))))))
E. not not ((not not ((Gold is a solid at room temperature.) or (not not (Uranus is the 5th planet from the Sun.)))) or ((not not ((119 is an odd number.) and (Chile is in Asia.))) or ((A octopus has 8 legs.) and (Saturn is the 6th planet from the Sun.))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 14710778,
"true_count": 4
},
"question": "Examine these expressions:\n\nA. not (not (((not not (not (Water is a liquid at room temperature.))) or (not (The 1948 Olympics were held in Tokyo.)) or ((((-6 * 10 + -9 * -10) < (-6 * -8) < (-7 * 1 - -9 * 2)) and ((2 ** 2) <= (10 * -15))) or ((The chemical symbol for Magnesium is Pb.) or ((2 * -7 - -4 * -4) == (11 - 2))))) or (not ((not not ((4 * 5) == (15 + 20))) and (54 is an even number.)))))\nB. not (((((not ((-12 + 15) < (2 * 1 - 5 * -7))) or ((10 + 8) <= (8 * 6 + -6 * -6))) and (The 1932 Olympics were held in Rome.)) or (not ((not not (Venus is the 2nd planet from the Sun.)) or (((-12 + 4) > (15 + -19)) or ((1 - -20) <= (-17 - 16) <= (9 + -18)))))) and (not not ((not (Spain is in Africa.)) or (Lightning never strikes the same place twice.))) and (not ((not not (The capital of Saudi Arabia is Mexico City.)) or (not ((A cod is a fish.) or (A spider has 100 legs.))))))\nC. not (not not (not not ((((1997 is a leap year.) or ((4 ** 2) >= (-5 - -9))) or (((2 ** 1) <= (10 - 2)) or ((19 - 20) == (5 ** 2)))) and (((-10 * -9 + 4 * 0) < (20 * 18)) and ((3 ** 3) >= (-14 - 5))) and ((((-14 * 10) < (-19 * 16) < (5 * 5 - 6 * -2)) and (The currency of Thailand is the Baht.)) or ((A lobster has 4 legs.) and ((15 * 6) >= (2 + -8)))))))\nD. (not not (not not (not ((A eagle is a bird.) or ((11 is a perfect square.) or (A pig has 10 legs.)))))) and (not not ((((10 + 15) < (-6 * -5 * 6 * 5)) or (not not (not not (The chemical symbol for Nitrogen is C.)))) and (((The Pacific Ocean is the largest ocean.) and (The 1960 Olympics were held in Tokyo.)) or ((4 * -7 - 5 * 1) <= (7 - -14)) or (not not ((-6 - -2) <= (-5 - 16) <= (-5 * 10 - -1 * 3))))))\nE. not not ((not not ((Gold is a solid at room temperature.) or (not not (Uranus is the 5th planet from the Sun.)))) or ((not not ((119 is an odd number.) and (Chile is in Asia.))) or ((A octopus has 8 legs.) and (Saturn is the 6th planet from the Sun.))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 14710778,
"true_count": 4
},
"seed": 14710778,
"task_id": 614710778,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (not not (((((葡萄牙的首都是巴西利亚。) or (铅的化学符号是Zn。)) and (((7 * 3 * 7 * 7) != (-9 + 19)) and ((-17 - 2) <= (-11 - 6)))) or ((蚊子是爬行动物。) or (1972年奥运会在慕尼黑举办。)) or ((1 - -11) != (-12 + -18))) and (((猫头鹰是鸟类。) or (古巴的首都是哈瓦那。)) and ((not ((-9 + -19) == (-10 + -10))) or ((1 ** 3) > (-15 * 18)))))) and (not not ((not (not ((鳕鱼是爬行动物。) and ((-8 + -12) <= (-5 * -8 + 9 * -2))))) and ((第二次世界大战结束发生在1946年。) or (((1 ** 3) == (3 ** 2)) and (柏林墙倒塌发生在1989年。)) or ((17 * 8) <= (3 ** 2)))))
B. (((not not ((9 + -12) <= (20 * -7))) and ((乌龟是哺乳动物。) and (人体有150块骨头。))) and (((((1920年奥运会在墨尔本举办。) or ((-1 + -15) <= (-10 + -9))) and (not not ((-15 * 8) <= (14 + 8)))) or ((瑞典的货币是兰特。) or (((4 ** 1) < (16 - -6)) and (罗马尼亚的首都是惠灵顿。)))) or (not ((二氧化碳在常温下是液体。) and (not ((4 ** 1) > (-8 * -5 * -2 * -7))))))) or (not (((冰的密度比液态水小。) and (not not ((1 * 9) < (-9 * 5 + 8 * -8)))) and (((氧气对人类生存是必需的。) or (not (2004年奥运会在雅典举办。))) or (((火星是距离太阳第6近的行星。) or (2098年是闰年。)) and (not (地球是距离太阳第3近的行星。))))))
C. not ((((2012年是闰年。) or ((12 - 17) > (-4 * -10))) or (((((-15 + 4) == (15 * -13)) or ((19 - -5) < (7 * 4 * -5 * -5))) or (not not (秘鲁位于南美洲。))) and ((5 - 15) < (-7 + 8)) and (not not ((声音无法在真空中传播。) or ((-15 + 11) <= (-15 + -17) <= (4 * 10 * 1 * 8)))))) or ((((not not (1988年奥运会在巴塞罗那举办。)) and ((2 * 8 * 3 * -1) < (18 + -4))) and (((38 % 10) > (-11 - 19)) or (氧气在常温下是固体。)) and (not not (螃蟹有8条腿。))) and ((1981年是闰年。) and (not (((4 ** 1) <= (3 - -8) <= (4 ** 3)) or (现代奥运会首届举办发生在1896年。))))))
D. not (not (((声音在真空中传播更快。) and (not not ((-4 - 15) == (-7 - 14))) and (not ((1997年是闰年。) or ((-9 * -3 + 6 * -7) != (-2 * -10 + -6 * -3))))) or (((3 - -14) < (17 + 6)) and (((蚱蜢是昆虫。) or ((6 * 6 * -8 * -1) >= (-5 * -2 * 2 * 0))) or (现代奥运会首届举办发生在1896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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 4,
"seed": 81688716,
"true_count": 2
},
"question": "给定以下布尔表达式：\n\nA. (not not (((((葡萄牙的首都是巴西利亚。) or (铅的化学符号是Zn。)) and (((7 * 3 * 7 * 7) != (-9 + 19)) and ((-17 - 2) <= (-11 - 6)))) or ((蚊子是爬行动物。) or (1972年奥运会在慕尼黑举办。)) or ((1 - -11) != (-12 + -18))) and (((猫头鹰是鸟类。) or (古巴的首都是哈瓦那。)) and ((not ((-9 + -19) == (-10 + -10))) or ((1 ** 3) > (-15 * 18)))))) and (not not ((not (not ((鳕鱼是爬行动物。) and ((-8 + -12) <= (-5 * -8 + 9 * -2))))) and ((第二次世界大战结束发生在1946年。) or (((1 ** 3) == (3 ** 2)) and (柏林墙倒塌发生在1989年。)) or ((17 * 8) <= (3 ** 2)))))\nB. (((not not ((9 + -12) <= (20 * -7))) and ((乌龟是哺乳动物。) and (人体有150块骨头。))) and (((((1920年奥运会在墨尔本举办。) or ((-1 + -15) <= (-10 + -9))) and (not not ((-15 * 8) <= (14 + 8)))) or ((瑞典的货币是兰特。) or (((4 ** 1) < (16 - -6)) and (罗马尼亚的首都是惠灵顿。)))) or (not ((二氧化碳在常温下是液体。) and (not ((4 ** 1) > (-8 * -5 * -2 * -7))))))) or (not (((冰的密度比液态水小。) and (not not ((1 * 9) < (-9 * 5 + 8 * -8)))) and (((氧气对人类生存是必需的。) or (not (2004年奥运会在雅典举办。))) or (((火星是距离太阳第6近的行星。) or (2098年是闰年。)) and (not (地球是距离太阳第3近的行星。))))))\nC. not ((((2012年是闰年。) or ((12 - 17) > (-4 * -10))) or (((((-15 + 4) == (15 * -13)) or ((19 - -5) < (7 * 4 * -5 * -5))) or (not not (秘鲁位于南美洲。))) and ((5 - 15) < (-7 + 8)) and (not not ((声音无法在真空中传播。) or ((-15 + 11) <= (-15 + -17) <= (4 * 10 * 1 * 8)))))) or ((((not not (1988年奥运会在巴塞罗那举办。)) and ((2 * 8 * 3 * -1) < (18 + -4))) and (((38 % 10) > (-11 - 19)) or (氧气在常温下是固体。)) and (not not (螃蟹有8条腿。))) and ((1981年是闰年。) and (not (((4 ** 1) <= (3 - -8) <= (4 ** 3)) or (现代奥运会首届举办发生在1896年。))))))\nD. not (not (((声音在真空中传播更快。) and (not not ((-4 - 15) == (-7 - 14))) and (not ((1997年是闰年。) or ((-9 * -3 + 6 * -7) != (-2 * -10 + -6 * -3))))) or (((3 - -14) < (17 + 6)) and (((蚱蜢是昆虫。) or ((6 * 6 * -8 * -1) >= (-5 * -2 * 2 * 0))) or (现代奥运会首届举办发生在1896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": 6,
"language": "cn",
"num_options": 4,
"seed": 81688716,
"true_count": 2
},
"seed": 81688716,
"task_id": 681688716,
"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 currency of Japan is the Naira.))))
B. not not (((The capital of Germany is Kyiv.) and (India is in South America.)) or (((Steam is a gas at room temperature.) or (Jupiter is the 5th planet from the Sun.)) and ((20 * -18) < (13 + -9))))
C. not (((not ((10 * -2 + -3 * -2) != (16 - -14))) and (((14 % 10) < (8 * -10 - 8 * -8) < (-4 * -17)) and ((9 * -2 * 1 * -5) >= (11 - 7)))) and (not not (not ((-6 * 5 * 8 * 7) < (-15 - 19) < (5 ** 2)))))
D. (((14 - -14) >= (-8 - -3)) and ((5 * -9 - 4 * -5) < (5 ** 1) < (7 % 8))) or (not not (((A kangaroo has 0 legs.) or (The speed of light is approximately 300,000 km/s.)) and ((The 1920 Olympics were held in Antwerp.) or ((3 ** 2) <= (20 - 6)))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 27256576,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (not (not (not (The currency of Japan is the Naira.))))\nB. not not (((The capital of Germany is Kyiv.) and (India is in South America.)) or (((Steam is a gas at room temperature.) or (Jupiter is the 5th planet from the Sun.)) and ((20 * -18) < (13 + -9))))\nC. not (((not ((10 * -2 + -3 * -2) != (16 - -14))) and (((14 % 10) < (8 * -10 - 8 * -8) < (-4 * -17)) and ((9 * -2 * 1 * -5) >= (11 - 7)))) and (not not (not ((-6 * 5 * 8 * 7) < (-15 - 19) < (5 ** 2)))))\nD. (((14 - -14) >= (-8 - -3)) and ((5 * -9 - 4 * -5) < (5 ** 1) < (7 % 8))) or (not not (((A kangaroo has 0 legs.) or (The speed of light is approximately 300,000 km/s.)) and ((The 1920 Olympics were held in Antwerp.) or ((3 ** 2) <= (20 - 6)))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 27256576,
"true_count": 4
},
"seed": 27256576,
"task_id": 627256576,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not ((((-1 + -13) >= (38 % 3)) and (Water is a liquid at room temperature.)) or ((The currency of New Zealand is the Dollar.) or (A bee is an insect.)))
B. not not ((((-9 * -13) >= (6 + 7)) and ((-15 + 20) < (12 % 3))) and ((Carbon dioxide is a solid at room temperature.) or ((1 - 19) == (30 % 10))))
C. (A beetle is a bird.) or ((77 is greater than 73.) and ((9 * 7 - -4 * -5) <= (3 ** 3) <= (17 - 19))) or ((not not (Copper is a liquid at room temperature.)) and (not ((20 + 8) != (19 * 2))))
D. not not (Ice is a gas at room temperature.)
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 5565521,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. not not ((((-1 + -13) >= (38 % 3)) and (Water is a liquid at room temperature.)) or ((The currency of New Zealand is the Dollar.) or (A bee is an insect.)))\nB. not not ((((-9 * -13) >= (6 + 7)) and ((-15 + 20) < (12 % 3))) and ((Carbon dioxide is a solid at room temperature.) or ((1 - 19) == (30 % 10))))\nC. (A beetle is a bird.) or ((77 is greater than 73.) and ((9 * 7 - -4 * -5) <= (3 ** 3) <= (17 - 19))) or ((not not (Copper is a liquid at room temperature.)) and (not ((20 + 8) != (19 * 2))))\nD. not not (Ice is a gas at room temperature.)\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 5565521,
"true_count": 1
},
"seed": 5565521,
"task_id": 605565521,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not ((not not (not not ((The capital of Sweden is Stockholm.) or ((-16 - -1) >= (19 % 5))))) or (Humans only use 10% of their brain.) or (((Chile is in Antarctica.) or (((1 * -6 * 0 * -4) >= (2 ** 2)) or ((-3 - -11) < (33 % 3) < (2 * -1 - 5 * 5)))) and ((not not ((6 * -8 * 10 * -2) != (4 ** 3))) or (not ((0 - -9) != (7 - -4))))))
B. not (not not (((not not ((14 - -13) > (-5 * 3 - -10 * -9))) or (The chemical symbol for Nickel is Ni.)) or (not not (((-16 - -18) < (-7 + -12)) and ((15 + 10) <= (-10 * 1 * 4 * -4))))))
C. not not (((not (not (The currency of Philippines is the Peso.))) or (Kenya is in South America.)) and (1945 is a leap year.) and (not ((1 * 17) <= (20 * 5) <= (2 ** 3))))
D. not (not ((Neptune is the 8th planet from the Sun.) and (((Colombia is in Antarctica.) or (The 1896 Olympics were held in Athens.)) or ((A pig is a mammal.) or (Antarctica is the coldest continent.)))))
E. not not ((not not (((Mercury is the 1st planet from the Sun.) and ((16 - -4) <= (2 * 3 + 7 * 3))) and (not not ((6 * -4) < (-15 - 13) < (-10 + -1))))) or ((not ((-10 * -8 + 1 * 5) <= (-15 + -20) <= (-18 - 5))) or ((Japan is in Asia.) or (A ladybug is an insect.))) or ((((The 1952 Olympics were held in Montreal.) and (80 is a prime number.)) or ((181 is a perfect square.) or (The 1904 Olympics were held in Athens.))) or ((46 % 8) < (10 + 4))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 5568303,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not not ((not not (not not ((The capital of Sweden is Stockholm.) or ((-16 - -1) >= (19 % 5))))) or (Humans only use 10% of their brain.) or (((Chile is in Antarctica.) or (((1 * -6 * 0 * -4) >= (2 ** 2)) or ((-3 - -11) < (33 % 3) < (2 * -1 - 5 * 5)))) and ((not not ((6 * -8 * 10 * -2) != (4 ** 3))) or (not ((0 - -9) != (7 - -4))))))\nB. not (not not (((not not ((14 - -13) > (-5 * 3 - -10 * -9))) or (The chemical symbol for Nickel is Ni.)) or (not not (((-16 - -18) < (-7 + -12)) and ((15 + 10) <= (-10 * 1 * 4 * -4))))))\nC. not not (((not (not (The currency of Philippines is the Peso.))) or (Kenya is in South America.)) and (1945 is a leap year.) and (not ((1 * 17) <= (20 * 5) <= (2 ** 3))))\nD. not (not ((Neptune is the 8th planet from the Sun.) and (((Colombia is in Antarctica.) or (The 1896 Olympics were held in Athens.)) or ((A pig is a mammal.) or (Antarctica is the coldest continent.)))))\nE. not not ((not not (((Mercury is the 1st planet from the Sun.) and ((16 - -4) <= (2 * 3 + 7 * 3))) and (not not ((6 * -4) < (-15 - 13) < (-10 + -1))))) or ((not ((-10 * -8 + 1 * 5) <= (-15 + -20) <= (-18 - 5))) or ((Japan is in Asia.) or (A ladybug is an insect.))) or ((((The 1952 Olympics were held in Montreal.) and (80 is a prime number.)) or ((181 is a perfect square.) or (The 1904 Olympics were held in Athens.))) or ((46 % 8) < (10 + 4))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 5568303,
"true_count": 3
},
"seed": 5568303,
"task_id": 605568303,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not not (not not (((((-4 * -14) == (-17 + -14)) or ((-5 * -5 - -1 * 4) > (9 - 9))) and ((A eagle is a bird.) or (There are 28 days in May.))) or (1981 is a leap year.) or ((20 + -17) < (3 - 2))))) or ((((The capital of France is Amsterdam.) or (not (not not (The capital of Mexico is Bogota.)))) and (((((49 % 2) <= (-10 + 10)) or ((8 * -4 * 9 * 3) < (2 * 10))) or ((-13 + 9) < (3 ** 1))) and (not ((-9 - 9) <= (-12 * 6) <= (-18 + 6))))) or (not not (not not (The Moon produces its own light.))))
B. not (not (not ((((Venus is the 2nd planet from the Sun.) or (Water is a liquid at room temperature.)) or ((4 ** 1) >= (-5 - 2))) or (The 1896 Olympics were held in Athens.) or ((The currency of Russia is the Ruble.) or (((23 % 10) >= (5 * 17)) or ((9 * -7 + -4 * 2) >= (0 * 3 - 8 * -7)))))))
C. not (((not not ((-12 * -18) < (-20 * 5))) and (not (not ((The currency of Norway is the Krone.) or ((18 + -17) < (20 % 2) < (-13 * -7)))))) and (not ((not (((10 * 1 - 2 * -7) == (18 * 19)) and ((-10 * -1 * -10 * -5) != (20 - -4)))) or (792 is a Fibonacci number.) or (Sound cannot travel through a vacuum.))))
D. not not ((not ((((The 1972 Olympics were held in Munich.) and ((-19 - 19) != (-10 - 4))) and ((-9 - -12) < (2 ** 2))) or ((3 * -8 + 9 * 1) != (1 * 15)))) and (((A flamingo is an insect.) or ((21 % 1) <= (5 ** 2) <= (-2 * -13))) and ((not ((4 ** 3) < (1 * -2) < (6 + -12))) and ((The first airplane flight by the Wright Brothers occurred in 1903.) or (not (The currency of Poland is the Yuan.))))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 13958360,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. (not not (not not (((((-4 * -14) == (-17 + -14)) or ((-5 * -5 - -1 * 4) > (9 - 9))) and ((A eagle is a bird.) or (There are 28 days in May.))) or (1981 is a leap year.) or ((20 + -17) < (3 - 2))))) or ((((The capital of France is Amsterdam.) or (not (not not (The capital of Mexico is Bogota.)))) and (((((49 % 2) <= (-10 + 10)) or ((8 * -4 * 9 * 3) < (2 * 10))) or ((-13 + 9) < (3 ** 1))) and (not ((-9 - 9) <= (-12 * 6) <= (-18 + 6))))) or (not not (not not (The Moon produces its own light.))))\nB. not (not (not ((((Venus is the 2nd planet from the Sun.) or (Water is a liquid at room temperature.)) or ((4 ** 1) >= (-5 - 2))) or (The 1896 Olympics were held in Athens.) or ((The currency of Russia is the Ruble.) or (((23 % 10) >= (5 * 17)) or ((9 * -7 + -4 * 2) >= (0 * 3 - 8 * -7)))))))\nC. not (((not not ((-12 * -18) < (-20 * 5))) and (not (not ((The currency of Norway is the Krone.) or ((18 + -17) < (20 % 2) < (-13 * -7)))))) and (not ((not (((10 * 1 - 2 * -7) == (18 * 19)) and ((-10 * -1 * -10 * -5) != (20 - -4)))) or (792 is a Fibonacci number.) or (Sound cannot travel through a vacuum.))))\nD. not not ((not ((((The 1972 Olympics were held in Munich.) and ((-19 - 19) != (-10 - 4))) and ((-9 - -12) < (2 ** 2))) or ((3 * -8 + 9 * 1) != (1 * 15)))) and (((A flamingo is an insect.) or ((21 % 1) <= (5 ** 2) <= (-2 * -13))) and ((not ((4 ** 3) < (1 * -2) < (6 + -12))) and ((The first airplane flight by the Wright Brothers occurred in 1903.) or (not (The currency of Poland is the Yuan.))))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 13958360,
"true_count": 2
},
"seed": 13958360,
"task_id": 613958360,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((not ((((12 * -16) < (5 ** 1)) or (德国位于欧洲。)) and ((141是完全平方数。) and (新加坡的货币是比索。)))) and (not not ((火星是距离太阳第6近的行星。) or (锡的化学符号是U。))) and ((not not ((第二次世界大战开始发生在1941年。) and (1972年奥运会在慕尼黑举办。))) or ((8 * -1 - -4 * -10) >= (14 - 10)) or ((not (磷的化学符号是Co。)) or (not not (智利的货币是比索。))))) or (not not (not not (not not (((7 * 3 * 10 * 6) >= (5 ** 3)) and ((-2 - -15) == (25 % 10))))))
B. 太平洋是最大的海洋。
C. not not (((2057年是闰年。) and (((中国长城是在一年内建成的。) and (62是质数。)) or (not ((5 ** 1) != (2 ** 3))))) and (((以色列的货币是谢克尔。) or (镍的化学符号是N。)) or (((-4 - 1) != (5 * 11)) and (苍蝇是昆虫。))) and (not (not (((-12 * 9) < (16 * -14) < (-9 * -8 + -7 * 9)) or ((7 * -13) > (17 + -12))))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 5829434,
"true_count": 1
},
"question": "分析以下逻辑表达式：\n\nA. ((not ((((12 * -16) < (5 ** 1)) or (德国位于欧洲。)) and ((141是完全平方数。) and (新加坡的货币是比索。)))) and (not not ((火星是距离太阳第6近的行星。) or (锡的化学符号是U。))) and ((not not ((第二次世界大战开始发生在1941年。) and (1972年奥运会在慕尼黑举办。))) or ((8 * -1 - -4 * -10) >= (14 - 10)) or ((not (磷的化学符号是Co。)) or (not not (智利的货币是比索。))))) or (not not (not not (not not (((7 * 3 * 10 * 6) >= (5 ** 3)) and ((-2 - -15) == (25 % 10))))))\nB. 太平洋是最大的海洋。\nC. not not (((2057年是闰年。) and (((中国长城是在一年内建成的。) and (62是质数。)) or (not ((5 ** 1) != (2 ** 3))))) and (((以色列的货币是谢克尔。) or (镍的化学符号是N。)) or (((-4 - 1) != (5 * 11)) and (苍蝇是昆虫。))) and (not (not (((-12 * 9) < (16 * -14) < (-9 * -8 + -7 * 9)) or ((7 * -13) > (17 + -12))))))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 5829434,
"true_count": 1
},
"seed": 5829434,
"task_id": 605829434,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. not (not (not ((The currency of Denmark is the Krone.) and (((21 % 5) <= (3 - -16)) and (2088 is a leap year.)) and (not not (2038 is a leap year.)))))
B. not (((not ((((4 ** 3) == (-14 * -6)) or (The first Olympic Games of modern era occurred in 1896.)) or ((Venus is the 2nd planet from the Sun.) and (The currency of Thailand is the Krona.)))) and ((not (((7 * -8 - -8 * -8) <= (4 * 7 - -2 * -2)) or ((-13 * 12) < (2 % 3) < (7 * 0 - 0 * 0)))) and ((3 * 10 + 5 * -1) >= (-8 * 9 * 8 * 1)))) or (not not (not not (The 1896 Olympics were held in Amsterdam.))))
C. not not ((not (not not ((35 % 9) != (3 - 18)))) or ((not (not not (not ((-10 - -19) >= (26 % 5))))) and ((not ((18 + 6) > (5 * 0 + 8 * 4))) or ((The chemical symbol for Magnesium is Pb.) or ((19 + 13) < (12 + 20)))) and ((((A swan is a reptile.) and (Germany is in Europe.)) and ((10 + 17) == (1 * -1))) or (Helium is a gas at room temperature.))))
D. not not ((not ((not ((Uranus is the 4th planet from the Sun.) and ((2 ** 1) != (14 % 10)))) and ((17 * 15) > (5 ** 1)) and ((0 - -14) == (-7 * 8 + 8 * 2)))) or (not (not not (not not (not not (The chemical symbol for Cobalt is Co.))))))
E. ((not (((not not (A butterfly has 6 legs.)) and (((15 % 6) <= (19 + 20) <= (42 % 4)) and (The chemical symbol for Sulfur is Mn.))) or ((-17 + 18) <= (20 + -4)))) and (not ((not (((29 % 6) >= (0 - 5)) or ((-8 + -16) > (9 * 3 + 1 * -4)))) or (not not ((3 ** 3) <= (8 * -12))) or ((3 * -14) != (-9 * -4 - -1 * 1))))) or (not not (not (not (not not (not ((19 + 10) > (15 % 5)))))))
F. not (not ((((The first airplane flight by the Wright Brothers occurred in 1903.) or ((1 ** 3) > (21 % 2))) or ((Oxygen is necessary for human survival.) and (107 is a perfect square.)) or (Wood is a solid at room temperature.)) and (((The capital of Czech Republic is Prague.) and (Mars is the closest planet to the Sun.)) or (not not (The capital of Ukraine is Rabat.)) or ((not not (A koala is an insect.)) and ((-5 - 4) >= (0 * -7))))))
G. not not (not not (not not (((((-14 * 4) < (3 * 3 * -1 * 3)) or (The capital of Brazil is Brasilia.)) and (56 is divisible by 7.)) or ((not not (2056 is a leap year.)) or (((3 ** 1) >= (3 ** 1)) or ((9 + 8) < (-17 * 0) < (-20 + 11)))))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 11909226,
"true_count": 5
},
"question": "Analyze these boolean expressions:\n\nA. not (not (not ((The currency of Denmark is the Krone.) and (((21 % 5) <= (3 - -16)) and (2088 is a leap year.)) and (not not (2038 is a leap year.)))))\nB. not (((not ((((4 ** 3) == (-14 * -6)) or (The first Olympic Games of modern era occurred in 1896.)) or ((Venus is the 2nd planet from the Sun.) and (The currency of Thailand is the Krona.)))) and ((not (((7 * -8 - -8 * -8) <= (4 * 7 - -2 * -2)) or ((-13 * 12) < (2 % 3) < (7 * 0 - 0 * 0)))) and ((3 * 10 + 5 * -1) >= (-8 * 9 * 8 * 1)))) or (not not (not not (The 1896 Olympics were held in Amsterdam.))))\nC. not not ((not (not not ((35 % 9) != (3 - 18)))) or ((not (not not (not ((-10 - -19) >= (26 % 5))))) and ((not ((18 + 6) > (5 * 0 + 8 * 4))) or ((The chemical symbol for Magnesium is Pb.) or ((19 + 13) < (12 + 20)))) and ((((A swan is a reptile.) and (Germany is in Europe.)) and ((10 + 17) == (1 * -1))) or (Helium is a gas at room temperature.))))\nD. not not ((not ((not ((Uranus is the 4th planet from the Sun.) and ((2 ** 1) != (14 % 10)))) and ((17 * 15) > (5 ** 1)) and ((0 - -14) == (-7 * 8 + 8 * 2)))) or (not (not not (not not (not not (The chemical symbol for Cobalt is Co.))))))\nE. ((not (((not not (A butterfly has 6 legs.)) and (((15 % 6) <= (19 + 20) <= (42 % 4)) and (The chemical symbol for Sulfur is Mn.))) or ((-17 + 18) <= (20 + -4)))) and (not ((not (((29 % 6) >= (0 - 5)) or ((-8 + -16) > (9 * 3 + 1 * -4)))) or (not not ((3 ** 3) <= (8 * -12))) or ((3 * -14) != (-9 * -4 - -1 * 1))))) or (not not (not (not (not not (not ((19 + 10) > (15 % 5)))))))\nF. not (not ((((The first airplane flight by the Wright Brothers occurred in 1903.) or ((1 ** 3) > (21 % 2))) or ((Oxygen is necessary for human survival.) and (107 is a perfect square.)) or (Wood is a solid at room temperature.)) and (((The capital of Czech Republic is Prague.) and (Mars is the closest planet to the Sun.)) or (not not (The capital of Ukraine is Rabat.)) or ((not not (A koala is an insect.)) and ((-5 - 4) >= (0 * -7))))))\nG. not not (not not (not not (((((-14 * 4) < (3 * 3 * -1 * 3)) or (The capital of Brazil is Brasilia.)) and (56 is divisible by 7.)) or ((not not (2056 is a leap year.)) or (((3 ** 1) >= (3 ** 1)) or ((9 + 8) < (-17 * 0) < (-20 + 11)))))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 11909226,
"true_count": 5
},
"seed": 11909226,
"task_id": 611909226,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not (((苏联解体发生在1991年。) and (丹麦的首都是哥本哈根。)) and ((12 * -11) < (-13 * 3) < (-9 * 16)))
B. (火星是距离太阳第2近的行星。) and (((-6 + -9) != (4 * -4 + 9 * 0)) and ((38 % 5) < (5 * -6 - -8 * 8) < (16 + 16))) and ((18 - -20) <= (8 * -1))
C. ((越南的货币是越南盾。) or (((-19 - -7) <= (16 * -14)) and (袋鼠有2条腿。))) and (not (not (71是偶数。)))
D. ((15 + -18) >= (6 + 12)) or (((39 % 3) == (16 - -12)) and (冰的密度比液态水小。)) or ((9 - 13) > (0 - 11))
E. ((0 * 9 * -6 * 4) < (8 * 4 + -10 * 4) < (-9 * 13)) or (((1896年奥运会在雅典举办。) and ((19 - -10) != (-2 * -6 - 10 * 0))) or ((银的化学符号是Mg。) or ((18 - 19) < (-10 + 7))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 61009014,
"true_count": 3
},
"question": "审视以下逻辑表达式：\n\nA. not (((苏联解体发生在1991年。) and (丹麦的首都是哥本哈根。)) and ((12 * -11) < (-13 * 3) < (-9 * 16)))\nB. (火星是距离太阳第2近的行星。) and (((-6 + -9) != (4 * -4 + 9 * 0)) and ((38 % 5) < (5 * -6 - -8 * 8) < (16 + 16))) and ((18 - -20) <= (8 * -1))\nC. ((越南的货币是越南盾。) or (((-19 - -7) <= (16 * -14)) and (袋鼠有2条腿。))) and (not (not (71是偶数。)))\nD. ((15 + -18) >= (6 + 12)) or (((39 % 3) == (16 - -12)) and (冰的密度比液态水小。)) or ((9 - 13) > (0 - 11))\nE. ((0 * 9 * -6 * 4) < (8 * 4 + -10 * 4) < (-9 * 13)) or (((1896年奥运会在雅典举办。) and ((19 - -10) != (-2 * -6 - 10 * 0))) or ((银的化学符号是Mg。) or ((18 - 19) < (-10 + 7))))\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": 5,
"seed": 61009014,
"true_count": 3
},
"seed": 61009014,
"task_id": 661009014,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. ((((Mercury is the 4th planet from the Sun.) and ((1 * -3) > (-18 + -19))) and ((The capital of Ukraine is Kyiv.) or (The Moon orbits the Earth.))) or ((The square root of 121 is 8.) and ((12 + 2) <= (12 - -1) <= (0 * -9 * 10 * 3))) or ((((3 ** 2) >= (-9 + -10)) and ((-6 + -19) == (-3 + 15))) or ((The chemical symbol for Lead is Al.) and (2048 is a leap year.)))) or ((The chemical symbol for Cobalt is Pb.) or (not not (The currency of China is the Yuan.)))
B. not not (not (Oxygen is necessary for human survival.))
C. (((11 * 14) < (9 + 13) < (20 % 9)) or (not (((1 - 8) != (-18 - -1)) or (There are 31 days in July.)))) and (((not not (The currency of Colombia is the Pound.)) and (184 is an odd number.)) or (not (not (The capital of Russia is Moscow.))))
D. not (((((16 - -14) > (3 ** 2)) and ((11 + 19) > (-12 - 9))) or ((Indonesia is in Asia.) and (Oil is a solid at room temperature.))) or ((not ((5 * 2 - -8 * -2) > (-1 * -19))) or (((5 ** 3) < (-10 * -3 + -10 * -5)) or (The chemical symbol for Sodium is Cr.))))
E. not not (not not ((((7 + -10) <= (-8 * 7 + 6 * -7)) and (Helium is a gas at room temperature.)) or (A lobster has 8 legs.)))
F. not (not not (((16 * 1) == (1 ** 2)) and ((1992 is a leap year.) and (Peru is in North America.))))
G. ((not not ((A crab has 10 legs.) and (The 1904 Olympics were held in St. Louis.))) and (not not (((-19 * -7) < (-20 + -1)) or (The 1984 Olympics were held in Berlin.)))) or (((The currency of Indonesia is the Rupiah.) and (The Soviet Union dissolved occurred in 1991.)) and (not ((-6 * 7) < (0 * -5) < (-19 + 2)))) or (not (not (((10 * 4 + -5 * -5) <= (19 + 7)) and (Uranus is the 7th planet from the Sun.))))
H. ((not ((The chemical symbol for Oxygen is O.) or ((-18 - 10) <= (-5 * 6 * -5 * -3)))) and ((Canada is in North America.) or (((2 * 9 * 4 * 2) <= (6 * 7 + 1 * 9)) and (The capital of Malaysia is Kyiv.)))) or ((((7 - 6) <= (-4 * 2 + 9 * 0)) and ((-1 - -12) == (-2 * 2))) and (not not ((5 % 6) < (46 % 8)))) or ((Mars is the 8th planet from the Sun.) or (not not (432 is a Fibonacci number.)) or (not ((6 * -6 * 5 * 8) < (3 ** 3) < (-8 - -4))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 5100387,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. ((((Mercury is the 4th planet from the Sun.) and ((1 * -3) > (-18 + -19))) and ((The capital of Ukraine is Kyiv.) or (The Moon orbits the Earth.))) or ((The square root of 121 is 8.) and ((12 + 2) <= (12 - -1) <= (0 * -9 * 10 * 3))) or ((((3 ** 2) >= (-9 + -10)) and ((-6 + -19) == (-3 + 15))) or ((The chemical symbol for Lead is Al.) and (2048 is a leap year.)))) or ((The chemical symbol for Cobalt is Pb.) or (not not (The currency of China is the Yuan.)))\nB. not not (not (Oxygen is necessary for human survival.))\nC. (((11 * 14) < (9 + 13) < (20 % 9)) or (not (((1 - 8) != (-18 - -1)) or (There are 31 days in July.)))) and (((not not (The currency of Colombia is the Pound.)) and (184 is an odd number.)) or (not (not (The capital of Russia is Moscow.))))\nD. not (((((16 - -14) > (3 ** 2)) and ((11 + 19) > (-12 - 9))) or ((Indonesia is in Asia.) and (Oil is a solid at room temperature.))) or ((not ((5 * 2 - -8 * -2) > (-1 * -19))) or (((5 ** 3) < (-10 * -3 + -10 * -5)) or (The chemical symbol for Sodium is Cr.))))\nE. not not (not not ((((7 + -10) <= (-8 * 7 + 6 * -7)) and (Helium is a gas at room temperature.)) or (A lobster has 8 legs.)))\nF. not (not not (((16 * 1) == (1 ** 2)) and ((1992 is a leap year.) and (Peru is in North America.))))\nG. ((not not ((A crab has 10 legs.) and (The 1904 Olympics were held in St. Louis.))) and (not not (((-19 * -7) < (-20 + -1)) or (The 1984 Olympics were held in Berlin.)))) or (((The currency of Indonesia is the Rupiah.) and (The Soviet Union dissolved occurred in 1991.)) and (not ((-6 * 7) < (0 * -5) < (-19 + 2)))) or (not (not (((10 * 4 + -5 * -5) <= (19 + 7)) and (Uranus is the 7th planet from the Sun.))))\nH. ((not ((The chemical symbol for Oxygen is O.) or ((-18 - 10) <= (-5 * 6 * -5 * -3)))) and ((Canada is in North America.) or (((2 * 9 * 4 * 2) <= (6 * 7 + 1 * 9)) and (The capital of Malaysia is Kyiv.)))) or ((((7 - 6) <= (-4 * 2 + 9 * 0)) and ((-1 - -12) == (-2 * 2))) and (not not ((5 % 6) < (46 % 8)))) or ((Mars is the 8th planet from the Sun.) or (not not (432 is a Fibonacci number.)) or (not ((6 * -6 * 5 * 8) < (3 ** 3) < (-8 - -4))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 5100387,
"true_count": 4
},
"seed": 5100387,
"task_id": 605100387,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not (not ((not ((3 * -10 + 1 * -6) > (4 * 20))) or (((((5 ** 2) >= (8 + 0)) and (481 is a Fibonacci number.)) or (((14 + 0) >= (5 % 2)) or (The 1988 Olympics were held in Moscow.))) and (Oxygen is necessary for human survival.))))
B. not (not not ((not not ((2063 is a leap year.) or (((13 * 6) <= (1 * 10 - 9 * 10)) or (The 2024 Olympics were held in Paris.)))) or ((not (not (Mercury is a liquid at room temperature.))) or (Ice is a solid at room temperature.))))
C. not not (not (not (not (The 1908 Olympics were held in Athens.))))
D. not ((not ((((2085 is a leap year.) and (The 1960 Olympics were held in Mexico City.)) and (not ((0 * -3 - 7 * 1) < (6 + -16)))) or (not (not (A human has 10 legs.))))) and (((The chemical symbol for Titanium is Ti.) and (((5 ** 1) >= (2 - -13)) and ((The currency of Peru is the Peso.) and (The capital of Hungary is Budapest.)))) and (((7 * 9 + 4 * 5) < (-9 - -20)) and (((World War II began occurred in 1939.) or (France is in Europe.)) or (not ((47 % 10) != (-10 + 9)))))))
E. not (not not ((not not ((-7 + 1) < (2 ** 2))) and ((Wood is a solid at room temperature.) and ((The currency of Brazil is the Zloty.) and ((The 1936 Olympics were held in Helsinki.) and ((2 ** 1) > (11 * -20)))))))
F. not ((((Indonesia is in Asia.) or ((The chemical symbol for Magnesium is Mn.) and (11 is greater than 36.))) and (A parrot is a bird.) and (not (((12 % 10) <= (2 + 5)) and ((The 1920 Olympics were held in Barcelona.) or (176 is a perfect square.))))) or (not not (((not not ((11 - 14) < (43 % 7))) or (((8 - -17) >= (-10 + 18)) and (A fish has 4 legs.))) or ((((0 + 20) < (21 % 2)) or (Oxygen is necessary for human survival.)) and (((11 - 16) != (22 % 2)) and ((-12 - 8) <= (30 % 6)))))))
G. (not ((((-4 * 9 + -8 * 3) > (-4 * -19)) or (not (Uranus is the 1st planet from the Sun.))) and (not not (not (not not ((-6 - -4) < (-8 + -15))))))) or (not (not (not (305 is a perfect square.))))
H. not (not not (not not (not (The 1924 Olympics were held in Antwerp.))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 96599957,
"true_count": 5
},
"question": "Below are several boolean expressions:\n\nA. not (not ((not ((3 * -10 + 1 * -6) > (4 * 20))) or (((((5 ** 2) >= (8 + 0)) and (481 is a Fibonacci number.)) or (((14 + 0) >= (5 % 2)) or (The 1988 Olympics were held in Moscow.))) and (Oxygen is necessary for human survival.))))\nB. not (not not ((not not ((2063 is a leap year.) or (((13 * 6) <= (1 * 10 - 9 * 10)) or (The 2024 Olympics were held in Paris.)))) or ((not (not (Mercury is a liquid at room temperature.))) or (Ice is a solid at room temperature.))))\nC. not not (not (not (not (The 1908 Olympics were held in Athens.))))\nD. not ((not ((((2085 is a leap year.) and (The 1960 Olympics were held in Mexico City.)) and (not ((0 * -3 - 7 * 1) < (6 + -16)))) or (not (not (A human has 10 legs.))))) and (((The chemical symbol for Titanium is Ti.) and (((5 ** 1) >= (2 - -13)) and ((The currency of Peru is the Peso.) and (The capital of Hungary is Budapest.)))) and (((7 * 9 + 4 * 5) < (-9 - -20)) and (((World War II began occurred in 1939.) or (France is in Europe.)) or (not ((47 % 10) != (-10 + 9)))))))\nE. not (not not ((not not ((-7 + 1) < (2 ** 2))) and ((Wood is a solid at room temperature.) and ((The currency of Brazil is the Zloty.) and ((The 1936 Olympics were held in Helsinki.) and ((2 ** 1) > (11 * -20)))))))\nF. not ((((Indonesia is in Asia.) or ((The chemical symbol for Magnesium is Mn.) and (11 is greater than 36.))) and (A parrot is a bird.) and (not (((12 % 10) <= (2 + 5)) and ((The 1920 Olympics were held in Barcelona.) or (176 is a perfect square.))))) or (not not (((not not ((11 - 14) < (43 % 7))) or (((8 - -17) >= (-10 + 18)) and (A fish has 4 legs.))) or ((((0 + 20) < (21 % 2)) or (Oxygen is necessary for human survival.)) and (((11 - 16) != (22 % 2)) and ((-12 - 8) <= (30 % 6)))))))\nG. (not ((((-4 * 9 + -8 * 3) > (-4 * -19)) or (not (Uranus is the 1st planet from the Sun.))) and (not not (not (not not ((-6 - -4) < (-8 + -15))))))) or (not (not (not (305 is a perfect square.))))\nH. not (not not (not not (not (The 1924 Olympics were held in Antwerp.))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 96599957,
"true_count": 5
},
"seed": 96599957,
"task_id": 696599957,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (((((-3 * 7 - 9 * 2) == (20 - 8)) or ((A bird has 100 legs.) and ((-10 * -7 + -6 * 10) < (19 + -7)))) and (not not (The chemical symbol for Gold is Au.))) or (((259 is a perfect square.) and ((-20 - 4) < (2 % 6) < (15 % 4))) or (((not ((11 - -8) != (19 - -19))) and ((Egypt is in Africa.) or (Whales are fish.))) or ((not not ((-14 * 2) >= (-20 + 2))) and (Gold is a gas at room temperature.)))))
B. not not ((not not ((((Plants produce oxygen through photosynthesis.) or (The capital of Vietnam is Moscow.)) or ((8 + -14) >= (5 * 0))) or (not not (A salmon is a fish.)))) and (not not (((((16 - 14) >= (3 ** 2)) and (Humans have five fingers on each hand.)) or (334 is a perfect square.)) and (176 is an odd number.) and (((-5 * -8 - 8 * 8) <= (2 ** 3)) or (((18 + -7) < (10 - -10)) or ((18 - 18) >= (7 * -4 + 4 * -6)))))))
C. not ((not (not not ((((0 * 2) <= (2 ** 2)) and (The 1956 Olympics were held in Melbourne.)) and (((7 * 4 - 3 * -5) > (-8 * 0)) or ((40 % 2) >= (-6 - -4)))))) and ((not ((184 is an even number.) or (The currency of South Africa is the Pound.))) or ((4 + -18) < (2 ** 3))) and (not not ((((1989 is a leap year.) or ((11 + -9) < (18 + 0))) or (Steam is a solid at room temperature.)) and ((((-7 - -13) <= (5 * 19) <= (18 * -11)) or ((-5 + 10) >= (16 * 19))) or (not ((9 - -3) >= (9 - 18)))))))
D. not (((not ((19 * -3) <= (-16 - 13))) and ((not ((The chemical symbol for Chlorine is Cl.) or ((-15 - -12) < (18 * -14) < (-4 * 2 * -3 * -6)))) or ((((-11 * 17) <= (-7 * 4 - -10 * -8)) and (The currency of European Union is the Dollar.)) and ((-9 * -8) != (-8 + -16))))) and (not not ((((There are 28 days in August.) and ((2 ** 3) >= (15 + -3))) and ((The Titanic sank occurred in 1912.) or (Uranus is the 5th planet from the Sun.))) and (not not ((5 ** 3) > (0 * 6 * 4 * 1))))))
E. not (((((((11 * 16) <= (0 * 8 + -1 * -10)) and (The chemical symbol for Chromium is Ne.)) or (not ((38 % 9) > (-7 - -12)))) or (88 is greater than 99.)) or (not ((17 * 9) >= (-10 * 13)))) or (not not ((2025 is a leap year.) and (Mercury is the 6th planet from the Sun.) and ((-6 * 16) == (-5 * 18)))))
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": 6,
"language": "en",
"num_options": 5,
"seed": 5631717,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (((((-3 * 7 - 9 * 2) == (20 - 8)) or ((A bird has 100 legs.) and ((-10 * -7 + -6 * 10) < (19 + -7)))) and (not not (The chemical symbol for Gold is Au.))) or (((259 is a perfect square.) and ((-20 - 4) < (2 % 6) < (15 % 4))) or (((not ((11 - -8) != (19 - -19))) and ((Egypt is in Africa.) or (Whales are fish.))) or ((not not ((-14 * 2) >= (-20 + 2))) and (Gold is a gas at room temperature.)))))\nB. not not ((not not ((((Plants produce oxygen through photosynthesis.) or (The capital of Vietnam is Moscow.)) or ((8 + -14) >= (5 * 0))) or (not not (A salmon is a fish.)))) and (not not (((((16 - 14) >= (3 ** 2)) and (Humans have five fingers on each hand.)) or (334 is a perfect square.)) and (176 is an odd number.) and (((-5 * -8 - 8 * 8) <= (2 ** 3)) or (((18 + -7) < (10 - -10)) or ((18 - 18) >= (7 * -4 + 4 * -6)))))))\nC. not ((not (not not ((((0 * 2) <= (2 ** 2)) and (The 1956 Olympics were held in Melbourne.)) and (((7 * 4 - 3 * -5) > (-8 * 0)) or ((40 % 2) >= (-6 - -4)))))) and ((not ((184 is an even number.) or (The currency of South Africa is the Pound.))) or ((4 + -18) < (2 ** 3))) and (not not ((((1989 is a leap year.) or ((11 + -9) < (18 + 0))) or (Steam is a solid at room temperature.)) and ((((-7 - -13) <= (5 * 19) <= (18 * -11)) or ((-5 + 10) >= (16 * 19))) or (not ((9 - -3) >= (9 - 18)))))))\nD. not (((not ((19 * -3) <= (-16 - 13))) and ((not ((The chemical symbol for Chlorine is Cl.) or ((-15 - -12) < (18 * -14) < (-4 * 2 * -3 * -6)))) or ((((-11 * 17) <= (-7 * 4 - -10 * -8)) and (The currency of European Union is the Dollar.)) and ((-9 * -8) != (-8 + -16))))) and (not not ((((There are 28 days in August.) and ((2 ** 3) >= (15 + -3))) and ((The Titanic sank occurred in 1912.) or (Uranus is the 5th planet from the Sun.))) and (not not ((5 ** 3) > (0 * 6 * 4 * 1))))))\nE. not (((((((11 * 16) <= (0 * 8 + -1 * -10)) and (The chemical symbol for Chromium is Ne.)) or (not ((38 % 9) > (-7 - -12)))) or (88 is greater than 99.)) or (not ((17 * 9) >= (-10 * 13)))) or (not not ((2025 is a leap year.) and (Mercury is the 6th planet from the Sun.) and ((-6 * 16) == (-5 * 18)))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 5631717,
"true_count": 2
},
"seed": 5631717,
"task_id": 605631717,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not ((((China is in Africa.) or (((-4 * 7 + 4 * 5) <= (17 * -15)) or (The capital of Chile is Santiago.))) or (not ((The chemical symbol for Chlorine is H.) and ((-16 * -20) < (3 * -1 + 7 * 5))))) or (not ((12 % 9) <= (9 * -8 + 9 * -8))) or (not ((not not ((-10 + 11) >= (8 * 2 * 0 * -1))) and (not not (Oil is a liquid at room temperature.)))))
B. not not (not ((1967 is a leap year.) or ((The chemical symbol for Zinc is Zn.) or ((4 ** 1) > (18 + -11)))))
C. not not ((((not (There are 31 days in July.)) or (not (The currency of Hungary is the Forint.))) or (not ((Brazil is in South America.) and (The 1980 Olympics were held in Beijing.)))) and ((((2076 is a leap year.) and ((9 * 2) == (2 * 6 + 4 * -7))) and (not (Water is a liquid at room temperature.))) and (Diamond is a gas at room temperature.)))
D. ((not not ((3 - -5) < (-15 * 3))) or (((Gold is a gas at room temperature.) or (not not (There are 30 days in September.))) or ((2100 is a leap year.) or (Morocco is in Africa.)))) or ((((1962 is a leap year.) and ((A ant has 6 legs.) and (2039 is a leap year.))) or (((-16 - 14) != (39 % 4)) or (Mercury is the 6th planet from the Sun.))) or ((not (not ((19 + -13) <= (4 + -17)))) and (((-16 - -17) >= (-17 - 12)) and (((-5 - 13) < (1 * 2 + -4 * 7)) and (The chemical symbol for Chromium is Pt.)))))
E. (((not (((11 + -12) != (3 - -20)) or ((10 * 0 * 1 * -10) != (-10 - 0)))) and (Steam is a solid at room temperature.)) or ((-6 * -3 + -3 * -6) != (16 - -7)) or (not ((((3 * 1 + 0 * 6) < (2 ** 3)) and (The 2004 Olympics were held in Rio de Janeiro.)) or (36 is divisible by 3.)))) or (not not (((Ice is less dense than liquid water.) or ((-10 - -1) == (-14 * -16))) or (The 1936 Olympics were held in Stockholm.)))
F. (((Wood is a gas at room temperature.) or (not not (There are 31 days in May.)) or ((4 * -5) >= (1 + 1))) or (((-4 * -9 - 3 * 5) <= (1 ** 1) <= (12 - -4)) and ((-19 - 18) > (8 * 7)))) and ((not (((17 * -20) <= (17 * 0)) and ((1 * 11) != (8 * 20)))) and ((The first Olympic Games of modern era occurred in 1896.) or ((-1 * -9) != (-6 * 7 + -5 * 6)) or ((1938 is a leap year.) or (The human body has 206 bones.))))
G. not (not not (((-7 - -3) < (-7 * -4 - 9 * -5)) and (not ((3 + 12) == (7 * -12)))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 21927552,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. not not ((((China is in Africa.) or (((-4 * 7 + 4 * 5) <= (17 * -15)) or (The capital of Chile is Santiago.))) or (not ((The chemical symbol for Chlorine is H.) and ((-16 * -20) < (3 * -1 + 7 * 5))))) or (not ((12 % 9) <= (9 * -8 + 9 * -8))) or (not ((not not ((-10 + 11) >= (8 * 2 * 0 * -1))) and (not not (Oil is a liquid at room temperature.)))))\nB. not not (not ((1967 is a leap year.) or ((The chemical symbol for Zinc is Zn.) or ((4 ** 1) > (18 + -11)))))\nC. not not ((((not (There are 31 days in July.)) or (not (The currency of Hungary is the Forint.))) or (not ((Brazil is in South America.) and (The 1980 Olympics were held in Beijing.)))) and ((((2076 is a leap year.) and ((9 * 2) == (2 * 6 + 4 * -7))) and (not (Water is a liquid at room temperature.))) and (Diamond is a gas at room temperature.)))\nD. ((not not ((3 - -5) < (-15 * 3))) or (((Gold is a gas at room temperature.) or (not not (There are 30 days in September.))) or ((2100 is a leap year.) or (Morocco is in Africa.)))) or ((((1962 is a leap year.) and ((A ant has 6 legs.) and (2039 is a leap year.))) or (((-16 - 14) != (39 % 4)) or (Mercury is the 6th planet from the Sun.))) or ((not (not ((19 + -13) <= (4 + -17)))) and (((-16 - -17) >= (-17 - 12)) and (((-5 - 13) < (1 * 2 + -4 * 7)) and (The chemical symbol for Chromium is Pt.)))))\nE. (((not (((11 + -12) != (3 - -20)) or ((10 * 0 * 1 * -10) != (-10 - 0)))) and (Steam is a solid at room temperature.)) or ((-6 * -3 + -3 * -6) != (16 - -7)) or (not ((((3 * 1 + 0 * 6) < (2 ** 3)) and (The 2004 Olympics were held in Rio de Janeiro.)) or (36 is divisible by 3.)))) or (not not (((Ice is less dense than liquid water.) or ((-10 - -1) == (-14 * -16))) or (The 1936 Olympics were held in Stockholm.)))\nF. (((Wood is a gas at room temperature.) or (not not (There are 31 days in May.)) or ((4 * -5) >= (1 + 1))) or (((-4 * -9 - 3 * 5) <= (1 ** 1) <= (12 - -4)) and ((-19 - 18) > (8 * 7)))) and ((not (((17 * -20) <= (17 * 0)) and ((1 * 11) != (8 * 20)))) and ((The first Olympic Games of modern era occurred in 1896.) or ((-1 * -9) != (-6 * 7 + -5 * 6)) or ((1938 is a leap year.) or (The human body has 206 bones.))))\nG. not (not not (((-7 - -3) < (-7 * -4 - 9 * -5)) and (not ((3 + 12) == (7 * -12)))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 21927552,
"true_count": 3
},
"seed": 21927552,
"task_id": 621927552,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. 光速比声速快。
B. (((水蒸气在常温下是气体。) or (((菲律宾的货币是越南盾。) or (哥伦比亚的货币是兹罗提。)) and (((-8 * 5 * -1 * 8) == (-2 * 3 * 1 * 6)) or ((1 - -16) > (41 % 5))))) or ((12 % 8) <= (17 * -16)) or (not not ((((-4 - -14) <= (5 * 1 + -2 * 10)) and (第二次世界大战结束发生在1944年。)) and (加拿大位于欧洲。)))) and (not (not (匈牙利的货币是索尔。)))
C. not not (not not (((((6 * -4) <= (5 ** 3)) or ((17 - 1) != (4 * -17))) or (not ((5 * -4 * 4 * -1) != (-3 * 8 - 7 * -2)))) and (((4 * 10 * -6 * -8) <= (10 * -3 * 6 * -4) <= (-19 + 1)) or ((20 + -2) >= (-17 + -15))) and ((not ((-16 - -10) <= (3 ** 1))) or (日本位于南美洲。))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 11203130,
"true_count": 1
},
"question": "下面是几个布尔表达式：\n\nA. 光速比声速快。\nB. (((水蒸气在常温下是气体。) or (((菲律宾的货币是越南盾。) or (哥伦比亚的货币是兹罗提。)) and (((-8 * 5 * -1 * 8) == (-2 * 3 * 1 * 6)) or ((1 - -16) > (41 % 5))))) or ((12 % 8) <= (17 * -16)) or (not not ((((-4 - -14) <= (5 * 1 + -2 * 10)) and (第二次世界大战结束发生在1944年。)) and (加拿大位于欧洲。)))) and (not (not (匈牙利的货币是索尔。)))\nC. not not (not not (((((6 * -4) <= (5 ** 3)) or ((17 - 1) != (4 * -17))) or (not ((5 * -4 * 4 * -1) != (-3 * 8 - 7 * -2)))) and (((4 * 10 * -6 * -8) <= (10 * -3 * 6 * -4) <= (-19 + 1)) or ((20 + -2) >= (-17 + -15))) and ((not ((-16 - -10) <= (3 ** 1))) or (日本位于南美洲。))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 11203130,
"true_count": 1
},
"seed": 11203130,
"task_id": 611203130,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not not (((((3 - -19) <= (0 * -7 + 1 * -6)) and (Alcohol is a solid at room temperature.)) or (The chemical symbol for Uranium is U.)) and (Russia is in Europe.) and (((3 ** 2) != (-12 - -12)) and (Light travels faster than sound.)))
B. (not ((not ((6 * -18) == (19 + 10))) or ((The capital of Mexico is Mexico City.) and (The currency of Philippines is the Peso.)))) and ((not not (Penguins can fly.)) or ((((3 + 17) > (2 ** 2)) or ((10 - 16) >= (-1 - 4))) or (((0 * 10 + -5 * 10) <= (17 % 9) <= (5 ** 3)) and ((9 % 5) > (20 - -2)))))
C. not ((Carbon dioxide is a gas at room temperature.) or ((-6 * -3 + 9 * 7) > (-14 * -13)))
D. not not (((((-15 - -18) < (0 * -2 * -8 * 6)) and ((0 - 5) != (-4 - -5))) or ((10 * 5 + -3 * 5) > (41 % 7))) and (not (Neptune is the 1st planet from the Sun.)) and ((2 + -14) < (-19 - 18)))
E. not not (not ((((18 * -17) >= (-10 * 1 - 5 * 3)) or ((-13 - -1) < (6 * -19) < (1 ** 2))) and (((9 * 1) <= (-10 * 0 + -5 * -9) <= (3 ** 3)) or ((5 * -9 + -9 * 5) != (16 - 4)))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 63804905,
"true_count": 2
},
"question": "Given the following boolean expressions:\n\nA. not not (((((3 - -19) <= (0 * -7 + 1 * -6)) and (Alcohol is a solid at room temperature.)) or (The chemical symbol for Uranium is U.)) and (Russia is in Europe.) and (((3 ** 2) != (-12 - -12)) and (Light travels faster than sound.)))\nB. (not ((not ((6 * -18) == (19 + 10))) or ((The capital of Mexico is Mexico City.) and (The currency of Philippines is the Peso.)))) and ((not not (Penguins can fly.)) or ((((3 + 17) > (2 ** 2)) or ((10 - 16) >= (-1 - 4))) or (((0 * 10 + -5 * 10) <= (17 % 9) <= (5 ** 3)) and ((9 % 5) > (20 - -2)))))\nC. not ((Carbon dioxide is a gas at room temperature.) or ((-6 * -3 + 9 * 7) > (-14 * -13)))\nD. not not (((((-15 - -18) < (0 * -2 * -8 * 6)) and ((0 - 5) != (-4 - -5))) or ((10 * 5 + -3 * 5) > (41 % 7))) and (not (Neptune is the 1st planet from the Sun.)) and ((2 + -14) < (-19 - 18)))\nE. not not (not ((((18 * -17) >= (-10 * 1 - 5 * 3)) or ((-13 - -1) < (6 * -19) < (1 ** 2))) and (((9 * 1) <= (-10 * 0 + -5 * -9) <= (3 ** 3)) or ((5 * -9 + -9 * 5) != (16 - 4)))))\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": 63804905,
"true_count": 2
},
"seed": 63804905,
"task_id": 663804905,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not (not not ((not ((not (The first iPhone was released occurred in 2007.)) and ((2048 is a leap year.) or (World War II began occurred in 1939.)))) and (((-12 * -16) < (15 - -3)) and ((-4 - 12) >= (1 ** 3)) and ((not not (A bear is a mammal.)) or (Steam is a solid at room temperature.)))))
B. not not ((not not (not not (not ((Spiders are insects.) or (2039 is a leap year.))))) and ((not not (((-14 + 19) > (12 * -11)) or ((The chemical symbol for Aluminum is Al.) or (Oxygen is necessary for human survival.)))) or ((((12 * -4) <= (-15 * 10) <= (-13 * 10)) or (not (Nitrogen is a liquid at room temperature.))) and (The 1900 Olympics were held in Paris.) and (not not (The chemical symbol for Carbon is C.)))))
C. (not (not ((((The currency of South Africa is the Krone.) or ((1 - -15) > (13 - -13))) or (((2 ** 1) != (-4 - -1)) or ((-17 + -16) < (-9 * -4 * -6 * 1)))) or (not ((-10 * -9 - 1 * -4) < (1 * 3 * 7 * -2) < (0 - -4))) or ((5 ** 2) != (-13 + -11))))) and ((not not (not not ((13 + 8) < (18 - -12)))) or (not (not ((The chemical symbol for Potassium is K.) or (Uranus is the 7th planet from the Sun.)))))
D. not not (not ((not not ((World War II began occurred in 1939.) and (((16 + 0) <= (16 - 17) <= (4 - 16)) and ((5 * -7) > (-8 + 16))))) or (((There are 31 days in July.) or ((17 * -18) <= (-2 * -6))) or (((11 % 4) != (-9 * 9 - 7 * 7)) or (A kangaroo is a mammal.))) or (not ((The capital of Belgium is Brussels.) and (not not (25 is a perfect square.))))))
E. not (not not (not (((((15 - -17) == (42 % 3)) and ((-2 + 3) > (39 % 8))) and (not (Plants produce oxygen through photosynthesis.))) and (not (((-20 * 4) == (17 - -18)) or ((-3 - -17) != (-4 * -12)))))))
F. not not ((not ((The currency of Hungary is the Yen.) or (not ((11 * -15) > (7 % 7))))) or (not (((((-7 - -7) <= (50 % 6)) and (A beetle is an insect.)) or (((5 % 8) <= (20 * -6) <= (5 ** 2)) or (Neptune is the 8th planet from the Sun.))) and ((not not ((9 * -1) != (3 * -5 * 10 * 2))) or (not ((14 + -6) != (0 * -5 + -7 * -3)))))))
G. not not (((not not (World War II ended occurred in 1945.)) and (((5 + 5) != (4 + -15)) or (Japan is in Asia.))) and (not (not not (((14 * 13) < (-12 - -5) < (0 * 4 + 10 * -8)) and ((20 + 4) >= (0 * -19))))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,B,C,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
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"seed": 14314237,
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"question": "Review these logical expressions:\n\nA. not (not not ((not ((not (The first iPhone was released occurred in 2007.)) and ((2048 is a leap year.) or (World War II began occurred in 1939.)))) and (((-12 * -16) < (15 - -3)) and ((-4 - 12) >= (1 ** 3)) and ((not not (A bear is a mammal.)) or (Steam is a solid at room temperature.)))))\nB. not not ((not not (not not (not ((Spiders are insects.) or (2039 is a leap year.))))) and ((not not (((-14 + 19) > (12 * -11)) or ((The chemical symbol for Aluminum is Al.) or (Oxygen is necessary for human survival.)))) or ((((12 * -4) <= (-15 * 10) <= (-13 * 10)) or (not (Nitrogen is a liquid at room temperature.))) and (The 1900 Olympics were held in Paris.) and (not not (The chemical symbol for Carbon is C.)))))\nC. (not (not ((((The currency of South Africa is the Krone.) or ((1 - -15) > (13 - -13))) or (((2 ** 1) != (-4 - -1)) or ((-17 + -16) < (-9 * -4 * -6 * 1)))) or (not ((-10 * -9 - 1 * -4) < (1 * 3 * 7 * -2) < (0 - -4))) or ((5 ** 2) != (-13 + -11))))) and ((not not (not not ((13 + 8) < (18 - -12)))) or (not (not ((The chemical symbol for Potassium is K.) or (Uranus is the 7th planet from the Sun.)))))\nD. not not (not ((not not ((World War II began occurred in 1939.) and (((16 + 0) <= (16 - 17) <= (4 - 16)) and ((5 * -7) > (-8 + 16))))) or (((There are 31 days in July.) or ((17 * -18) <= (-2 * -6))) or (((11 % 4) != (-9 * 9 - 7 * 7)) or (A kangaroo is a mammal.))) or (not ((The capital of Belgium is Brussels.) and (not not (25 is a perfect square.))))))\nE. not (not not (not (((((15 - -17) == (42 % 3)) and ((-2 + 3) > (39 % 8))) and (not (Plants produce oxygen through photosynthesis.))) and (not (((-20 * 4) == (17 - -18)) or ((-3 - -17) != (-4 * -12)))))))\nF. not not ((not ((The currency of Hungary is the Yen.) or (not ((11 * -15) > (7 % 7))))) or (not (((((-7 - -7) <= (50 % 6)) and (A beetle is an insect.)) or (((5 % 8) <= (20 * -6) <= (5 ** 2)) or (Neptune is the 8th planet from the Sun.))) and ((not not ((9 * -1) != (3 * -5 * 10 * 2))) or (not ((14 + -6) != (0 * -5 + -7 * -3)))))))\nG. not not (((not not (World War II ended occurred in 1945.)) and (((5 + 5) != (4 + -15)) or (Japan is in Asia.))) and (not (not not (((14 * 13) < (-12 - -5) < (0 * 4 + 10 * -8)) and ((20 + 4) >= (0 * -19))))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
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"language": "en",
"num_options": 7,
"seed": 14314237,
"true_count": 4
},
"seed": 14314237,
"task_id": 614314237,
"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. 美国的货币是埃及镑。
B. (((-1 * 15) <= (-17 * 19)) and ((-13 + 12) > (-10 * -10))) and (阿根廷的首都是布宜诺斯艾利斯。)
C. 章鱼有8条腿。
D. not not (肯尼亚的首都是首尔。)
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 54888778,
"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. 美国的货币是埃及镑。\nB. (((-1 * 15) <= (-17 * 19)) and ((-13 + 12) > (-10 * -10))) and (阿根廷的首都是布宜诺斯艾利斯。)\nC. 章鱼有8条腿。\nD. not not (肯尼亚的首都是首尔。)\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": 54888778,
"true_count": 1
},
"seed": 54888778,
"task_id": 654888778,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not (not (not not ((-10 * 9 - -6 * -8) <= (6 - 10) <= (12 + 5))))) or (not not (not ((not not (((3 ** 1) < (6 * 1 * 8 * -6)) or (The capital of Australia is Berlin.))) and ((not ((17 + 15) < (-6 * 6 + -8 * 7))) and (((-7 + -9) <= (-18 * -7)) and (Water is a solid at room temperature.))))))
B. not (not not ((not not (not not (((14 * -3) <= (7 + 20)) and ((18 + 16) != (-10 - -13))))) and ((Christopher Columbus reached America occurred in 1492.) and ((((1 * -3 * 9 * 10) < (7 - -19) < (-7 * -1 * -4 * -1)) or ((3 * 2 - 9 * 2) <= (12 - 12))) and (((-14 - -8) < (-3 + -2) < (5 ** 2)) or (7 is an odd number.))))))
C. not (not not (((The currency of South Korea is the Won.) and (2024 is a leap year.)) or (((not not (The currency of Canada is the Rand.)) and (((18 % 4) == (18 * 14)) or ((-12 + -12) < (5 ** 1)))) and (The 2004 Olympics were held in Athens.))))
D. not ((not (not (((-7 * -9 - -1 * -10) == (-10 - 0)) or (((-14 * 18) >= (-8 * -4)) or (The United States declared independence occurred in 1776.))))) or (not not ((not (not not ((36 % 5) <= (18 % 9)))) or ((-18 + -13) < (1 ** 2)))))
E. not not (not not (((1979 is a leap year.) or ((5 ** 2) > (12 * -20)) or (not (not ((-7 * 3 * -7 * -10) != (-8 * 9 + 5 * 9))))) and (not not ((4 - -16) <= (-10 - 19)))))
F. not ((not not ((Mars is the closest planet to the Sun.) or (((18 * 20) > (1 * -5 - -5 * 4)) and (The currency of South Africa is the Shekel.)))) or (not (not not ((World War I began occurred in 1914.) or (((-15 * 2) <= (13 + -1)) and (The 1908 Olympics were held in Tokyo.))))))
G. not not ((not not (((10 + 7) != (3 ** 3)) or (not not ((Mars is the 4th planet from the Sun.) and (The chemical symbol for Silicon is Sn.))))) or ((((not ((8 + 4) <= (23 % 1))) or ((The chemical symbol for Magnesium is Pb.) and (72 is an odd number.))) or (38 is an even number.)) or ((not not ((Air is a solid at room temperature.) and ((-5 * -7 - 8 * 4) != (39 % 6)))) and (A iguana is a reptile.))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
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"answer": "A,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 66493377,
"true_count": 3
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"question": "Below are several boolean expressions:\n\nA. (not (not (not not ((-10 * 9 - -6 * -8) <= (6 - 10) <= (12 + 5))))) or (not not (not ((not not (((3 ** 1) < (6 * 1 * 8 * -6)) or (The capital of Australia is Berlin.))) and ((not ((17 + 15) < (-6 * 6 + -8 * 7))) and (((-7 + -9) <= (-18 * -7)) and (Water is a solid at room temperature.))))))\nB. not (not not ((not not (not not (((14 * -3) <= (7 + 20)) and ((18 + 16) != (-10 - -13))))) and ((Christopher Columbus reached America occurred in 1492.) and ((((1 * -3 * 9 * 10) < (7 - -19) < (-7 * -1 * -4 * -1)) or ((3 * 2 - 9 * 2) <= (12 - 12))) and (((-14 - -8) < (-3 + -2) < (5 ** 2)) or (7 is an odd number.))))))\nC. not (not not (((The currency of South Korea is the Won.) and (2024 is a leap year.)) or (((not not (The currency of Canada is the Rand.)) and (((18 % 4) == (18 * 14)) or ((-12 + -12) < (5 ** 1)))) and (The 2004 Olympics were held in Athens.))))\nD. not ((not (not (((-7 * -9 - -1 * -10) == (-10 - 0)) or (((-14 * 18) >= (-8 * -4)) or (The United States declared independence occurred in 1776.))))) or (not not ((not (not not ((36 % 5) <= (18 % 9)))) or ((-18 + -13) < (1 ** 2)))))\nE. not not (not not (((1979 is a leap year.) or ((5 ** 2) > (12 * -20)) or (not (not ((-7 * 3 * -7 * -10) != (-8 * 9 + 5 * 9))))) and (not not ((4 - -16) <= (-10 - 19)))))\nF. not ((not not ((Mars is the closest planet to the Sun.) or (((18 * 20) > (1 * -5 - -5 * 4)) and (The currency of South Africa is the Shekel.)))) or (not (not not ((World War I began occurred in 1914.) or (((-15 * 2) <= (13 + -1)) and (The 1908 Olympics were held in Tokyo.))))))\nG. not not ((not not (((10 + 7) != (3 ** 3)) or (not not ((Mars is the 4th planet from the Sun.) and (The chemical symbol for Silicon is Sn.))))) or ((((not ((8 + 4) <= (23 % 1))) or ((The chemical symbol for Magnesium is Pb.) and (72 is an odd number.))) or (38 is an even number.)) or ((not not ((Air is a solid at room temperature.) and ((-5 * -7 - 8 * 4) != (39 % 6)))) and (A iguana is a reptile.))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
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"language": "en",
"num_options": 7,
"seed": 66493377,
"true_count": 3
},
"seed": 66493377,
"task_id": 666493377,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not not ((not ((((14 * 12) != (-18 + -9)) and ((37 % 4) < (5 ** 2))) and (not (The currency of Argentina is the Peso.)))) and (not (not not (not (The chemical symbol for Neon is O.)))))
B. not not (((((The chemical symbol for Hydrogen is U.) and (A pig has 4 legs.)) or ((-18 - 18) != (17 - -2))) and (Oil is a liquid at room temperature.) and (not not (((-9 - -3) < (12 - -16) < (-7 * 2 + 9 * -8)) and ((2 * -6 * -8 * 6) >= (-9 * 1 + -10 * -1))))) or ((not (not ((-9 * 9 + -8 * 9) > (-19 * -2)))) or (The currency of Brazil is the Real.)))
C. ((not ((The chemical symbol for Titanium is He.) or (The Great Wall of China was built in one year.))) and (not not (The chemical symbol for Titanium is Ti.))) or ((not (not not (((2 * 18) <= (4 - 5) <= (4 ** 3)) and ((-5 * 10 - 3 * 4) <= (4 * -4 - -7 * 4))))) and (not (((The capital of Portugal is Lisbon.) or (Neptune is the 3rd planet from the Sun.)) or (((7 * -11) < (-3 * 9 - 8 * 0) < (2 ** 1)) or (Air is a liquid at room temperature.)))))
D. not ((((-17 - 2) <= (10 * 8 - 9 * -9)) or ((not not (The 2024 Olympics were held in Athens.)) and ((3 * 2 - 0 * 1) <= (10 - 15) <= (-3 + -12)))) or ((-12 + 0) >= (10 * -8 - -4 * 6)) or ((not (The currency of Czech Republic is the Koruna.)) and ((not (Ice is a liquid at room temperature.)) and ((The 1972 Olympics were held in Beijing.) and (The currency of Colombia is the Ruble.)))))
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": 5,
"language": "en",
"num_options": 4,
"seed": 51681960,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. not not ((not ((((14 * 12) != (-18 + -9)) and ((37 % 4) < (5 ** 2))) and (not (The currency of Argentina is the Peso.)))) and (not (not not (not (The chemical symbol for Neon is O.)))))\nB. not not (((((The chemical symbol for Hydrogen is U.) and (A pig has 4 legs.)) or ((-18 - 18) != (17 - -2))) and (Oil is a liquid at room temperature.) and (not not (((-9 - -3) < (12 - -16) < (-7 * 2 + 9 * -8)) and ((2 * -6 * -8 * 6) >= (-9 * 1 + -10 * -1))))) or ((not (not ((-9 * 9 + -8 * 9) > (-19 * -2)))) or (The currency of Brazil is the Real.)))\nC. ((not ((The chemical symbol for Titanium is He.) or (The Great Wall of China was built in one year.))) and (not not (The chemical symbol for Titanium is Ti.))) or ((not (not not (((2 * 18) <= (4 - 5) <= (4 ** 3)) and ((-5 * 10 - 3 * 4) <= (4 * -4 - -7 * 4))))) and (not (((The capital of Portugal is Lisbon.) or (Neptune is the 3rd planet from the Sun.)) or (((7 * -11) < (-3 * 9 - 8 * 0) < (2 ** 1)) or (Air is a liquid at room temperature.)))))\nD. not ((((-17 - 2) <= (10 * 8 - 9 * -9)) or ((not not (The 2024 Olympics were held in Athens.)) and ((3 * 2 - 0 * 1) <= (10 - 15) <= (-3 + -12)))) or ((-12 + 0) >= (10 * -8 - -4 * 6)) or ((not (The currency of Czech Republic is the Koruna.)) and ((not (Ice is a liquid at room temperature.)) and ((The 1972 Olympics were held in Beijing.) and (The currency of Colombia is the Ruble.)))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 51681960,
"true_count": 2
},
"seed": 51681960,
"task_id": 651681960,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. not not (not (((6 - -15) < (8 * 7 + 1 * -9)) and (钛的化学符号是Ti。)))
B. (((镍的化学符号是Ni。) and ((2 % 8) >= (0 * -10 - -4 * 5))) and (天王星是距离太阳第7近的行星。)) and (海王星是距离太阳第8近的行星。)
C. (((十二月有31天。) and (1968年奥运会在洛杉矶举办。)) and (not not (人类每只手有五个手指。))) or ((人类每只手有五个手指。) or (not not ((-2 - 13) > (-10 * -2 * 8 * -6))))
D. (not (not (英国的货币是美元。))) or (((欧盟的货币是欧元。) or ((5 ** 3) >= (10 + 1))) or ((-5 * 10 * 9 * -10) == (-12 * -18)))
E. (not not ((-2 * -10 + 2 * 0) < (1 ** 2))) and ((中国长城是在一年内建成的。) and (中国位于亚洲。)) and (((金星是距离太阳第2近的行星。) or (汞在常温下是液体。)) or ((4 * -3 * 5 * 7) < (-10 - 10) < (0 * 0 - 1 * -3)))
F. ((not not ((-4 * -6) == (4 - -18))) or (((7 * 4 - -5 * 7) > (-15 * -14)) and (木头在常温下是液体。))) or (蟑螂是鱼类。) or (((3 ** 3) == (2 * 5 + 9 * -1)) or ((天鹅是昆虫。) and (人体有150块骨头。)))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 84068120,
"true_count": 2
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"question": "考虑以下布尔表达式：\n\nA. not not (not (((6 - -15) < (8 * 7 + 1 * -9)) and (钛的化学符号是Ti。)))\nB. (((镍的化学符号是Ni。) and ((2 % 8) >= (0 * -10 - -4 * 5))) and (天王星是距离太阳第7近的行星。)) and (海王星是距离太阳第8近的行星。)\nC. (((十二月有31天。) and (1968年奥运会在洛杉矶举办。)) and (not not (人类每只手有五个手指。))) or ((人类每只手有五个手指。) or (not not ((-2 - 13) > (-10 * -2 * 8 * -6))))\nD. (not (not (英国的货币是美元。))) or (((欧盟的货币是欧元。) or ((5 ** 3) >= (10 + 1))) or ((-5 * 10 * 9 * -10) == (-12 * -18)))\nE. (not not ((-2 * -10 + 2 * 0) < (1 ** 2))) and ((中国长城是在一年内建成的。) and (中国位于亚洲。)) and (((金星是距离太阳第2近的行星。) or (汞在常温下是液体。)) or ((4 * -3 * 5 * 7) < (-10 - 10) < (0 * 0 - 1 * -3)))\nF. ((not not ((-4 * -6) == (4 - -18))) or (((7 * 4 - -5 * 7) > (-15 * -14)) and (木头在常温下是液体。))) or (蟑螂是鱼类。) or (((3 ** 3) == (2 * 5 + 9 * -1)) or ((天鹅是昆虫。) and (人体有150块骨头。)))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 84068120,
"true_count": 2
},
"seed": 84068120,
"task_id": 684068120,
"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 (锌的化学符号是Zn。))
B. (铜在常温下是气体。) or (not ((-7 * 20) >= (16 + 8))) or (((-2 * -6 - 0 * 6) > (-9 * 9 * 4 * -2)) or (金星是距离太阳第2近的行星。))
C. (not not ((1920年奥运会在慕尼黑举办。) and (912是斐波那契数。))) or (((156是完全平方数。) and (鲸鱼是鱼类。)) or (((-7 * 2 * 0 * -6) <= (-17 + 10)) or ((-17 - 14) < (2 * 3 * -5 * 2) < (4 - -1))))
D. (not ((18 * 8) == (44 % 4))) and (海王星是距离太阳第7近的行星。)
E. not (not ((俄罗斯的货币是卢布。) and (菲律宾的货币是克朗。)))
F. (((50小于等于19。) and ((15 - 4) < (-20 - 20) < (-2 * -2 + 0 * 8))) and (木星是距离太阳第6近的行星。)) and (水星是距离太阳第1近的行星。) and (法国大革命开始发生在1789年。)
G. (((-5 - 14) <= (-3 * 19) <= (4 ** 2)) and ((瑞士的货币是印尼盾。) and (南极洲是最冷的大陆。))) and (((25 % 6) > (-2 + -3)) or (((1 * 2 - 5 * -9) < (2 ** 3)) and (酒精在常温下是液体。)))
H. (((1920年奥运会在罗马举办。) or ((3 ** 3) <= (4 - -15))) and ((莱特兄弟首次飞行发生在1903年。) or (2008年奥运会在北京举办。))) or ((32 % 8) == (3 ** 2)) or (((狗有4条腿。) or (狗有4条腿。)) and ((-4 + 16) != (6 - -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": {
"answer": "A,B,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 93180332,
"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 (锌的化学符号是Zn。))\nB. (铜在常温下是气体。) or (not ((-7 * 20) >= (16 + 8))) or (((-2 * -6 - 0 * 6) > (-9 * 9 * 4 * -2)) or (金星是距离太阳第2近的行星。))\nC. (not not ((1920年奥运会在慕尼黑举办。) and (912是斐波那契数。))) or (((156是完全平方数。) and (鲸鱼是鱼类。)) or (((-7 * 2 * 0 * -6) <= (-17 + 10)) or ((-17 - 14) < (2 * 3 * -5 * 2) < (4 - -1))))\nD. (not ((18 * 8) == (44 % 4))) and (海王星是距离太阳第7近的行星。)\nE. not (not ((俄罗斯的货币是卢布。) and (菲律宾的货币是克朗。)))\nF. (((50小于等于19。) and ((15 - 4) < (-20 - 20) < (-2 * -2 + 0 * 8))) and (木星是距离太阳第6近的行星。)) and (水星是距离太阳第1近的行星。) and (法国大革命开始发生在1789年。)\nG. (((-5 - 14) <= (-3 * 19) <= (4 ** 2)) and ((瑞士的货币是印尼盾。) and (南极洲是最冷的大陆。))) and (((25 % 6) > (-2 + -3)) or (((1 * 2 - 5 * -9) < (2 ** 3)) and (酒精在常温下是液体。)))\nH. (((1920年奥运会在罗马举办。) or ((3 ** 3) <= (4 - -15))) and ((莱特兄弟首次飞行发生在1903年。) or (2008年奥运会在北京举办。))) or ((32 % 8) == (3 ** 2)) or (((狗有4条腿。) or (狗有4条腿。)) and ((-4 + 16) != (6 - -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。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 93180332,
"true_count": 3
},
"seed": 93180332,
"task_id": 693180332,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. ((((not (not ((47 % 8) > (-5 * 4 + 8 * -3)))) or (not not ((钠的化学符号是P。) or ((-5 - 16) <= (3 * -4 + 7 * 6))))) and (not not (((氖的化学符号是S。) or ((2 % 9) >= (-16 * -19))) and ((水星是距离太阳第1近的行星。) and (1928年奥运会在阿姆斯特丹举办。))))) and (not not (((8 * 7 * 7 * 7) > (4 ** 1)) or (((-13 * -3) < (6 * -8 + 8 * -6) < (-18 * -9)) or ((43 % 2) == (-13 - 11)))))) or ((not not (not not ((not not (铅的化学符号是H。)) and (not not ((19 % 3) >= (4 % 10)))))) and (not (((-6 - -13) != (10 - 18)) and (羊是哺乳动物。))))
B. not (((not not ((2085年是闰年。) and (2004年奥运会在巴黎举办。))) and (not (阿根廷位于南美洲。))) and (not not (not not ((8 * 9 * -7 * 6) <= (-3 + -1)))))
C. (not ((((-13 * -12) > (-17 * 9)) or (((第二次世界大战结束发生在1943年。) or (泰坦尼克号沉没发生在1912年。)) and ((海豚是哺乳动物。) and ((-17 - 16) <= (5 * 10 * 9 * -4))))) and ((海王星是距离太阳第8近的行星。) or ((-3 * -9 * 5 * -8) > (9 + 15)) or (((-19 + -1) <= (-20 - 6)) and (((-14 - 6) <= (-6 * 3 + -7 * 9) <= (3 + 2)) or ((-6 * -5 + 8 * -10) >= (-12 * -20))))))) and ((not (not not ((10 % 7) > (-3 * -3)))) or (not (((-5 - -5) < (11 * 19)) and (not not ((8 - -1) == (0 - -6))))))
D. not not (((not (not ((-13 + 14) >= (19 * 4)))) and ((not ((苏联解体发生在1996年。) or (英国位于欧洲。))) and (not not (21能被12整除。)) and (((澳大利亚的首都是堪培拉。) and ((-8 * 4) != (10 * -4))) or (((-4 - -10) < (7 + 5)) and (1931年是闰年。))))) or ((not ((not not ((0 + 2) > (49 % 7))) or (not ((17 % 7) >= (-7 * -4))))) and (((not not ((-4 * 10 - -9 * 1) <= (-12 - -7))) or (((6 + -17) <= (-1 * 4 - -7 * -7)) and (鳄鱼是爬行动物。))) or ((1 * 10) <= (-4 * 6 + -1 * 0)))))
E. not not (not (not not (((十一月有30天。) or ((-8 * 8) == (2 * -6 - 10 * -1))) or ((((17 % 2) >= (-9 * 19)) and (古巴的首都是哈瓦那。)) and ((200是奇数。) and ((-3 + -5) <= (-3 * -7 - 6 * 9) <= (-9 - 5)))))))
F. not ((not (not ((木头在常温下是固体。) and ((银在常温下是固体。) and (韩国的货币是欧元。))))) and (not (not ((钛的化学符号是O。) or (((14 - 20) != (-11 + -6)) or ((14 + -19) <= (3 - -20)))))))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"seed": 33754282,
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},
"question": "给定以下布尔表达式：\n\nA. ((((not (not ((47 % 8) > (-5 * 4 + 8 * -3)))) or (not not ((钠的化学符号是P。) or ((-5 - 16) <= (3 * -4 + 7 * 6))))) and (not not (((氖的化学符号是S。) or ((2 % 9) >= (-16 * -19))) and ((水星是距离太阳第1近的行星。) and (1928年奥运会在阿姆斯特丹举办。))))) and (not not (((8 * 7 * 7 * 7) > (4 ** 1)) or (((-13 * -3) < (6 * -8 + 8 * -6) < (-18 * -9)) or ((43 % 2) == (-13 - 11)))))) or ((not not (not not ((not not (铅的化学符号是H。)) and (not not ((19 % 3) >= (4 % 10)))))) and (not (((-6 - -13) != (10 - 18)) and (羊是哺乳动物。))))\nB. not (((not not ((2085年是闰年。) and (2004年奥运会在巴黎举办。))) and (not (阿根廷位于南美洲。))) and (not not (not not ((8 * 9 * -7 * 6) <= (-3 + -1)))))\nC. (not ((((-13 * -12) > (-17 * 9)) or (((第二次世界大战结束发生在1943年。) or (泰坦尼克号沉没发生在1912年。)) and ((海豚是哺乳动物。) and ((-17 - 16) <= (5 * 10 * 9 * -4))))) and ((海王星是距离太阳第8近的行星。) or ((-3 * -9 * 5 * -8) > (9 + 15)) or (((-19 + -1) <= (-20 - 6)) and (((-14 - 6) <= (-6 * 3 + -7 * 9) <= (3 + 2)) or ((-6 * -5 + 8 * -10) >= (-12 * -20))))))) and ((not (not not ((10 % 7) > (-3 * -3)))) or (not (((-5 - -5) < (11 * 19)) and (not not ((8 - -1) == (0 - -6))))))\nD. not not (((not (not ((-13 + 14) >= (19 * 4)))) and ((not ((苏联解体发生在1996年。) or (英国位于欧洲。))) and (not not (21能被12整除。)) and (((澳大利亚的首都是堪培拉。) and ((-8 * 4) != (10 * -4))) or (((-4 - -10) < (7 + 5)) and (1931年是闰年。))))) or ((not ((not not ((0 + 2) > (49 % 7))) or (not ((17 % 7) >= (-7 * -4))))) and (((not not ((-4 * 10 - -9 * 1) <= (-12 - -7))) or (((6 + -17) <= (-1 * 4 - -7 * -7)) and (鳄鱼是爬行动物。))) or ((1 * 10) <= (-4 * 6 + -1 * 0)))))\nE. not not (not (not not (((十一月有30天。) or ((-8 * 8) == (2 * -6 - 10 * -1))) or ((((17 % 2) >= (-9 * 19)) and (古巴的首都是哈瓦那。)) and ((200是奇数。) and ((-3 + -5) <= (-3 * -7 - 6 * 9) <= (-9 - 5)))))))\nF. not ((not (not ((木头在常温下是固体。) and ((银在常温下是固体。) and (韩国的货币是欧元。))))) and (not (not ((钛的化学符号是O。) or (((14 - 20) != (-11 + -6)) or ((14 + -19) <= (3 - -20)))))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
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"language": "cn",
"num_options": 6,
"seed": 33754282,
"true_count": 2
},
"seed": 33754282,
"task_id": 633754282,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not ((1 ** 3) == (-8 + 15))
B. not (((45 % 7) <= (4 + 4) <= (-1 * 4)) or (not ((18 % 8) == (1 - 4))))
C. ((Chile is in Europe.) or ((46 % 5) >= (-17 * -5))) and ((not ((7 + -11) < (8 * -10 * 4 * 4))) and (The capital of Thailand is New Delhi.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 25042122,
"true_count": 1
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"question": "Examine these expressions:\n\nA. not ((1 ** 3) == (-8 + 15))\nB. not (((45 % 7) <= (4 + 4) <= (-1 * 4)) or (not ((18 % 8) == (1 - 4))))\nC. ((Chile is in Europe.) or ((46 % 5) >= (-17 * -5))) and ((not ((7 + -11) < (8 * -10 * 4 * 4))) and (The capital of Thailand is New Delhi.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 25042122,
"true_count": 1
},
"seed": 25042122,
"task_id": 625042122,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not (not not (not (((((-3 + 11) != (17 * -18)) and ((2 * -13) >= (4 * 1 - 4 * 2))) or ((大象有4条腿。) or (2052年是闰年。))) or ((697是斐波那契数。) or ((十月有31天。) or ((2 ** 3) <= (2 * -4 + -5 * -5) <= (7 + 11)))))))
B. (not not (((((160是奇数。) and (二氧化碳在常温下是气体。)) or (16是质数。)) and ((2013年是闰年。) and ((8 % 3) < (-4 + 15) < (44 % 10))) and ((20 * -3) == (-4 - -16))) or (not (1976年奥运会在亚特兰大举办。)))) and (not not (not not (((not not ((40 % 3) == (-8 - 7))) and ((越南位于亚洲。) and ((14 + 12) == (5 - 0)))) or (not not (美国位于南美洲。)) or (((海王星是距离太阳第8近的行星。) or (1920年奥运会在安特卫普举办。)) or ((-5 * -1 * -2 * 2) <= (1 * 6 + 4 * 0))))))
C. (not not ((not ((((-11 - 18) > (8 - -10)) and ((9 * 5 * -6 * -1) > (-8 * 8))) or ((锌的化学符号是Ca。) and (氧气对人类生存是必需的。)))) and (((((2 * 20) <= (-9 * 8 * -7 * 2)) or ((14 * 15) != (8 * 15))) and ((鲸鱼是哺乳动物。) and ((10 + -17) != (4 * -18)))) or ((62是质数。) and (not not ((9 * -10) >= (-4 + 11))))))) and (not ((not not (水星是距离太阳第1近的行星。)) and (not ((0 - 8) >= (-20 + 20)))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
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"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "cn",
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"seed": 78128734,
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"question": "下面是几个布尔表达式：\n\nA. not (not not (not (((((-3 + 11) != (17 * -18)) and ((2 * -13) >= (4 * 1 - 4 * 2))) or ((大象有4条腿。) or (2052年是闰年。))) or ((697是斐波那契数。) or ((十月有31天。) or ((2 ** 3) <= (2 * -4 + -5 * -5) <= (7 + 11)))))))\nB. (not not (((((160是奇数。) and (二氧化碳在常温下是气体。)) or (16是质数。)) and ((2013年是闰年。) and ((8 % 3) < (-4 + 15) < (44 % 10))) and ((20 * -3) == (-4 - -16))) or (not (1976年奥运会在亚特兰大举办。)))) and (not not (not not (((not not ((40 % 3) == (-8 - 7))) and ((越南位于亚洲。) and ((14 + 12) == (5 - 0)))) or (not not (美国位于南美洲。)) or (((海王星是距离太阳第8近的行星。) or (1920年奥运会在安特卫普举办。)) or ((-5 * -1 * -2 * 2) <= (1 * 6 + 4 * 0))))))\nC. (not not ((not ((((-11 - 18) > (8 - -10)) and ((9 * 5 * -6 * -1) > (-8 * 8))) or ((锌的化学符号是Ca。) and (氧气对人类生存是必需的。)))) and (((((2 * 20) <= (-9 * 8 * -7 * 2)) or ((14 * 15) != (8 * 15))) and ((鲸鱼是哺乳动物。) and ((10 + -17) != (4 * -18)))) or ((62是质数。) and (not not ((9 * -10) >= (-4 + 11))))))) and (not ((not not (水星是距离太阳第1近的行星。)) and (not ((0 - 8) >= (-20 + 20)))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 78128734,
"true_count": 2
},
"seed": 78128734,
"task_id": 678128734,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. (not not ((not not (not (The 1924 Olympics were held in Paris.))) and (The currency of Norway is the Krone.))) or ((not not (not not ((1 + 12) >= (13 - 13)))) and (not (((9 + 3) <= (-4 + 10)) and (Bats are blind.)))) or (((not ((The 1920 Olympics were held in Antwerp.) or (Neptune is the 8th planet from the Sun.))) and (The capital of South Korea is Seoul.)) or (not not (not (((5 * 8 * 6 * 2) > (18 * 11)) or (The chemical symbol for Aluminum is Pb.)))))
B. ((((((12 - 15) < (50 % 4) < (13 % 3)) and (The first iPhone was released occurred in 2007.)) or (((2 * 4 + -10 * -8) <= (-11 - 1)) and (2080 is a leap year.))) or (not not (not ((2 + -7) > (13 + 0))))) or ((not not (A cockroach is a fish.)) and (not not ((A crocodile is a fish.) or ((7 * 11) >= (10 * -4 - 0 * 1)))))) and (not (not not ((The 1932 Olympics were held in Rio de Janeiro.) and (not ((-14 * -11) >= (-7 + -3))))))
C. not not ((not not ((-8 * 2 - -5 * 0) > (6 + 14))) or (((((-7 * -1 * -10 * 2) <= (-7 + -2) <= (17 - 8)) and (The first moon landing occurred in 1969.)) and (not not ((17 * -18) == (15 % 6)))) or ((A cat has 4 legs.) and (The 1908 Olympics were held in London.)) or ((not (1920 is a leap year.)) or ((2094 is a leap year.) or ((21 % 2) < (6 * 5 * -2 * 1))))))
D. not not ((((-4 + 9) >= (4 - 7)) and ((-3 * 16) >= (4 % 5))) or (The capital of India is Moscow.) or (not not ((-13 + 2) <= (-5 * 3))))
E. not not ((((Water is a gas at room temperature.) and (((11 - 7) >= (1 - -3)) and ((44 % 5) > (-2 * -1 - 7 * -10)))) and ((Neptune is the 8th planet from the Sun.) and (((-7 - 2) >= (-2 * -6 - 4 * 3)) and ((-17 + 2) != (-10 * 4 + 8 * -3))))) or (not (not not (The Great Fire of London occurred in 1666.))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 15541385,
"true_count": 3
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"question": "Evaluate each expression below:\n\nA. (not not ((not not (not (The 1924 Olympics were held in Paris.))) and (The currency of Norway is the Krone.))) or ((not not (not not ((1 + 12) >= (13 - 13)))) and (not (((9 + 3) <= (-4 + 10)) and (Bats are blind.)))) or (((not ((The 1920 Olympics were held in Antwerp.) or (Neptune is the 8th planet from the Sun.))) and (The capital of South Korea is Seoul.)) or (not not (not (((5 * 8 * 6 * 2) > (18 * 11)) or (The chemical symbol for Aluminum is Pb.)))))\nB. ((((((12 - 15) < (50 % 4) < (13 % 3)) and (The first iPhone was released occurred in 2007.)) or (((2 * 4 + -10 * -8) <= (-11 - 1)) and (2080 is a leap year.))) or (not not (not ((2 + -7) > (13 + 0))))) or ((not not (A cockroach is a fish.)) and (not not ((A crocodile is a fish.) or ((7 * 11) >= (10 * -4 - 0 * 1)))))) and (not (not not ((The 1932 Olympics were held in Rio de Janeiro.) and (not ((-14 * -11) >= (-7 + -3))))))\nC. not not ((not not ((-8 * 2 - -5 * 0) > (6 + 14))) or (((((-7 * -1 * -10 * 2) <= (-7 + -2) <= (17 - 8)) and (The first moon landing occurred in 1969.)) and (not not ((17 * -18) == (15 % 6)))) or ((A cat has 4 legs.) and (The 1908 Olympics were held in London.)) or ((not (1920 is a leap year.)) or ((2094 is a leap year.) or ((21 % 2) < (6 * 5 * -2 * 1))))))\nD. not not ((((-4 + 9) >= (4 - 7)) and ((-3 * 16) >= (4 % 5))) or (The capital of India is Moscow.) or (not not ((-13 + 2) <= (-5 * 3))))\nE. not not ((((Water is a gas at room temperature.) and (((11 - 7) >= (1 - -3)) and ((44 % 5) > (-2 * -1 - 7 * -10)))) and ((Neptune is the 8th planet from the Sun.) and (((-7 - 2) >= (-2 * -6 - 4 * 3)) and ((-17 + 2) != (-10 * 4 + 8 * -3))))) or (not (not not (The Great Fire of London occurred in 1666.))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
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"language": "en",
"num_options": 5,
"seed": 15541385,
"true_count": 3
},
"seed": 15541385,
"task_id": 615541385,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not not ((not not (Mercury is the 1st planet from the Sun.)) and (((-11 + -11) >= (3 ** 1)) and (Mars is the 5th planet from the Sun.)))
B. ((7 + 8) > (5 * -1)) and ((((1 + -13) >= (-6 * -5 - 5 * 6)) or ((9 * -9 - -6 * -2) > (-4 * -1 + -9 * 5))) or ((Mercury is a liquid at room temperature.) and ((2 * -3 + -6 * 7) < (-14 + 7))))
C. ((A day on Earth is 24 hours.) and (((1 + 2) <= (20 * -6)) and ((-11 * -16) <= (-8 - 8) <= (-18 + -9)))) or (not ((17 - -4) > (3 * 16))) or ((0 * -1 + 10 * -3) < (9 * -10 * 0 * 1) < (-3 * -5 * 9 * 8))
D. (((1925 is a leap year.) or ((5 ** 2) < (40 % 4))) and (The chemical symbol for Potassium is Ti.)) or ((The currency of Chile is the Peso.) or (2050 is a leap year.)) or ((not not ((-12 - 14) == (1 + -4))) or (The capital of Russia is Canberra.))
E. not ((-2 * 2 + -2 * -3) < (0 - 20) < (49 % 9))
F. (((South Africa is in Africa.) and ((19 * 20) > (11 % 6))) and (not ((8 * 9) > (-15 + -19)))) and ((not not (Egypt is in Africa.)) and (892 is a Fibonacci number.))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 10524391,
"true_count": 4
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"question": "Below are several boolean expressions:\n\nA. not not ((not not (Mercury is the 1st planet from the Sun.)) and (((-11 + -11) >= (3 ** 1)) and (Mars is the 5th planet from the Sun.)))\nB. ((7 + 8) > (5 * -1)) and ((((1 + -13) >= (-6 * -5 - 5 * 6)) or ((9 * -9 - -6 * -2) > (-4 * -1 + -9 * 5))) or ((Mercury is a liquid at room temperature.) and ((2 * -3 + -6 * 7) < (-14 + 7))))\nC. ((A day on Earth is 24 hours.) and (((1 + 2) <= (20 * -6)) and ((-11 * -16) <= (-8 - 8) <= (-18 + -9)))) or (not ((17 - -4) > (3 * 16))) or ((0 * -1 + 10 * -3) < (9 * -10 * 0 * 1) < (-3 * -5 * 9 * 8))\nD. (((1925 is a leap year.) or ((5 ** 2) < (40 % 4))) and (The chemical symbol for Potassium is Ti.)) or ((The currency of Chile is the Peso.) or (2050 is a leap year.)) or ((not not ((-12 - 14) == (1 + -4))) or (The capital of Russia is Canberra.))\nE. not ((-2 * 2 + -2 * -3) < (0 - 20) < (49 % 9))\nF. (((South Africa is in Africa.) and ((19 * 20) > (11 % 6))) and (not ((8 * 9) > (-15 + -19)))) and ((not not (Egypt is in Africa.)) and (892 is a Fibonacci number.))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 10524391,
"true_count": 4
},
"seed": 10524391,
"task_id": 610524391,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (((-13 + -9) <= (-11 + -19) <= (4 ** 2)) and ((0 + 18) > (-7 * 1 + -10 * -5))) or (((2008年奥运会在北京举办。) and ((2 * 1) <= (-17 - -7))) and ((17 - -9) >= (43 % 6)))
B. ((((-9 + -19) <= (-20 - -4) <= (-17 + -16)) and ((4 * 4 + -1 * 0) >= (-12 + 6))) and (((-13 + -7) != (11 % 9)) or (722是斐波那契数。))) and (not not (((11 + 2) < (-9 * 3 - -6 * -4)) or (挪威的首都是奥斯陆。)))
C. not (((钻石在常温下是固体。) or ((10 * -12) >= (9 + 5))) and (((5 ** 1) != (3 - 3)) or (锡的化学符号是Pt。)))
D. not not (not not (((-20 * -4) >= (-17 + -9)) or (十一月有28天。)))
E. (((银在常温下是固体。) or (9小于等于67。)) or ((0 * -4) <= (-16 + 6) <= (-2 + 1))) and ((-9 * -5 - -1 * -10) != (-6 * 4 + -2 * 8))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 34061152,
"true_count": 2
},
"question": "考虑以下布尔表达式：\n\nA. (((-13 + -9) <= (-11 + -19) <= (4 ** 2)) and ((0 + 18) > (-7 * 1 + -10 * -5))) or (((2008年奥运会在北京举办。) and ((2 * 1) <= (-17 - -7))) and ((17 - -9) >= (43 % 6)))\nB. ((((-9 + -19) <= (-20 - -4) <= (-17 + -16)) and ((4 * 4 + -1 * 0) >= (-12 + 6))) and (((-13 + -7) != (11 % 9)) or (722是斐波那契数。))) and (not not (((11 + 2) < (-9 * 3 - -6 * -4)) or (挪威的首都是奥斯陆。)))\nC. not (((钻石在常温下是固体。) or ((10 * -12) >= (9 + 5))) and (((5 ** 1) != (3 - 3)) or (锡的化学符号是Pt。)))\nD. not not (not not (((-20 * -4) >= (-17 + -9)) or (十一月有28天。)))\nE. (((银在常温下是固体。) or (9小于等于67。)) or ((0 * -4) <= (-16 + 6) <= (-2 + 1))) and ((-9 * -5 - -1 * -10) != (-6 * 4 + -2 * 8))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 34061152,
"true_count": 2
},
"seed": 34061152,
"task_id": 634061152,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((-6 * 4) <= (-16 + 14)) or ((32 % 9) < (6 - 16))
B. (((九月有28天。) and ((12 * 12) >= (31 % 8))) and ((新西兰位于大洋洲。) and (墨西哥的首都是布加勒斯特。))) and (((8 * -2 + -9 * 0) == (5 ** 3)) and (现代奥运会首届举办发生在1896年。))
C. (not ((水在海平面上的沸点是100摄氏度。) or ((17 % 8) > (5 ** 2)))) and (not not (第二次世界大战开始发生在1938年。)) and ((大象有4条腿。) or (沙特阿拉伯位于亚洲。))
D. not not (蝙蝠是瞎的。)
E. ((not not (加拿大的货币是越南盾。)) and ((意大利位于欧洲。) or (氦气在常温下是气体。))) or (9的平方根是1。) or (海王星是距离太阳第2近的行星。)
F. ((日本的货币是日元。) and ((声音在真空中传播更快。) or ((29 % 8) < (-15 * 8)))) and (((-9 * 2 * 0 * 2) == (2 * 7 + -6 * 0)) and (酒精在常温下是液体。))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 92202384,
"true_count": 1
},
"question": "下面是几个布尔表达式：\n\nA. ((-6 * 4) <= (-16 + 14)) or ((32 % 9) < (6 - 16))\nB. (((九月有28天。) and ((12 * 12) >= (31 % 8))) and ((新西兰位于大洋洲。) and (墨西哥的首都是布加勒斯特。))) and (((8 * -2 + -9 * 0) == (5 ** 3)) and (现代奥运会首届举办发生在1896年。))\nC. (not ((水在海平面上的沸点是100摄氏度。) or ((17 % 8) > (5 ** 2)))) and (not not (第二次世界大战开始发生在1938年。)) and ((大象有4条腿。) or (沙特阿拉伯位于亚洲。))\nD. not not (蝙蝠是瞎的。)\nE. ((not not (加拿大的货币是越南盾。)) and ((意大利位于欧洲。) or (氦气在常温下是气体。))) or (9的平方根是1。) or (海王星是距离太阳第2近的行星。)\nF. ((日本的货币是日元。) and ((声音在真空中传播更快。) or ((29 % 8) < (-15 * 8)))) and (((-9 * 2 * 0 * 2) == (2 * 7 + -6 * 0)) and (酒精在常温下是液体。))\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": 3,
"language": "cn",
"num_options": 6,
"seed": 92202384,
"true_count": 1
},
"seed": 92202384,
"task_id": 692202384,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (-14 * 12) < (-17 * -14)
B. (((-5 + -2) >= (20 * 4)) and ((12 * -3) != (9 * 8 + 4 * 10))) and ((-20 - -17) >= (10 + 18))
C. (((11 + -1) == (3 - 1)) and (氯的化学符号是Cl。)) and ((4 ** 3) != (-18 - 12))
D. (((9 - 12) <= (-17 * 4)) and (20是偶数。)) or ((龙虾有0条腿。) or ((13 - -8) <= (3 + -4)))
E. (英国的货币是英镑。) and (马来西亚的货币是瑞士法郎。)
F. (2是完全平方数。) and (加拿大位于亚洲。)
G. not (not (汞在常温下是气体。))
H. (2 * -7 - -8 * -3) > (-10 * 0 + 9 * -8)
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,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 3441425,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. (-14 * 12) < (-17 * -14)\nB. (((-5 + -2) >= (20 * 4)) and ((12 * -3) != (9 * 8 + 4 * 10))) and ((-20 - -17) >= (10 + 18))\nC. (((11 + -1) == (3 - 1)) and (氯的化学符号是Cl。)) and ((4 ** 3) != (-18 - 12))\nD. (((9 - 12) <= (-17 * 4)) and (20是偶数。)) or ((龙虾有0条腿。) or ((13 - -8) <= (3 + -4)))\nE. (英国的货币是英镑。) and (马来西亚的货币是瑞士法郎。)\nF. (2是完全平方数。) and (加拿大位于亚洲。)\nG. not (not (汞在常温下是气体。))\nH. (2 * -7 - -8 * -3) > (-10 * 0 + 9 * -8)\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 3441425,
"true_count": 2
},
"seed": 3441425,
"task_id": 603441425,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. ((((3 - -9) >= (-2 - -16)) and (((3 ** 2) >= (-12 + -1)) and (not ((21 % 2) >= (12 * 0))))) or (not not (((第一次世界大战开始发生在1914年。) or (猫有4条腿。)) and (((-7 + 8) > (8 * -6 - 6 * -3)) and (哥伦比亚位于南美洲。))))) or (((not not (((2 ** 2) > (-10 * -5 - -10 * 9)) or (第二次世界大战结束发生在1945年。))) and ((-15 - -15) > (9 + 3))) and (not not ((3 - -11) < (-3 * -1 - -4 * -2) < (-20 * -10))) and (not not ((((-1 * -8 - -9 * -2) == (38 % 2)) and (海王星是距离太阳第1近的行星。)) or (((-2 - -3) < (-5 - 16) < (31 % 9)) and (瑞典的货币是比索。)))))
B. (not (((14 % 4) != (-10 * -20)) and (1992年奥运会在巴塞罗那举办。))) and ((not not ((声音在真空中传播更快。) and ((天王星是距离太阳第7近的行星。) and (地球是距离太阳第3近的行星。)))) and (146是奇数。) and (not ((((-15 - -12) < (10 - 0) < (2 - -14)) or (219是斐波那契数。)) or (((0 * -7) >= (-4 * -7 + 6 * -2)) or (匈牙利的货币是福林。)))))
C. (not (((挪威的首都是奥斯陆。) and (not not (海王星是距离太阳第4近的行星。))) or ((印度位于欧洲。) and (2004年奥运会在雅典举办。)) or (not not ((-2 * 7 + 9 * 7) == (45 % 4))))) or (((not not (not ((16 + -1) != (9 * -1 * 8 * -6)))) and (not (1912年奥运会在赫尔辛基举办。)) and ((木头在常温下是液体。) or ((43是斐波那契数。) or (现代奥运会首届举办发生在1891年。)))) and ((not not ((9 * 4 + 3 * 10) <= (-6 * 7))) or ((9 * -2 - -10 * 5) >= (5 - -10))) and ((((土耳其的首都是基辅。) or (希腊的首都是圣地亚哥。)) and (((3 ** 3) >= (5 * -5 * 2 * -4)) or (秘鲁的货币是索尔。))) and (泰国的货币是埃及镑。)))
D. (((泰国的货币是泰铢。) or ((泰国的首都是布鲁塞尔。) or ((0 * -9 + 8 * 0) < (11 % 8))) or ((((-13 + -19) < (0 * 3 - 7 * -1)) or (人体有206块骨头。)) or ((1936年奥运会在柏林举办。) or ((21 % 4) < (5 * 1 - 5 * -9))))) or (not (人类有三个肺。))) and (((((14 * 4) <= (-6 + -9)) or (not (1904年奥运会在圣路易斯举办。))) and (not not ((17 - -1) != (-9 * -6 - -6 * -4)))) and ((中国长城是在一年内建成的。) and (二氧化碳在常温下是固体。)))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 33939306,
"true_count": 2
},
"question": "考虑以下布尔表达式：\n\nA. ((((3 - -9) >= (-2 - -16)) and (((3 ** 2) >= (-12 + -1)) and (not ((21 % 2) >= (12 * 0))))) or (not not (((第一次世界大战开始发生在1914年。) or (猫有4条腿。)) and (((-7 + 8) > (8 * -6 - 6 * -3)) and (哥伦比亚位于南美洲。))))) or (((not not (((2 ** 2) > (-10 * -5 - -10 * 9)) or (第二次世界大战结束发生在1945年。))) and ((-15 - -15) > (9 + 3))) and (not not ((3 - -11) < (-3 * -1 - -4 * -2) < (-20 * -10))) and (not not ((((-1 * -8 - -9 * -2) == (38 % 2)) and (海王星是距离太阳第1近的行星。)) or (((-2 - -3) < (-5 - 16) < (31 % 9)) and (瑞典的货币是比索。)))))\nB. (not (((14 % 4) != (-10 * -20)) and (1992年奥运会在巴塞罗那举办。))) and ((not not ((声音在真空中传播更快。) and ((天王星是距离太阳第7近的行星。) and (地球是距离太阳第3近的行星。)))) and (146是奇数。) and (not ((((-15 - -12) < (10 - 0) < (2 - -14)) or (219是斐波那契数。)) or (((0 * -7) >= (-4 * -7 + 6 * -2)) or (匈牙利的货币是福林。)))))\nC. (not (((挪威的首都是奥斯陆。) and (not not (海王星是距离太阳第4近的行星。))) or ((印度位于欧洲。) and (2004年奥运会在雅典举办。)) or (not not ((-2 * 7 + 9 * 7) == (45 % 4))))) or (((not not (not ((16 + -1) != (9 * -1 * 8 * -6)))) and (not (1912年奥运会在赫尔辛基举办。)) and ((木头在常温下是液体。) or ((43是斐波那契数。) or (现代奥运会首届举办发生在1891年。)))) and ((not not ((9 * 4 + 3 * 10) <= (-6 * 7))) or ((9 * -2 - -10 * 5) >= (5 - -10))) and ((((土耳其的首都是基辅。) or (希腊的首都是圣地亚哥。)) and (((3 ** 3) >= (5 * -5 * 2 * -4)) or (秘鲁的货币是索尔。))) and (泰国的货币是埃及镑。)))\nD. (((泰国的货币是泰铢。) or ((泰国的首都是布鲁塞尔。) or ((0 * -9 + 8 * 0) < (11 % 8))) or ((((-13 + -19) < (0 * 3 - 7 * -1)) or (人体有206块骨头。)) or ((1936年奥运会在柏林举办。) or ((21 % 4) < (5 * 1 - 5 * -9))))) or (not (人类有三个肺。))) and (((((14 * 4) <= (-6 + -9)) or (not (1904年奥运会在圣路易斯举办。))) and (not not ((17 - -1) != (-9 * -6 - -6 * -4)))) and ((中国长城是在一年内建成的。) and (二氧化碳在常温下是固体。)))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 33939306,
"true_count": 2
},
"seed": 33939306,
"task_id": 633939306,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((((6 * 19) > (7 - 0)) or (not not (碳的化学符号是C。))) and (not ((芬兰的首都是赫尔辛基。) or ((12 - -17) != (-16 * -2))))) and (not (((地球绕太阳运转。) and ((-13 * 3) > (30 % 3))) or (not not ((-18 - 2) == (10 * -9)))))) and (((((58是偶数。) and (印度的货币是卢比。)) or ((南非位于非洲。) and (猫头鹰是昆虫。))) and (not ((384是斐波那契数。) and (168是奇数。)))) and ((5 * -10 - 4 * -5) == (-18 + -9)) and (not ((((11 - -19) > (-7 - 20)) and (美国的货币是美元。)) or (((-4 * 3) <= (9 * 17) <= (-7 * 1 * 7 * 4)) or (1976年奥运会在巴黎举办。)))))
B. not (((2004年奥运会在斯德哥尔摩举办。) or ((新西兰位于欧洲。) or ((水蒸气在常温下是气体。) and ((2 ** 3) <= (-15 * -10) <= (40 % 9))))) or (((((-18 * 16) < (-1 * 1 + -8 * 5)) and ((17 * -6) != (5 ** 1))) and (((19 - 17) <= (-19 * -11)) or (锰的化学符号是Pt。))) or (泰坦尼克号沉没发生在1912年。) or (((-19 * 2) == (9 + 18)) and (苏联解体发生在1989年。))))
C. not (not not (not not ((((-14 + -13) <= (1 * 4)) or ((2 % 3) < (-1 * -15))) and ((3 ** 3) == (24 % 4)))))
D. not ((not (((法国大革命开始发生在1787年。) or ((-7 * -10 - 9 * 3) <= (0 - -12))) and (((43 % 10) < (4 ** 3) < (5 * 8 + 8 * -4)) or (欧盟的货币是欧元。)))) or ((not not (not not (智利的货币是克朗。))) and (((7 - 7) >= (5 - 4)) or (奥地利的首都是维也纳。)) and (摩洛哥的首都是利雅得。)))
E. not (not not (not ((not (油在常温下是固体。)) and ((-1 - -9) != (-11 + -12)))))
F. ((not (第二次世界大战开始发生在1939年。)) and (not not (not not ((12 + 5) < (-6 + 13) < (-9 * -7 - 7 * -3)))) and (((((19 + -17) != (16 + 16)) or (土星是距离太阳第6近的行星。)) or (not (德国的首都是赫尔辛基。))) or ((not not ((0 * -7 + 2 * 6) == (-7 * 7))) or (((7 * 8) >= (-5 * -10 + -6 * 0)) and ((-9 * 14) > (-8 - -6)))))) or ((((-4 - -9) < (9 * -4 + -5 * 8)) or ((((6 - 20) == (-4 * 3 + 10 * -2)) or (铀的化学符号是Ne。)) and (((13 - 6) != (-5 + 0)) or (俄罗斯位于南美洲。)))) and (not not (欧盟的货币是欧元。)))
G. (((not ((五月有28天。) or (哥伦布到达美洲发生在1482年。))) or (not not ((8 - -14) <= (15 * 0))) or (((钠的化学符号是Ne。) or (氮的化学符号是N。)) or (not (摩洛哥位于非洲。)))) or ((海王星是距离太阳第8近的行星。) or ((((-1 + -10) <= (10 * -3)) and (1936年奥运会在柏林举办。)) or (((-4 * -14) <= (-4 * -1)) and ((-10 * 6 - -3 * -7) > (8 - 8)))))) and ((not (((9 * -5 * 3 * 0) <= (2 ** 2)) or ((天王星是距离太阳第7近的行星。) or (墨西哥位于北美洲。)))) or ((((10 - 15) <= (-3 * 0 + 4 * 9)) or (not (泰国位于亚洲。))) and (英国位于欧洲。)))
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": "C,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 8381750,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. (((((6 * 19) > (7 - 0)) or (not not (碳的化学符号是C。))) and (not ((芬兰的首都是赫尔辛基。) or ((12 - -17) != (-16 * -2))))) and (not (((地球绕太阳运转。) and ((-13 * 3) > (30 % 3))) or (not not ((-18 - 2) == (10 * -9)))))) and (((((58是偶数。) and (印度的货币是卢比。)) or ((南非位于非洲。) and (猫头鹰是昆虫。))) and (not ((384是斐波那契数。) and (168是奇数。)))) and ((5 * -10 - 4 * -5) == (-18 + -9)) and (not ((((11 - -19) > (-7 - 20)) and (美国的货币是美元。)) or (((-4 * 3) <= (9 * 17) <= (-7 * 1 * 7 * 4)) or (1976年奥运会在巴黎举办。)))))\nB. not (((2004年奥运会在斯德哥尔摩举办。) or ((新西兰位于欧洲。) or ((水蒸气在常温下是气体。) and ((2 ** 3) <= (-15 * -10) <= (40 % 9))))) or (((((-18 * 16) < (-1 * 1 + -8 * 5)) and ((17 * -6) != (5 ** 1))) and (((19 - 17) <= (-19 * -11)) or (锰的化学符号是Pt。))) or (泰坦尼克号沉没发生在1912年。) or (((-19 * 2) == (9 + 18)) and (苏联解体发生在1989年。))))\nC. not (not not (not not ((((-14 + -13) <= (1 * 4)) or ((2 % 3) < (-1 * -15))) and ((3 ** 3) == (24 % 4)))))\nD. not ((not (((法国大革命开始发生在1787年。) or ((-7 * -10 - 9 * 3) <= (0 - -12))) and (((43 % 10) < (4 ** 3) < (5 * 8 + 8 * -4)) or (欧盟的货币是欧元。)))) or ((not not (not not (智利的货币是克朗。))) and (((7 - 7) >= (5 - 4)) or (奥地利的首都是维也纳。)) and (摩洛哥的首都是利雅得。)))\nE. not (not not (not ((not (油在常温下是固体。)) and ((-1 - -9) != (-11 + -12)))))\nF. ((not (第二次世界大战开始发生在1939年。)) and (not not (not not ((12 + 5) < (-6 + 13) < (-9 * -7 - 7 * -3)))) and (((((19 + -17) != (16 + 16)) or (土星是距离太阳第6近的行星。)) or (not (德国的首都是赫尔辛基。))) or ((not not ((0 * -7 + 2 * 6) == (-7 * 7))) or (((7 * 8) >= (-5 * -10 + -6 * 0)) and ((-9 * 14) > (-8 - -6)))))) or ((((-4 - -9) < (9 * -4 + -5 * 8)) or ((((6 - 20) == (-4 * 3 + 10 * -2)) or (铀的化学符号是Ne。)) and (((13 - 6) != (-5 + 0)) or (俄罗斯位于南美洲。)))) and (not not (欧盟的货币是欧元。)))\nG. (((not ((五月有28天。) or (哥伦布到达美洲发生在1482年。))) or (not not ((8 - -14) <= (15 * 0))) or (((钠的化学符号是Ne。) or (氮的化学符号是N。)) or (not (摩洛哥位于非洲。)))) or ((海王星是距离太阳第8近的行星。) or ((((-1 + -10) <= (10 * -3)) and (1936年奥运会在柏林举办。)) or (((-4 * -14) <= (-4 * -1)) and ((-10 * 6 - -3 * -7) > (8 - 8)))))) and ((not (((9 * -5 * 3 * 0) <= (2 ** 2)) or ((天王星是距离太阳第7近的行星。) or (墨西哥位于北美洲。)))) or ((((10 - 15) <= (-3 * 0 + 4 * 9)) or (not (泰国位于亚洲。))) and (英国位于欧洲。)))\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": 5,
"language": "cn",
"num_options": 7,
"seed": 8381750,
"true_count": 3
},
"seed": 8381750,
"task_id": 608381750,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. ((not not (not not (not not (The capital of Venezuela is Jakarta.)))) or ((The Great Wall of China was built in one year.) or (not ((-11 - -1) != (-10 * -15))) or (not not (The capital of France is Paris.)))) and ((not (((7 + -14) > (-4 * -10)) or (not (A cat has 4 legs.)))) and (not not ((not not ((4 * -5 - 0 * 7) <= (8 * -2 * -3 * -10))) and ((1979 is a leap year.) and ((2 ** 1) <= (4 + 8))))))
B. not not (((((-5 * -1 - -8 * -7) != (47 % 4)) and (Nitrogen is a gas at room temperature.)) or (not (The currency of Denmark is the Sol.))) and ((4 % 4) < (-3 * 6 + -10 * -5)) and (not ((22 % 5) == (-17 * -3))))
C. not (((((-12 * -9) < (31 % 3)) and (not not (United States is in Oceania.))) or ((((-5 * -7 * 5 * 8) > (3 ** 2)) or (The 2024 Olympics were held in Paris.)) or (((13 + 0) == (24 % 2)) or (5 is a perfect square.)))) and (((((2 ** 1) < (19 % 5)) or ((-1 * -3 + 10 * -5) <= (-18 * -15))) and (not ((10 * -5 - 2 * 0) < (-4 + -17) < (5 ** 2)))) and (not not ((-2 - -18) < (6 * 7 + -9 * -7)))))
D. not (not not (((A day on Earth is 24 hours.) or (((11 - -1) > (-15 + -1)) or (Indonesia is in Asia.))) or (The currency of United Kingdom is the Pound.) or (Oxygen is a solid at room temperature.)))
E. not not (((((13 - 14) < (1 ** 1)) and (A spider has 8 legs.)) and ((((-5 * 3) <= (-14 - 10)) or (The chemical symbol for Potassium is K.)) or ((The first moon landing occurred in 1969.) and ((-15 + -9) > (2 ** 1))))) or (((Mercury is the 1st planet from the Sun.) and ((-9 * 6 * 5 * -7) < (3 + -14) < (19 + 1))) or (37 is divisible by 11.) or (((The capital of Malaysia is Kuala Lumpur.) or (The French Revolution began occurred in 1789.)) or (not (312 is a Fibonacci number.)))))
F. (not (not not (((-3 * 6 + -1 * 7) < (14 % 5)) and ((7 * 10) < (-17 * -4) < (-6 + 2))))) and (not not (not not ((The chemical symbol for Potassium is Cr.) or (not (The currency of Hungary is the Forint.)))))
G. not not (not (not not (((Silver is a solid at room temperature.) and (237 is a perfect square.)) or (not not ((-14 + -11) > (-17 * -16))))))
H. not not (not (((((4 % 6) <= (-3 * 8 + -8 * -5)) and ((0 - -3) >= (42 % 4))) or (not (Nitrogen is a gas at room temperature.))) or (The United States declared independence occurred in 1776.)))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 58383843,
"true_count": 4
},
"question": "Consider the following logical expressions:\n\nA. ((not not (not not (not not (The capital of Venezuela is Jakarta.)))) or ((The Great Wall of China was built in one year.) or (not ((-11 - -1) != (-10 * -15))) or (not not (The capital of France is Paris.)))) and ((not (((7 + -14) > (-4 * -10)) or (not (A cat has 4 legs.)))) and (not not ((not not ((4 * -5 - 0 * 7) <= (8 * -2 * -3 * -10))) and ((1979 is a leap year.) and ((2 ** 1) <= (4 + 8))))))\nB. not not (((((-5 * -1 - -8 * -7) != (47 % 4)) and (Nitrogen is a gas at room temperature.)) or (not (The currency of Denmark is the Sol.))) and ((4 % 4) < (-3 * 6 + -10 * -5)) and (not ((22 % 5) == (-17 * -3))))\nC. not (((((-12 * -9) < (31 % 3)) and (not not (United States is in Oceania.))) or ((((-5 * -7 * 5 * 8) > (3 ** 2)) or (The 2024 Olympics were held in Paris.)) or (((13 + 0) == (24 % 2)) or (5 is a perfect square.)))) and (((((2 ** 1) < (19 % 5)) or ((-1 * -3 + 10 * -5) <= (-18 * -15))) and (not ((10 * -5 - 2 * 0) < (-4 + -17) < (5 ** 2)))) and (not not ((-2 - -18) < (6 * 7 + -9 * -7)))))\nD. not (not not (((A day on Earth is 24 hours.) or (((11 - -1) > (-15 + -1)) or (Indonesia is in Asia.))) or (The currency of United Kingdom is the Pound.) or (Oxygen is a solid at room temperature.)))\nE. not not (((((13 - 14) < (1 ** 1)) and (A spider has 8 legs.)) and ((((-5 * 3) <= (-14 - 10)) or (The chemical symbol for Potassium is K.)) or ((The first moon landing occurred in 1969.) and ((-15 + -9) > (2 ** 1))))) or (((Mercury is the 1st planet from the Sun.) and ((-9 * 6 * 5 * -7) < (3 + -14) < (19 + 1))) or (37 is divisible by 11.) or (((The capital of Malaysia is Kuala Lumpur.) or (The French Revolution began occurred in 1789.)) or (not (312 is a Fibonacci number.)))))\nF. (not (not not (((-3 * 6 + -1 * 7) < (14 % 5)) and ((7 * 10) < (-17 * -4) < (-6 + 2))))) and (not not (not not ((The chemical symbol for Potassium is Cr.) or (not (The currency of Hungary is the Forint.)))))\nG. not not (not (not not (((Silver is a solid at room temperature.) and (237 is a perfect square.)) or (not not ((-14 + -11) > (-17 * -16))))))\nH. not not (not (((((4 % 6) <= (-3 * 8 + -8 * -5)) and ((0 - -3) >= (42 % 4))) or (not (Nitrogen is a gas at room temperature.))) or (The United States declared independence occurred in 1776.)))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 58383843,
"true_count": 4
},
"seed": 58383843,
"task_id": 658383843,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. not not (not not (not not (((not (63能被12整除。)) or (新西兰的货币是新西兰元。)) and (((-13 + -11) >= (33 % 4)) or ((14 - 1) <= (-10 - 1) <= (17 + 17))) and (((金的化学符号是Au。) and (比利时的首都是布鲁塞尔。)) or (not not (植物通过光合作用产生氧气。))))))
B. not ((((not not (鲨鱼是哺乳动物。)) and (not (not not (鸟有2条腿。)))) and (((((-5 * -7 - 9 * -3) != (4 ** 1)) or ((14 + -10) == (-5 - -14))) and (鲨鱼是哺乳动物。)) or (not not (火烈鸟是鸟类。)))) or ((((木星是距离太阳第5近的行星。) and (二氧化碳在常温下是液体。)) or ((-12 + 8) == (1 * 5 - -5 * 6))) or (not (光速约为每秒30万公里。))))
C. not not (((not not ((9 * -1 + 4 * -6) > (-19 - 18))) and (((3 ** 2) <= (15 * 7)) or (尼日利亚位于亚洲。))) and (((not not ((4 * 5 + 7 * -8) <= (-1 + 18))) or (((5 + 19) > (-6 - -7)) and ((-6 * 15) <= (-19 - -11) <= (13 % 1)))) or (not (40能被8整除。))) and (not not ((((-4 * 4 + -10 * -1) < (7 - 11)) or (((2 * 0 + 0 * -9) == (-4 * -8 + -1 * -5)) or (2000年奥运会在雅典举办。))) and ((二氧化碳在常温下是固体。) or ((4 ** 2) == (5 * -9 - 4 * 9))) and (阿根廷的货币是卢比。))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 9715126,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. not not (not not (not not (((not (63能被12整除。)) or (新西兰的货币是新西兰元。)) and (((-13 + -11) >= (33 % 4)) or ((14 - 1) <= (-10 - 1) <= (17 + 17))) and (((金的化学符号是Au。) and (比利时的首都是布鲁塞尔。)) or (not not (植物通过光合作用产生氧气。))))))\nB. not ((((not not (鲨鱼是哺乳动物。)) and (not (not not (鸟有2条腿。)))) and (((((-5 * -7 - 9 * -3) != (4 ** 1)) or ((14 + -10) == (-5 - -14))) and (鲨鱼是哺乳动物。)) or (not not (火烈鸟是鸟类。)))) or ((((木星是距离太阳第5近的行星。) and (二氧化碳在常温下是液体。)) or ((-12 + 8) == (1 * 5 - -5 * 6))) or (not (光速约为每秒30万公里。))))\nC. not not (((not not ((9 * -1 + 4 * -6) > (-19 - 18))) and (((3 ** 2) <= (15 * 7)) or (尼日利亚位于亚洲。))) and (((not not ((4 * 5 + 7 * -8) <= (-1 + 18))) or (((5 + 19) > (-6 - -7)) and ((-6 * 15) <= (-19 - -11) <= (13 % 1)))) or (not (40能被8整除。))) and (not not ((((-4 * 4 + -10 * -1) < (7 - 11)) or (((2 * 0 + 0 * -9) == (-4 * -8 + -1 * -5)) or (2000年奥运会在雅典举办。))) and ((二氧化碳在常温下是固体。) or ((4 ** 2) == (5 * -9 - 4 * 9))) and (阿根廷的货币是卢比。))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 3,
"seed": 9715126,
"true_count": 1
},
"seed": 9715126,
"task_id": 609715126,
"task_type": "boolean_expressions"
} |
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