env stringclasses 1 value | prompt stringlengths 85 3.69k | extra dict |
|---|---|---|
logic-v2 | Analyze these boolean expressions:
A. (((((-18 * -13) == (6 - 18)) or ((-10 - -3) < (1 - 4) < (-6 * -2 * -8 * -5))) and (not not (51 is an even number.))) or (Steam is a liquid at room temperature.)) or (not not (not (not not (The Pacific Ocean is the largest ocean.))))
B. not ((not (India is in Asia.)) or (((The square root of 4 is 8.) and (Mars is the 4th planet from the Sun.)) and ((The capital of Argentina is Buenos Aires.) and ((5 * 17) > (2 * 8 * -7 * -1)))))
C. ((Nitrogen is a gas at room temperature.) or ((-6 - 6) == (1 ** 2)) or (The chemical symbol for Platinum is Pt.)) and (not ((not not (There are 31 days in September.)) and (((-20 * 4) > (11 - -13)) or (Sharks are mammals.))))
D. ((((The 2012 Olympics were held in London.) or ((-6 * 19) < (17 - -16))) or (not (Thailand is in Asia.))) or (((The currency of Singapore is the Ringgit.) or (South Korea is in Asia.)) or (((17 * 15) < (-6 * 2 + -6 * 1)) or (Alcohol is a liquid at room temperature.)))) or (not (((Mars is the 4th planet from the Sun.) and ((2 * -18) <= (2 + 20))) or (((8 * 18) != (-8 - -7)) or (Spain is in Europe.))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 19248142,
"true_count": 3
},
"question": "Analyze these boolean expressions:\n\nA. (((((-18 * -13) == (6 - 18)) or ((-10 - -3) < (1 - 4) < (-6 * -2 * -8 * -5))) and (not not (51 is an even number.))) or (Steam is a liquid at room temperature.)) or (not not (not (not not (The Pacific Ocean is the largest ocean.))))\nB. not ((not (India is in Asia.)) or (((The square root of 4 is 8.) and (Mars is the 4th planet from the Sun.)) and ((The capital of Argentina is Buenos Aires.) and ((5 * 17) > (2 * 8 * -7 * -1)))))\nC. ((Nitrogen is a gas at room temperature.) or ((-6 - 6) == (1 ** 2)) or (The chemical symbol for Platinum is Pt.)) and (not ((not not (There are 31 days in September.)) and (((-20 * 4) > (11 - -13)) or (Sharks are mammals.))))\nD. ((((The 2012 Olympics were held in London.) or ((-6 * 19) < (17 - -16))) or (not (Thailand is in Asia.))) or (((The currency of Singapore is the Ringgit.) or (South Korea is in Asia.)) or (((17 * 15) < (-6 * 2 + -6 * 1)) or (Alcohol is a liquid at room temperature.)))) or (not (((Mars is the 4th planet from the Sun.) and ((2 * -18) <= (2 + 20))) or (((8 * 18) != (-8 - -7)) or (Spain is in Europe.))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 19248142,
"true_count": 3
},
"seed": 19248142,
"task_id": 619248142,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. ((0 - 15) <= (-20 * -6)) or (not (The capital of Malaysia is Nairobi.)) or (not ((80 is divisible by 12.) or (Ice is a solid at room temperature.)))
B. (not ((There are 31 days in July.) or ((-10 + -1) >= (4 * 20)))) and (not (((2 * -4 - -1 * 10) != (10 + 6)) and ((37 % 4) >= (0 * -6))))
C. not (not ((The capital of Nigeria is Kyiv.) or ((47 % 2) >= (-11 * -4))))
D. ((not not ((-3 * 0) <= (10 * -3 - 5 * 9))) and (((5 * 8 - -6 * -8) >= (16 * 10)) or (The capital of Ireland is Rabat.))) and ((not ((41 % 6) > (-19 - -14))) and (((-7 * -3 * -6 * -8) <= (8 - -15)) or ((19 * 16) != (4 ** 2))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 38792062,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. ((0 - 15) <= (-20 * -6)) or (not (The capital of Malaysia is Nairobi.)) or (not ((80 is divisible by 12.) or (Ice is a solid at room temperature.)))\nB. (not ((There are 31 days in July.) or ((-10 + -1) >= (4 * 20)))) and (not (((2 * -4 - -1 * 10) != (10 + 6)) and ((37 % 4) >= (0 * -6))))\nC. not (not ((The capital of Nigeria is Kyiv.) or ((47 % 2) >= (-11 * -4))))\nD. ((not not ((-3 * 0) <= (10 * -3 - 5 * 9))) and (((5 * 8 - -6 * -8) >= (16 * 10)) or (The capital of Ireland is Rabat.))) and ((not ((41 % 6) > (-19 - -14))) and (((-7 * -3 * -6 * -8) <= (8 - -15)) or ((19 * 16) != (4 ** 2))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 38792062,
"true_count": 1
},
"seed": 38792062,
"task_id": 638792062,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not (The 1900 Olympics were held in Paris.)) or ((Australia is in Oceania.) and (((42 % 4) == (11 + 5)) and (The chemical symbol for Silver is Pb.)))
B. not (not (not not (not (28 is divisible by 8.))))
C. (((50 % 2) <= (-4 * 3 + -7 * -8)) and ((((-10 * -6 - -9 * 1) <= (-18 * 1)) or (The chemical symbol for Silicon is Ca.)) or (((-20 - -2) != (-16 + 19)) or (The capital of Germany is Berlin.)))) or (((19 % 9) != (-18 + 16)) or ((The chemical symbol for Manganese is Pb.) or ((5 * -4 + -2 * 0) < (3 - -11) < (4 ** 1)))) or (not not ((((-11 - 2) < (1 * 4 + 3 * 5)) or (Mercury is the 1st planet from the Sun.)) or ((15 - 4) <= (2 ** 3))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 23250437,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. (not (The 1900 Olympics were held in Paris.)) or ((Australia is in Oceania.) and (((42 % 4) == (11 + 5)) and (The chemical symbol for Silver is Pb.)))\nB. not (not (not not (not (28 is divisible by 8.))))\nC. (((50 % 2) <= (-4 * 3 + -7 * -8)) and ((((-10 * -6 - -9 * 1) <= (-18 * 1)) or (The chemical symbol for Silicon is Ca.)) or (((-20 - -2) != (-16 + 19)) or (The capital of Germany is Berlin.)))) or (((19 % 9) != (-18 + 16)) or ((The chemical symbol for Manganese is Pb.) or ((5 * -4 + -2 * 0) < (3 - -11) < (4 ** 1)))) or (not not ((((-11 - 2) < (1 * 4 + 3 * 5)) or (Mercury is the 1st planet from the Sun.)) or ((15 - 4) <= (2 ** 3))))\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": 23250437,
"true_count": 2
},
"seed": 23250437,
"task_id": 623250437,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not ((not ((World War II began occurred in 1939.) or (The chemical symbol for Chlorine is Cl.))) and (((A iguana is a reptile.) or ((14 + -8) < (7 * 9 - 5 * 3))) and (not not (The chemical symbol for Titanium is Ti.))))) and (((43 is a prime number.) or (2 is a prime number.) or (The chemical symbol for Sodium is Na.)) or (not not (((-2 + -4) < (9 * 17)) and (not not (Diamond is a liquid at room temperature.)))))
B. (not not (not not (((The Titanic sank occurred in 1912.) and ((-19 + 3) >= (15 * 0))) and (((17 * -20) < (5 ** 2)) and ((6 % 9) < (20 * -12) < (-9 * 0 - 9 * 0)))))) and ((not not (((4 * -10) < (1 * 7) < (-10 * -5 + -8 * -3)) and (Venus is the 3rd planet from the Sun.))) or ((not (The 1980 Olympics were held in Moscow.)) or ((-13 - -13) == (-11 - -12))) or (((18 % 8) != (-16 - -16)) or ((2 ** 1) >= (-19 - 3))))
C. (not not (not not (((18 + -8) <= (14 - -7) <= (7 + 14)) or (not ((14 * 15) <= (7 + 16) <= (-4 * 0 * -9 * 9)))))) and (not ((The 2008 Olympics were held in Beijing.) and ((((5 ** 1) > (18 + -10)) or ((26 % 4) != (50 % 7))) or (((10 * -6 - 3 * 0) == (27 % 3)) and (There are 29 days in June.)))))
D. not not (((((12 + 7) != (-18 + 18)) or ((1 ** 3) > (19 % 7))) and ((not not ((4 ** 1) != (-10 * -1 + 10 * -6))) or ((Germany is in Africa.) or ((-12 - 9) == (-10 + -10))))) or ((((2052 is a leap year.) and ((16 - 0) != (-6 * 9 + 6 * 9))) and (not not (2033 is a leap year.))) and (not (Gold is a gas at room temperature.))))
E. not not ((((((-3 * 9 * 4 * -6) == (18 + -17)) and (A crocodile is an insect.)) and ((Mexico is in North America.) or (Oxygen is a gas at room temperature.))) or ((not ((-9 * -10 - 6 * 7) != (12 + -17))) and ((Venus is the 5th planet from the Sun.) or (Humans only use 10% of their brain.)))) or (((-3 - -7) == (1 ** 2)) and (not not (Uranus is the 7th planet from the Sun.)) and (((The 1908 Olympics were held in London.) and (There are 29 days in September.)) or (not not ((15 * 20) < (3 ** 2))))))
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": 5,
"language": "en",
"num_options": 5,
"seed": 13537989,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. (not ((not ((World War II began occurred in 1939.) or (The chemical symbol for Chlorine is Cl.))) and (((A iguana is a reptile.) or ((14 + -8) < (7 * 9 - 5 * 3))) and (not not (The chemical symbol for Titanium is Ti.))))) and (((43 is a prime number.) or (2 is a prime number.) or (The chemical symbol for Sodium is Na.)) or (not not (((-2 + -4) < (9 * 17)) and (not not (Diamond is a liquid at room temperature.)))))\nB. (not not (not not (((The Titanic sank occurred in 1912.) and ((-19 + 3) >= (15 * 0))) and (((17 * -20) < (5 ** 2)) and ((6 % 9) < (20 * -12) < (-9 * 0 - 9 * 0)))))) and ((not not (((4 * -10) < (1 * 7) < (-10 * -5 + -8 * -3)) and (Venus is the 3rd planet from the Sun.))) or ((not (The 1980 Olympics were held in Moscow.)) or ((-13 - -13) == (-11 - -12))) or (((18 % 8) != (-16 - -16)) or ((2 ** 1) >= (-19 - 3))))\nC. (not not (not not (((18 + -8) <= (14 - -7) <= (7 + 14)) or (not ((14 * 15) <= (7 + 16) <= (-4 * 0 * -9 * 9)))))) and (not ((The 2008 Olympics were held in Beijing.) and ((((5 ** 1) > (18 + -10)) or ((26 % 4) != (50 % 7))) or (((10 * -6 - 3 * 0) == (27 % 3)) and (There are 29 days in June.)))))\nD. not not (((((12 + 7) != (-18 + 18)) or ((1 ** 3) > (19 % 7))) and ((not not ((4 ** 1) != (-10 * -1 + 10 * -6))) or ((Germany is in Africa.) or ((-12 - 9) == (-10 + -10))))) or ((((2052 is a leap year.) and ((16 - 0) != (-6 * 9 + 6 * 9))) and (not not (2033 is a leap year.))) and (not (Gold is a gas at room temperature.))))\nE. not not ((((((-3 * 9 * 4 * -6) == (18 + -17)) and (A crocodile is an insect.)) and ((Mexico is in North America.) or (Oxygen is a gas at room temperature.))) or ((not ((-9 * -10 - 6 * 7) != (12 + -17))) and ((Venus is the 5th planet from the Sun.) or (Humans only use 10% of their brain.)))) or (((-3 - -7) == (1 ** 2)) and (not not (Uranus is the 7th planet from the Sun.)) and (((The 1908 Olympics were held in London.) and (There are 29 days in September.)) or (not not ((15 * 20) < (3 ** 2))))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 13537989,
"true_count": 2
},
"seed": 13537989,
"task_id": 613537989,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (not not (not (Lightning never strikes the same place twice.))) or ((not (((6 - -18) < (-9 * 6 - 9 * 4)) or (The capital of Finland is Helsinki.))) and (Nigeria is in Asia.)) or (not ((((8 * -15) > (11 + 20)) and (((14 - -17) > (6 - -19)) or ((50 % 10) <= (21 % 2)))) or (not not (not ((-16 - 11) >= (13 + -17))))))
B. not not (not not ((The 2008 Olympics were held in Beijing.) or (not not (The currency of Philippines is the Peso.))))
C. not not (not not ((((-2 * -1) < (-3 * 2 + 10 * 6)) or ((The chemical symbol for Lead is Hg.) or ((19 - -11) > (6 - -1)))) or ((((24 % 5) >= (-13 * -2)) or (1984 is a leap year.)) or (Canada is in North America.))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 56474985,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. (not not (not (Lightning never strikes the same place twice.))) or ((not (((6 - -18) < (-9 * 6 - 9 * 4)) or (The capital of Finland is Helsinki.))) and (Nigeria is in Asia.)) or (not ((((8 * -15) > (11 + 20)) and (((14 - -17) > (6 - -19)) or ((50 % 10) <= (21 % 2)))) or (not not (not ((-16 - 11) >= (13 + -17))))))\nB. not not (not not ((The 2008 Olympics were held in Beijing.) or (not not (The currency of Philippines is the Peso.))))\nC. not not (not not ((((-2 * -1) < (-3 * 2 + 10 * 6)) or ((The chemical symbol for Lead is Hg.) or ((19 - -11) > (6 - -1)))) or ((((24 % 5) >= (-13 * -2)) or (1984 is a leap year.)) or (Canada is in North America.))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 56474985,
"true_count": 3
},
"seed": 56474985,
"task_id": 656474985,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. (-10 * 10) == (-4 * 2 + 7 * 3)
B. There are 31 days in August.
C. ((There are 30 days in November.) and (The chemical symbol for Calcium is Ca.)) or ((The 1964 Olympics were held in Athens.) or ((13 + -9) <= (11 % 8)))
D. not not ((Sound travels faster in a vacuum.) or (Mercury is the 5th planet from the Sun.))
E. (The capital of Venezuela is Caracas.) and (not not (337 is a perfect square.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 36236945,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. (-10 * 10) == (-4 * 2 + 7 * 3)\nB. There are 31 days in August.\nC. ((There are 30 days in November.) and (The chemical symbol for Calcium is Ca.)) or ((The 1964 Olympics were held in Athens.) or ((13 + -9) <= (11 % 8)))\nD. not not ((Sound travels faster in a vacuum.) or (Mercury is the 5th planet from the Sun.))\nE. (The capital of Venezuela is Caracas.) and (not not (337 is a perfect square.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 36236945,
"true_count": 2
},
"seed": 36236945,
"task_id": 636236945,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (not (Electricity flows faster than light.))
B. (33 % 9) != (-7 * 5 - 8 * -10)
C. Uranus is the 7th planet from the Sun.
D. not not ((The currency of United States is the Dollar.) or (World War I began occurred in 1914.))
E. (Chile is in Antarctica.) or ((Venus is the 7th planet from the Sun.) or (A tuna is a fish.))
F. (((-1 - 16) == (5 ** 3)) and (Vietnam is in Asia.)) and ((Oxygen is a liquid at room temperature.) and (A crow is an insect.))
G. (((12 - -8) == (-4 - 12)) and (91 is less than or equal to 23.)) and ((China is in Asia.) or ((-16 + -14) < (2 % 5) < (-11 + -19)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 30402837,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not (Electricity flows faster than light.))\nB. (33 % 9) != (-7 * 5 - 8 * -10)\nC. Uranus is the 7th planet from the Sun.\nD. not not ((The currency of United States is the Dollar.) or (World War I began occurred in 1914.))\nE. (Chile is in Antarctica.) or ((Venus is the 7th planet from the Sun.) or (A tuna is a fish.))\nF. (((-1 - 16) == (5 ** 3)) and (Vietnam is in Asia.)) and ((Oxygen is a liquid at room temperature.) and (A crow is an insect.))\nG. (((12 - -8) == (-4 - 12)) and (91 is less than or equal to 23.)) and ((China is in Asia.) or ((-16 + -14) < (2 % 5) < (-11 + -19)))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 30402837,
"true_count": 4
},
"seed": 30402837,
"task_id": 630402837,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not not (A octopus has 8 legs.)
B. (19 + 18) < (10 * -3 + 9 * 3)
C. not (not not (Kenya is in Africa.))
D. (not (Alcohol is a solid at room temperature.)) and (((-19 * -8) != (5 - -16)) and ((7 - -1) == (0 * -5 - 3 * 8)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 89200889,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. not not (A octopus has 8 legs.)\nB. (19 + 18) < (10 * -3 + 9 * 3)\nC. not (not not (Kenya is in Africa.))\nD. (not (Alcohol is a solid at room temperature.)) and (((-19 * -8) != (5 - -16)) and ((7 - -1) == (0 * -5 - 3 * 8)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 89200889,
"true_count": 1
},
"seed": 89200889,
"task_id": 689200889,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((The capital of Nigeria is Warsaw.) and ((-10 * 1 - 8 * 2) != (-10 * 0 - 10 * -6))) or (not not ((The currency of Nigeria is the Forint.) or (Chile is in South America.)))
B. (not (((1 % 7) != (20 + 18)) or (Diamonds are made of carbon.))) or ((17 * -15) >= (2 % 5))
C. ((2 + 10) <= (2 ** 2)) or ((not ((3 ** 3) >= (19 + -8))) or (((12 - 6) < (-4 - 15) < (16 - 14)) or (The currency of Switzerland is the Franc.)))
D. (996 is a Fibonacci number.) or ((0 * -6 + -4 * 10) >= (2 ** 3))
E. not (((Water boils at 100 degrees Celsius at sea level.) or (Water boils at 100 degrees Celsius at sea level.)) or ((The capital of Philippines is Manila.) and (A lobster has 8 legs.)))
F. not not (((-5 * 4 * 9 * -6) <= (-6 - -7)) and ((-11 - 12) == (3 + 11)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 38195724,
"true_count": 2
},
"question": "Given the following boolean expressions:\n\nA. ((The capital of Nigeria is Warsaw.) and ((-10 * 1 - 8 * 2) != (-10 * 0 - 10 * -6))) or (not not ((The currency of Nigeria is the Forint.) or (Chile is in South America.)))\nB. (not (((1 % 7) != (20 + 18)) or (Diamonds are made of carbon.))) or ((17 * -15) >= (2 % 5))\nC. ((2 + 10) <= (2 ** 2)) or ((not ((3 ** 3) >= (19 + -8))) or (((12 - 6) < (-4 - 15) < (16 - 14)) or (The currency of Switzerland is the Franc.)))\nD. (996 is a Fibonacci number.) or ((0 * -6 + -4 * 10) >= (2 ** 3))\nE. not (((Water boils at 100 degrees Celsius at sea level.) or (Water boils at 100 degrees Celsius at sea level.)) or ((The capital of Philippines is Manila.) and (A lobster has 8 legs.)))\nF. not not (((-5 * 4 * 9 * -6) <= (-6 - -7)) and ((-11 - 12) == (3 + 11)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 38195724,
"true_count": 2
},
"seed": 38195724,
"task_id": 638195724,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (The capital of Peru is Lima.)
B. (The capital of Romania is Bucharest.) and (not not ((-14 - 13) <= (14 - -16)))
C. (((6 + 17) <= (36 % 5) <= (5 * -2 + 8 * 9)) or ((-7 * 10 + 9 * 9) <= (3 + 3))) or ((The capital of Venezuela is Lisbon.) and (The Soviet Union dissolved occurred in 1991.))
D. (((3 ** 1) <= (1 * 1 * 0 * -7) <= (18 * 4)) and (Silver is a gas at room temperature.)) and ((6 % 2) < (39 % 8))
E. 67 is greater than 69.
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 43078860,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (The capital of Peru is Lima.)\nB. (The capital of Romania is Bucharest.) and (not not ((-14 - 13) <= (14 - -16)))\nC. (((6 + 17) <= (36 % 5) <= (5 * -2 + 8 * 9)) or ((-7 * 10 + 9 * 9) <= (3 + 3))) or ((The capital of Venezuela is Lisbon.) and (The Soviet Union dissolved occurred in 1991.))\nD. (((3 ** 1) <= (1 * 1 * 0 * -7) <= (18 * 4)) and (Silver is a gas at room temperature.)) and ((6 % 2) < (39 % 8))\nE. 67 is greater than 69.\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 43078860,
"true_count": 1
},
"seed": 43078860,
"task_id": 643078860,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (The Sun revolves around the Earth.)
B. not (((-15 + 11) >= (20 - -17)) or (not (Mercury is the 1st planet from the Sun.)))
C. (Sound travels faster in a vacuum.) and (((The 1964 Olympics were held in Mexico City.) and ((5 % 9) >= (1 + 19))) and (not (Venus is the 4th planet from the Sun.)))
D. (((The 2020 Olympics were held in Tokyo.) or ((-4 * -3 + -7 * 1) < (-8 * -19))) and ((-9 * 10 * -2 * -8) <= (-10 - 2))) or ((-5 - 5) > (-18 + -18))
E. not (not not (not ((3 ** 2) <= (31 % 10))))
F. not ((There are 31 days in March.) and (((-18 - -12) < (36 % 10)) and (The human body has 206 bones.)))
G. ((not not ((-10 * -3 - -2 * -1) <= (15 * -19) <= (-1 * 1))) or ((The currency of Canada is the Dollar.) or ((-1 + -5) < (3 * 5 - 2 * 4)))) and (The capital of Portugal is Lisbon.)
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,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 57716068,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (The Sun revolves around the Earth.)\nB. not (((-15 + 11) >= (20 - -17)) or (not (Mercury is the 1st planet from the Sun.)))\nC. (Sound travels faster in a vacuum.) and (((The 1964 Olympics were held in Mexico City.) and ((5 % 9) >= (1 + 19))) and (not (Venus is the 4th planet from the Sun.)))\nD. (((The 2020 Olympics were held in Tokyo.) or ((-4 * -3 + -7 * 1) < (-8 * -19))) and ((-9 * 10 * -2 * -8) <= (-10 - 2))) or ((-5 - 5) > (-18 + -18))\nE. not (not not (not ((3 ** 2) <= (31 % 10))))\nF. not ((There are 31 days in March.) and (((-18 - -12) < (36 % 10)) and (The human body has 206 bones.)))\nG. ((not not ((-10 * -3 - -2 * -1) <= (15 * -19) <= (-1 * 1))) or ((The currency of Canada is the Dollar.) or ((-1 + -5) < (3 * 5 - 2 * 4)))) and (The capital of Portugal is Lisbon.)\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 57716068,
"true_count": 4
},
"seed": 57716068,
"task_id": 657716068,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (((0 + -3) > (8 * -20)) and ((not not (The chemical symbol for Copper is Cu.)) and ((Ice is a solid at room temperature.) and ((1 ** 2) >= (22 % 2)))))
B. (((-10 + -4) < (-10 * -2 + 5 * -10)) or (France is in Europe.)) or ((((Helium is a liquid at room temperature.) and (Earth is the 3rd planet from the Sun.)) or (not not ((-17 + -15) != (4 + -13)))) or (not ((The chemical symbol for Magnesium is U.) or (Mars is the 4th planet from the Sun.))))
C. not not ((((Carbon dioxide is a gas at room temperature.) and ((3 - -10) != (-11 * 3))) and (A fish has 2 legs.)) and ((World War I began occurred in 1914.) or (((-1 + 15) < (-12 - 4)) or ((13 + -16) != (-18 + 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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 84077951,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (((0 + -3) > (8 * -20)) and ((not not (The chemical symbol for Copper is Cu.)) and ((Ice is a solid at room temperature.) and ((1 ** 2) >= (22 % 2)))))\nB. (((-10 + -4) < (-10 * -2 + 5 * -10)) or (France is in Europe.)) or ((((Helium is a liquid at room temperature.) and (Earth is the 3rd planet from the Sun.)) or (not not ((-17 + -15) != (4 + -13)))) or (not ((The chemical symbol for Magnesium is U.) or (Mars is the 4th planet from the Sun.))))\nC. not not ((((Carbon dioxide is a gas at room temperature.) and ((3 - -10) != (-11 * 3))) and (A fish has 2 legs.)) and ((World War I began occurred in 1914.) or (((-1 + 15) < (-12 - 4)) or ((13 + -16) != (-18 + 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": 3,
"seed": 84077951,
"true_count": 2
},
"seed": 84077951,
"task_id": 684077951,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not not (not ((17 + 7) < (17 * 18))))
B. (not not ((6 is a prime number.) or (Christopher Columbus reached America occurred in 1492.))) and (The 1912 Olympics were held in Stockholm.)
C. ((-16 + -9) == (-2 * 8 * -9 * 0)) or (not not ((The 1896 Olympics were held in Rome.) and (The capital of Belgium is Bern.)))
D. not (((A cow has 4 legs.) or ((4 * 17) > (2 * -5 * 1 * 9))) and (Mexico is in North America.))
E. (not ((Sound cannot travel through a vacuum.) or ((-7 - -9) != (-16 + 1)))) and (The 1936 Olympics were held in Berlin.)
F. not (not (((-5 * -2 + 2 * -8) < (-15 + 2) < (3 ** 1)) and ((1 ** 1) == (19 % 3))))
G. not (A cockroach is an insect.)
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 67326778,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. not (not not (not ((17 + 7) < (17 * 18))))\nB. (not not ((6 is a prime number.) or (Christopher Columbus reached America occurred in 1492.))) and (The 1912 Olympics were held in Stockholm.)\nC. ((-16 + -9) == (-2 * 8 * -9 * 0)) or (not not ((The 1896 Olympics were held in Rome.) and (The capital of Belgium is Bern.)))\nD. not (((A cow has 4 legs.) or ((4 * 17) > (2 * -5 * 1 * 9))) and (Mexico is in North America.))\nE. (not ((Sound cannot travel through a vacuum.) or ((-7 - -9) != (-16 + 1)))) and (The 1936 Olympics were held in Berlin.)\nF. not (not (((-5 * -2 + 2 * -8) < (-15 + 2) < (3 ** 1)) and ((1 ** 1) == (19 % 3))))\nG. not (A cockroach is an insect.)\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 67326778,
"true_count": 2
},
"seed": 67326778,
"task_id": 667326778,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (not not (not ((((-19 - -20) < (-15 * 19)) and (Saturn is the 6th planet from the Sun.)) and (not not ((-10 + -5) == (19 + -18)))))) and (not not (not not ((not not ((40 % 5) <= (-18 * 9))) or (79 is greater than 13.))))
B. not ((not ((not not ((-14 - 20) >= (6 + -8))) and (((-3 + -10) <= (20 - -2)) and (192 is a perfect square.)))) and ((not not (((5 ** 2) == (8 * 6 - 9 * -7)) and (A trout is a bird.))) or ((Gold is a gas at room temperature.) and (not (The human body has 150 bones.)))))
C. not not ((((not not ((1 * -9 - 0 * 10) >= (38 % 4))) and ((Vietnam is in Asia.) and (Earth is the 3rd planet from the Sun.))) or ((The 2016 Olympics were held in London.) and (not (Argentina is in South America.)))) and (not not ((not ((1 ** 1) != (12 + 10))) or ((36 is greater than 14.) or ((1 * -20) != (-16 * 2))))))
D. (not ((2025 is a leap year.) or (((9 + 17) < (-17 - 20)) or (not ((1 ** 2) == (-15 + 18)))))) and ((((Bats are blind.) or (Saudi Arabia is in Asia.)) or (Penguins can fly.)) and (2023 is a leap year.)) and (not not (((2090 is a leap year.) and ((The capital of Egypt is Lima.) or (The chemical symbol for Manganese is H.))) and ((14 * 20) >= (-5 * -7 + 1 * -1))))
E. not (not ((((9 - -5) >= (-14 - 15)) and ((19 + -8) <= (33 % 4))) and ((19 - 1) < (-10 * -8))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 73308237,
"true_count": 2
},
"question": "Review these logical expressions:\n\nA. (not not (not ((((-19 - -20) < (-15 * 19)) and (Saturn is the 6th planet from the Sun.)) and (not not ((-10 + -5) == (19 + -18)))))) and (not not (not not ((not not ((40 % 5) <= (-18 * 9))) or (79 is greater than 13.))))\nB. not ((not ((not not ((-14 - 20) >= (6 + -8))) and (((-3 + -10) <= (20 - -2)) and (192 is a perfect square.)))) and ((not not (((5 ** 2) == (8 * 6 - 9 * -7)) and (A trout is a bird.))) or ((Gold is a gas at room temperature.) and (not (The human body has 150 bones.)))))\nC. not not ((((not not ((1 * -9 - 0 * 10) >= (38 % 4))) and ((Vietnam is in Asia.) and (Earth is the 3rd planet from the Sun.))) or ((The 2016 Olympics were held in London.) and (not (Argentina is in South America.)))) and (not not ((not ((1 ** 1) != (12 + 10))) or ((36 is greater than 14.) or ((1 * -20) != (-16 * 2))))))\nD. (not ((2025 is a leap year.) or (((9 + 17) < (-17 - 20)) or (not ((1 ** 2) == (-15 + 18)))))) and ((((Bats are blind.) or (Saudi Arabia is in Asia.)) or (Penguins can fly.)) and (2023 is a leap year.)) and (not not (((2090 is a leap year.) and ((The capital of Egypt is Lima.) or (The chemical symbol for Manganese is H.))) and ((14 * 20) >= (-5 * -7 + 1 * -1))))\nE. not (not ((((9 - -5) >= (-14 - 15)) and ((19 + -8) <= (33 % 4))) and ((19 - 1) < (-10 * -8))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 73308237,
"true_count": 2
},
"seed": 73308237,
"task_id": 673308237,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (not not ((2 * 7 + 6 * 5) > (4 * -6 * -1 * -7))) and (not not (((20 * 0) != (3 * -17)) and (Spain is in Europe.))) and ((not not (The chemical symbol for Chlorine is Cl.)) and (((-13 * 12) < (41 % 2)) or ((15 - -18) <= (1 % 9))) and (((Uranus is the 3rd planet from the Sun.) or ((-12 + -7) != (-8 - -19))) or ((-15 + -11) == (8 * 8 - -8 * -2))))
B. (((not not (Lightning never strikes the same place twice.)) and (((-20 - -13) == (6 * -8 * 0 * 9)) or (The capital of Finland is Athens.))) or (The 1912 Olympics were held in Munich.)) and (not ((2 ** 3) <= (-17 - 14))) and (((((22 % 2) != (43 % 9)) or ((0 * -8 * 4 * 10) <= (7 - 2))) or (((1 * -9) >= (-20 * -16)) and (The currency of United Kingdom is the Pound.))) and (Uranus is the 1st planet from the Sun.) and (The capital of Chile is Canberra.))
C. (((1 * -7) == (20 - -17)) or (The chemical symbol for Magnesium is S.)) or (((South Africa is in Europe.) or ((-19 + 2) < (-16 + 15))) and ((The currency of South Africa is the Rand.) or (There are 30 days in November.))) or (not (((Diamonds are made of carbon.) or ((-2 - 1) == (-18 - -20))) or (The chemical symbol for Helium is He.)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 14510134,
"true_count": 2
},
"question": "Review these logical expressions:\n\nA. (not not ((2 * 7 + 6 * 5) > (4 * -6 * -1 * -7))) and (not not (((20 * 0) != (3 * -17)) and (Spain is in Europe.))) and ((not not (The chemical symbol for Chlorine is Cl.)) and (((-13 * 12) < (41 % 2)) or ((15 - -18) <= (1 % 9))) and (((Uranus is the 3rd planet from the Sun.) or ((-12 + -7) != (-8 - -19))) or ((-15 + -11) == (8 * 8 - -8 * -2))))\nB. (((not not (Lightning never strikes the same place twice.)) and (((-20 - -13) == (6 * -8 * 0 * 9)) or (The capital of Finland is Athens.))) or (The 1912 Olympics were held in Munich.)) and (not ((2 ** 3) <= (-17 - 14))) and (((((22 % 2) != (43 % 9)) or ((0 * -8 * 4 * 10) <= (7 - 2))) or (((1 * -9) >= (-20 * -16)) and (The currency of United Kingdom is the Pound.))) and (Uranus is the 1st planet from the Sun.) and (The capital of Chile is Canberra.))\nC. (((1 * -7) == (20 - -17)) or (The chemical symbol for Magnesium is S.)) or (((South Africa is in Europe.) or ((-19 + 2) < (-16 + 15))) and ((The currency of South Africa is the Rand.) or (There are 30 days in November.))) or (not (((Diamonds are made of carbon.) or ((-2 - 1) == (-18 - -20))) or (The chemical symbol for Helium is He.)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 14510134,
"true_count": 2
},
"seed": 14510134,
"task_id": 614510134,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. The 1980 Olympics were held in Atlanta.
B. (-18 + 9) <= (-2 * 0 - -6 * -8) <= (8 % 10)
C. ((3 ** 1) < (13 * -18) < (-2 + 11)) and (((4 ** 1) <= (-5 * 0 * -8 * -7) <= (40 % 8)) and (91 is divisible by 10.))
D. not (((-3 * -8 + -7 * -7) > (15 - -15)) or (Colombia is in South America.))
E. (9 * -1 + 4 * -7) <= (3 * 10 + 5 * 7)
F. (((4 ** 1) < (-8 - 3)) or (73 is an even number.)) and (130 is an odd number.)
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 22831798,
"true_count": 1
},
"question": "Evaluate each expression below:\n\nA. The 1980 Olympics were held in Atlanta.\nB. (-18 + 9) <= (-2 * 0 - -6 * -8) <= (8 % 10)\nC. ((3 ** 1) < (13 * -18) < (-2 + 11)) and (((4 ** 1) <= (-5 * 0 * -8 * -7) <= (40 % 8)) and (91 is divisible by 10.))\nD. not (((-3 * -8 + -7 * -7) > (15 - -15)) or (Colombia is in South America.))\nE. (9 * -1 + 4 * -7) <= (3 * 10 + 5 * 7)\nF. (((4 ** 1) < (-8 - 3)) or (73 is an even number.)) and (130 is an odd number.)\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 22831798,
"true_count": 1
},
"seed": 22831798,
"task_id": 622831798,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. The 1920 Olympics were held in Antwerp.
B. ((3 ** 2) != (-7 * -15)) or (A lobster has 10 legs.)
C. ((35 is a prime number.) or (The capital of Japan is Tokyo.)) and (not (2022 is a leap year.))
D. ((1 * 1 * -10 * -9) <= (4 ** 1)) and ((4 ** 3) > (0 + -1))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 91974961,
"true_count": 3
},
"question": "Here are some boolean expressions to evaluate:\n\nA. The 1920 Olympics were held in Antwerp.\nB. ((3 ** 2) != (-7 * -15)) or (A lobster has 10 legs.)\nC. ((35 is a prime number.) or (The capital of Japan is Tokyo.)) and (not (2022 is a leap year.))\nD. ((1 * 1 * -10 * -9) <= (4 ** 1)) and ((4 ** 3) > (0 + -1))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 91974961,
"true_count": 3
},
"seed": 91974961,
"task_id": 691974961,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. Whales are fish.
B. not not ((-5 - 13) >= (3 ** 2))
C. (((-7 * 0 * -4 * -3) >= (-9 - -11)) or ((3 - 3) > (21 % 9))) or ((There are 28 days in June.) and (A salmon is a mammal.))
D. (7 + 20) > (-4 - 19)
E. (not not (There are 31 days in May.)) or (not ((1 * 2) == (-14 - 8)))
F. not not ((A trout is a fish.) or (Carbon dioxide is a gas at room temperature.))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 93501584,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. Whales are fish.\nB. not not ((-5 - 13) >= (3 ** 2))\nC. (((-7 * 0 * -4 * -3) >= (-9 - -11)) or ((3 - 3) > (21 % 9))) or ((There are 28 days in June.) and (A salmon is a mammal.))\nD. (7 + 20) > (-4 - 19)\nE. (not not (There are 31 days in May.)) or (not ((1 * 2) == (-14 - 8)))\nF. not not ((A trout is a fish.) or (Carbon dioxide is a gas at room temperature.))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 93501584,
"true_count": 3
},
"seed": 93501584,
"task_id": 693501584,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (not (Germany is in Asia.))
B. (not ((The currency of China is the Yuan.) or (Mercury is the 7th planet from the Sun.))) and (68 is a prime number.)
C. (not not (not ((7 % 5) > (6 * -13)))) or ((((15 - -10) > (13 * 0)) and (A mosquito is a bird.)) or (Mars is the 4th planet from the Sun.))
D. ((not ((-5 * 7 * -1 * -3) <= (-10 * 2 + 10 * 5))) or (72 is divisible by 6.)) and (((2008 is a leap year.) and (The chemical symbol for Zinc is Zn.)) or (The 2020 Olympics were held in Amsterdam.))
E. (not not (not (The chemical symbol for Magnesium is Mg.))) or ((The Soviet Union dissolved occurred in 1991.) and ((-19 - 20) < (20 * 7) < (-4 * -4 * 4 * -5))) or (There are 28 days in February.)
F. (Mars is the 4th planet from the Sun.) or ((-16 - -16) != (8 * -7 * -6 * 2))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 94392365,
"true_count": 5
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (not (Germany is in Asia.))\nB. (not ((The currency of China is the Yuan.) or (Mercury is the 7th planet from the Sun.))) and (68 is a prime number.)\nC. (not not (not ((7 % 5) > (6 * -13)))) or ((((15 - -10) > (13 * 0)) and (A mosquito is a bird.)) or (Mars is the 4th planet from the Sun.))\nD. ((not ((-5 * 7 * -1 * -3) <= (-10 * 2 + 10 * 5))) or (72 is divisible by 6.)) and (((2008 is a leap year.) and (The chemical symbol for Zinc is Zn.)) or (The 2020 Olympics were held in Amsterdam.))\nE. (not not (not (The chemical symbol for Magnesium is Mg.))) or ((The Soviet Union dissolved occurred in 1991.) and ((-19 - 20) < (20 * 7) < (-4 * -4 * 4 * -5))) or (There are 28 days in February.)\nF. (Mars is the 4th planet from the Sun.) or ((-16 - -16) != (8 * -7 * -6 * 2))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 94392365,
"true_count": 5
},
"seed": 94392365,
"task_id": 694392365,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not (((0 * 9 * -1 * 4) == (0 * -8 + -2 * -7)) and (((4 * 7 - -4 * -8) <= (34 % 5) <= (-20 + -13)) or (A parrot is a mammal.)))) and (((((0 * -4 * -8 * 3) > (2 * -13)) and (The chemical symbol for Calcium is U.)) or (The chemical symbol for Tin is Sn.)) and (The capital of South Korea is Bucharest.))
B. (((The currency of Denmark is the Yuan.) or ((There are 29 days in August.) and (The currency of China is the Rand.))) or (not not (((-4 * 19) <= (8 * 1 - -2 * 8)) or (Oxygen is a solid at room temperature.)))) and ((Kenya is in Africa.) or (((-4 * 7 * 10 * 10) != (20 * -18)) and (((0 * -1 + 9 * 8) < (-5 * 5 + 9 * 4)) and (The chemical symbol for Chromium is Cu.))))
C. (not (not not ((-9 * -17) < (1 * 3 - -2 * 10)))) or ((((Humans have five fingers on each hand.) or ((-2 * -3) <= (-9 * 0 - 1 * 8))) or (Neptune is the 8th planet from the Sun.)) and (((Nigeria is in Africa.) and (The chemical symbol for Chlorine is Zn.)) and (Ice is a solid at room temperature.)))
D. (not not ((-9 * -14) >= (-8 * -4 + 8 * 5))) and (not not (Mars is the 8th planet from the Sun.))
E. not (not (((-6 - -8) != (6 + 8)) or (((1 - 5) == (3 % 5)) or (The currency of Denmark is the Krone.))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 30802318,
"true_count": 3
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (not (((0 * 9 * -1 * 4) == (0 * -8 + -2 * -7)) and (((4 * 7 - -4 * -8) <= (34 % 5) <= (-20 + -13)) or (A parrot is a mammal.)))) and (((((0 * -4 * -8 * 3) > (2 * -13)) and (The chemical symbol for Calcium is U.)) or (The chemical symbol for Tin is Sn.)) and (The capital of South Korea is Bucharest.))\nB. (((The currency of Denmark is the Yuan.) or ((There are 29 days in August.) and (The currency of China is the Rand.))) or (not not (((-4 * 19) <= (8 * 1 - -2 * 8)) or (Oxygen is a solid at room temperature.)))) and ((Kenya is in Africa.) or (((-4 * 7 * 10 * 10) != (20 * -18)) and (((0 * -1 + 9 * 8) < (-5 * 5 + 9 * 4)) and (The chemical symbol for Chromium is Cu.))))\nC. (not (not not ((-9 * -17) < (1 * 3 - -2 * 10)))) or ((((Humans have five fingers on each hand.) or ((-2 * -3) <= (-9 * 0 - 1 * 8))) or (Neptune is the 8th planet from the Sun.)) and (((Nigeria is in Africa.) and (The chemical symbol for Chlorine is Zn.)) and (Ice is a solid at room temperature.)))\nD. (not not ((-9 * -14) >= (-8 * -4 + 8 * 5))) and (not not (Mars is the 8th planet from the Sun.))\nE. not (not (((-6 - -8) != (6 + 8)) or (((1 - 5) == (3 % 5)) or (The currency of Denmark is the Krone.))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 30802318,
"true_count": 3
},
"seed": 30802318,
"task_id": 630802318,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not ((((35 % 6) > (15 + -19)) or ((-11 - 20) <= (-15 - -10))) or ((The capital of Egypt is Cairo.) and (United Kingdom is in Oceania.)))) and (not not (((18 + -2) == (2 * -9 + -6 * -2)) or ((The chemical symbol for Copper is Cu.) or (Silver is a solid at room temperature.))))
B. (not not (((1956 is a leap year.) or ((30 % 10) <= (-8 * -1 + 0 * 0) <= (15 - -18))) and ((The square root of 36 is 6.) or (The chemical symbol for Tin is Sn.)))) and (not (((A mosquito is an insect.) or (1976 is a leap year.)) or (not (France is in Europe.))))
C. (((((-9 * 1 - 10 * -9) == (-2 + 20)) and (The 1964 Olympics were held in Tokyo.)) and ((Electricity flows faster than light.) and (Mars is the 4th planet from the Sun.))) and (not not (not (Carbon dioxide is a gas at room temperature.)))) or ((The chemical symbol for Silver is Ca.) or (not ((44 % 2) <= (-14 - -15)))) or (not ((41 % 2) <= (7 * -3 - -1 * 3)))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 88880940,
"true_count": 1
},
"question": "Analyze these boolean expressions:\n\nA. (not ((((35 % 6) > (15 + -19)) or ((-11 - 20) <= (-15 - -10))) or ((The capital of Egypt is Cairo.) and (United Kingdom is in Oceania.)))) and (not not (((18 + -2) == (2 * -9 + -6 * -2)) or ((The chemical symbol for Copper is Cu.) or (Silver is a solid at room temperature.))))\nB. (not not (((1956 is a leap year.) or ((30 % 10) <= (-8 * -1 + 0 * 0) <= (15 - -18))) and ((The square root of 36 is 6.) or (The chemical symbol for Tin is Sn.)))) and (not (((A mosquito is an insect.) or (1976 is a leap year.)) or (not (France is in Europe.))))\nC. (((((-9 * 1 - 10 * -9) == (-2 + 20)) and (The 1964 Olympics were held in Tokyo.)) and ((Electricity flows faster than light.) and (Mars is the 4th planet from the Sun.))) and (not not (not (Carbon dioxide is a gas at room temperature.)))) or ((The chemical symbol for Silver is Ca.) or (not ((44 % 2) <= (-14 - -15)))) or (not ((41 % 2) <= (7 * -3 - -1 * 3)))\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": 88880940,
"true_count": 1
},
"seed": 88880940,
"task_id": 688880940,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. ((10 - 5) != (-19 + -8)) or (((4 ** 1) != (-11 * -16)) or (A day on Earth is 24 hours.))
B. ((A trout is an insect.) or ((3 ** 3) == (4 % 6))) or ((Water is a gas at room temperature.) or (The 1976 Olympics were held in Rio de Janeiro.))
C. ((The chemical symbol for Manganese is Mn.) or ((-6 * 10 * -1 * 0) <= (2 ** 2))) or (((18 - 3) > (3 ** 3)) and (The chemical symbol for Manganese is Co.))
D. ((The capital of New Zealand is Warsaw.) and ((6 + 12) < (-9 + 0) < (-18 - -5))) and (((36 % 9) != (-15 + 10)) or ((33 % 4) <= (0 + 0) <= (-20 * 10)))
E. 91 is an odd number.
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 51719448,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. ((10 - 5) != (-19 + -8)) or (((4 ** 1) != (-11 * -16)) or (A day on Earth is 24 hours.))\nB. ((A trout is an insect.) or ((3 ** 3) == (4 % 6))) or ((Water is a gas at room temperature.) or (The 1976 Olympics were held in Rio de Janeiro.))\nC. ((The chemical symbol for Manganese is Mn.) or ((-6 * 10 * -1 * 0) <= (2 ** 2))) or (((18 - 3) > (3 ** 3)) and (The chemical symbol for Manganese is Co.))\nD. ((The capital of New Zealand is Warsaw.) and ((6 + 12) < (-9 + 0) < (-18 - -5))) and (((36 % 9) != (-15 + 10)) or ((33 % 4) <= (0 + 0) <= (-20 * 10)))\nE. 91 is an odd number.\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 51719448,
"true_count": 3
},
"seed": 51719448,
"task_id": 651719448,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. The square root of 225 is 1.
B. not (((17 + 9) <= (-10 * -6 + -8 * -8) <= (-11 - 0)) and (Gold is a liquid at room temperature.))
C. (not not (The 1928 Olympics were held in Amsterdam.)) or (((3 ** 3) > (22 % 10)) or (India is in North America.))
D. (The chemical symbol for Gold is Cr.) and (not ((14 * 14) == (10 - -7)))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 76666540,
"true_count": 2
},
"question": "Analyze these boolean expressions:\n\nA. The square root of 225 is 1.\nB. not (((17 + 9) <= (-10 * -6 + -8 * -8) <= (-11 - 0)) and (Gold is a liquid at room temperature.))\nC. (not not (The 1928 Olympics were held in Amsterdam.)) or (((3 ** 3) > (22 % 10)) or (India is in North America.))\nD. (The chemical symbol for Gold is Cr.) and (not ((14 * 14) == (10 - -7)))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 76666540,
"true_count": 2
},
"seed": 76666540,
"task_id": 676666540,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. The capital of Singapore is Paris.
B. The square root of 81 is 9.
C. (not ((14 - -7) > (-2 * -2))) and (not (There are 31 days in May.))
D. ((The capital of Hungary is Budapest.) or ((-16 + 2) < (3 ** 2))) and ((1 + 8) != (-3 - 10))
E. (17 + 13) != (16 + -1)
F. United States is in North America.
G. (The currency of Egypt is the Lira.) or ((1 * 0 + -1 * 7) >= (-19 + 13))
H. (The chemical symbol for Lead is Pb.) and (The capital of Nigeria is Paris.)
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 14129964,
"true_count": 4
},
"question": "Examine these expressions:\n\nA. The capital of Singapore is Paris.\nB. The square root of 81 is 9.\nC. (not ((14 - -7) > (-2 * -2))) and (not (There are 31 days in May.))\nD. ((The capital of Hungary is Budapest.) or ((-16 + 2) < (3 ** 2))) and ((1 + 8) != (-3 - 10))\nE. (17 + 13) != (16 + -1)\nF. United States is in North America.\nG. (The currency of Egypt is the Lira.) or ((1 * 0 + -1 * 7) >= (-19 + 13))\nH. (The chemical symbol for Lead is Pb.) and (The capital of Nigeria is Paris.)\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 14129964,
"true_count": 4
},
"seed": 14129964,
"task_id": 614129964,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not (not ((-6 * -8) >= (-19 - 9)))
B. ((not (not (The chemical symbol for Chlorine is Cl.))) or (1969 is a leap year.)) and ((not (Mercury is the 1st planet from the Sun.)) and (The 2024 Olympics were held in Paris.)) and (((7 * 20) == (46 % 4)) and ((40 % 10) <= (2 ** 1)))
C. ((not not (The 1896 Olympics were held in Mexico City.)) or ((((3 ** 1) != (-20 + 12)) and ((2 + 18) > (5 ** 3))) and (((12 + 1) <= (2 ** 1)) or (The capital of Brazil is Rome.)))) or ((not not (((48 % 6) < (2 ** 2) < (4 ** 3)) and ((20 - 16) < (10 * 3 - 0 * 7)))) or (1968 is a leap year.) or ((-9 * -10 * 1 * 10) >= (19 % 4)))
D. ((((Copper is a solid at room temperature.) and (59 is a prime number.)) and ((-13 + 0) == (7 % 4))) or (((2 + 20) <= (5 - -17)) or ((The currency of India is the Rupiah.) and (There are 30 days in November.)))) or (not ((The chemical symbol for Aluminum is O.) or (((5 ** 1) == (4 % 10)) and (100 is divisible by 6.))))
E. (((not (Humans only use 10% of their brain.)) or ((The capital of China is Beijing.) and ((3 * 2 + -10 * 10) != (15 - -3)))) and (The 1920 Olympics were held in Beijing.)) and (((15 + -15) <= (5 ** 3) <= (-3 * -16)) or (59 is divisible by 5.))
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": 4,
"language": "en",
"num_options": 5,
"seed": 63889079,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not (not ((-6 * -8) >= (-19 - 9)))\nB. ((not (not (The chemical symbol for Chlorine is Cl.))) or (1969 is a leap year.)) and ((not (Mercury is the 1st planet from the Sun.)) and (The 2024 Olympics were held in Paris.)) and (((7 * 20) == (46 % 4)) and ((40 % 10) <= (2 ** 1)))\nC. ((not not (The 1896 Olympics were held in Mexico City.)) or ((((3 ** 1) != (-20 + 12)) and ((2 + 18) > (5 ** 3))) and (((12 + 1) <= (2 ** 1)) or (The capital of Brazil is Rome.)))) or ((not not (((48 % 6) < (2 ** 2) < (4 ** 3)) and ((20 - 16) < (10 * 3 - 0 * 7)))) or (1968 is a leap year.) or ((-9 * -10 * 1 * 10) >= (19 % 4)))\nD. ((((Copper is a solid at room temperature.) and (59 is a prime number.)) and ((-13 + 0) == (7 % 4))) or (((2 + 20) <= (5 - -17)) or ((The currency of India is the Rupiah.) and (There are 30 days in November.)))) or (not ((The chemical symbol for Aluminum is O.) or (((5 ** 1) == (4 % 10)) and (100 is divisible by 6.))))\nE. (((not (Humans only use 10% of their brain.)) or ((The capital of China is Beijing.) and ((3 * 2 + -10 * 10) != (15 - -3)))) and (The 1920 Olympics were held in Beijing.)) and (((15 + -15) <= (5 ** 3) <= (-3 * -16)) or (59 is divisible by 5.))\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": 63889079,
"true_count": 2
},
"seed": 63889079,
"task_id": 663889079,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (not not (not ((-1 + -19) > (-8 + 20)))) or (not not (((-3 - 18) >= (-5 * 8 * -3 * 0)) and (Uranus is the 7th planet from the Sun.)))
B. (((14 * -1) > (-13 - 16)) and (not not (The capital of Argentina is Buenos Aires.))) or ((12 * 11) < (7 + -5) < (-13 * 14)) or ((49 % 10) <= (3 + -2) <= (2 ** 3))
C. ((-11 * 9) > (7 + -17)) or (Indonesia is in Asia.)
D. (The capital of Morocco is Havana.) and (The capital of Argentina is Budapest.) and (not (not not (The 1956 Olympics were held in Tokyo.)))
E. not (The chemical symbol for Sulfur is Sn.)
F. ((The Moon produces its own light.) or ((The capital of Norway is Oslo.) and (Oil is a gas at room temperature.))) and ((Mars is the 4th planet from the Sun.) and ((The currency of India is the Dollar.) or ((-10 - 11) <= (2 - -13) <= (-13 - 7))))
G. ((not not ((-2 * -2 + -1 * 2) <= (8 - -15) <= (5 * 5 + 10 * 1))) and ((5 + 19) < (-1 * -4 + -3 * 6) < (-10 * 13))) or ((A cow has 6 legs.) or (Kenya is in Oceania.)) or ((not not (The currency of United Kingdom is the Pound.)) or ((The 2000 Olympics were held in Sydney.) or (Sharks are mammals.)))
H. not ((not (The capital of Venezuela is Hanoi.)) or (((-7 * -18) == (18 + -3)) or ((4 * 2 * -9 * -3) <= (0 * 16))))
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,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 71859976,
"true_count": 5
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (not not (not ((-1 + -19) > (-8 + 20)))) or (not not (((-3 - 18) >= (-5 * 8 * -3 * 0)) and (Uranus is the 7th planet from the Sun.)))\nB. (((14 * -1) > (-13 - 16)) and (not not (The capital of Argentina is Buenos Aires.))) or ((12 * 11) < (7 + -5) < (-13 * 14)) or ((49 % 10) <= (3 + -2) <= (2 ** 3))\nC. ((-11 * 9) > (7 + -17)) or (Indonesia is in Asia.)\nD. (The capital of Morocco is Havana.) and (The capital of Argentina is Budapest.) and (not (not not (The 1956 Olympics were held in Tokyo.)))\nE. not (The chemical symbol for Sulfur is Sn.)\nF. ((The Moon produces its own light.) or ((The capital of Norway is Oslo.) and (Oil is a gas at room temperature.))) and ((Mars is the 4th planet from the Sun.) and ((The currency of India is the Dollar.) or ((-10 - 11) <= (2 - -13) <= (-13 - 7))))\nG. ((not not ((-2 * -2 + -1 * 2) <= (8 - -15) <= (5 * 5 + 10 * 1))) and ((5 + 19) < (-1 * -4 + -3 * 6) < (-10 * 13))) or ((A cow has 6 legs.) or (Kenya is in Oceania.)) or ((not not (The currency of United Kingdom is the Pound.)) or ((The 2000 Olympics were held in Sydney.) or (Sharks are mammals.)))\nH. not ((not (The capital of Venezuela is Hanoi.)) or (((-7 * -18) == (18 + -3)) or ((4 * 2 * -9 * -3) <= (0 * 16))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 71859976,
"true_count": 5
},
"seed": 71859976,
"task_id": 671859976,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not not ((not not ((The currency of United Kingdom is the Peso.) and (Earth is the 7th planet from the Sun.))) and (not ((20 + -14) == (-9 + -6))))) and (((((-14 * -7) != (4 * -1 + -2 * -4)) or ((The currency of Czech Republic is the Dollar.) or ((-17 + 9) < (-2 - 16)))) and (not ((12 * -19) <= (-8 * -10 + 10 * 3) <= (-8 * -3 - 2 * -5)))) and (((not not ((9 * -8) < (19 * 16))) and (A chicken has 0 legs.)) or ((The chemical symbol for Platinum is Pt.) or (The chemical symbol for Lead is Cr.))))
B. (((The currency of Israel is the Pound.) or ((-17 - -3) < (46 % 1) < (1 * 6 * -1 * -3))) and ((The 2008 Olympics were held in Beijing.) and ((not ((3 % 1) < (-4 - -2))) and (((-14 * -17) != (-12 + -14)) and (The 2008 Olympics were held in Mexico City.))))) or (not ((not not (Saturn is the 5th planet from the Sun.)) or (A kangaroo has 4 legs.)))
C. not (((not not (not not (The capital of Ukraine is Vienna.))) and (((-6 * 5 * -2 * -5) >= (-10 + -3)) or (96 is less than or equal to 21.))) or (not (The currency of Egypt is the Shekel.)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 66265834,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. (not not ((not not ((The currency of United Kingdom is the Peso.) and (Earth is the 7th planet from the Sun.))) and (not ((20 + -14) == (-9 + -6))))) and (((((-14 * -7) != (4 * -1 + -2 * -4)) or ((The currency of Czech Republic is the Dollar.) or ((-17 + 9) < (-2 - 16)))) and (not ((12 * -19) <= (-8 * -10 + 10 * 3) <= (-8 * -3 - 2 * -5)))) and (((not not ((9 * -8) < (19 * 16))) and (A chicken has 0 legs.)) or ((The chemical symbol for Platinum is Pt.) or (The chemical symbol for Lead is Cr.))))\nB. (((The currency of Israel is the Pound.) or ((-17 - -3) < (46 % 1) < (1 * 6 * -1 * -3))) and ((The 2008 Olympics were held in Beijing.) and ((not ((3 % 1) < (-4 - -2))) and (((-14 * -17) != (-12 + -14)) and (The 2008 Olympics were held in Mexico City.))))) or (not ((not not (Saturn is the 5th planet from the Sun.)) or (A kangaroo has 4 legs.)))\nC. not (((not not (not not (The capital of Ukraine is Vienna.))) and (((-6 * 5 * -2 * -5) >= (-10 + -3)) or (96 is less than or equal to 21.))) or (not (The currency of Egypt is the Shekel.)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 66265834,
"true_count": 1
},
"seed": 66265834,
"task_id": 666265834,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (1958 is a leap year.) or (not ((38 % 6) > (8 * 4 * 10 * 4))) or (not not ((-4 + 15) < (4 + -3)))
B. (((3 ** 3) <= (0 * -20)) and (not ((-16 + -14) < (-13 * -4) < (6 * -1 * -3 * 10)))) or (((The square root of 4 is 12.) and ((4 ** 2) > (0 - -9))) and ((There are 29 days in August.) and ((1 ** 2) > (17 + 13))))
C. (((5 + -10) < (1 * 9 - 4 * -10) < (-8 * -2 * 3 * 10)) or (Oxygen is necessary for human survival.)) or ((Water boils at 100 degrees Celsius at sea level.) or (The 2020 Olympics were held in Los Angeles.)) or (((There are 31 days in October.) and (The human body has 206 bones.)) and ((-3 + -5) <= (11 * -14)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 20966804,
"true_count": 2
},
"question": "Review these logical expressions:\n\nA. (1958 is a leap year.) or (not ((38 % 6) > (8 * 4 * 10 * 4))) or (not not ((-4 + 15) < (4 + -3)))\nB. (((3 ** 3) <= (0 * -20)) and (not ((-16 + -14) < (-13 * -4) < (6 * -1 * -3 * 10)))) or (((The square root of 4 is 12.) and ((4 ** 2) > (0 - -9))) and ((There are 29 days in August.) and ((1 ** 2) > (17 + 13))))\nC. (((5 + -10) < (1 * 9 - 4 * -10) < (-8 * -2 * 3 * 10)) or (Oxygen is necessary for human survival.)) or ((Water boils at 100 degrees Celsius at sea level.) or (The 2020 Olympics were held in Los Angeles.)) or (((There are 31 days in October.) and (The human body has 206 bones.)) and ((-3 + -5) <= (11 * -14)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 20966804,
"true_count": 2
},
"seed": 20966804,
"task_id": 620966804,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (The 1964 Olympics were held in Tokyo.) or (((3 + -19) == (1 % 2)) or ((-1 - -7) < (-3 + -16)))
B. (((16 + 8) != (3 ** 2)) and ((5 * 7 * 2 * -6) == (-3 * 9))) and ((795 is a Fibonacci number.) and ((18 - 17) > (2 ** 2)))
C. ((Earth is the 3rd planet from the Sun.) or (Uranus is the 7th planet from the Sun.)) and ((Alcohol is a liquid at room temperature.) and ((-5 - -3) >= (2 * 5 * 7 * 9)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 3404850,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. (The 1964 Olympics were held in Tokyo.) or (((3 + -19) == (1 % 2)) or ((-1 - -7) < (-3 + -16)))\nB. (((16 + 8) != (3 ** 2)) and ((5 * 7 * 2 * -6) == (-3 * 9))) and ((795 is a Fibonacci number.) and ((18 - 17) > (2 ** 2)))\nC. ((Earth is the 3rd planet from the Sun.) or (Uranus is the 7th planet from the Sun.)) and ((Alcohol is a liquid at room temperature.) and ((-5 - -3) >= (2 * 5 * 7 * 9)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 3404850,
"true_count": 1
},
"seed": 3404850,
"task_id": 603404850,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. The speed of light is approximately 300,000 km/s.
B. (-10 - -15) < (-2 * 2 * 2 * 6) < (3 - -16)
C. (not not (The currency of Sweden is the Franc.)) or (not not ((9 * 2 + -7 * 10) < (10 * -15)))
D. ((The human body has 206 bones.) and ((18 + -11) >= (21 % 10))) or (not (The 1948 Olympics were held in London.))
E. not ((The chemical symbol for Manganese is Cu.) and (Steam is a liquid at room temperature.))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 91627837,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. The speed of light is approximately 300,000 km/s.\nB. (-10 - -15) < (-2 * 2 * 2 * 6) < (3 - -16)\nC. (not not (The currency of Sweden is the Franc.)) or (not not ((9 * 2 + -7 * 10) < (10 * -15)))\nD. ((The human body has 206 bones.) and ((18 + -11) >= (21 % 10))) or (not (The 1948 Olympics were held in London.))\nE. not ((The chemical symbol for Manganese is Cu.) and (Steam is a liquid at room temperature.))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 91627837,
"true_count": 3
},
"seed": 91627837,
"task_id": 691627837,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not (not ((There are 31 days in October.) or (((17 + 10) != (38 % 2)) and ((18 * 8) <= (31 % 1)))))
B. (((((1 % 2) == (3 ** 1)) and (Mercury is the 1st planet from the Sun.)) or (77 is an odd number.)) or ((not not (The chemical symbol for Gold is Au.)) and (The chemical symbol for Silver is Na.))) and (not not ((19 * 5) <= (-2 - -19))) and (not (not not (((-16 * 8) != (1 * 10 - 1 * 7)) or (A cat has 100 legs.))))
C. not not (((0 + -20) >= (12 % 1)) or ((((-10 + -13) != (12 % 9)) and (90 is divisible by 12.)) or ((-9 - 18) == (-12 - -6))))
D. ((The capital of New Zealand is Wellington.) or (The capital of Switzerland is Bern.) or (The capital of Saudi Arabia is Riyadh.)) or (not not (not (not not (The chemical symbol for Nitrogen is N.))))
E. not ((((-19 * 16) < (2 ** 3)) and (((2 ** 1) >= (13 * -19)) and ((1 * 18) != (-2 - 3)))) and (93 is a perfect square.))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 62245920,
"true_count": 3
},
"question": "Review these logical expressions:\n\nA. not (not ((There are 31 days in October.) or (((17 + 10) != (38 % 2)) and ((18 * 8) <= (31 % 1)))))\nB. (((((1 % 2) == (3 ** 1)) and (Mercury is the 1st planet from the Sun.)) or (77 is an odd number.)) or ((not not (The chemical symbol for Gold is Au.)) and (The chemical symbol for Silver is Na.))) and (not not ((19 * 5) <= (-2 - -19))) and (not (not not (((-16 * 8) != (1 * 10 - 1 * 7)) or (A cat has 100 legs.))))\nC. not not (((0 + -20) >= (12 % 1)) or ((((-10 + -13) != (12 % 9)) and (90 is divisible by 12.)) or ((-9 - 18) == (-12 - -6))))\nD. ((The capital of New Zealand is Wellington.) or (The capital of Switzerland is Bern.) or (The capital of Saudi Arabia is Riyadh.)) or (not not (not (not not (The chemical symbol for Nitrogen is N.))))\nE. not ((((-19 * 16) < (2 ** 3)) and (((2 ** 1) >= (13 * -19)) and ((1 * 18) != (-2 - 3)))) and (93 is a perfect square.))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 62245920,
"true_count": 3
},
"seed": 62245920,
"task_id": 662245920,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (((11 % 10) <= (-20 + -2) <= (-10 * -17)) or (((-9 * -2) <= (6 * -4 + 8 * 9)) and ((15 - -3) <= (10 + -9) <= (-3 * 17)))) or (((10 - -10) <= (5 * 11)) or ((The currency of Russia is the Ruble.) or ((19 + -12) < (19 - 6))))
B. (((The Sun revolves around the Earth.) and (48 is divisible by 10.)) or (182 is an odd number.)) and (There are 31 days in October.)
C. (The chemical symbol for Mercury is Hg.) and (not not (((-13 + -15) < (2 * -9)) and ((18 * 16) == (-17 + -11))))
D. (((The chemical symbol for Helium is Mn.) and (Peru is in South America.)) and (The capital of Norway is Seoul.)) and (not (((2 ** 3) < (36 % 5) < (7 * -1 * 9 * -2)) and ((0 * 9) >= (-10 - 4))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 8975528,
"true_count": 1
},
"question": "Analyze these boolean expressions:\n\nA. (((11 % 10) <= (-20 + -2) <= (-10 * -17)) or (((-9 * -2) <= (6 * -4 + 8 * 9)) and ((15 - -3) <= (10 + -9) <= (-3 * 17)))) or (((10 - -10) <= (5 * 11)) or ((The currency of Russia is the Ruble.) or ((19 + -12) < (19 - 6))))\nB. (((The Sun revolves around the Earth.) and (48 is divisible by 10.)) or (182 is an odd number.)) and (There are 31 days in October.)\nC. (The chemical symbol for Mercury is Hg.) and (not not (((-13 + -15) < (2 * -9)) and ((18 * 16) == (-17 + -11))))\nD. (((The chemical symbol for Helium is Mn.) and (Peru is in South America.)) and (The capital of Norway is Seoul.)) and (not (((2 ** 3) < (36 % 5) < (7 * -1 * 9 * -2)) and ((0 * 9) >= (-10 - 4))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 4,
"seed": 8975528,
"true_count": 1
},
"seed": 8975528,
"task_id": 608975528,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (((18 % 5) < (11 % 10)) or (Sharks are mammals.)) or (not (((-15 + -20) == (-5 + 14)) and ((16 + -2) < (5 ** 1)))) or ((The 1968 Olympics were held in Athens.) or (not not ((Water is a liquid at room temperature.) and (The chemical symbol for Mercury is Hg.))))
B. (((2 ** 3) == (-1 + -4)) or (The capital of Venezuela is Caracas.)) or (not not ((not not (Uranus is the 6th planet from the Sun.)) or (((-2 * 3 * 10 * 1) < (4 - 10)) and ((18 % 3) != (-14 - 14)))))
C. not ((The chemical symbol for Chromium is Cr.) or (A dog has 4 legs.) or (not (((-3 * -6) <= (-10 * 3 * 3 * 6)) and ((4 ** 3) == (10 - -17)))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 28785872,
"true_count": 2
},
"question": "Consider the following logical expressions:\n\nA. (((18 % 5) < (11 % 10)) or (Sharks are mammals.)) or (not (((-15 + -20) == (-5 + 14)) and ((16 + -2) < (5 ** 1)))) or ((The 1968 Olympics were held in Athens.) or (not not ((Water is a liquid at room temperature.) and (The chemical symbol for Mercury is Hg.))))\nB. (((2 ** 3) == (-1 + -4)) or (The capital of Venezuela is Caracas.)) or (not not ((not not (Uranus is the 6th planet from the Sun.)) or (((-2 * 3 * 10 * 1) < (4 - 10)) and ((18 % 3) != (-14 - 14)))))\nC. not ((The chemical symbol for Chromium is Cr.) or (A dog has 4 legs.) or (not (((-3 * -6) <= (-10 * 3 * 3 * 6)) and ((4 ** 3) == (10 - -17)))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 3,
"seed": 28785872,
"true_count": 2
},
"seed": 28785872,
"task_id": 628785872,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((-20 + -15) < (17 + 16)) and (A chicken has 2 legs.)
B. (not ((17 + -1) < (-4 - 4))) or (((-4 * 2 - -3 * -6) <= (34 % 9)) and (not (The capital of Philippines is Singapore.)))
C. ((The Pacific Ocean is the largest ocean.) and (There are 30 days in September.)) and (((Helium is a gas at room temperature.) or ((4 ** 2) != (-10 - 18))) and (not not ((-15 + 13) != (10 * 10 * 9 * 0))))
D. (((5 * -4 - 3 * -4) >= (5 * -5)) and ((Saturn is the 5th planet from the Sun.) or ((5 ** 3) > (20 % 8)))) or ((13 * -2) <= (38 % 10) <= (13 + -20)) or ((((-14 - -10) >= (8 * -5 * 5 * 0)) and (The capital of France is Paris.)) and (((32 % 5) == (47 % 6)) and ((19 - -12) < (-2 * 3 * -6 * 4))))
E. not (((Alcohol is a liquid at room temperature.) or (Mercury is the 4th planet from the Sun.)) and (((6 + -11) > (5 + -3)) or ((-20 * -1) > (17 * -15))))
F. (India is in Asia.) or (The Moon produces its own light.) or (((5 - 19) == (-16 * 9)) or ((Jupiter is the 8th planet from the Sun.) or ((3 * -3) != (2 * 5 + 10 * -8))))
G. ((((8 - -9) > (8 + 19)) or (1975 is a leap year.)) and (not not (The currency of Norway is the Krone.))) or (((Egypt is in South America.) or ((16 * -2) != (-13 + -13))) and (((6 % 3) > (25 % 5)) or ((6 - -2) <= (1 - 19) <= (-8 * 6 - 2 * 7))))
H. (not not ((2 - -8) != (8 * -18))) and (The currency of New Zealand is the Koruna.)
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 39948767,
"true_count": 5
},
"question": "Given the following boolean expressions:\n\nA. ((-20 + -15) < (17 + 16)) and (A chicken has 2 legs.)\nB. (not ((17 + -1) < (-4 - 4))) or (((-4 * 2 - -3 * -6) <= (34 % 9)) and (not (The capital of Philippines is Singapore.)))\nC. ((The Pacific Ocean is the largest ocean.) and (There are 30 days in September.)) and (((Helium is a gas at room temperature.) or ((4 ** 2) != (-10 - 18))) and (not not ((-15 + 13) != (10 * 10 * 9 * 0))))\nD. (((5 * -4 - 3 * -4) >= (5 * -5)) and ((Saturn is the 5th planet from the Sun.) or ((5 ** 3) > (20 % 8)))) or ((13 * -2) <= (38 % 10) <= (13 + -20)) or ((((-14 - -10) >= (8 * -5 * 5 * 0)) and (The capital of France is Paris.)) and (((32 % 5) == (47 % 6)) and ((19 - -12) < (-2 * 3 * -6 * 4))))\nE. not (((Alcohol is a liquid at room temperature.) or (Mercury is the 4th planet from the Sun.)) and (((6 + -11) > (5 + -3)) or ((-20 * -1) > (17 * -15))))\nF. (India is in Asia.) or (The Moon produces its own light.) or (((5 - 19) == (-16 * 9)) or ((Jupiter is the 8th planet from the Sun.) or ((3 * -3) != (2 * 5 + 10 * -8))))\nG. ((((8 - -9) > (8 + 19)) or (1975 is a leap year.)) and (not not (The currency of Norway is the Krone.))) or (((Egypt is in South America.) or ((16 * -2) != (-13 + -13))) and (((6 % 3) > (25 % 5)) or ((6 - -2) <= (1 - 19) <= (-8 * 6 - 2 * 7))))\nH. (not not ((2 - -8) != (8 * -18))) and (The currency of New Zealand is the Koruna.)\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 39948767,
"true_count": 5
},
"seed": 39948767,
"task_id": 639948767,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (A chicken has 6 legs.)
B. ((-20 - 0) == (6 * 0 * -5 * 10)) or ((42 % 3) != (-17 - 17)) or (not (((7 * 3 + 4 * -2) < (-13 - -10) < (18 - -8)) or (The Great Wall of China was built in one year.)))
C. (((The currency of United States is the Dollar.) and ((-2 + -3) <= (7 * -20))) and (((-9 * -9 - 0 * -2) != (-12 * -18)) or ((3 ** 3) <= (6 * -18)))) and (The currency of United Kingdom is the Pound.) and (((The chemical symbol for Chlorine is Cl.) or (49 is an odd number.)) or (((2 * -5 - -2 * -3) > (1 ** 2)) or ((12 * -14) <= (-4 * 1 - 8 * -10))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 55964359,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. not (A chicken has 6 legs.)\nB. ((-20 - 0) == (6 * 0 * -5 * 10)) or ((42 % 3) != (-17 - 17)) or (not (((7 * 3 + 4 * -2) < (-13 - -10) < (18 - -8)) or (The Great Wall of China was built in one year.)))\nC. (((The currency of United States is the Dollar.) and ((-2 + -3) <= (7 * -20))) and (((-9 * -9 - 0 * -2) != (-12 * -18)) or ((3 ** 3) <= (6 * -18)))) and (The currency of United Kingdom is the Pound.) and (((The chemical symbol for Chlorine is Cl.) or (49 is an odd number.)) or (((2 * -5 - -2 * -3) > (1 ** 2)) or ((12 * -14) <= (-4 * 1 - 8 * -10))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 55964359,
"true_count": 2
},
"seed": 55964359,
"task_id": 655964359,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not ((1 * -8 - 1 * -9) < (6 * 4 * -10 * -7))
B. (((-4 * 8 + -3 * -1) <= (16 % 1)) or (not (The currency of Turkey is the Lira.))) and ((South Korea is in Asia.) or (not not ((4 ** 2) != (44 % 4))))
C. not (((Spiders are insects.) or ((11 % 9) <= (14 - -3))) and (((-5 - 17) == (5 % 2)) and (The 1976 Olympics were held in London.)))
D. not not ((1 ** 2) < (50 % 2))
E. ((((-12 + 2) == (-16 * 13)) and ((-4 - -16) > (-11 + 17))) and ((5 * 10 - -5 * 2) == (4 * -2 * -10 * -1))) and ((((-4 + -16) > (0 * 6)) and ((1 + -1) <= (18 + 18))) or (Humans have three lungs.))
F. (Uranus is the 4th planet from the Sun.) and ((not (Uranus is the 7th planet from the Sun.)) or ((Vietnam is in Asia.) or ((14 - 2) < (9 % 2) < (-20 * 20))))
G. ((not ((-17 + 9) < (3 + 1) < (1 ** 1))) and ((2 + 0) == (-5 * -6))) and (not not ((Oxygen is a gas at room temperature.) and ((-4 * 2) < (37 % 2))))
H. (not not ((14 + -16) != (8 + -9))) and (not not ((France is in Europe.) and ((-3 * 5) != (10 * -9))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 91758109,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. not ((1 * -8 - 1 * -9) < (6 * 4 * -10 * -7))\nB. (((-4 * 8 + -3 * -1) <= (16 % 1)) or (not (The currency of Turkey is the Lira.))) and ((South Korea is in Asia.) or (not not ((4 ** 2) != (44 % 4))))\nC. not (((Spiders are insects.) or ((11 % 9) <= (14 - -3))) and (((-5 - 17) == (5 % 2)) and (The 1976 Olympics were held in London.)))\nD. not not ((1 ** 2) < (50 % 2))\nE. ((((-12 + 2) == (-16 * 13)) and ((-4 - -16) > (-11 + 17))) and ((5 * 10 - -5 * 2) == (4 * -2 * -10 * -1))) and ((((-4 + -16) > (0 * 6)) and ((1 + -1) <= (18 + 18))) or (Humans have three lungs.))\nF. (Uranus is the 4th planet from the Sun.) and ((not (Uranus is the 7th planet from the Sun.)) or ((Vietnam is in Asia.) or ((14 - 2) < (9 % 2) < (-20 * 20))))\nG. ((not ((-17 + 9) < (3 + 1) < (1 ** 1))) and ((2 + 0) == (-5 * -6))) and (not not ((Oxygen is a gas at room temperature.) and ((-4 * 2) < (37 % 2))))\nH. (not not ((14 + -16) != (8 + -9))) and (not not ((France is in Europe.) and ((-3 * 5) != (10 * -9))))\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": 91758109,
"true_count": 3
},
"seed": 91758109,
"task_id": 691758109,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not (not ((not not (45 is an even number.)) or (not ((-7 * 5) < (9 % 9) < (6 * -6 + 10 * 6)))))
B. not (not (not not (The chemical symbol for Uranium is U.)))
C. (not not (Jupiter is the 5th planet from the Sun.)) and (not ((1 ** 2) < (2 + -15)))
D. ((not ((Diamonds are made of carbon.) and ((2 ** 3) == (4 - 5)))) and (World War II began occurred in 1939.)) or (((345 is a perfect square.) or (The Great Fire of London occurred in 1666.)) and ((39 % 3) >= (-20 + 20))) or (((((3 ** 1) < (-2 + -5)) and ((9 * 4 + -1 * 0) == (5 + -3))) and ((-3 - 3) < (45 % 6) < (7 * 5 + -5 * -5))) and ((((1 - -15) == (-10 * -6 * 2 * 5)) and (The Moon produces its own light.)) and ((1 ** 3) <= (9 * -4 + -6 * 0))))
E. ((((Sound cannot travel through a vacuum.) and ((-4 + 11) < (13 % 4))) and ((Peru is in South America.) and ((3 % 9) <= (10 - -2) <= (-14 * -1)))) and (((1 ** 1) >= (3 ** 2)) and ((-8 * -6 + -8 * -4) != (19 * 1)))) or (not ((((-15 + -14) < (9 * -5 - 6 * 6)) or (The Great Wall of China was built in one year.)) or (not not (The square root of 36 is 6.))))
F. (not not (The Moon produces its own light.)) or (((not ((-7 * -2 * -6 * -2) == (1 ** 2))) and (Oil is a liquid at room temperature.)) or ((83 is a prime number.) and (South Africa is in Antarctica.)) or (Diamonds are made of carbon.))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 38715032,
"true_count": 5
},
"question": "Evaluate each expression below:\n\nA. not not (not ((not not (45 is an even number.)) or (not ((-7 * 5) < (9 % 9) < (6 * -6 + 10 * 6)))))\nB. not (not (not not (The chemical symbol for Uranium is U.)))\nC. (not not (Jupiter is the 5th planet from the Sun.)) and (not ((1 ** 2) < (2 + -15)))\nD. ((not ((Diamonds are made of carbon.) and ((2 ** 3) == (4 - 5)))) and (World War II began occurred in 1939.)) or (((345 is a perfect square.) or (The Great Fire of London occurred in 1666.)) and ((39 % 3) >= (-20 + 20))) or (((((3 ** 1) < (-2 + -5)) and ((9 * 4 + -1 * 0) == (5 + -3))) and ((-3 - 3) < (45 % 6) < (7 * 5 + -5 * -5))) and ((((1 - -15) == (-10 * -6 * 2 * 5)) and (The Moon produces its own light.)) and ((1 ** 3) <= (9 * -4 + -6 * 0))))\nE. ((((Sound cannot travel through a vacuum.) and ((-4 + 11) < (13 % 4))) and ((Peru is in South America.) and ((3 % 9) <= (10 - -2) <= (-14 * -1)))) and (((1 ** 1) >= (3 ** 2)) and ((-8 * -6 + -8 * -4) != (19 * 1)))) or (not ((((-15 + -14) < (9 * -5 - 6 * 6)) or (The Great Wall of China was built in one year.)) or (not not (The square root of 36 is 6.))))\nF. (not not (The Moon produces its own light.)) or (((not ((-7 * -2 * -6 * -2) == (1 ** 2))) and (Oil is a liquid at room temperature.)) or ((83 is a prime number.) and (South Africa is in Antarctica.)) or (Diamonds are made of carbon.))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 38715032,
"true_count": 5
},
"seed": 38715032,
"task_id": 638715032,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. ((not not ((The United States declared independence occurred in 1776.) and (A dolphin is a mammal.))) and (((Uranus is the 6th planet from the Sun.) or ((-1 * 3 * -4 * -2) > (10 + -20))) and (not ((-4 + -13) <= (3 % 8))))) or (not (not (The 1984 Olympics were held in Los Angeles.)))
B. (((The square root of 9 is 3.) and (1908 is a leap year.)) and ((not not ((-15 * 17) >= (1 ** 2))) and ((The chemical symbol for Helium is He.) and ((-5 + 10) >= (-11 + 16))))) and ((((17 + -17) != (-3 + -13)) and (Steam is a gas at room temperature.)) and ((((-11 + 7) >= (-20 - -8)) or (A snake is a reptile.)) or ((-6 + -1) == (18 - 5))))
C. (not (((The currency of Switzerland is the Franc.) and ((3 ** 2) < (5 - 9) < (1 - -17))) and (((23 % 9) <= (1 * -7 * 10 * -7) <= (-13 + -14)) and ((-1 + 7) < (5 * -10 + 8 * -1) < (-10 + 16))))) and ((not (not not (Uranus is the 6th planet from the Sun.))) and (not not ((A cat is a mammal.) or (The chemical symbol for Nickel is Cr.))))
D. ((((5 - -8) > (4 ** 2)) and ((Thailand is in Asia.) and (The currency of Singapore is the Pound.))) or ((The chemical symbol for Calcium is Ca.) and ((The currency of Canada is the Won.) or (The 1960 Olympics were held in Munich.)))) and ((Vietnam is in Asia.) or (A beetle is an insect.))
E. ((((-8 * 7 - 9 * -10) >= (9 + 16)) or ((Ice is a solid at room temperature.) or ((-6 - 7) != (14 + -13)))) or ((not not ((12 * 9) == (20 % 8))) or ((Wood is a liquid at room temperature.) or (Colombia is in North America.)))) and (not ((-2 * 7) == (2 % 5)))
F. not ((There are 29 days in July.) and ((not ((-6 * 7 * 2 * 0) > (-12 * -5))) or (A pig has 4 legs.)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 17613745,
"true_count": 4
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. ((not not ((The United States declared independence occurred in 1776.) and (A dolphin is a mammal.))) and (((Uranus is the 6th planet from the Sun.) or ((-1 * 3 * -4 * -2) > (10 + -20))) and (not ((-4 + -13) <= (3 % 8))))) or (not (not (The 1984 Olympics were held in Los Angeles.)))\nB. (((The square root of 9 is 3.) and (1908 is a leap year.)) and ((not not ((-15 * 17) >= (1 ** 2))) and ((The chemical symbol for Helium is He.) and ((-5 + 10) >= (-11 + 16))))) and ((((17 + -17) != (-3 + -13)) and (Steam is a gas at room temperature.)) and ((((-11 + 7) >= (-20 - -8)) or (A snake is a reptile.)) or ((-6 + -1) == (18 - 5))))\nC. (not (((The currency of Switzerland is the Franc.) and ((3 ** 2) < (5 - 9) < (1 - -17))) and (((23 % 9) <= (1 * -7 * 10 * -7) <= (-13 + -14)) and ((-1 + 7) < (5 * -10 + 8 * -1) < (-10 + 16))))) and ((not (not not (Uranus is the 6th planet from the Sun.))) and (not not ((A cat is a mammal.) or (The chemical symbol for Nickel is Cr.))))\nD. ((((5 - -8) > (4 ** 2)) and ((Thailand is in Asia.) and (The currency of Singapore is the Pound.))) or ((The chemical symbol for Calcium is Ca.) and ((The currency of Canada is the Won.) or (The 1960 Olympics were held in Munich.)))) and ((Vietnam is in Asia.) or (A beetle is an insect.))\nE. ((((-8 * 7 - 9 * -10) >= (9 + 16)) or ((Ice is a solid at room temperature.) or ((-6 - 7) != (14 + -13)))) or ((not not ((12 * 9) == (20 % 8))) or ((Wood is a liquid at room temperature.) or (Colombia is in North America.)))) and (not ((-2 * 7) == (2 % 5)))\nF. not ((There are 29 days in July.) and ((not ((-6 * 7 * 2 * 0) > (-12 * -5))) or (A pig has 4 legs.)))\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": 6,
"seed": 17613745,
"true_count": 4
},
"seed": 17613745,
"task_id": 617613745,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not (73 is less than or equal to 88.)) or ((not (1951 is a leap year.)) or (((The chemical symbol for Nitrogen is N.) and ((-13 - 19) > (-12 - 7))) or (((5 ** 3) < (2 ** 1) < (-3 + 12)) or (The currency of Nigeria is the Naira.))))
B. (((((7 * 8) != (13 * 7)) or (The 1956 Olympics were held in Rio de Janeiro.)) and (((10 * 2 * 2 * -1) > (-9 * 7 * 6 * -10)) and (The chemical symbol for Aluminum is Ne.))) or (not not ((The currency of Nigeria is the Peso.) or ((40 % 2) >= (14 + -8))))) or ((The chemical symbol for Potassium is K.) and (((-1 * 7 - -2 * 9) <= (19 - 4)) or ((5 ** 3) == (18 - -20)))) or (not (World War II ended occurred in 1945.))
C. ((not not ((-10 - 14) >= (12 - 11))) or ((not (The chemical symbol for Sodium is Na.)) or ((38 % 3) > (9 + 5)))) and ((((A bee is an insect.) and ((14 + -8) <= (-3 * 10))) or ((25 % 6) == (1 * 8 - 10 * -10))) or (not not (((-2 * 9 - -7 * -8) >= (4 ** 3)) or (The capital of Morocco is Rome.))))
D. ((The 1920 Olympics were held in Mexico City.) and (((The 1988 Olympics were held in Seoul.) and ((-1 * 2 - 5 * 1) == (-20 * -8))) and ((The chemical symbol for Manganese is Mn.) or (Ice is a gas at room temperature.)))) or (((-9 * -10 + 3 * -9) != (23 % 7)) and (not not (Saturn is the 6th planet from the Sun.)) and (((The chemical symbol for Chlorine is Au.) and (The chemical symbol for Nitrogen is N.)) and ((46 % 3) < (32 % 2))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 94556891,
"true_count": 2
},
"question": "Study the following logical statements:\n\nA. (not (73 is less than or equal to 88.)) or ((not (1951 is a leap year.)) or (((The chemical symbol for Nitrogen is N.) and ((-13 - 19) > (-12 - 7))) or (((5 ** 3) < (2 ** 1) < (-3 + 12)) or (The currency of Nigeria is the Naira.))))\nB. (((((7 * 8) != (13 * 7)) or (The 1956 Olympics were held in Rio de Janeiro.)) and (((10 * 2 * 2 * -1) > (-9 * 7 * 6 * -10)) and (The chemical symbol for Aluminum is Ne.))) or (not not ((The currency of Nigeria is the Peso.) or ((40 % 2) >= (14 + -8))))) or ((The chemical symbol for Potassium is K.) and (((-1 * 7 - -2 * 9) <= (19 - 4)) or ((5 ** 3) == (18 - -20)))) or (not (World War II ended occurred in 1945.))\nC. ((not not ((-10 - 14) >= (12 - 11))) or ((not (The chemical symbol for Sodium is Na.)) or ((38 % 3) > (9 + 5)))) and ((((A bee is an insect.) and ((14 + -8) <= (-3 * 10))) or ((25 % 6) == (1 * 8 - 10 * -10))) or (not not (((-2 * 9 - -7 * -8) >= (4 ** 3)) or (The capital of Morocco is Rome.))))\nD. ((The 1920 Olympics were held in Mexico City.) and (((The 1988 Olympics were held in Seoul.) and ((-1 * 2 - 5 * 1) == (-20 * -8))) and ((The chemical symbol for Manganese is Mn.) or (Ice is a gas at room temperature.)))) or (((-9 * -10 + 3 * -9) != (23 % 7)) and (not not (Saturn is the 6th planet from the Sun.)) and (((The chemical symbol for Chlorine is Au.) and (The chemical symbol for Nitrogen is N.)) and ((46 % 3) < (32 % 2))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 94556891,
"true_count": 2
},
"seed": 94556891,
"task_id": 694556891,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. not ((9 * -2 + 3 * 5) > (20 * 12))
B. ((The United States declared independence occurred in 1776.) or ((3 * -1 - 9 * 8) <= (-2 * 18))) or ((23 % 3) > (10 - 20))
C. (15 + 12) > (-5 * 4)
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 60892008,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. not ((9 * -2 + 3 * 5) > (20 * 12))\nB. ((The United States declared independence occurred in 1776.) or ((3 * -1 - 9 * 8) <= (-2 * 18))) or ((23 % 3) > (10 - 20))\nC. (15 + 12) > (-5 * 4)\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 60892008,
"true_count": 3
},
"seed": 60892008,
"task_id": 660892008,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. ((132 is an even number.) or (Mercury is the 1st planet from the Sun.)) and (not (not not ((2 ** 2) == (1 ** 3))))
B. (((not not (The 1956 Olympics were held in Paris.)) and ((Copper is a solid at room temperature.) or (The Great Wall of China was built in one year.))) or (((Mercury is a liquid at room temperature.) and ((-14 - 14) > (4 * 9 - -6 * -3))) or (80 is a prime number.))) or ((((10 * 11) > (-11 * -18)) and (Oxygen is necessary for human survival.)) or (not not ((-19 * -18) < (0 * 16)))) or (not not ((not ((4 * 3 + -5 * 1) == (13 * -5))) and (not ((-1 * -7 * 3 * -1) <= (3 ** 2)))))
C. (not not (not not ((Canada is in North America.) and (The chemical symbol for Gold is Cl.)))) or (not ((not not (Helium is a gas at room temperature.)) and ((-9 * 10) <= (20 * -1) <= (-5 - 10))))
D. not not ((not not ((10 * 9) != (1 ** 1))) and (The currency of United Kingdom is the Pound.) and ((((3 % 2) > (12 + 10)) or (Saudi Arabia is in North America.)) and ((The human body has 206 bones.) and (Morocco is in Antarctica.))))
E. not not (((-9 * -8) >= (-8 * 2 * 1 * 6)) or (The capital of Canada is Paris.))
F. (((A human has 4 legs.) and ((-12 * 18) != (10 + -13))) or (The capital of Brazil is Brasilia.)) or (((A butterfly has 6 legs.) and ((0 * 7 + -9 * -7) < (25 % 2))) and (2009 is a leap year.))
G. (((((-3 * 1 - 6 * -7) >= (-9 - 6)) and (World War I began occurred in 1914.)) and (not not (2087 is a leap year.))) and ((-15 - 15) > (-17 * -1))) or ((((20 - 14) <= (21 % 7)) and (not not (The capital of Thailand is Bangkok.))) and (not ((-10 - -7) != (6 * -2 * -7 * 5))) and ((Saturn is the 6th planet from the Sun.) or ((46 % 1) != (-20 - -13))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 87331597,
"true_count": 3
},
"question": "Review these logical expressions:\n\nA. ((132 is an even number.) or (Mercury is the 1st planet from the Sun.)) and (not (not not ((2 ** 2) == (1 ** 3))))\nB. (((not not (The 1956 Olympics were held in Paris.)) and ((Copper is a solid at room temperature.) or (The Great Wall of China was built in one year.))) or (((Mercury is a liquid at room temperature.) and ((-14 - 14) > (4 * 9 - -6 * -3))) or (80 is a prime number.))) or ((((10 * 11) > (-11 * -18)) and (Oxygen is necessary for human survival.)) or (not not ((-19 * -18) < (0 * 16)))) or (not not ((not ((4 * 3 + -5 * 1) == (13 * -5))) and (not ((-1 * -7 * 3 * -1) <= (3 ** 2)))))\nC. (not not (not not ((Canada is in North America.) and (The chemical symbol for Gold is Cl.)))) or (not ((not not (Helium is a gas at room temperature.)) and ((-9 * 10) <= (20 * -1) <= (-5 - 10))))\nD. not not ((not not ((10 * 9) != (1 ** 1))) and (The currency of United Kingdom is the Pound.) and ((((3 % 2) > (12 + 10)) or (Saudi Arabia is in North America.)) and ((The human body has 206 bones.) and (Morocco is in Antarctica.))))\nE. not not (((-9 * -8) >= (-8 * 2 * 1 * 6)) or (The capital of Canada is Paris.))\nF. (((A human has 4 legs.) and ((-12 * 18) != (10 + -13))) or (The capital of Brazil is Brasilia.)) or (((A butterfly has 6 legs.) and ((0 * 7 + -9 * -7) < (25 % 2))) and (2009 is a leap year.))\nG. (((((-3 * 1 - 6 * -7) >= (-9 - 6)) and (World War I began occurred in 1914.)) and (not not (2087 is a leap year.))) and ((-15 - 15) > (-17 * -1))) or ((((20 - 14) <= (21 % 7)) and (not not (The capital of Thailand is Bangkok.))) and (not ((-10 - -7) != (6 * -2 * -7 * 5))) and ((Saturn is the 6th planet from the Sun.) or ((46 % 1) != (-20 - -13))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 87331597,
"true_count": 3
},
"seed": 87331597,
"task_id": 687331597,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (not ((A cow has 8 legs.) and (not not ((6 * -4 - 8 * 5) <= (-4 - 15))) and (((The French Revolution began occurred in 1789.) or (297 is a perfect square.)) and (The capital of Belgium is Brussels.)))) and (((The chemical symbol for Uranium is U.) and (A elephant has 4 legs.)) or (((-4 * 5 - 2 * -9) < (0 + -2) < (18 + 4)) or (not not (Mars is the 4th planet from the Sun.))) or (not not (Jupiter is the 2nd planet from the Sun.)))
B. ((not not (((Helium is a solid at room temperature.) or (Uranus is the 7th planet from the Sun.)) and (India is in North America.))) and ((The currency of Colombia is the Peso.) and ((((19 - -5) <= (17 * 5)) and (The chemical symbol for Phosphorus is P.)) and ((2 + 5) >= (-8 * 1 * 8 * -1))))) or ((not not (The chemical symbol for Sodium is U.)) and (not (not not ((-11 + -13) > (6 * -5 * 5 * -8)))) and (not not ((The square root of 36 is 6.) or (not not (Argentina is in South America.)))))
C. (not (((11 * 0) <= (-8 * -10 + 1 * 3)) and (((8 * 2 * 8 * -3) != (6 % 5)) or ((Diamonds are made of carbon.) and (Ice is a liquid at room temperature.))))) or (not not (not not (not not ((7 + -17) < (4 - -15) < (2 ** 3)))))
D. ((((not (Italy is in Africa.)) or (Iron is a solid at room temperature.)) and ((The 1900 Olympics were held in Los Angeles.) and (not not ((2 * -7 - 8 * 0) != (5 - 3))))) and (not not (Carbon dioxide is a gas at room temperature.))) and (not ((A horse has 4 legs.) or ((-9 - 5) > (25 % 2))))
E. not not (((((South Africa is in Africa.) and (A ladybug is a fish.)) and (1955 is a leap year.)) or ((not not (Ice is a solid at room temperature.)) or ((-10 * -9) < (-12 * -18) < (3 ** 1)))) and (not (not not (((29 % 1) >= (-6 * 6 + 7 * 3)) and (The human body has 206 bones.)))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 79298617,
"true_count": 1
},
"question": "Consider the following logical expressions:\n\nA. (not ((A cow has 8 legs.) and (not not ((6 * -4 - 8 * 5) <= (-4 - 15))) and (((The French Revolution began occurred in 1789.) or (297 is a perfect square.)) and (The capital of Belgium is Brussels.)))) and (((The chemical symbol for Uranium is U.) and (A elephant has 4 legs.)) or (((-4 * 5 - 2 * -9) < (0 + -2) < (18 + 4)) or (not not (Mars is the 4th planet from the Sun.))) or (not not (Jupiter is the 2nd planet from the Sun.)))\nB. ((not not (((Helium is a solid at room temperature.) or (Uranus is the 7th planet from the Sun.)) and (India is in North America.))) and ((The currency of Colombia is the Peso.) and ((((19 - -5) <= (17 * 5)) and (The chemical symbol for Phosphorus is P.)) and ((2 + 5) >= (-8 * 1 * 8 * -1))))) or ((not not (The chemical symbol for Sodium is U.)) and (not (not not ((-11 + -13) > (6 * -5 * 5 * -8)))) and (not not ((The square root of 36 is 6.) or (not not (Argentina is in South America.)))))\nC. (not (((11 * 0) <= (-8 * -10 + 1 * 3)) and (((8 * 2 * 8 * -3) != (6 % 5)) or ((Diamonds are made of carbon.) and (Ice is a liquid at room temperature.))))) or (not not (not not (not not ((7 + -17) < (4 - -15) < (2 ** 3)))))\nD. ((((not (Italy is in Africa.)) or (Iron is a solid at room temperature.)) and ((The 1900 Olympics were held in Los Angeles.) and (not not ((2 * -7 - 8 * 0) != (5 - 3))))) and (not not (Carbon dioxide is a gas at room temperature.))) and (not ((A horse has 4 legs.) or ((-9 - 5) > (25 % 2))))\nE. not not (((((South Africa is in Africa.) and (A ladybug is a fish.)) and (1955 is a leap year.)) or ((not not (Ice is a solid at room temperature.)) or ((-10 * -9) < (-12 * -18) < (3 ** 1)))) and (not (not not (((29 % 1) >= (-6 * 6 + 7 * 3)) and (The human body has 206 bones.)))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 79298617,
"true_count": 1
},
"seed": 79298617,
"task_id": 679298617,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. ((((-5 - -20) == (7 + 1)) and (The 1948 Olympics were held in Los Angeles.)) and ((27 % 7) < (-7 - -19) < (-6 - -12))) and ((-3 * -2) != (5 - -10)) and ((-10 - 5) > (25 % 9))
B. not ((((-17 + 19) != (-9 * 1 + 4 * 2)) or (The currency of China is the Dong.)) and ((1991 is a leap year.) or ((16 * 16) < (-14 + -15))))
C. (not (((-8 * -3 * -9 * -1) >= (-4 * -3 + 8 * -1)) or ((1 * 7 - -6 * -10) >= (5 - -3)))) or (Humans only use 10% of their brain.) or (not ((Plants produce oxygen through photosynthesis.) and (Nitrogen is a gas at room temperature.)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 1416736,
"true_count": 1
},
"question": "Examine these expressions:\n\nA. ((((-5 - -20) == (7 + 1)) and (The 1948 Olympics were held in Los Angeles.)) and ((27 % 7) < (-7 - -19) < (-6 - -12))) and ((-3 * -2) != (5 - -10)) and ((-10 - 5) > (25 % 9))\nB. not ((((-17 + 19) != (-9 * 1 + 4 * 2)) or (The currency of China is the Dong.)) and ((1991 is a leap year.) or ((16 * 16) < (-14 + -15))))\nC. (not (((-8 * -3 * -9 * -1) >= (-4 * -3 + 8 * -1)) or ((1 * 7 - -6 * -10) >= (5 - -3)))) or (Humans only use 10% of their brain.) or (not ((Plants produce oxygen through photosynthesis.) and (Nitrogen is a gas at room temperature.)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 3,
"seed": 1416736,
"true_count": 1
},
"seed": 1416736,
"task_id": 601416736,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (((17 + 9) <= (5 + -5)) or (The 1980 Olympics were held in Moscow.)) and (not not (The 1912 Olympics were held in Stockholm.))
B. not (not not (The capital of Spain is Madrid.))
C. There are 28 days in February.
D. not ((2 % 2) > (-4 * -5))
E. (((20 % 4) <= (2 ** 3) <= (13 * -7)) and (Wood is a liquid at room temperature.)) and (((4 ** 3) >= (0 - 1)) or ((0 * -12) < (20 * 4) < (-14 * -2)))
F. (((0 * -8 - 8 * -9) <= (-13 * 12)) and ((43 % 1) < (1 ** 3))) or (not not ((3 % 7) == (1 * -20)))
G. The first iPhone was released occurred in 2007.
H. (The chemical symbol for Silver is Al.) and (not (The chemical symbol for Chromium is Pb.))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 40565920,
"true_count": 4
},
"question": "Study the following logical statements:\n\nA. (((17 + 9) <= (5 + -5)) or (The 1980 Olympics were held in Moscow.)) and (not not (The 1912 Olympics were held in Stockholm.))\nB. not (not not (The capital of Spain is Madrid.))\nC. There are 28 days in February.\nD. not ((2 % 2) > (-4 * -5))\nE. (((20 % 4) <= (2 ** 3) <= (13 * -7)) and (Wood is a liquid at room temperature.)) and (((4 ** 3) >= (0 - 1)) or ((0 * -12) < (20 * 4) < (-14 * -2)))\nF. (((0 * -8 - 8 * -9) <= (-13 * 12)) and ((43 % 1) < (1 ** 3))) or (not not ((3 % 7) == (1 * -20)))\nG. The first iPhone was released occurred in 2007.\nH. (The chemical symbol for Silver is Al.) and (not (The chemical symbol for Chromium is Pb.))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 40565920,
"true_count": 4
},
"seed": 40565920,
"task_id": 640565920,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (not ((意大利的首都是罗马。) or (鲸鱼是鱼类。))) and ((((2是完全平方数。) and (2020年奥运会在东京举办。)) and (2024年奥运会在赫尔辛基举办。)) and (594是斐波那契数。)) and ((((((-11 * -7) < (0 - -15)) or (一月有28天。)) or ((金星是距离太阳第4近的行星。) or (822是斐波那契数。))) and ((1972年奥运会在亚特兰大举办。) or (((3 * 0) <= (5 * 7 * -4 * 1)) or (第一次世界大战结束发生在1918年。)))) or (not not ((1 + 15) >= (12 + 11))))
B. ((not (秘鲁位于南美洲。)) or (((氮的化学符号是N。) and ((碳的化学符号是C。) or ((30 % 3) < (5 % 4)))) or (not not ((54是奇数。) or (南极洲是最冷的大陆。))))) and (not not ((310是斐波那契数。) or ((第一次世界大战结束发生在1913年。) and (水星是距离太阳第4近的行星。)))) and (not ((not not (not (光速比声速快。))) and (((地球是距离太阳第3近的行星。) or (土星是距离太阳第7近的行星。)) or (not not ((8 * -10 * 10 * -10) > (5 + 13))))))
C. not ((not (not (1920年奥运会在巴黎举办。))) and (((((-1 + -20) <= (2 ** 2)) and (水在海平面上的沸点是100摄氏度。)) or (((-18 + -10) != (1 * 0 - 1 * -9)) and ((42 % 6) <= (17 - 15)))) and (not (((-15 + 18) < (16 + -17) < (-3 * -1 - 10 * 5)) or ((20 + 12) >= (11 * -12))))))
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": 54699797,
"true_count": 1
},
"question": "下面是几个布尔表达式：\n\nA. (not ((意大利的首都是罗马。) or (鲸鱼是鱼类。))) and ((((2是完全平方数。) and (2020年奥运会在东京举办。)) and (2024年奥运会在赫尔辛基举办。)) and (594是斐波那契数。)) and ((((((-11 * -7) < (0 - -15)) or (一月有28天。)) or ((金星是距离太阳第4近的行星。) or (822是斐波那契数。))) and ((1972年奥运会在亚特兰大举办。) or (((3 * 0) <= (5 * 7 * -4 * 1)) or (第一次世界大战结束发生在1918年。)))) or (not not ((1 + 15) >= (12 + 11))))\nB. ((not (秘鲁位于南美洲。)) or (((氮的化学符号是N。) and ((碳的化学符号是C。) or ((30 % 3) < (5 % 4)))) or (not not ((54是奇数。) or (南极洲是最冷的大陆。))))) and (not not ((310是斐波那契数。) or ((第一次世界大战结束发生在1913年。) and (水星是距离太阳第4近的行星。)))) and (not ((not not (not (光速比声速快。))) and (((地球是距离太阳第3近的行星。) or (土星是距离太阳第7近的行星。)) or (not not ((8 * -10 * 10 * -10) > (5 + 13))))))\nC. not ((not (not (1920年奥运会在巴黎举办。))) and (((((-1 + -20) <= (2 ** 2)) and (水在海平面上的沸点是100摄氏度。)) or (((-18 + -10) != (1 * 0 - 1 * -9)) and ((42 % 6) <= (17 - 15)))) and (not (((-15 + 18) < (16 + -17) < (-3 * -1 - 10 * 5)) or ((20 + 12) >= (11 * -12))))))\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": 54699797,
"true_count": 1
},
"seed": 54699797,
"task_id": 654699797,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (not not ((意大利位于欧洲。) and ((4 + -1) < (-17 - 16) < (10 + 5)) and ((-19 + -13) < (35 % 9)))) or (((螃蟹有10条腿。) or (((19 + 5) <= (4 ** 1)) or (((4 ** 3) >= (12 - -3)) or (蜘蛛是昆虫。)))) or (not not ((-8 * 4 * -8 * 9) >= (-8 - 11))) or (((铜在常温下是固体。) or ((58是偶数。) or ((15 % 2) < (12 + -2)))) and (三月有29天。) and ((0 * -1 + 10 * -4) < (-1 * 20) < (16 + -6))))
B. (not (((17 * 9) != (-16 * 18)) and ((1948年是闰年。) or (中国长城是在一年内建成的。)))) and (((not not (not (木星是距离太阳第3近的行星。))) and (not not (法国大革命开始发生在1787年。))) and (not (((16 - -2) >= (10 + -4)) or ((19 * -12) != (-10 + -13)))) and (((((5 ** 2) == (0 * -9 - -5 * 8)) or ((19 % 3) >= (3 * -7 - -6 * 2))) and (((17 * 5) > (-3 - 8)) or ((0 + -18) <= (4 * 1 + 2 * -3) <= (-4 * -15)))) and ((-4 * -6 * -9 * 1) == (41 % 9))))
C. (not ((579是斐波那契数。) and (水星是距离太阳第1近的行星。))) or ((((企鹅能飞翔。) and ((150是偶数。) or (金枪鱼是鸟类。))) or ((天王星是距离太阳第4近的行星。) and (not not (太平洋是最大的海洋。)))) and (((-8 * 1 - -1 * 4) >= (8 * 14)) and (63能被6整除。)))
D. (not not ((汞在常温下是液体。) or ((2039年是闰年。) and (土耳其的首都是安卡拉。)) or ((人类只使用了大脑的10%。) and (((2 + 15) <= (5 * 4)) and ((-3 * 4) < (5 ** 2)))))) and (not not (not not (((-13 - -11) <= (-8 * -3 * 10 * 3)) and ((狗有100条腿。) and (铜在常温下是固体。)))))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 83679344,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. (not not ((意大利位于欧洲。) and ((4 + -1) < (-17 - 16) < (10 + 5)) and ((-19 + -13) < (35 % 9)))) or (((螃蟹有10条腿。) or (((19 + 5) <= (4 ** 1)) or (((4 ** 3) >= (12 - -3)) or (蜘蛛是昆虫。)))) or (not not ((-8 * 4 * -8 * 9) >= (-8 - 11))) or (((铜在常温下是固体。) or ((58是偶数。) or ((15 % 2) < (12 + -2)))) and (三月有29天。) and ((0 * -1 + 10 * -4) < (-1 * 20) < (16 + -6))))\nB. (not (((17 * 9) != (-16 * 18)) and ((1948年是闰年。) or (中国长城是在一年内建成的。)))) and (((not not (not (木星是距离太阳第3近的行星。))) and (not not (法国大革命开始发生在1787年。))) and (not (((16 - -2) >= (10 + -4)) or ((19 * -12) != (-10 + -13)))) and (((((5 ** 2) == (0 * -9 - -5 * 8)) or ((19 % 3) >= (3 * -7 - -6 * 2))) and (((17 * 5) > (-3 - 8)) or ((0 + -18) <= (4 * 1 + 2 * -3) <= (-4 * -15)))) and ((-4 * -6 * -9 * 1) == (41 % 9))))\nC. (not ((579是斐波那契数。) and (水星是距离太阳第1近的行星。))) or ((((企鹅能飞翔。) and ((150是偶数。) or (金枪鱼是鸟类。))) or ((天王星是距离太阳第4近的行星。) and (not not (太平洋是最大的海洋。)))) and (((-8 * 1 - -1 * 4) >= (8 * 14)) and (63能被6整除。)))\nD. (not not ((汞在常温下是液体。) or ((2039年是闰年。) and (土耳其的首都是安卡拉。)) or ((人类只使用了大脑的10%。) and (((2 + 15) <= (5 * 4)) and ((-3 * 4) < (5 ** 2)))))) and (not not (not not (((-13 - -11) <= (-8 * -3 * 10 * 3)) and ((狗有100条腿。) and (铜在常温下是固体。)))))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 83679344,
"true_count": 2
},
"seed": 83679344,
"task_id": 683679344,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not not (((硫的化学符号是S。) and (人类首次登月发生在1979年。)) or (秘鲁位于北美洲。))
B. ((冰在常温下是固体。) or (((-7 + 13) < (-5 - -14)) or (氦气在常温下是气体。))) or (not (((-10 + 4) >= (2 ** 2)) or (甲虫是哺乳动物。)))
C. (not (13是质数。)) or (not not (捷克的货币是卢布。)) or ((((-7 + 2) == (15 - -10)) or ((4 * -9 * 8 * -4) <= (4 ** 2))) or (((0 * 6 - -10 * -3) != (12 - -11)) or (八月有29天。)))
D. (第二次世界大战开始发生在1944年。) or (英国位于欧洲。) or ((((-8 * -2 - 2 * 8) <= (5 ** 1) <= (3 * 9 + 10 * 0)) or ((-11 * 0) <= (-2 * -5 - -10 * -4))) or ((第二次世界大战开始发生在1939年。) and (九月有29天。)))
E. ((not not ((-16 - 11) == (0 - -16))) or (((2 * -7 - -4 * 5) == (-5 - -19)) or ((-3 * -12) > (10 * 3 - -2 * 3)))) and ((347是完全平方数。) and (1909年是闰年。))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 93835205,
"true_count": 3
},
"question": "给定以下布尔表达式：\n\nA. not not (((硫的化学符号是S。) and (人类首次登月发生在1979年。)) or (秘鲁位于北美洲。))\nB. ((冰在常温下是固体。) or (((-7 + 13) < (-5 - -14)) or (氦气在常温下是气体。))) or (not (((-10 + 4) >= (2 ** 2)) or (甲虫是哺乳动物。)))\nC. (not (13是质数。)) or (not not (捷克的货币是卢布。)) or ((((-7 + 2) == (15 - -10)) or ((4 * -9 * 8 * -4) <= (4 ** 2))) or (((0 * 6 - -10 * -3) != (12 - -11)) or (八月有29天。)))\nD. (第二次世界大战开始发生在1944年。) or (英国位于欧洲。) or ((((-8 * -2 - 2 * 8) <= (5 ** 1) <= (3 * 9 + 10 * 0)) or ((-11 * 0) <= (-2 * -5 - -10 * -4))) or ((第二次世界大战开始发生在1939年。) and (九月有29天。)))\nE. ((not not ((-16 - 11) == (0 - -16))) or (((2 * -7 - -4 * 5) == (-5 - -19)) or ((-3 * -12) > (10 * 3 - -2 * 3)))) and ((347是完全平方数。) and (1909年是闰年。))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 93835205,
"true_count": 3
},
"seed": 93835205,
"task_id": 693835205,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (not ((not not ((47 % 9) <= (16 + -9))) and ((The chemical symbol for Mercury is C.) and ((13 * -8) != (1 - -17))) and (not ((16 * -11) >= (-15 - -15)))))
B. (not ((not not (not not (Australia is in Oceania.))) or (((The Titanic sank occurred in 1912.) or (Uranus is the 6th planet from the Sun.)) and ((Wood is a solid at room temperature.) and ((-12 + 5) <= (-10 + 10) <= (14 + 9)))))) or ((not (Saturn is the 2nd planet from the Sun.)) or (not not (not not ((29 % 3) == (-8 * 1 - -5 * -8)))))
C. not not (((Alcohol is a liquid at room temperature.) or (not not ((The 1896 Olympics were held in Athens.) and (There are 30 days in April.)))) and ((A human has 10 legs.) and (((-19 + -2) <= (-6 * 9 * 6 * -6)) and ((2 * -4) < (-7 * -2 + -6 * 9) < (14 * 19)))))
D. ((not ((4 ** 2) == (-19 + -2))) or (A human has 2 legs.) or (not ((5 ** 2) == (-1 * 10 + -5 * 1)))) or ((not (((The 1952 Olympics were held in Helsinki.) and (The currency of South Africa is the Rand.)) and (not (The chemical symbol for Copper is Cu.)))) and ((not not (There are 28 days in October.)) or ((((1 ** 2) > (-11 * -1)) or (69 is an even number.)) or (Gold is a solid at room temperature.))))
E. (not ((not not (((-18 + 10) <= (12 + 1) <= (13 * 7)) and (The 1988 Olympics were held in Tokyo.))) or (((3 - -18) < (-6 * 3 - 2 * 1)) and ((10 + 7) != (15 + 14))))) and (((not ((The capital of Argentina is Prague.) and (Mercury is the 1st planet from the Sun.))) or (((-16 - -16) == (-14 + -19)) or (The chemical symbol for Copper is Cu.)) or (Thailand is in Europe.)) and (((-15 - 14) <= (4 ** 2)) or (not not ((10 * -1 + -8 * -5) <= (29 % 2)))) and (not (World War I began occurred in 1914.)))
F. not ((not ((((12 - 3) < (5 * -7 + -6 * -1)) or ((5 - 3) <= (-3 * 9 * -8 * -7) <= (34 % 6))) and ((-20 + 18) >= (-17 + -17)))) and (((((3 ** 3) <= (-12 + 17)) and ((-14 - -1) == (10 * -7))) or (not (The currency of United Kingdom is the Ruble.))) or ((Wood is a solid at room temperature.) or (((0 * 1 * -4 * 9) == (8 + 14)) or (The currency of South Korea is the Dollar.)))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 52321560,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. not not (not ((not not ((47 % 9) <= (16 + -9))) and ((The chemical symbol for Mercury is C.) and ((13 * -8) != (1 - -17))) and (not ((16 * -11) >= (-15 - -15)))))\nB. (not ((not not (not not (Australia is in Oceania.))) or (((The Titanic sank occurred in 1912.) or (Uranus is the 6th planet from the Sun.)) and ((Wood is a solid at room temperature.) and ((-12 + 5) <= (-10 + 10) <= (14 + 9)))))) or ((not (Saturn is the 2nd planet from the Sun.)) or (not not (not not ((29 % 3) == (-8 * 1 - -5 * -8)))))\nC. not not (((Alcohol is a liquid at room temperature.) or (not not ((The 1896 Olympics were held in Athens.) and (There are 30 days in April.)))) and ((A human has 10 legs.) and (((-19 + -2) <= (-6 * 9 * 6 * -6)) and ((2 * -4) < (-7 * -2 + -6 * 9) < (14 * 19)))))\nD. ((not ((4 ** 2) == (-19 + -2))) or (A human has 2 legs.) or (not ((5 ** 2) == (-1 * 10 + -5 * 1)))) or ((not (((The 1952 Olympics were held in Helsinki.) and (The currency of South Africa is the Rand.)) and (not (The chemical symbol for Copper is Cu.)))) and ((not not (There are 28 days in October.)) or ((((1 ** 2) > (-11 * -1)) or (69 is an even number.)) or (Gold is a solid at room temperature.))))\nE. (not ((not not (((-18 + 10) <= (12 + 1) <= (13 * 7)) and (The 1988 Olympics were held in Tokyo.))) or (((3 - -18) < (-6 * 3 - 2 * 1)) and ((10 + 7) != (15 + 14))))) and (((not ((The capital of Argentina is Prague.) and (Mercury is the 1st planet from the Sun.))) or (((-16 - -16) == (-14 + -19)) or (The chemical symbol for Copper is Cu.)) or (Thailand is in Europe.)) and (((-15 - 14) <= (4 ** 2)) or (not not ((10 * -1 + -8 * -5) <= (29 % 2)))) and (not (World War I began occurred in 1914.)))\nF. not ((not ((((12 - 3) < (5 * -7 + -6 * -1)) or ((5 - 3) <= (-3 * 9 * -8 * -7) <= (34 % 6))) and ((-20 + 18) >= (-17 + -17)))) and (((((3 ** 3) <= (-12 + 17)) and ((-14 - -1) == (10 * -7))) or (not (The currency of United Kingdom is the Ruble.))) or ((Wood is a solid at room temperature.) or (((0 * 1 * -4 * 9) == (8 + 14)) or (The currency of South Korea is the Dollar.)))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 52321560,
"true_count": 3
},
"seed": 52321560,
"task_id": 652321560,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. ((捷克的首都是利马。) and (第二次世界大战开始发生在1939年。)) and ((-13 + -1) == (19 % 9)) and (not not ((not not ((-18 - 5) == (7 * 1 * -2 * -4))) and ((二月有30天。) and ((10 - 8) < (5 * 7 - -9 * 5)))))
B. (not (not not (not (美国的货币是美元。)))) or ((not not (挪威的首都是新加坡。)) or (not not (not ((-6 + -6) <= (-7 * -10 - 0 * 9)))))
C. not not ((((-14 - 15) > (18 * -9)) or (((15 + -5) < (-14 + 5) < (-2 - 13)) and ((1 ** 1) < (-14 + -1)))) and (((9 - 17) < (21 % 10)) or ((十一月有31天。) or (莱特兄弟首次飞行发生在1903年。))))
D. not not (((龙虾有10条腿。) or (not (鹦鹉是鸟类。))) and (((印度位于亚洲。) and ((-13 - 2) <= (4 * 11))) or (not ((9 * -4 + 3 * -2) < (43 % 9)))))
E. (not (not not ((哥伦比亚位于南美洲。) or ((-5 + -17) < (1 ** 2))))) and (not ((-3 * -10 + 6 * 6) > (-4 * -6))) and ((((-6 * -5 - 6 * -5) < (12 % 5)) and ((锡的化学符号是Sn。) and ((-6 + 12) == (20 - -14)))) or ((秘鲁的货币是林吉特。) and (((1 ** 2) <= (39 % 10)) or (光速比声速快。))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 50785973,
"true_count": 3
},
"question": "审视以下逻辑表达式：\n\nA. ((捷克的首都是利马。) and (第二次世界大战开始发生在1939年。)) and ((-13 + -1) == (19 % 9)) and (not not ((not not ((-18 - 5) == (7 * 1 * -2 * -4))) and ((二月有30天。) and ((10 - 8) < (5 * 7 - -9 * 5)))))\nB. (not (not not (not (美国的货币是美元。)))) or ((not not (挪威的首都是新加坡。)) or (not not (not ((-6 + -6) <= (-7 * -10 - 0 * 9)))))\nC. not not ((((-14 - 15) > (18 * -9)) or (((15 + -5) < (-14 + 5) < (-2 - 13)) and ((1 ** 1) < (-14 + -1)))) and (((9 - 17) < (21 % 10)) or ((十一月有31天。) or (莱特兄弟首次飞行发生在1903年。))))\nD. not not (((龙虾有10条腿。) or (not (鹦鹉是鸟类。))) and (((印度位于亚洲。) and ((-13 - 2) <= (4 * 11))) or (not ((9 * -4 + 3 * -2) < (43 % 9)))))\nE. (not (not not ((哥伦比亚位于南美洲。) or ((-5 + -17) < (1 ** 2))))) and (not ((-3 * -10 + 6 * 6) > (-4 * -6))) and ((((-6 * -5 - 6 * -5) < (12 % 5)) and ((锡的化学符号是Sn。) and ((-6 + 12) == (20 - -14)))) or ((秘鲁的货币是林吉特。) and (((1 ** 2) <= (39 % 10)) or (光速比声速快。))))\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": 50785973,
"true_count": 3
},
"seed": 50785973,
"task_id": 650785973,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((-11 - -1) == (-1 * -1 + -9 * -6)) or ((7 + -17) < (-17 + 18))
B. not (not not (not not (铁在常温下是气体。)))
C. ((-8 - -15) >= (18 * -14)) and ((英国位于南美洲。) and ((水蒸气在常温下是固体。) or ((46 % 1) >= (12 + -5))))
D. (((91是奇数。) or (光速约为每秒30万公里。)) or (((12 * 8) != (6 * -9 - 4 * 10)) or ((5 - -5) < (-9 - 8)))) or ((智利的货币是比索。) or (金的化学符号是H。)) or (not (((4 ** 3) > (2 - 11)) or (中国的首都是北京。)))
E. (印度尼西亚位于亚洲。) and ((not (光速比声速快。)) and (((-17 + 13) <= (-1 - 8)) and (1924年奥运会在巴黎举办。)))
F. ((5 ** 2) == (15 + 12)) and ((20能被9整除。) and ((1964年奥运会在东京举办。) or (五月有28天。)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 25619336,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. ((-11 - -1) == (-1 * -1 + -9 * -6)) or ((7 + -17) < (-17 + 18))\nB. not (not not (not not (铁在常温下是气体。)))\nC. ((-8 - -15) >= (18 * -14)) and ((英国位于南美洲。) and ((水蒸气在常温下是固体。) or ((46 % 1) >= (12 + -5))))\nD. (((91是奇数。) or (光速约为每秒30万公里。)) or (((12 * 8) != (6 * -9 - 4 * 10)) or ((5 - -5) < (-9 - 8)))) or ((智利的货币是比索。) or (金的化学符号是H。)) or (not (((4 ** 3) > (2 - 11)) or (中国的首都是北京。)))\nE. (印度尼西亚位于亚洲。) and ((not (光速比声速快。)) and (((-17 + 13) <= (-1 - 8)) and (1924年奥运会在巴黎举办。)))\nF. ((5 ** 2) == (15 + 12)) and ((20能被9整除。) and ((1964年奥运会在东京举办。) or (五月有28天。)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 25619336,
"true_count": 3
},
"seed": 25619336,
"task_id": 625619336,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (4 ** 1) == (30 % 9)
B. not not ((土星是距离太阳第6近的行星。) and ((-12 - 1) == (3 ** 2)))
C. (((16 - -1) < (4 + -6)) or (电流比光速更快。)) and (水在海平面上的沸点是100摄氏度。)
D. 氧气对人类生存是必需的。
E. (墨西哥的首都是哈瓦那。) and ((8 - 10) >= (17 * 11))
F. (-15 * 2) > (18 * 15)
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 27086764,
"true_count": 1
},
"question": "审视以下逻辑表达式：\n\nA. (4 ** 1) == (30 % 9)\nB. not not ((土星是距离太阳第6近的行星。) and ((-12 - 1) == (3 ** 2)))\nC. (((16 - -1) < (4 + -6)) or (电流比光速更快。)) and (水在海平面上的沸点是100摄氏度。)\nD. 氧气对人类生存是必需的。\nE. (墨西哥的首都是哈瓦那。) and ((8 - 10) >= (17 * 11))\nF. (-15 * 2) > (18 * 15)\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 27086764,
"true_count": 1
},
"seed": 27086764,
"task_id": 627086764,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((((-20 * 6) >= (-4 - -11)) or ((第一部iPhone发布发生在2007年。) and (俄罗斯的货币是兰特。))) or ((12 + -16) == (1 ** 3)) or (美国的货币是瑞士法郎。)) and ((1924年奥运会在斯德哥尔摩举办。) or ((not (美国宣布独立发生在1776年。)) or ((十二月有31天。) or ((-6 + -16) <= (10 * 12)))))
B. ((not (海王星是距离太阳第4近的行星。)) or (not not (12是质数。)) or ((not not (镍的化学符号是Ni。)) or (not not ((7 + 1) > (17 * 2))))) or (((not ((4 * 15) == (13 + -3))) or ((硫的化学符号是Pt。) and ((9 % 4) < (1 ** 2) < (6 * 0 - 9 * 2)))) and (not ((碳的化学符号是Na。) or ((-4 + 9) == (0 * 6 - 10 * -3)))))
C. (((not not ((11 - 11) >= (7 * -3))) and (((6 * 17) == (-12 - 1)) and ((1 ** 3) > (-10 * 3 - 3 * 8)))) or ((-10 - 15) != (16 + 13))) and (not ((((2 ** 1) == (8 + -19)) or ((2 ** 2) <= (-9 + -16))) and ((1936年奥运会在巴黎举办。) or ((-2 * -5 + -3 * 8) > (8 * 6 * 2 * 4)))))
D. ((铜在常温下是液体。) and (not not ((1908年奥运会在伦敦举办。) or ((-20 - -2) < (3 ** 3) < (-15 - -13))))) and ((第二次世界大战结束发生在1945年。) and ((not not (海王星是距离太阳第6近的行星。)) and ((现代奥运会首届举办发生在1891年。) or (铁在常温下是固体。))))
E. (not (((中国的首都是马尼拉。) or (比利时的首都是雅加达。)) and (((-13 * -9) < (17 % 3)) or ((-2 * 0 - -5 * -9) != (19 + -6))))) or (not (钴的化学符号是Co。)) or (((not not (越南的货币是澳元。)) or (not (水在常温下是液体。))) and (越南位于亚洲。))
F. not ((not (天王星是距离太阳第4近的行星。)) or (鲨鱼是哺乳动物。))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 99590592,
"true_count": 3
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. ((((-20 * 6) >= (-4 - -11)) or ((第一部iPhone发布发生在2007年。) and (俄罗斯的货币是兰特。))) or ((12 + -16) == (1 ** 3)) or (美国的货币是瑞士法郎。)) and ((1924年奥运会在斯德哥尔摩举办。) or ((not (美国宣布独立发生在1776年。)) or ((十二月有31天。) or ((-6 + -16) <= (10 * 12)))))\nB. ((not (海王星是距离太阳第4近的行星。)) or (not not (12是质数。)) or ((not not (镍的化学符号是Ni。)) or (not not ((7 + 1) > (17 * 2))))) or (((not ((4 * 15) == (13 + -3))) or ((硫的化学符号是Pt。) and ((9 % 4) < (1 ** 2) < (6 * 0 - 9 * 2)))) and (not ((碳的化学符号是Na。) or ((-4 + 9) == (0 * 6 - 10 * -3)))))\nC. (((not not ((11 - 11) >= (7 * -3))) and (((6 * 17) == (-12 - 1)) and ((1 ** 3) > (-10 * 3 - 3 * 8)))) or ((-10 - 15) != (16 + 13))) and (not ((((2 ** 1) == (8 + -19)) or ((2 ** 2) <= (-9 + -16))) and ((1936年奥运会在巴黎举办。) or ((-2 * -5 + -3 * 8) > (8 * 6 * 2 * 4)))))\nD. ((铜在常温下是液体。) and (not not ((1908年奥运会在伦敦举办。) or ((-20 - -2) < (3 ** 3) < (-15 - -13))))) and ((第二次世界大战结束发生在1945年。) and ((not not (海王星是距离太阳第6近的行星。)) and ((现代奥运会首届举办发生在1891年。) or (铁在常温下是固体。))))\nE. (not (((中国的首都是马尼拉。) or (比利时的首都是雅加达。)) and (((-13 * -9) < (17 % 3)) or ((-2 * 0 - -5 * -9) != (19 + -6))))) or (not (钴的化学符号是Co。)) or (((not not (越南的货币是澳元。)) or (not (水在常温下是液体。))) and (越南位于亚洲。))\nF. not ((not (天王星是距离太阳第4近的行星。)) or (鲨鱼是哺乳动物。))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 99590592,
"true_count": 3
},
"seed": 99590592,
"task_id": 699590592,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((not (not (((9 * 11) < (3 * -2 - 10 * 1) < (5 - 2)) and (The Soviet Union dissolved occurred in 1991.)))) and (The currency of India is the Shekel.) and (((not not ((12 - -5) != (4 * -7 - -7 * 7))) or (United States is in Antarctica.)) and ((((8 + 12) > (-4 * 7 - 5 * 10)) and (The capital of Singapore is Moscow.)) or ((2 % 4) > (-7 - 14))))) or (not not (not not ((-9 * 7 * 7 * 10) <= (-11 - 8))))
B. ((not ((((2 * -5) > (1 ** 2)) or ((4 - 9) < (-17 * -11))) and (A octopus has 8 legs.))) and (not not (((7 * 9 + -6 * 0) < (7 - 19) < (-10 * 14)) and ((-9 * -6 + 7 * -8) == (20 + -12))))) or (((11 + -10) <= (10 * 1 + 10 * -1) <= (-10 * -6 - 0 * -5)) or (The capital of Hungary is Budapest.) or (not not ((20 * 15) >= (-10 * -6)))) or (not ((((-18 * -3) < (18 - 8)) or ((-8 * 19) == (18 + 0))) or ((7 * -1 - 5 * 10) < (-17 * 14) < (5 ** 3))))
C. not (not ((65 is a prime number.) or ((59 is divisible by 4.) or ((4 - -15) >= (8 * 6))) or (The Great Fire of London occurred in 1666.)))
D. ((not not ((not ((1 * 7 + 7 * 2) < (-5 * -18))) or ((-14 * 12) < (1 * -7 + -8 * -3)))) or (((The chemical symbol for Titanium is Pt.) or ((-18 + 16) <= (-5 * -2 - -2 * -8))) and (not (((1 ** 1) <= (-17 - -11)) or (The square root of 121 is 11.))))) and (not ((not (The first Olympic Games of modern era occurred in 1896.)) and ((-14 + 14) == (7 * -5 * 1 * -7)))) and (not (not ((7 + -1) != (-3 - -4))))
E. not ((((There are 30 days in October.) or (not not (The Berlin Wall fell occurred in 1989.))) and ((6 * 0) != (7 * -5 * 3 * -9))) and ((((2 + 15) != (2 * -1 + -4 * -3)) and (not not (The capital of Australia is Canberra.))) or (The currency of Hungary is the Forint.)))
F. not not (not not ((Helium is a gas at room temperature.) and (A horse is a fish.)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 36576956,
"true_count": 4
},
"question": "Given the following boolean expressions:\n\nA. ((not (not (((9 * 11) < (3 * -2 - 10 * 1) < (5 - 2)) and (The Soviet Union dissolved occurred in 1991.)))) and (The currency of India is the Shekel.) and (((not not ((12 - -5) != (4 * -7 - -7 * 7))) or (United States is in Antarctica.)) and ((((8 + 12) > (-4 * 7 - 5 * 10)) and (The capital of Singapore is Moscow.)) or ((2 % 4) > (-7 - 14))))) or (not not (not not ((-9 * 7 * 7 * 10) <= (-11 - 8))))\nB. ((not ((((2 * -5) > (1 ** 2)) or ((4 - 9) < (-17 * -11))) and (A octopus has 8 legs.))) and (not not (((7 * 9 + -6 * 0) < (7 - 19) < (-10 * 14)) and ((-9 * -6 + 7 * -8) == (20 + -12))))) or (((11 + -10) <= (10 * 1 + 10 * -1) <= (-10 * -6 - 0 * -5)) or (The capital of Hungary is Budapest.) or (not not ((20 * 15) >= (-10 * -6)))) or (not ((((-18 * -3) < (18 - 8)) or ((-8 * 19) == (18 + 0))) or ((7 * -1 - 5 * 10) < (-17 * 14) < (5 ** 3))))\nC. not (not ((65 is a prime number.) or ((59 is divisible by 4.) or ((4 - -15) >= (8 * 6))) or (The Great Fire of London occurred in 1666.)))\nD. ((not not ((not ((1 * 7 + 7 * 2) < (-5 * -18))) or ((-14 * 12) < (1 * -7 + -8 * -3)))) or (((The chemical symbol for Titanium is Pt.) or ((-18 + 16) <= (-5 * -2 - -2 * -8))) and (not (((1 ** 1) <= (-17 - -11)) or (The square root of 121 is 11.))))) and (not ((not (The first Olympic Games of modern era occurred in 1896.)) and ((-14 + 14) == (7 * -5 * 1 * -7)))) and (not (not ((7 + -1) != (-3 - -4))))\nE. not ((((There are 30 days in October.) or (not not (The Berlin Wall fell occurred in 1989.))) and ((6 * 0) != (7 * -5 * 3 * -9))) and ((((2 + 15) != (2 * -1 + -4 * -3)) and (not not (The capital of Australia is Canberra.))) or (The currency of Hungary is the Forint.)))\nF. not not (not not ((Helium is a gas at room temperature.) and (A horse is a fish.)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 36576956,
"true_count": 4
},
"seed": 36576956,
"task_id": 636576956,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. (((not not (2024年奥运会在伦敦举办。)) and (not not (加拿大的货币是加元。))) and (((13 % 4) > (-10 * 3)) and (金星是距离太阳第2近的行星。))) and (not (not (not ((-2 * -13) >= (-19 * -19)))))
B. not not (not not (丹麦的货币是克朗。))
C. not not ((not not (((-2 * 8 * 10 * -8) <= (2 ** 3) <= (-6 * 3 - -3 * -5)) and (2004年奥运会在亚特兰大举办。))) or (((-12 - -9) == (14 - -10)) or ((2 - -16) < (-6 * -9 - -3 * -10))) or (not not ((丹麦的首都是哥本哈根。) and ((-20 - 10) <= (5 % 7)))))
D. not ((((0 - 17) != (32 % 6)) and ((摩洛哥的首都是拉巴特。) and ((4 * -8 * 5 * 4) < (3 ** 1) < (17 - 8)))) or (((中国的货币是克朗。) and ((6 * 20) <= (-18 * -8) <= (18 - 13))) or (not not ((2 ** 1) > (-17 + 4)))))
E. not (((天王星是距离太阳第7近的行星。) and (((-3 * 17) == (-5 * 0 - 8 * 4)) and (意大利位于欧洲。))) and (not not (((1 ** 2) < (6 - 5) < (1 ** 1)) or (2093年是闰年。))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 77500475,
"true_count": 3
},
"question": "审视以下逻辑表达式：\n\nA. (((not not (2024年奥运会在伦敦举办。)) and (not not (加拿大的货币是加元。))) and (((13 % 4) > (-10 * 3)) and (金星是距离太阳第2近的行星。))) and (not (not (not ((-2 * -13) >= (-19 * -19)))))\nB. not not (not not (丹麦的货币是克朗。))\nC. not not ((not not (((-2 * 8 * 10 * -8) <= (2 ** 3) <= (-6 * 3 - -3 * -5)) and (2004年奥运会在亚特兰大举办。))) or (((-12 - -9) == (14 - -10)) or ((2 - -16) < (-6 * -9 - -3 * -10))) or (not not ((丹麦的首都是哥本哈根。) and ((-20 - 10) <= (5 % 7)))))\nD. not ((((0 - 17) != (32 % 6)) and ((摩洛哥的首都是拉巴特。) and ((4 * -8 * 5 * 4) < (3 ** 1) < (17 - 8)))) or (((中国的货币是克朗。) and ((6 * 20) <= (-18 * -8) <= (18 - 13))) or (not not ((2 ** 1) > (-17 + 4)))))\nE. not (((天王星是距离太阳第7近的行星。) and (((-3 * 17) == (-5 * 0 - 8 * 4)) and (意大利位于欧洲。))) and (not not (((1 ** 2) < (6 - 5) < (1 ** 1)) or (2093年是闰年。))))\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": 77500475,
"true_count": 3
},
"seed": 77500475,
"task_id": 677500475,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. ((((-7 * 5) > (14 - 19)) and ((-9 * -10 + -6 * 2) <= (13 * -8))) or (((1977 is a leap year.) and ((-3 + -15) <= (-7 * 11))) and ((The currency of Canada is the Dollar.) or ((-1 * 4 * 5 * 7) > (-17 * -10))))) or (not not (The Soviet Union dissolved occurred in 1991.))
B. (((not (The capital of Thailand is Wellington.)) or (The capital of Ukraine is Caracas.)) and (The square root of 144 is 13.)) or ((not not (((-17 + -15) < (7 * -16)) and ((-20 + -9) <= (5 + -6)))) and (not not ((The capital of Cuba is Havana.) and (The chemical symbol for Uranium is U.))))
C. not (not not (not not ((South Africa is in Antarctica.) or (The capital of Singapore is Singapore.))))
D. not ((The currency of Japan is the Yen.) and (not not (((-3 * -9 * 6 * -8) >= (17 % 10)) or ((-1 + -7) >= (4 + 5)))))
E. (((not not (There are 30 days in July.)) and ((1996 is a leap year.) and (The chemical symbol for Silver is Co.))) and (759 is a Fibonacci number.)) and (not (not (Earth is the 3rd planet from the Sun.)))
F. (((not not ((47 % 9) != (-13 - 10))) or (((10 + -17) != (7 - 2)) or (Diamonds are made of carbon.))) or ((((1 % 9) < (-12 + 12)) or ((4 * 2 - 10 * -4) <= (4 ** 2))) and ((Jupiter is the 5th planet from the Sun.) or ((-14 - -3) == (-9 + -18))))) and ((((41 % 3) <= (-10 + -6)) or (Venus is the 2nd planet from the Sun.)) or (not not ((7 * -4 + -2 * 5) < (11 + 10)))) and (not not (((Nitrogen is a gas at room temperature.) or (A frog has 100 legs.)) and ((-3 + -15) < (2 ** 2) < (-7 + -13))))
G. not not ((Water is a gas at room temperature.) and (not not (not ((-17 + -18) >= (5 ** 2)))))
H. (((12 * -13) != (-7 - 15)) and (((The chemical symbol for Chromium is Cr.) or (The 2004 Olympics were held in Rome.)) and (The 1948 Olympics were held in London.))) and (((not not (Mars is the 4th planet from the Sun.)) or (((12 - -2) != (3 ** 1)) and ((1 % 2) >= (-10 * 2 - 8 * -3)))) or ((Ice is a liquid at room temperature.) and ((8 * 9 + 5 * -5) >= (10 * -8))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,D,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 96206628,
"true_count": 3
},
"question": "Analyze these boolean expressions:\n\nA. ((((-7 * 5) > (14 - 19)) and ((-9 * -10 + -6 * 2) <= (13 * -8))) or (((1977 is a leap year.) and ((-3 + -15) <= (-7 * 11))) and ((The currency of Canada is the Dollar.) or ((-1 * 4 * 5 * 7) > (-17 * -10))))) or (not not (The Soviet Union dissolved occurred in 1991.))\nB. (((not (The capital of Thailand is Wellington.)) or (The capital of Ukraine is Caracas.)) and (The square root of 144 is 13.)) or ((not not (((-17 + -15) < (7 * -16)) and ((-20 + -9) <= (5 + -6)))) and (not not ((The capital of Cuba is Havana.) and (The chemical symbol for Uranium is U.))))\nC. not (not not (not not ((South Africa is in Antarctica.) or (The capital of Singapore is Singapore.))))\nD. not ((The currency of Japan is the Yen.) and (not not (((-3 * -9 * 6 * -8) >= (17 % 10)) or ((-1 + -7) >= (4 + 5)))))\nE. (((not not (There are 30 days in July.)) and ((1996 is a leap year.) and (The chemical symbol for Silver is Co.))) and (759 is a Fibonacci number.)) and (not (not (Earth is the 3rd planet from the Sun.)))\nF. (((not not ((47 % 9) != (-13 - 10))) or (((10 + -17) != (7 - 2)) or (Diamonds are made of carbon.))) or ((((1 % 9) < (-12 + 12)) or ((4 * 2 - 10 * -4) <= (4 ** 2))) and ((Jupiter is the 5th planet from the Sun.) or ((-14 - -3) == (-9 + -18))))) and ((((41 % 3) <= (-10 + -6)) or (Venus is the 2nd planet from the Sun.)) or (not not ((7 * -4 + -2 * 5) < (11 + 10)))) and (not not (((Nitrogen is a gas at room temperature.) or (A frog has 100 legs.)) and ((-3 + -15) < (2 ** 2) < (-7 + -13))))\nG. not not ((Water is a gas at room temperature.) and (not not (not ((-17 + -18) >= (5 ** 2)))))\nH. (((12 * -13) != (-7 - 15)) and (((The chemical symbol for Chromium is Cr.) or (The 2004 Olympics were held in Rome.)) and (The 1948 Olympics were held in London.))) and (((not not (Mars is the 4th planet from the Sun.)) or (((12 - -2) != (3 ** 1)) and ((1 % 2) >= (-10 * 2 - 8 * -3)))) or ((Ice is a liquid at room temperature.) and ((8 * 9 + 5 * -5) >= (10 * -8))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 96206628,
"true_count": 3
},
"seed": 96206628,
"task_id": 696206628,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. not (((((15 - -4) > (1 * -10 + -8 * -2)) and ((-6 + -17) < (2 + -1))) and (((-6 - -11) > (12 % 10)) or (氦气在常温下是气体。))) and ((1920年奥运会在亚特兰大举办。) or (not not (丹麦的货币是克朗。))))
B. (((((19 * -12) < (1 ** 2) < (-19 - 13)) and (埃及的货币是雷亚尔。)) and (考拉是鸟类。)) and (((-10 * -5) < (-8 - -8)) or ((121的平方根是11。) and (加拿大的货币是比索。)))) or ((not (猪有4条腿。)) or ((火星是距离太阳第4近的行星。) and (2096年是闰年。)) or (not (not (印度的首都是布拉格。))))
C. (((((-19 * 15) != (3 % 5)) and (伦敦大火发生在1661年。)) or (not ((-2 + -12) == (3 * 5)))) or (((-16 * -11) > (-16 - -14)) or (哥伦比亚的货币是比索。))) and (((地球是距离太阳第6近的行星。) and ((水在常温下是液体。) and (加拿大的货币是加元。))) or ((((-4 - -20) > (-6 * 8 + 1 * -10)) or (金枪鱼是鱼类。)) and (not (第一次世界大战结束发生在1918年。))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 3,
"seed": 98288064,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. not (((((15 - -4) > (1 * -10 + -8 * -2)) and ((-6 + -17) < (2 + -1))) and (((-6 - -11) > (12 % 10)) or (氦气在常温下是气体。))) and ((1920年奥运会在亚特兰大举办。) or (not not (丹麦的货币是克朗。))))\nB. (((((19 * -12) < (1 ** 2) < (-19 - 13)) and (埃及的货币是雷亚尔。)) and (考拉是鸟类。)) and (((-10 * -5) < (-8 - -8)) or ((121的平方根是11。) and (加拿大的货币是比索。)))) or ((not (猪有4条腿。)) or ((火星是距离太阳第4近的行星。) and (2096年是闰年。)) or (not (not (印度的首都是布拉格。))))\nC. (((((-19 * 15) != (3 % 5)) and (伦敦大火发生在1661年。)) or (not ((-2 + -12) == (3 * 5)))) or (((-16 * -11) > (-16 - -14)) or (哥伦比亚的货币是比索。))) and (((地球是距离太阳第6近的行星。) and ((水在常温下是液体。) and (加拿大的货币是加元。))) or ((((-4 - -20) > (-6 * 8 + 1 * -10)) or (金枪鱼是鱼类。)) and (not (第一次世界大战结束发生在1918年。))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 3,
"seed": 98288064,
"true_count": 1
},
"seed": 98288064,
"task_id": 698288064,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. ((not not (1974 is a leap year.)) and ((((Japan is in Asia.) and ((13 * 2) <= (-9 * -4) <= (-3 - -8))) and (((2 * -16) <= (3 * -8 - 9 * 1)) and (Water is a liquid at room temperature.))) and (not ((Sound travels faster in a vacuum.) and ((12 % 8) != (8 % 6)))))) and ((not ((not not (54 is less than or equal to 29.)) or ((17 % 7) < (-7 * 6 - 1 * 2) < (-19 * 20)))) or (((8 - 14) < (8 % 4) < (-1 - -18)) or ((-5 * -2) != (5 ** 1))))
B. not (((((The capital of Singapore is Abuja.) or (The chemical symbol for Tin is Sn.)) and (((5 * 1 * 6 * -6) == (-4 * -4)) and ((18 * 3) < (16 + -6)))) and (Jupiter is the 5th planet from the Sun.)) or (not not (Silver is a solid at room temperature.)))
C. (not ((not (Oxygen is necessary for human survival.)) or ((The chemical symbol for Sulfur is S.) or (The square root of 36 is 6.)) or ((20 + 6) < (-17 + -16)))) and ((((-4 * 17) > (13 * -8)) and (not (The capital of Nigeria is Abuja.))) and ((not not (((-16 + -6) == (-16 - 1)) or (A crab has 10 legs.))) and ((35 % 9) < (17 + 7))))
D. not (not not (((4 - -15) >= (-9 - -2)) or (not ((Canada is in Africa.) or (The currency of South Korea is the Euro.)))))
E. not not (not (not not (not (((-12 + 8) > (12 + 1)) and ((0 * -5 * -6 * -4) < (-19 + -5))))))
F. not not ((not (((The currency of China is the Krone.) and (The 2024 Olympics were held in Paris.)) or ((The human body has 150 bones.) or ((5 * 9 * 4 * 2) == (-4 - 5))))) or (Uranus is the 7th planet from the Sun.) or (((9 * 7 + 1 * -1) == (-6 - -18)) and ((not not ((-7 * 20) > (4 * -14))) and (not (163 is an odd number.)))))
G. not ((not not ((not ((10 + 17) < (-3 + 1) < (10 * 4 - -3 * 10))) or (not not (99 is a prime number.)))) or (not ((((16 * -17) == (-3 + -2)) or ((19 - -18) > (1 ** 3))) or ((A crab has 10 legs.) and ((-9 + -20) < (-20 - -14))))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 7,
"seed": 31914960,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. ((not not (1974 is a leap year.)) and ((((Japan is in Asia.) and ((13 * 2) <= (-9 * -4) <= (-3 - -8))) and (((2 * -16) <= (3 * -8 - 9 * 1)) and (Water is a liquid at room temperature.))) and (not ((Sound travels faster in a vacuum.) and ((12 % 8) != (8 % 6)))))) and ((not ((not not (54 is less than or equal to 29.)) or ((17 % 7) < (-7 * 6 - 1 * 2) < (-19 * 20)))) or (((8 - 14) < (8 % 4) < (-1 - -18)) or ((-5 * -2) != (5 ** 1))))\nB. not (((((The capital of Singapore is Abuja.) or (The chemical symbol for Tin is Sn.)) and (((5 * 1 * 6 * -6) == (-4 * -4)) and ((18 * 3) < (16 + -6)))) and (Jupiter is the 5th planet from the Sun.)) or (not not (Silver is a solid at room temperature.)))\nC. (not ((not (Oxygen is necessary for human survival.)) or ((The chemical symbol for Sulfur is S.) or (The square root of 36 is 6.)) or ((20 + 6) < (-17 + -16)))) and ((((-4 * 17) > (13 * -8)) and (not (The capital of Nigeria is Abuja.))) and ((not not (((-16 + -6) == (-16 - 1)) or (A crab has 10 legs.))) and ((35 % 9) < (17 + 7))))\nD. not (not not (((4 - -15) >= (-9 - -2)) or (not ((Canada is in Africa.) or (The currency of South Korea is the Euro.)))))\nE. not not (not (not not (not (((-12 + 8) > (12 + 1)) and ((0 * -5 * -6 * -4) < (-19 + -5))))))\nF. not not ((not (((The currency of China is the Krone.) and (The 2024 Olympics were held in Paris.)) or ((The human body has 150 bones.) or ((5 * 9 * 4 * 2) == (-4 - 5))))) or (Uranus is the 7th planet from the Sun.) or (((9 * 7 + 1 * -1) == (-6 - -18)) and ((not not ((-7 * 20) > (4 * -14))) and (not (163 is an odd number.)))))\nG. not ((not not ((not ((10 + 17) < (-3 + 1) < (10 * 4 - -3 * 10))) or (not not (99 is a prime number.)))) or (not ((((16 * -17) == (-3 + -2)) or ((19 - -18) > (1 ** 3))) or ((A crab has 10 legs.) and ((-9 + -20) < (-20 - -14))))))\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": 7,
"seed": 31914960,
"true_count": 1
},
"seed": 31914960,
"task_id": 631914960,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (not not ((not not (not ((-5 - 16) <= (7 % 2)))) or ((The Titanic sank occurred in 1912.) or (A lizard is a bird.)) or (((-16 * -2) <= (37 % 10)) and (The 1948 Olympics were held in Sydney.)))) and ((((19 + -16) == (27 % 3)) and (((Humans have three lungs.) or ((-10 * 6 + -7 * -2) < (-12 + 13) < (36 % 7))) or ((The capital of Nigeria is Abuja.) or ((6 * -6) <= (-15 * 12) <= (7 * -3))))) and (((not not ((1 ** 2) > (14 * -20))) or ((26 % 4) >= (-15 + -3))) or (not not (A cod is a fish.))))
B. not ((not not ((-3 * -10 - -1 * -5) != (28 % 8))) or ((not ((There are 31 days in December.) and ((15 * -9) != (13 + -12)))) and ((not (The capital of South Korea is Seoul.)) or (The 2004 Olympics were held in Athens.))))
C. not (((((The 1988 Olympics were held in Seoul.) or ((-2 * 12) < (2 ** 3))) and (not (China is in Asia.))) or ((2 ** 3) >= (5 ** 2)) or (Humans have five fingers on each hand.)) or ((((1 ** 1) <= (23 % 3)) and (not not (There are 30 days in April.))) and ((1 ** 2) != (20 - 13)) and ((Mercury is a liquid at room temperature.) or (The currency of South Africa is the Zloty.))))
D. not not (not ((Spain is in Europe.) and (not ((0 * -15) <= (1 ** 1))) and (not not ((The Soviet Union dissolved occurred in 1991.) and ((-3 - -12) < (4 ** 2))))))
E. (not not ((Iron is a solid at room temperature.) and ((22 % 9) < (-4 * -5 * -7 * -6)))) and (not not (not (not not (The speed of light is approximately 300,000 km/s.))))
F. not ((not (not (((27 % 5) == (5 ** 3)) and ((-9 * 5 * 1 * 5) >= (-18 + -10))))) or (not not (The capital of Finland is Jakarta.)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 77102843,
"true_count": 2
},
"question": "Given the following boolean expressions:\n\nA. (not not ((not not (not ((-5 - 16) <= (7 % 2)))) or ((The Titanic sank occurred in 1912.) or (A lizard is a bird.)) or (((-16 * -2) <= (37 % 10)) and (The 1948 Olympics were held in Sydney.)))) and ((((19 + -16) == (27 % 3)) and (((Humans have three lungs.) or ((-10 * 6 + -7 * -2) < (-12 + 13) < (36 % 7))) or ((The capital of Nigeria is Abuja.) or ((6 * -6) <= (-15 * 12) <= (7 * -3))))) and (((not not ((1 ** 2) > (14 * -20))) or ((26 % 4) >= (-15 + -3))) or (not not (A cod is a fish.))))\nB. not ((not not ((-3 * -10 - -1 * -5) != (28 % 8))) or ((not ((There are 31 days in December.) and ((15 * -9) != (13 + -12)))) and ((not (The capital of South Korea is Seoul.)) or (The 2004 Olympics were held in Athens.))))\nC. not (((((The 1988 Olympics were held in Seoul.) or ((-2 * 12) < (2 ** 3))) and (not (China is in Asia.))) or ((2 ** 3) >= (5 ** 2)) or (Humans have five fingers on each hand.)) or ((((1 ** 1) <= (23 % 3)) and (not not (There are 30 days in April.))) and ((1 ** 2) != (20 - 13)) and ((Mercury is a liquid at room temperature.) or (The currency of South Africa is the Zloty.))))\nD. not not (not ((Spain is in Europe.) and (not ((0 * -15) <= (1 ** 1))) and (not not ((The Soviet Union dissolved occurred in 1991.) and ((-3 - -12) < (4 ** 2))))))\nE. (not not ((Iron is a solid at room temperature.) and ((22 % 9) < (-4 * -5 * -7 * -6)))) and (not not (not (not not (The speed of light is approximately 300,000 km/s.))))\nF. not ((not (not (((27 % 5) == (5 ** 3)) and ((-9 * 5 * 1 * 5) >= (-18 + -10))))) or (not not (The capital of Finland is Jakarta.)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 6,
"seed": 77102843,
"true_count": 2
},
"seed": 77102843,
"task_id": 677102843,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. 土星是距离太阳第4近的行星。
B. 51是质数。
C. (63是质数。) and (((4 - 2) == (7 * 9 + 9 * 6)) or (芬兰的首都是吉隆坡。))
D. (((19 % 2) < (-5 * -6 + 6 * -4)) or (柏林墙倒塌发生在1999年。)) and (not not ((5 * 2 - -8 * 6) != (-18 - -3)))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 66269033,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. 土星是距离太阳第4近的行星。\nB. 51是质数。\nC. (63是质数。) and (((4 - 2) == (7 * 9 + 9 * 6)) or (芬兰的首都是吉隆坡。))\nD. (((19 % 2) < (-5 * -6 + 6 * -4)) or (柏林墙倒塌发生在1999年。)) and (not not ((5 * 2 - -8 * 6) != (-18 - -3)))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 66269033,
"true_count": 1
},
"seed": 66269033,
"task_id": 666269033,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (not ((not ((-16 - -8) != (1 * -12))) or (not ((2 + -13) <= (-13 + 3))))) and ((((海王星是距离太阳第2近的行星。) and (第一部iPhone发布发生在2006年。)) and (not not ((19 % 3) != (-10 - 2)))) and ((-19 + -14) > (7 + -3)) and (((2012年奥运会在伦敦举办。) and ((11 - -2) != (8 * 5 + -5 * -7))) and (not not (1924年奥运会在巴黎举办。))))
B. ((9是质数。) or (((莱特兄弟首次飞行发生在1903年。) or (龙虾有10条腿。)) or (((-6 - -2) > (9 + 7)) or (澳大利亚位于大洋洲。)))) and (not not (铜在常温下是固体。))
C. (not not ((((10 * 3 + 5 * 4) >= (2 * 8 + -8 * -6)) or (1988年奥运会在伦敦举办。)) and (not not ((6 * 9 * -2 * -6) < (18 - -20))))) and (not not ((铀的化学符号是U。) or ((1935年是闰年。) or (2003年是闰年。))))
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": 4,
"language": "cn",
"num_options": 3,
"seed": 78743032,
"true_count": 1
},
"question": "分析以下逻辑表达式：\n\nA. (not ((not ((-16 - -8) != (1 * -12))) or (not ((2 + -13) <= (-13 + 3))))) and ((((海王星是距离太阳第2近的行星。) and (第一部iPhone发布发生在2006年。)) and (not not ((19 % 3) != (-10 - 2)))) and ((-19 + -14) > (7 + -3)) and (((2012年奥运会在伦敦举办。) and ((11 - -2) != (8 * 5 + -5 * -7))) and (not not (1924年奥运会在巴黎举办。))))\nB. ((9是质数。) or (((莱特兄弟首次飞行发生在1903年。) or (龙虾有10条腿。)) or (((-6 - -2) > (9 + 7)) or (澳大利亚位于大洋洲。)))) and (not not (铜在常温下是固体。))\nC. (not not ((((10 * 3 + 5 * 4) >= (2 * 8 + -8 * -6)) or (1988年奥运会在伦敦举办。)) and (not not ((6 * 9 * -2 * -6) < (18 - -20))))) and (not not ((铀的化学符号是U。) or ((1935年是闰年。) or (2003年是闰年。))))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 3,
"seed": 78743032,
"true_count": 1
},
"seed": 78743032,
"task_id": 678743032,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. ((-12 + 16) <= (5 * -2) <= (-8 - 5)) or (not not (((-9 * 20) == (-4 * 3 - 9 * -1)) and ((3 ** 1) == (2 * -10 - -3 * 8))))
B. ((钻石由碳元素组成。) or ((-2 - -6) < (1 ** 3) < (6 * 18))) and (not not (((12 + 14) < (-15 + -15)) and ((-6 - -9) == (3 ** 3))))
C. 人类每只手有五个手指。
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 15842582,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. ((-12 + 16) <= (5 * -2) <= (-8 - 5)) or (not not (((-9 * 20) == (-4 * 3 - 9 * -1)) and ((3 ** 1) == (2 * -10 - -3 * 8))))\nB. ((钻石由碳元素组成。) or ((-2 - -6) < (1 ** 3) < (6 * 18))) and (not not (((12 + 14) < (-15 + -15)) and ((-6 - -9) == (3 ** 3))))\nC. 人类每只手有五个手指。\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": 15842582,
"true_count": 1
},
"seed": 15842582,
"task_id": 615842582,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (((((泰国的首都是曼谷。) and ((2 ** 1) == (6 - 16))) or (not not (五月有31天。))) or (水在常温下是液体。)) or (not not (not not (((20 - 12) == (1 + -2)) or ((19 - 5) <= (7 - 17)))))) or (((((狮子是哺乳动物。) and ((-2 + -10) <= (-2 * 4 + 6 * -10))) and (not not ((-3 - -18) >= (10 - -4)))) or ((337是完全平方数。) and (第一次世界大战开始发生在1904年。)) or ((14 - 0) >= (7 * -1 + 7 * -2))) and (not not ((((5 ** 1) != (14 + 15)) or ((1 * -8 + -2 * 0) == (4 ** 1))) or ((哥伦布到达美洲发生在1492年。) or (瑞士的货币是瑞士法郎。)))))
B. not ((((企鹅能飞翔。) and (((17 * -17) < (0 * 2)) and ((-13 - 16) == (-9 * 8 * -1 * 9)))) or ((((-18 - 20) >= (-8 - 18)) and (水星是距离太阳第1近的行星。)) or (not not (2005年是闰年。)))) or (not ((钾的化学符号是K。) or ((碳的化学符号是Zn。) or (墨西哥位于南美洲。)))))
C. not (((((氧气在常温下是气体。) and ((37 % 3) != (3 ** 1))) or (铅的化学符号是Mg。)) or ((((4 ** 1) >= (0 - -18)) and (墨西哥位于北美洲。)) and (not not ((15 - 2) <= (2 ** 2) <= (-2 + 16))))) or ((1 - -17) == (-18 * -2)) or ((十月有28天。) or (not not (((-8 - 8) >= (9 - -4)) and ((-15 * 7) >= (-19 * -9))))))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 75241974,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. (((((泰国的首都是曼谷。) and ((2 ** 1) == (6 - 16))) or (not not (五月有31天。))) or (水在常温下是液体。)) or (not not (not not (((20 - 12) == (1 + -2)) or ((19 - 5) <= (7 - 17)))))) or (((((狮子是哺乳动物。) and ((-2 + -10) <= (-2 * 4 + 6 * -10))) and (not not ((-3 - -18) >= (10 - -4)))) or ((337是完全平方数。) and (第一次世界大战开始发生在1904年。)) or ((14 - 0) >= (7 * -1 + 7 * -2))) and (not not ((((5 ** 1) != (14 + 15)) or ((1 * -8 + -2 * 0) == (4 ** 1))) or ((哥伦布到达美洲发生在1492年。) or (瑞士的货币是瑞士法郎。)))))\nB. not ((((企鹅能飞翔。) and (((17 * -17) < (0 * 2)) and ((-13 - 16) == (-9 * 8 * -1 * 9)))) or ((((-18 - 20) >= (-8 - 18)) and (水星是距离太阳第1近的行星。)) or (not not (2005年是闰年。)))) or (not ((钾的化学符号是K。) or ((碳的化学符号是Zn。) or (墨西哥位于南美洲。)))))\nC. not (((((氧气在常温下是气体。) and ((37 % 3) != (3 ** 1))) or (铅的化学符号是Mg。)) or ((((4 ** 1) >= (0 - -18)) and (墨西哥位于北美洲。)) and (not not ((15 - 2) <= (2 ** 2) <= (-2 + 16))))) or ((1 - -17) == (-18 * -2)) or ((十月有28天。) or (not not (((-8 - 8) >= (9 - -4)) and ((-15 * 7) >= (-19 * -9))))))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 75241974,
"true_count": 2
},
"seed": 75241974,
"task_id": 675241974,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. 2016年奥运会在里约热内卢举办。
B. (not not (声音无法在真空中传播。)) or (not not ((-4 * 4) != (-8 - -2)))
C. not (((5 * 1 - -3 * -2) > (18 - -13)) or (铁在常温下是液体。))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 51721515,
"true_count": 3
},
"question": "分析以下逻辑表达式：\n\nA. 2016年奥运会在里约热内卢举办。\nB. (not not (声音无法在真空中传播。)) or (not not ((-4 * 4) != (-8 - -2)))\nC. not (((5 * 1 - -3 * -2) > (18 - -13)) or (铁在常温下是液体。))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 51721515,
"true_count": 3
},
"seed": 51721515,
"task_id": 651721515,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (not not ((((油在常温下是气体。) or (881是斐波那契数。)) and ((金鱼是爬行动物。) and ((16 + -3) <= (18 % 10)))) or ((火星是距离太阳第4近的行星。) or (新西兰的货币是比索。)) or (((20大于98。) and (苏联解体发生在1992年。)) or ((尼日利亚的货币是奈拉。) or (第二次世界大战结束发生在1935年。))))) or (not not ((((中国长城是在一年内建成的。) or (匈牙利的货币是卢布。)) or ((印度尼西亚位于南极洲。) or ((1 ** 1) <= (-5 * -6 * 3 * 1)))) and ((((14 + 11) == (12 % 1)) and (木头在常温下是液体。)) or ((木头在常温下是液体。) or (2016年是闰年。)))))
B. (((十一月有29天。) and (not not (not not ((13 * 12) >= (43 % 6))))) or (((not not (印度尼西亚的货币是印尼盾。)) and ((金枪鱼是鱼类。) or (冰的密度比液态水小。))) or ((-8 - 16) >= (12 - 0)))) or (not not (((2 + 19) < (-5 * -5)) and (not (西班牙的首都是马德里。))))
C. (not ((not not (((-1 * -5 + 4 * -7) < (6 + -15)) and ((1 ** 3) >= (15 * 15)))) and ((not (酒精在常温下是液体。)) and (1924年奥运会在赫尔辛基举办。)))) or ((not (((-4 - 0) > (16 * 5)) or ((4 * -17) != (3 - -1)))) or (((not ((-4 * -10 + 6 * 5) != (-9 * 5 * 9 * -7))) and (第二次世界大战结束发生在1945年。)) and ((not not ((-15 + 7) <= (6 * 9 * -4 * 3))) and ((57是质数。) or (人类首次登月发生在1971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": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 14414261,
"true_count": 3
},
"question": "给定以下布尔表达式：\n\nA. (not not ((((油在常温下是气体。) or (881是斐波那契数。)) and ((金鱼是爬行动物。) and ((16 + -3) <= (18 % 10)))) or ((火星是距离太阳第4近的行星。) or (新西兰的货币是比索。)) or (((20大于98。) and (苏联解体发生在1992年。)) or ((尼日利亚的货币是奈拉。) or (第二次世界大战结束发生在1935年。))))) or (not not ((((中国长城是在一年内建成的。) or (匈牙利的货币是卢布。)) or ((印度尼西亚位于南极洲。) or ((1 ** 1) <= (-5 * -6 * 3 * 1)))) and ((((14 + 11) == (12 % 1)) and (木头在常温下是液体。)) or ((木头在常温下是液体。) or (2016年是闰年。)))))\nB. (((十一月有29天。) and (not not (not not ((13 * 12) >= (43 % 6))))) or (((not not (印度尼西亚的货币是印尼盾。)) and ((金枪鱼是鱼类。) or (冰的密度比液态水小。))) or ((-8 - 16) >= (12 - 0)))) or (not not (((2 + 19) < (-5 * -5)) and (not (西班牙的首都是马德里。))))\nC. (not ((not not (((-1 * -5 + 4 * -7) < (6 + -15)) and ((1 ** 3) >= (15 * 15)))) and ((not (酒精在常温下是液体。)) and (1924年奥运会在赫尔辛基举办。)))) or ((not (((-4 - 0) > (16 * 5)) or ((4 * -17) != (3 - -1)))) or (((not ((-4 * -10 + 6 * 5) != (-9 * 5 * 9 * -7))) and (第二次世界大战结束发生在1945年。)) and ((not not ((-15 + 7) <= (6 * 9 * -4 * 3))) and ((57是质数。) or (人类首次登月发生在1971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": 5,
"language": "cn",
"num_options": 3,
"seed": 14414261,
"true_count": 3
},
"seed": 14414261,
"task_id": 614414261,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not not (二氧化碳在常温下是气体。)
B. (83是质数。) or (not ((10 - 10) >= (-16 * -15)))
C. not (not (22能被3整除。))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 23351258,
"true_count": 2
},
"question": "给定以下布尔表达式：\n\nA. not not (二氧化碳在常温下是气体。)\nB. (83是质数。) or (not ((10 - 10) >= (-16 * -15)))\nC. not (not (22能被3整除。))\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": 2,
"language": "cn",
"num_options": 3,
"seed": 23351258,
"true_count": 2
},
"seed": 23351258,
"task_id": 623351258,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. not not (((not (以色列的货币是印尼盾。)) or ((金在常温下是固体。) and (现代奥运会首届举办发生在1886年。))) and ((101是奇数。) and (哥伦布到达美洲发生在1492年。)) and (伦敦大火发生在1666年。))
B. (not (以色列的货币是里亚尔。)) or (((土星是距离太阳第6近的行星。) or ((0 - 20) < (8 * -8 - 2 * 6))) and ((not ((-15 * -7) <= (14 + -2))) and (水星是距离太阳第1近的行星。)))
C. ((not ((1 * -10 - -10 * -1) < (-5 - -5) < (20 % 2))) and (not (俄罗斯的货币是卢布。)) and ((((-10 * -7 + -7 * -9) <= (7 * -2 * 0 * -3)) and (924是斐波那契数。)) and ((-3 + -20) < (11 - -20) < (-9 * -6 + -7 * -3)))) or ((((10 - -9) > (-18 * 4)) and ((39 % 9) >= (-11 * 3))) or (西班牙位于欧洲。)) or ((((南极洲是最冷的大陆。) and ((0 * 1 - -9 * -7) <= (14 * 20))) or ((水在常温下是气体。) or (2021年是闰年。))) and (((4 ** 3) < (-8 + -8)) and (((-8 * 10 + -5 * 8) != (-15 * -14)) or (金星是距离太阳第2近的行星。))))
D. (not not ((阿根廷的首都是布宜诺斯艾利斯。) or ((美国的货币是印尼盾。) and (企鹅能飞翔。)))) and (((0 - 16) > (-9 - 1)) or (not not (((4 ** 1) != (-18 - 18)) and (氢的化学符号是Hg。))))
E. (((-16 - -7) <= (2 * 4 - 6 * -1) <= (15 + 11)) and (菲律宾的首都是马尼拉。) and (not not ((苏联解体发生在1996年。) and ((1 - -2) > (6 + -6))))) or (not not ((日本位于亚洲。) and (not not ((40 % 6) >= (24 % 7)))))
F. ((((0 - 9) < (-14 - 16)) or ((9 * -15) != (-10 * -6))) or ((-17 * 18) == (-18 + -4)) or (((狗有8条腿。) or (225的平方根是7。)) and ((13 + -12) >= (11 + -10)))) and (not (((2 + -2) > (-3 + 4)) and (加拿大的货币是加元。))) and (not not (((地球是距离太阳第3近的行星。) and (火星是距离太阳第6近的行星。)) and (((12 - 7) >= (-9 * 6 - -2 * -4)) or (地球是距离太阳第7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,B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 99343986,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. not not (((not (以色列的货币是印尼盾。)) or ((金在常温下是固体。) and (现代奥运会首届举办发生在1886年。))) and ((101是奇数。) and (哥伦布到达美洲发生在1492年。)) and (伦敦大火发生在1666年。))\nB. (not (以色列的货币是里亚尔。)) or (((土星是距离太阳第6近的行星。) or ((0 - 20) < (8 * -8 - 2 * 6))) and ((not ((-15 * -7) <= (14 + -2))) and (水星是距离太阳第1近的行星。)))\nC. ((not ((1 * -10 - -10 * -1) < (-5 - -5) < (20 % 2))) and (not (俄罗斯的货币是卢布。)) and ((((-10 * -7 + -7 * -9) <= (7 * -2 * 0 * -3)) and (924是斐波那契数。)) and ((-3 + -20) < (11 - -20) < (-9 * -6 + -7 * -3)))) or ((((10 - -9) > (-18 * 4)) and ((39 % 9) >= (-11 * 3))) or (西班牙位于欧洲。)) or ((((南极洲是最冷的大陆。) and ((0 * 1 - -9 * -7) <= (14 * 20))) or ((水在常温下是气体。) or (2021年是闰年。))) and (((4 ** 3) < (-8 + -8)) and (((-8 * 10 + -5 * 8) != (-15 * -14)) or (金星是距离太阳第2近的行星。))))\nD. (not not ((阿根廷的首都是布宜诺斯艾利斯。) or ((美国的货币是印尼盾。) and (企鹅能飞翔。)))) and (((0 - 16) > (-9 - 1)) or (not not (((4 ** 1) != (-18 - 18)) and (氢的化学符号是Hg。))))\nE. (((-16 - -7) <= (2 * 4 - 6 * -1) <= (15 + 11)) and (菲律宾的首都是马尼拉。) and (not not ((苏联解体发生在1996年。) and ((1 - -2) > (6 + -6))))) or (not not ((日本位于亚洲。) and (not not ((40 % 6) >= (24 % 7)))))\nF. ((((0 - 9) < (-14 - 16)) or ((9 * -15) != (-10 * -6))) or ((-17 * 18) == (-18 + -4)) or (((狗有8条腿。) or (225的平方根是7。)) and ((13 + -12) >= (11 + -10)))) and (not (((2 + -2) > (-3 + 4)) and (加拿大的货币是加元。))) and (not not (((地球是距离太阳第3近的行星。) and (火星是距离太阳第6近的行星。)) and (((12 - 7) >= (-9 * 6 - -2 * -4)) or (地球是距离太阳第7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": 4,
"language": "cn",
"num_options": 6,
"seed": 99343986,
"true_count": 4
},
"seed": 99343986,
"task_id": 699343986,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((尼日利亚的货币是奈拉。) or (钴的化学符号是Co。)) and (not (第一部iPhone发布发生在2007年。))) or (((8 * 1 - 10 * -9) < (17 + -9)) or (not (闪电不会两次击中同一个地方。)))
B. not (((鸟有0条腿。) or ((9 * -5 * -4 * -9) <= (-7 - -4))) or (not ((-7 * 8 + 2 * 6) > (-2 * -8 - -2 * 7))))
C. not (((1964年奥运会在东京举办。) or (企鹅能飞翔。)) or ((5 - -7) < (1 * 7 - 6 * -1)))
D. ((((-8 - -2) != (-5 - -18)) and (1932年奥运会在洛杉矶举办。)) or ((泰坦尼克号沉没发生在1914年。) or (金星是距离太阳第2近的行星。))) or (((-8 * -9) > (4 * -6 - 4 * 5)) and (not (印度尼西亚的货币是兰特。)))
E. (2004年奥运会在雅典举办。) and ((天王星是距离太阳第7近的行星。) or (1933年是闰年。))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 50790833,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. (((尼日利亚的货币是奈拉。) or (钴的化学符号是Co。)) and (not (第一部iPhone发布发生在2007年。))) or (((8 * 1 - 10 * -9) < (17 + -9)) or (not (闪电不会两次击中同一个地方。)))\nB. not (((鸟有0条腿。) or ((9 * -5 * -4 * -9) <= (-7 - -4))) or (not ((-7 * 8 + 2 * 6) > (-2 * -8 - -2 * 7))))\nC. not (((1964年奥运会在东京举办。) or (企鹅能飞翔。)) or ((5 - -7) < (1 * 7 - 6 * -1)))\nD. ((((-8 - -2) != (-5 - -18)) and (1932年奥运会在洛杉矶举办。)) or ((泰坦尼克号沉没发生在1914年。) or (金星是距离太阳第2近的行星。))) or (((-8 * -9) > (4 * -6 - 4 * 5)) and (not (印度尼西亚的货币是兰特。)))\nE. (2004年奥运会在雅典举办。) and ((天王星是距离太阳第7近的行星。) or (1933年是闰年。))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 50790833,
"true_count": 3
},
"seed": 50790833,
"task_id": 650790833,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (16 - -2) >= (0 * -10 + 4 * -7)
B. (((-20 * 4) >= (3 + -11)) or ((-15 - 13) <= (8 + -17))) or (((-17 - -16) != (-17 - 11)) or ((2 + 3) > (0 * 3 + 2 * -5)))
C. 蜘蛛是昆虫。
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 57202079,
"true_count": 2
},
"question": "下面是几个布尔表达式：\n\nA. (16 - -2) >= (0 * -10 + 4 * -7)\nB. (((-20 * 4) >= (3 + -11)) or ((-15 - 13) <= (8 + -17))) or (((-17 - -16) != (-17 - 11)) or ((2 + 3) > (0 * 3 + 2 * -5)))\nC. 蜘蛛是昆虫。\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 57202079,
"true_count": 2
},
"seed": 57202079,
"task_id": 657202079,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. 现代奥运会首届举办发生在1896年。
B. (-10 * 4 - 3 * -10) < (-2 - -16)
C. (((-5 * 13) == (9 * 8 - 5 * -5)) or (人类首次登月发生在1968年。)) or ((金在常温下是固体。) or (波兰的货币是兹罗提。))
D. not not (not (1992年奥运会在巴塞罗那举办。))
E. (5 * 9 + -2 * 6) != (5 + 11)
F. (not ((3 ** 2) >= (-6 * -15))) or (not ((0 * -10) < (-14 * 12)))
G. ((2小于等于57。) and (新西兰的首都是墨西哥城。)) and ((蟑螂是哺乳动物。) or (智利的货币是比索。))
H. ((68是完全平方数。) and (4是质数。)) and (not ((4 ** 2) < (-19 * 13)))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 9763651,
"true_count": 5
},
"question": "研究以下逻辑语句：\n\nA. 现代奥运会首届举办发生在1896年。\nB. (-10 * 4 - 3 * -10) < (-2 - -16)\nC. (((-5 * 13) == (9 * 8 - 5 * -5)) or (人类首次登月发生在1968年。)) or ((金在常温下是固体。) or (波兰的货币是兹罗提。))\nD. not not (not (1992年奥运会在巴塞罗那举办。))\nE. (5 * 9 + -2 * 6) != (5 + 11)\nF. (not ((3 ** 2) >= (-6 * -15))) or (not ((0 * -10) < (-14 * 12)))\nG. ((2小于等于57。) and (新西兰的首都是墨西哥城。)) and ((蟑螂是哺乳动物。) or (智利的货币是比索。))\nH. ((68是完全平方数。) and (4是质数。)) and (not ((4 ** 2) < (-19 * 13)))\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": 9763651,
"true_count": 5
},
"seed": 9763651,
"task_id": 609763651,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (not ((not (1936年奥运会在柏林举办。)) or (韩国的货币是韩元。))) and ((((19 + -15) > (-5 - 4)) or (((-14 + -7) <= (-9 * -8 - 9 * -7)) or (土耳其的首都是布鲁塞尔。))) or ((铝的化学符号是U。) or ((火星是距离太阳第5近的行星。) and (地球上一天是24小时。))))
B. (((not (韩国的货币是韩元。)) and (月球自己发光。)) or (((13 - -14) > (4 % 1)) or ((0 * -5 * -3 * -7) >= (7 * -8 - -3 * 1))) or (木头在常温下是固体。)) and (((((-1 + 15) == (37 % 8)) and (2064年是闰年。)) and (not (钻石在常温下是气体。))) and (金的化学符号是Au。))
C. ((not (((15 * 7) != (23 % 10)) and ((38 % 6) == (-13 * -1)))) and (64的平方根是8。)) and ((not (not not ((9 * -4 * -8 * -1) < (4 + -5)))) or ((-3 * 5) >= (2 + 18)) or ((1976年奥运会在蒙特利尔举办。) and ((6 * 6 + 2 * 3) >= (4 + 19))))
D. not not ((酒精在常温下是固体。) and ((-8 * 0 - -2 * -1) == (17 + 5)))
E. (((锌的化学符号是Zn。) or (not not ((2 ** 2) == (16 * 7)))) and (((十二月有28天。) and ((-13 - 13) != (-16 * -4))) or (九月有30天。))) or ((not (金枪鱼是昆虫。)) or ((((10 * 5 + 3 * -6) < (9 + -11)) and (酒精在常温下是气体。)) or ((1904年奥运会在圣路易斯举办。) or (月球自己发光。))))
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": "C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 41803715,
"true_count": 2
},
"question": "给定以下布尔表达式：\n\nA. (not ((not (1936年奥运会在柏林举办。)) or (韩国的货币是韩元。))) and ((((19 + -15) > (-5 - 4)) or (((-14 + -7) <= (-9 * -8 - 9 * -7)) or (土耳其的首都是布鲁塞尔。))) or ((铝的化学符号是U。) or ((火星是距离太阳第5近的行星。) and (地球上一天是24小时。))))\nB. (((not (韩国的货币是韩元。)) and (月球自己发光。)) or (((13 - -14) > (4 % 1)) or ((0 * -5 * -3 * -7) >= (7 * -8 - -3 * 1))) or (木头在常温下是固体。)) and (((((-1 + 15) == (37 % 8)) and (2064年是闰年。)) and (not (钻石在常温下是气体。))) and (金的化学符号是Au。))\nC. ((not (((15 * 7) != (23 % 10)) and ((38 % 6) == (-13 * -1)))) and (64的平方根是8。)) and ((not (not not ((9 * -4 * -8 * -1) < (4 + -5)))) or ((-3 * 5) >= (2 + 18)) or ((1976年奥运会在蒙特利尔举办。) and ((6 * 6 + 2 * 3) >= (4 + 19))))\nD. not not ((酒精在常温下是固体。) and ((-8 * 0 - -2 * -1) == (17 + 5)))\nE. (((锌的化学符号是Zn。) or (not not ((2 ** 2) == (16 * 7)))) and (((十二月有28天。) and ((-13 - 13) != (-16 * -4))) or (九月有30天。))) or ((not (金枪鱼是昆虫。)) or ((((10 * 5 + 3 * -6) < (9 + -11)) and (酒精在常温下是气体。)) or ((1904年奥运会在圣路易斯举办。) or (月球自己发光。))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 5,
"seed": 41803715,
"true_count": 2
},
"seed": 41803715,
"task_id": 641803715,
"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 Indonesia is the Rupiah.) or ((A bat is a mammal.) and (The 1912 Olympics were held in Stockholm.))) or (((0 * 5) <= (4 ** 3)) and ((The currency of Sweden is the Shekel.) or ((14 * 6) <= (1 + -2) <= (-10 * -4 + 0 * -5))))))
B. not not (((((The chemical symbol for Platinum is Sn.) and (92 is less than or equal to 22.)) or (Humans have three lungs.)) and (((7 * 4) < (12 + -5)) and (The chemical symbol for Silver is Ag.)) and ((18 - -12) <= (43 % 8) <= (-14 * -12))) or ((The capital of Morocco is Rabat.) and (The 1924 Olympics were held in Tokyo.)))
C. not ((((-3 * -5 + -4 * -8) >= (6 * 4 + 0 * 0)) or (not (((3 - 11) != (12 * 3)) and ((3 ** 1) <= (-18 * 18) <= (-5 * 1 * -4 * 6))))) and (((Copper is a solid at room temperature.) and (Diamonds are made of carbon.)) and (((20 * 5) != (4 ** 3)) and (Water boils at 100 degrees Celsius at sea level.))) and (not (The currency of Saudi Arabia is the Riyal.)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 3,
"seed": 37892576,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (not not (((The currency of Indonesia is the Rupiah.) or ((A bat is a mammal.) and (The 1912 Olympics were held in Stockholm.))) or (((0 * 5) <= (4 ** 3)) and ((The currency of Sweden is the Shekel.) or ((14 * 6) <= (1 + -2) <= (-10 * -4 + 0 * -5))))))\nB. not not (((((The chemical symbol for Platinum is Sn.) and (92 is less than or equal to 22.)) or (Humans have three lungs.)) and (((7 * 4) < (12 + -5)) and (The chemical symbol for Silver is Ag.)) and ((18 - -12) <= (43 % 8) <= (-14 * -12))) or ((The capital of Morocco is Rabat.) and (The 1924 Olympics were held in Tokyo.)))\nC. not ((((-3 * -5 + -4 * -8) >= (6 * 4 + 0 * 0)) or (not (((3 - 11) != (12 * 3)) and ((3 ** 1) <= (-18 * 18) <= (-5 * 1 * -4 * 6))))) and (((Copper is a solid at room temperature.) and (Diamonds are made of carbon.)) and (((20 * 5) != (4 ** 3)) and (Water boils at 100 degrees Celsius at sea level.))) and (not (The currency of Saudi Arabia is the Riyal.)))\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": 3,
"seed": 37892576,
"true_count": 1
},
"seed": 37892576,
"task_id": 637892576,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. ((奥地利的首都是波哥大。) and (肯尼亚位于非洲。)) or ((水星是距离太阳第1近的行星。) and (1908年奥运会在伦敦举办。))
B. not ((1958年是闰年。) or (2012年奥运会在伦敦举办。))
C. (((-16 * 3) <= (10 % 7) <= (50 % 5)) or (埃及位于非洲。)) or ((蜥蜴是爬行动物。) and (八月有31天。))
D. (not (苏联解体发生在1991年。)) and ((0 * -7 * -7 * 1) < (-4 - 0) < (4 * 3))
E. 柏林墙倒塌发生在1989年。
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
"game_data": {
"answer": "A,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 89636395,
"true_count": 3
},
"question": "审视以下逻辑表达式：\n\nA. ((奥地利的首都是波哥大。) and (肯尼亚位于非洲。)) or ((水星是距离太阳第1近的行星。) and (1908年奥运会在伦敦举办。))\nB. not ((1958年是闰年。) or (2012年奥运会在伦敦举办。))\nC. (((-16 * 3) <= (10 % 7) <= (50 % 5)) or (埃及位于非洲。)) or ((蜥蜴是爬行动物。) and (八月有31天。))\nD. (not (苏联解体发生在1991年。)) and ((0 * -7 * -7 * 1) < (-4 - 0) < (4 * 3))\nE. 柏林墙倒塌发生在1989年。\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 89636395,
"true_count": 3
},
"seed": 89636395,
"task_id": 689636395,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (((not not (哥伦布到达美洲发生在1492年。)) and ((1920年奥运会在巴黎举办。) or ((二氧化碳在常温下是液体。) or (越南的货币是越南盾。)))) and ((2016年奥运会在里约热内卢举办。) and (摩洛哥的首都是新德里。) and ((0 - 3) != (4 - 18)))) and ((not not (not (not not (铝的化学符号是Al。)))) or ((not ((蚂蚁是昆虫。) or ((-9 * -5 * 5 * -3) != (8 - -14)))) and ((火星是距离太阳第7近的行星。) and (((8 * 12) > (3 % 2)) or (电流比光速更快。)))))
B. (not not (((10 * 5 + -8 * -2) >= (-3 * 16)) or (not ((铜在常温下是气体。) and (土星是距离太阳第8近的行星。))))) and ((not not ((匈牙利的首都是布达佩斯。) and ((5 * 7 + -7 * -6) >= (-14 * -9)))) or (not not (((4 ** 2) < (14 - -4) < (10 + -11)) or ((2 ** 1) < (-8 * 18))))) and (not (not not (((第二次世界大战结束发生在1945年。) or ((5 ** 3) < (-1 - -1))) or (not ((4 % 9) == (2 * -6 * -10 * 2))))))
C. 地球上一天是24小时。
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": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 3,
"seed": 62804811,
"true_count": 1
},
"question": "给定以下布尔表达式：\n\nA. (((not not (哥伦布到达美洲发生在1492年。)) and ((1920年奥运会在巴黎举办。) or ((二氧化碳在常温下是液体。) or (越南的货币是越南盾。)))) and ((2016年奥运会在里约热内卢举办。) and (摩洛哥的首都是新德里。) and ((0 - 3) != (4 - 18)))) and ((not not (not (not not (铝的化学符号是Al。)))) or ((not ((蚂蚁是昆虫。) or ((-9 * -5 * 5 * -3) != (8 - -14)))) and ((火星是距离太阳第7近的行星。) and (((8 * 12) > (3 % 2)) or (电流比光速更快。)))))\nB. (not not (((10 * 5 + -8 * -2) >= (-3 * 16)) or (not ((铜在常温下是气体。) and (土星是距离太阳第8近的行星。))))) and ((not not ((匈牙利的首都是布达佩斯。) and ((5 * 7 + -7 * -6) >= (-14 * -9)))) or (not not (((4 ** 2) < (14 - -4) < (10 + -11)) or ((2 ** 1) < (-8 * 18))))) and (not (not not (((第二次世界大战结束发生在1945年。) or ((5 ** 3) < (-1 - -1))) or (not ((4 % 9) == (2 * -6 * -10 * 2))))))\nC. 地球上一天是24小时。\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": 62804811,
"true_count": 1
},
"seed": 62804811,
"task_id": 662804811,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (-17 * 19) > (-6 + -10)
B. 火星是距离太阳第2近的行星。
C. 人类每只手有五个手指。
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 24916686,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. (-17 * 19) > (-6 + -10)\nB. 火星是距离太阳第2近的行星。\nC. 人类每只手有五个手指。\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 24916686,
"true_count": 1
},
"seed": 24916686,
"task_id": 624916686,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. not not (金星是距离太阳第2近的行星。)
B. ((水星是距离太阳第4近的行星。) or ((1 ** 2) == (4 * 1 - 1 * 9))) and (金的化学符号是Au。)
C. (((9的平方根是1。) or ((2 * -6) != (16 + -18))) and (((9 * 6 + 6 * 6) == (3 - -3)) and (光速比声速快。))) or ((16 * -2) >= (-14 - -5))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 79414396,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. not not (金星是距离太阳第2近的行星。)\nB. ((水星是距离太阳第4近的行星。) or ((1 ** 2) == (4 * 1 - 1 * 9))) and (金的化学符号是Au。)\nC. (((9的平方根是1。) or ((2 * -6) != (16 + -18))) and (((9 * 6 + 6 * 6) == (3 - -3)) and (光速比声速快。))) or ((16 * -2) >= (-14 - -5))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 79414396,
"true_count": 1
},
"seed": 79414396,
"task_id": 679414396,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. 1988年奥运会在首尔举办。
B. (((4 * 4) <= (7 * 6 + 6 * 1)) or (瑞典的货币是克朗。)) and (银的化学符号是Ne。)
C. (((-12 * -7) <= (-14 + 4)) or ((1 + -7) == (41 % 8))) and ((1 + 16) <= (-7 * -10))
D. not not (not not ((-9 * 10 + -3 * -1) >= (20 * -9)))
E. ((-9 * -4) < (9 * -3 * 2 * 9) < (-6 - 20)) and ((1995年是闰年。) and (波兰的货币是瑞士法郎。))
F. (((-11 - 7) != (-8 * -10 + -10 * 2)) or (瑞士的货币是韩元。)) or ((泰国的货币是泰铢。) and ((18 + 5) == (2 ** 3)))
G. (((9 * -2 + 1 * -1) <= (49 % 5) <= (28 % 4)) and ((-20 + 2) < (27 % 5))) or ((0 - 3) >= (44 % 6))
H. (瑞典的首都是斯德哥尔摩。) and (((2 * 7 + 2 * 1) == (1 * 8 + 5 * 2)) or (2052年是闰年。))
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,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 31486229,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. 1988年奥运会在首尔举办。\nB. (((4 * 4) <= (7 * 6 + 6 * 1)) or (瑞典的货币是克朗。)) and (银的化学符号是Ne。)\nC. (((-12 * -7) <= (-14 + 4)) or ((1 + -7) == (41 % 8))) and ((1 + 16) <= (-7 * -10))\nD. not not (not not ((-9 * 10 + -3 * -1) >= (20 * -9)))\nE. ((-9 * -4) < (9 * -3 * 2 * 9) < (-6 - 20)) and ((1995年是闰年。) and (波兰的货币是瑞士法郎。))\nF. (((-11 - 7) != (-8 * -10 + -10 * 2)) or (瑞士的货币是韩元。)) or ((泰国的货币是泰铢。) and ((18 + 5) == (2 ** 3)))\nG. (((9 * -2 + 1 * -1) <= (49 % 5) <= (28 % 4)) and ((-20 + 2) < (27 % 5))) or ((0 - 3) >= (44 % 6))\nH. (瑞典的首都是斯德哥尔摩。) and (((2 * 7 + 2 * 1) == (1 * 8 + 5 * 2)) or (2052年是闰年。))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 31486229,
"true_count": 4
},
"seed": 31486229,
"task_id": 631486229,
"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 ((-20 - -1) > (20 * -4))
B. ((((4 ** 2) < (6 * 11)) or ((14 % 9) == (-4 + 4))) and ((芬兰的首都是马德里。) or ((-19 - 13) <= (-15 - 18)))) or ((埃及的货币是卢布。) or ((31 % 3) == (26 % 6)))
C. not not (((铝的化学符号是Al。) and ((2 * -7 - 7 * -5) < (20 * -2))) or (not ((-9 - 20) > (2 * 8 - 9 * 10))))
D. not (not not (not ((5 - 7) <= (3 + 17))))
E. ((((4 * 9 * 1 * 0) <= (19 + -13)) or (酒精在常温下是液体。)) and ((铜的化学符号是Cu。) and (水蒸气在常温下是固体。))) and (海王星是距离太阳第8近的行星。) and (((25 % 7) <= (-20 * 7)) and ((4 ** 2) >= (2 + -3)))
F. (((火星是距离太阳第4近的行星。) or (铜的化学符号是Na。)) and ((新西兰位于非洲。) or (中国位于亚洲。))) and (((狗有4条腿。) and (氢的化学符号是Ag。)) or ((西班牙位于欧洲。) and ((-15 + -15) < (5 * 0 * 2 * -1))))
G. ((0 * -7 * 0 * -6) == (3 - 3)) or (铀的化学符号是U。)
H. ((11 - 7) <= (1 - 2)) or ((马来西亚的首都是吉隆坡。) and ((巴西位于欧洲。) and (9的平方根是3。)))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "D,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 36692920,
"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 ((-20 - -1) > (20 * -4))\nB. ((((4 ** 2) < (6 * 11)) or ((14 % 9) == (-4 + 4))) and ((芬兰的首都是马德里。) or ((-19 - 13) <= (-15 - 18)))) or ((埃及的货币是卢布。) or ((31 % 3) == (26 % 6)))\nC. not not (((铝的化学符号是Al。) and ((2 * -7 - 7 * -5) < (20 * -2))) or (not ((-9 - 20) > (2 * 8 - 9 * 10))))\nD. not (not not (not ((5 - 7) <= (3 + 17))))\nE. ((((4 * 9 * 1 * 0) <= (19 + -13)) or (酒精在常温下是液体。)) and ((铜的化学符号是Cu。) and (水蒸气在常温下是固体。))) and (海王星是距离太阳第8近的行星。) and (((25 % 7) <= (-20 * 7)) and ((4 ** 2) >= (2 + -3)))\nF. (((火星是距离太阳第4近的行星。) or (铜的化学符号是Na。)) and ((新西兰位于非洲。) or (中国位于亚洲。))) and (((狗有4条腿。) and (氢的化学符号是Ag。)) or ((西班牙位于欧洲。) and ((-15 + -15) < (5 * 0 * 2 * -1))))\nG. ((0 * -7 * 0 * -6) == (3 - 3)) or (铀的化学符号是U。)\nH. ((11 - 7) <= (1 - 2)) or ((马来西亚的首都是吉隆坡。) and ((巴西位于欧洲。) and (9的平方根是3。)))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 36692920,
"true_count": 3
},
"seed": 36692920,
"task_id": 636692920,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. 变色龙是爬行动物。
B. (not not ((-14 - -15) < (3 * -4) < (-1 * 5 - 1 * -8))) and (not not ((1 ** 3) > (-1 + -1)))
C. (not not ((42 % 7) == (-19 + -4))) and (((-7 * -7) < (10 * -15) < (-20 + 7)) or ((48 % 5) < (-3 * 10 * -3 * 8)))
D. (3 + 6) <= (18 + 19)
E. 印度尼西亚位于亚洲。
F. (not not ((-13 * 12) > (4 ** 2))) or ((1 - -14) == (16 - -11))
G. ((越南位于欧洲。) and ((15 + -11) == (10 - -5))) and ((-20 + 6) <= (18 + -9))
H. (not (壁虎是爬行动物。)) or (((2 + -8) < (13 * 11) < (2 ** 3)) or (四月有30天。))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "A,D,E,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 53308353,
"true_count": 4
},
"question": "评估以下每个表达式：\n\nA. 变色龙是爬行动物。\nB. (not not ((-14 - -15) < (3 * -4) < (-1 * 5 - 1 * -8))) and (not not ((1 ** 3) > (-1 + -1)))\nC. (not not ((42 % 7) == (-19 + -4))) and (((-7 * -7) < (10 * -15) < (-20 + 7)) or ((48 % 5) < (-3 * 10 * -3 * 8)))\nD. (3 + 6) <= (18 + 19)\nE. 印度尼西亚位于亚洲。\nF. (not not ((-13 * 12) > (4 ** 2))) or ((1 - -14) == (16 - -11))\nG. ((越南位于欧洲。) and ((15 + -11) == (10 - -5))) and ((-20 + 6) <= (18 + -9))\nH. (not (壁虎是爬行动物。)) or (((2 + -8) < (13 * 11) < (2 ** 3)) or (四月有30天。))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 53308353,
"true_count": 4
},
"seed": 53308353,
"task_id": 653308353,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not (((378是完全平方数。) and (鬣蜥是爬行动物。)) and ((智利位于南美洲。) and ((-1 + -12) > (18 + 7))))
B. ((巴西的货币是比索。) and (氦气在常温下是气体。)) and (((二月有29天。) and ((17 + -5) > (21 % 10))) or ((17 + -3) >= (5 - 9)))
C. (((木头在常温下是固体。) or ((-6 * -5 * 8 * 8) <= (3 - -2))) and ((1984年奥运会在洛杉矶举办。) and (印度尼西亚的货币是印尼盾。))) and (not (((17 - -15) > (-17 * -6)) or ((15 - 20) <= (-9 * 7 + -7 * -9))))
D. ((((16 * -12) >= (9 * -4)) and ((-10 * 5 - -3 * 9) == (39 % 9))) and (not not ((14 - -13) < (9 * -3 + -9 * 4) < (3 - 17)))) and ((4 * 2 * -8 * -6) != (-6 * -2 * 2 * -8))
E. not (韩国的首都是首尔。)
F. not ((((9 + -6) == (-1 * 8)) and (1928年奥运会在赫尔辛基举办。)) or ((法国的首都是巴西利亚。) or ((-8 * -12) >= (-8 - 7))))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 17440266,
"true_count": 1
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not (((378是完全平方数。) and (鬣蜥是爬行动物。)) and ((智利位于南美洲。) and ((-1 + -12) > (18 + 7))))\nB. ((巴西的货币是比索。) and (氦气在常温下是气体。)) and (((二月有29天。) and ((17 + -5) > (21 % 10))) or ((17 + -3) >= (5 - 9)))\nC. (((木头在常温下是固体。) or ((-6 * -5 * 8 * 8) <= (3 - -2))) and ((1984年奥运会在洛杉矶举办。) and (印度尼西亚的货币是印尼盾。))) and (not (((17 - -15) > (-17 * -6)) or ((15 - 20) <= (-9 * 7 + -7 * -9))))\nD. ((((16 * -12) >= (9 * -4)) and ((-10 * 5 - -3 * 9) == (39 % 9))) and (not not ((14 - -13) < (9 * -3 + -9 * 4) < (3 - 17)))) and ((4 * 2 * -8 * -6) != (-6 * -2 * 2 * -8))\nE. not (韩国的首都是首尔。)\nF. not ((((9 + -6) == (-1 * 8)) and (1928年奥运会在赫尔辛基举办。)) or ((法国的首都是巴西利亚。) or ((-8 * -12) >= (-8 - 7))))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 17440266,
"true_count": 1
},
"seed": 17440266,
"task_id": 617440266,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((鸡是鸟类。) and ((1988年奥运会在圣路易斯举办。) or (1964年奥运会在伦敦举办。))) and (天王星是距离太阳第7近的行星。)) or (大象有2条腿。) or (not not (((20 % 5) == (5 ** 2)) and ((意大利位于欧洲。) or (泰坦尼克号沉没发生在1914年。))))
B. not not (((螃蟹有10条腿。) or (not ((-15 - -12) < (-1 * -4 - 8 * -4) < (2 ** 1)))) and (((氮的化学符号是N。) and ((0 * -1) > (3 * -9))) and ((七月有31天。) and (猫是哺乳动物。))))
C. not not ((((2008年奥运会在北京举办。) and (酒精在常温下是液体。)) and (南非的货币是兰特。)) or (((法国大革命开始发生在1791年。) and ((1 ** 1) < (37 % 10) < (-5 * 5))) and ((银在常温下是液体。) or ((-13 - 17) < (-8 - -13) < (-13 * -1)))))
D. (((not not (1984年奥运会在洛杉矶举办。)) and ((金星是距离太阳第3近的行星。) or ((36 % 3) != (7 * 2 * 8 * 4)))) or (((-4 * -9 + 6 * 1) == (18 + 6)) and ((月球绕地球运转。) or ((7 - -12) < (-11 + 8))))) or (not not ((760是斐波那契数。) and (鲨鱼是鱼类。))) or (((6 * -14) < (-13 + -17) < (-1 * -10)) and ((3 * 8 + -4 * 2) < (-10 + 15)) and (not not ((1920年奥运会在墨西哥城举办。) and ((12 - 20) < (-10 + 14) < (-6 - 0)))))
E. ((((酒精在常温下是液体。) or ((8 * -4) > (8 + 9))) or (美国宣布独立发生在1774年。)) and ((二月有28天。) or ((孔雀是哺乳动物。) or (2084年是闰年。)))) or (not not (((-7 * 8 - -1 * -8) < (8 * -18) < (8 - -12)) and (not not ((-11 + -5) != (4 ** 1)))))
F. ((中国的首都是渥太华。) and ((not ((5 ** 2) < (-20 - 15))) or ((15 - 17) > (1 - -13)))) and (not ((9 % 5) < (1 - 0)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 84293707,
"true_count": 4
},
"question": "检验这些表达式：\n\nA. (((鸡是鸟类。) and ((1988年奥运会在圣路易斯举办。) or (1964年奥运会在伦敦举办。))) and (天王星是距离太阳第7近的行星。)) or (大象有2条腿。) or (not not (((20 % 5) == (5 ** 2)) and ((意大利位于欧洲。) or (泰坦尼克号沉没发生在1914年。))))\nB. not not (((螃蟹有10条腿。) or (not ((-15 - -12) < (-1 * -4 - 8 * -4) < (2 ** 1)))) and (((氮的化学符号是N。) and ((0 * -1) > (3 * -9))) and ((七月有31天。) and (猫是哺乳动物。))))\nC. not not ((((2008年奥运会在北京举办。) and (酒精在常温下是液体。)) and (南非的货币是兰特。)) or (((法国大革命开始发生在1791年。) and ((1 ** 1) < (37 % 10) < (-5 * 5))) and ((银在常温下是液体。) or ((-13 - 17) < (-8 - -13) < (-13 * -1)))))\nD. (((not not (1984年奥运会在洛杉矶举办。)) and ((金星是距离太阳第3近的行星。) or ((36 % 3) != (7 * 2 * 8 * 4)))) or (((-4 * -9 + 6 * 1) == (18 + 6)) and ((月球绕地球运转。) or ((7 - -12) < (-11 + 8))))) or (not not ((760是斐波那契数。) and (鲨鱼是鱼类。))) or (((6 * -14) < (-13 + -17) < (-1 * -10)) and ((3 * 8 + -4 * 2) < (-10 + 15)) and (not not ((1920年奥运会在墨西哥城举办。) and ((12 - 20) < (-10 + 14) < (-6 - 0)))))\nE. ((((酒精在常温下是液体。) or ((8 * -4) > (8 + 9))) or (美国宣布独立发生在1774年。)) and ((二月有28天。) or ((孔雀是哺乳动物。) or (2084年是闰年。)))) or (not not (((-7 * 8 - -1 * -8) < (8 * -18) < (8 - -12)) and (not not ((-11 + -5) != (4 ** 1)))))\nF. ((中国的首都是渥太华。) and ((not ((5 ** 2) < (-20 - 15))) or ((15 - 17) > (1 - -13)))) and (not ((9 % 5) < (1 - 0)))\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": 84293707,
"true_count": 4
},
"seed": 84293707,
"task_id": 684293707,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((((16 - -4) < (-9 * 9)) and (23能被11整除。)) or ((-20 * 17) < (8 - 19) < (-6 - -3))) or (((((13 - -8) == (13 * -13)) and ((2 ** 2) == (-5 + 5))) and (((9 + -4) != (-17 - 12)) or ((-10 * -9 * -5 * -2) < (-4 * -7 * -9 * -6) < (10 - 5)))) and (not not ((15能被9整除。) or (九月有30天。))))) and (not not ((((24 % 3) == (-14 - -16)) and (((22 % 10) != (18 * 11)) and (阿根廷位于南美洲。))) and (not not ((7 % 4) > (-3 - 20))) and (not (not not ((-7 + 11) < (-16 * -18))))))
B. (not (not not (新加坡的货币是奈拉。))) and ((((-8 * 2) > (0 + 11)) or (越南的货币是越南盾。)) or ((8 * -10 * -6 * -7) == (6 * -9 * -6 * -8))) and (not not ((((-15 + -15) <= (3 ** 1)) or (青蛙有10条腿。)) and (((10 * 0) == (13 - -13)) or ((-4 * -9) <= (13 * 20))) and (((2086年是闰年。) or (1992年奥运会在巴塞罗那举办。)) or (not (钴的化学符号是Ag。)))))
C. (((鱼有0条腿。) or (not not (not not ((-3 * 7) <= (-11 - 1))))) and ((not (64的平方根是8。)) and ((氢的化学符号是H。) and ((-19 - -7) < (12 * 7) < (-1 + -15))) and (not not ((10 * -5 - -9 * -2) != (-18 - 5))))) or ((not not ((not not (挪威的首都是雅加达。)) or (not not (木星是距离太阳第5近的行星。)))) or (not not (((2 % 2) <= (13 * 20)) or ((-2 * -7 - -6 * 0) <= (8 * -1 * -9 * -8)))) or (not not (鸡有2条腿。)))
D. (not (not not (((闪电不会两次击中同一个地方。) and (2004年奥运会在雅典举办。)) and (马来西亚的货币是林吉特。)))) and ((((not not (加拿大的首都是渥太华。)) and (蝙蝠是瞎的。)) and ((47 % 9) < (17 + 10)) and ((-19 - 18) > (-18 * 6))) or ((((电流比光速更快。) or ((-7 - 18) < (24 % 10))) and (not (2008年奥运会在伦敦举办。))) and (((-9 * -3 * 7 * -1) == (4 * -10 * 9 * 0)) or (167是完全平方数。)) and (((氧气对人类生存是必需的。) and (锡的化学符号是H。)) or (水星是距离太阳第1近的行星。))))
E. not (not ((((-16 + -3) > (5 * 7 * -6 * -8)) or ((7 + -8) <= (8 % 10))) or ((摩洛哥位于南极洲。) or (not (四月有30天。)))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 70121284,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. (((((16 - -4) < (-9 * 9)) and (23能被11整除。)) or ((-20 * 17) < (8 - 19) < (-6 - -3))) or (((((13 - -8) == (13 * -13)) and ((2 ** 2) == (-5 + 5))) and (((9 + -4) != (-17 - 12)) or ((-10 * -9 * -5 * -2) < (-4 * -7 * -9 * -6) < (10 - 5)))) and (not not ((15能被9整除。) or (九月有30天。))))) and (not not ((((24 % 3) == (-14 - -16)) and (((22 % 10) != (18 * 11)) and (阿根廷位于南美洲。))) and (not not ((7 % 4) > (-3 - 20))) and (not (not not ((-7 + 11) < (-16 * -18))))))\nB. (not (not not (新加坡的货币是奈拉。))) and ((((-8 * 2) > (0 + 11)) or (越南的货币是越南盾。)) or ((8 * -10 * -6 * -7) == (6 * -9 * -6 * -8))) and (not not ((((-15 + -15) <= (3 ** 1)) or (青蛙有10条腿。)) and (((10 * 0) == (13 - -13)) or ((-4 * -9) <= (13 * 20))) and (((2086年是闰年。) or (1992年奥运会在巴塞罗那举办。)) or (not (钴的化学符号是Ag。)))))\nC. (((鱼有0条腿。) or (not not (not not ((-3 * 7) <= (-11 - 1))))) and ((not (64的平方根是8。)) and ((氢的化学符号是H。) and ((-19 - -7) < (12 * 7) < (-1 + -15))) and (not not ((10 * -5 - -9 * -2) != (-18 - 5))))) or ((not not ((not not (挪威的首都是雅加达。)) or (not not (木星是距离太阳第5近的行星。)))) or (not not (((2 % 2) <= (13 * 20)) or ((-2 * -7 - -6 * 0) <= (8 * -1 * -9 * -8)))) or (not not (鸡有2条腿。)))\nD. (not (not not (((闪电不会两次击中同一个地方。) and (2004年奥运会在雅典举办。)) and (马来西亚的货币是林吉特。)))) and ((((not not (加拿大的首都是渥太华。)) and (蝙蝠是瞎的。)) and ((47 % 9) < (17 + 10)) and ((-19 - 18) > (-18 * 6))) or ((((电流比光速更快。) or ((-7 - 18) < (24 % 10))) and (not (2008年奥运会在伦敦举办。))) and (((-9 * -3 * 7 * -1) == (4 * -10 * 9 * 0)) or (167是完全平方数。)) and (((氧气对人类生存是必需的。) and (锡的化学符号是H。)) or (水星是距离太阳第1近的行星。))))\nE. not (not ((((-16 + -3) > (5 * 7 * -6 * -8)) or ((7 + -8) <= (8 % 10))) or ((摩洛哥位于南极洲。) or (not (四月有30天。)))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 70121284,
"true_count": 3
},
"seed": 70121284,
"task_id": 670121284,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (-4 + 18) <= (-17 - 7)
B. (4 ** 1) >= (1 % 2)
C. (((-9 * 8 - -7 * -2) > (5 * 1 - 10 * -6)) or ((-10 - -10) >= (9 * 7))) and (not (氯的化学符号是Cl。))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 78717652,
"true_count": 1
},
"question": "下面是几个布尔表达式：\n\nA. (-4 + 18) <= (-17 - 7)\nB. (4 ** 1) >= (1 % 2)\nC. (((-9 * 8 - -7 * -2) > (5 * 1 - 10 * -6)) or ((-10 - -10) >= (9 * 7))) and (not (氯的化学符号是Cl。))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 78717652,
"true_count": 1
},
"seed": 78717652,
"task_id": 678717652,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (土星是距离太阳第6近的行星。) or (((葡萄牙的首都是东京。) or (2024年奥运会在巴黎举办。)) and (第二次世界大战结束发生在1945年。))
B. not not (((智利的货币是里拉。) or ((-8 * -9) > (30 % 5))) and (第一部iPhone发布发生在2007年。))
C. not ((not not (钾的化学符号是K。)) or (((9 * 7 + 2 * 6) != (5 ** 1)) or ((-5 * -4 - -9 * -9) == (7 * 9 - 8 * 2))))
D. (((325是完全平方数。) and (1928年奥运会在阿姆斯特丹举办。)) and (((8 + -10) >= (13 - -12)) or ((-6 * -17) > (12 - -6)))) and ((-4 * 9) == (10 % 1))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 94073217,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. (土星是距离太阳第6近的行星。) or (((葡萄牙的首都是东京。) or (2024年奥运会在巴黎举办。)) and (第二次世界大战结束发生在1945年。))\nB. not not (((智利的货币是里拉。) or ((-8 * -9) > (30 % 5))) and (第一部iPhone发布发生在2007年。))\nC. not ((not not (钾的化学符号是K。)) or (((9 * 7 + 2 * 6) != (5 ** 1)) or ((-5 * -4 - -9 * -9) == (7 * 9 - 8 * 2))))\nD. (((325是完全平方数。) and (1928年奥运会在阿姆斯特丹举办。)) and (((8 + -10) >= (13 - -12)) or ((-6 * -17) > (12 - -6)))) and ((-4 * 9) == (10 % 1))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 94073217,
"true_count": 2
},
"seed": 94073217,
"task_id": 694073217,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. 68是质数。
B. ((1928年奥运会在阿姆斯特丹举办。) or (人类首次登月发生在1969年。)) and (not ((9 - -5) <= (-8 + -20)))
C. (((47 % 7) == (12 * -4)) and (巴西位于南美洲。)) and (((-7 - -17) < (20 % 4) < (-7 + -19)) and (现代奥运会首届举办发生在1886年。))
D. ((3 ** 2) <= (3 - 13) <= (3 ** 2)) or (中国位于亚洲。)
E. (3 * -6 + 0 * -8) <= (19 + -8)
F. ((蚂蚁是爬行动物。) and (氮气在常温下是气体。)) and ((55能被11整除。) or ((-8 - 5) != (15 - 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": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 19258339,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. 68是质数。\nB. ((1928年奥运会在阿姆斯特丹举办。) or (人类首次登月发生在1969年。)) and (not ((9 - -5) <= (-8 + -20)))\nC. (((47 % 7) == (12 * -4)) and (巴西位于南美洲。)) and (((-7 - -17) < (20 % 4) < (-7 + -19)) and (现代奥运会首届举办发生在1886年。))\nD. ((3 ** 2) <= (3 - 13) <= (3 ** 2)) or (中国位于亚洲。)\nE. (3 * -6 + 0 * -8) <= (19 + -8)\nF. ((蚂蚁是爬行动物。) and (氮气在常温下是气体。)) and ((55能被11整除。) or ((-8 - 5) != (15 - 8)))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 19258339,
"true_count": 3
},
"seed": 19258339,
"task_id": 619258339,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (-6 * 10 - 3 * 10) == (10 * 6 + -10 * -7)
B. The 1932 Olympics were held in Montreal.
C. (4 * 17) >= (-8 * -11)
D. not not (((4 * -3 + 1 * 1) <= (39 % 4) <= (3 ** 1)) and (Neptune is the 8th planet from the Sun.))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 44024787,
"true_count": 1
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (-6 * 10 - 3 * 10) == (10 * 6 + -10 * -7)\nB. The 1932 Olympics were held in Montreal.\nC. (4 * 17) >= (-8 * -11)\nD. not not (((4 * -3 + 1 * 1) <= (39 % 4) <= (3 ** 1)) and (Neptune is the 8th planet from the Sun.))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 4,
"seed": 44024787,
"true_count": 1
},
"seed": 44024787,
"task_id": 644024787,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. (15 - 13) != (14 * 15)
B. (((3 - -19) < (-5 + 19) < (15 + 19)) and ((3 ** 3) <= (20 - 7))) or (((6 * 11) == (0 * 5 - 8 * 8)) and ((-19 * 13) <= (-4 * 7 - -7 * -8)))
C. ((1976年奥运会在巴黎举办。) and (日本的首都是东京。)) and ((地球绕太阳运转。) or ((-16 + 0) > (-14 * -3)))
D. ((-20 * 3) > (8 + 17)) and (((41 % 4) <= (13 * 19) <= (-8 - -5)) and (266是斐波那契数。))
E. (((-3 - 14) < (2 * 8 * 2 * 7)) or (荷兰的首都是渥太华。)) and (((-8 * -9 + -3 * 9) == (-1 + 5)) or (水蒸气在常温下是气体。))
F. (not not (章鱼有8条腿。)) and ((-5 * 4 - 7 * 9) < (13 - 13))
G. 人体有206块骨头。
H. (1928年奥运会在巴黎举办。) or (乌克兰的首都是基辅。)
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,E,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 79755817,
"true_count": 5
},
"question": "给定以下布尔表达式：\n\nA. (15 - 13) != (14 * 15)\nB. (((3 - -19) < (-5 + 19) < (15 + 19)) and ((3 ** 3) <= (20 - 7))) or (((6 * 11) == (0 * 5 - 8 * 8)) and ((-19 * 13) <= (-4 * 7 - -7 * -8)))\nC. ((1976年奥运会在巴黎举办。) and (日本的首都是东京。)) and ((地球绕太阳运转。) or ((-16 + 0) > (-14 * -3)))\nD. ((-20 * 3) > (8 + 17)) and (((41 % 4) <= (13 * 19) <= (-8 - -5)) and (266是斐波那契数。))\nE. (((-3 - 14) < (2 * 8 * 2 * 7)) or (荷兰的首都是渥太华。)) and (((-8 * -9 + -3 * 9) == (-1 + 5)) or (水蒸气在常温下是气体。))\nF. (not not (章鱼有8条腿。)) and ((-5 * 4 - 7 * 9) < (13 - 13))\nG. 人体有206块骨头。\nH. (1928年奥运会在巴黎举办。) or (乌克兰的首都是基辅。)\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": 2,
"language": "cn",
"num_options": 8,
"seed": 79755817,
"true_count": 5
},
"seed": 79755817,
"task_id": 679755817,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. 天王星是距离太阳第2近的行星。
B. (15 + -18) <= (18 - -10) <= (5 ** 3)
C. ((8 * 2 * 8 * -5) >= (-3 - -18)) or (((-12 * 10) != (21 % 4)) and ((9 + 19) <= (-4 * -6 * -3 * 10)))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 78948999,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. 天王星是距离太阳第2近的行星。\nB. (15 + -18) <= (18 - -10) <= (5 ** 3)\nC. ((8 * 2 * 8 * -5) >= (-3 - -18)) or (((-12 * 10) != (21 % 4)) and ((9 + 19) <= (-4 * -6 * -3 * 10)))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 78948999,
"true_count": 1
},
"seed": 78948999,
"task_id": 678948999,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not not (not (((12 * -12) > (-20 + 3)) and (256 is a perfect square.)))) and ((((4 ** 2) == (-10 - -14)) or ((46 % 8) != (3 ** 2))) and ((The 2024 Olympics were held in Paris.) and ((-13 - 14) >= (-1 * -12)))) and ((not not ((9 + -19) < (5 * 2 - -10 * -5))) or ((-5 + 12) < (8 % 5) < (1 + -6)) or (not ((Sharks are mammals.) or (The speed of light is approximately 300,000 km/s.))))
B. not not ((93 is a prime number.) or ((-19 + 3) <= (8 * -6 * -7 * -2) <= (14 - 20)))
C. (not ((6 * 3) < (-12 - 0) < (-8 * -7 * -2 * -3))) and ((((11 - 6) <= (18 - 20) <= (4 - -7)) and ((3 * -1) == (-17 * -9))) or ((A beetle is an insect.) and (Peru is in South America.))) and (not ((30 % 8) < (-6 + 0)))
D. ((not (The currency of Canada is the Rupiah.)) and ((((10 + -13) > (4 ** 2)) or (2043 is a leap year.)) and (not not ((18 - 14) < (-4 - -14))))) or (not (not not (Wood 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": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 4,
"seed": 81643178,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. (not not (not (((12 * -12) > (-20 + 3)) and (256 is a perfect square.)))) and ((((4 ** 2) == (-10 - -14)) or ((46 % 8) != (3 ** 2))) and ((The 2024 Olympics were held in Paris.) and ((-13 - 14) >= (-1 * -12)))) and ((not not ((9 + -19) < (5 * 2 - -10 * -5))) or ((-5 + 12) < (8 % 5) < (1 + -6)) or (not ((Sharks are mammals.) or (The speed of light is approximately 300,000 km/s.))))\nB. not not ((93 is a prime number.) or ((-19 + 3) <= (8 * -6 * -7 * -2) <= (14 - 20)))\nC. (not ((6 * 3) < (-12 - 0) < (-8 * -7 * -2 * -3))) and ((((11 - 6) <= (18 - 20) <= (4 - -7)) and ((3 * -1) == (-17 * -9))) or ((A beetle is an insect.) and (Peru is in South America.))) and (not ((30 % 8) < (-6 + 0)))\nD. ((not (The currency of Canada is the Rupiah.)) and ((((10 + -13) > (4 ** 2)) or (2043 is a leap year.)) and (not not ((18 - 14) < (-4 - -14))))) or (not (not not (Wood 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": 4,
"language": "en",
"num_options": 4,
"seed": 81643178,
"true_count": 1
},
"seed": 81643178,
"task_id": 681643178,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not ((The Great Wall of China was built in one year.) and (not not (((5 * -1 * 4 * 9) < (18 * 9)) or (The currency of Saudi Arabia is the Krone.))))) or ((not (not ((The currency of Saudi Arabia is the Rupiah.) or ((-7 * -3) == (10 * -7 + -7 * -5))))) and (not ((5 * -15) == (-2 * -4 - -5 * -5))))
B. not (((not ((-1 + -10) == (-17 * 1))) or (The chemical symbol for Sulfur is Pt.) or (2032 is a leap year.)) and (not not (not not ((Japan is in South America.) and (The 1896 Olympics were held in Athens.)))))
C. not not ((not not (((China is in Asia.) or ((7 % 8) <= (-3 * 4 - 8 * 1) <= (-6 * 5))) or (A eagle is a bird.))) and (((South Korea is in North America.) and ((The capital of Colombia is Bogota.) and (Venus is the 2nd planet from the Sun.))) or ((2 - -14) == (14 + -9))))
D. not not (((not (A kangaroo has 10 legs.)) and ((9 * -5 + -8 * -2) < (3 ** 1) < (16 * -15)) and (The chemical symbol for Copper is Cu.)) or ((not (((42 % 9) < (11 * -2) < (-4 * -5 - -8 * 1)) or ((16 + 6) == (25 % 2)))) and (((5 * 2 + -5 * 4) < (13 + -11)) and (The chemical symbol for Copper is Cr.)) and ((13 * 18) < (9 + -20))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
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"seed": 28546767,
"true_count": 2
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"question": "Study the following logical statements:\n\nA. (not ((The Great Wall of China was built in one year.) and (not not (((5 * -1 * 4 * 9) < (18 * 9)) or (The currency of Saudi Arabia is the Krone.))))) or ((not (not ((The currency of Saudi Arabia is the Rupiah.) or ((-7 * -3) == (10 * -7 + -7 * -5))))) and (not ((5 * -15) == (-2 * -4 - -5 * -5))))\nB. not (((not ((-1 + -10) == (-17 * 1))) or (The chemical symbol for Sulfur is Pt.) or (2032 is a leap year.)) and (not not (not not ((Japan is in South America.) and (The 1896 Olympics were held in Athens.)))))\nC. not not ((not not (((China is in Asia.) or ((7 % 8) <= (-3 * 4 - 8 * 1) <= (-6 * 5))) or (A eagle is a bird.))) and (((South Korea is in North America.) and ((The capital of Colombia is Bogota.) and (Venus is the 2nd planet from the Sun.))) or ((2 - -14) == (14 + -9))))\nD. not not (((not (A kangaroo has 10 legs.)) and ((9 * -5 + -8 * -2) < (3 ** 1) < (16 * -15)) and (The chemical symbol for Copper is Cu.)) or ((not (((42 % 9) < (11 * -2) < (-4 * -5 - -8 * 1)) or ((16 + 6) == (25 % 2)))) and (((5 * 2 + -5 * 4) < (13 + -11)) and (The chemical symbol for Copper is Cr.)) and ((13 * 18) < (9 + -20))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 28546767,
"true_count": 2
},
"seed": 28546767,
"task_id": 628546767,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (-2 * -1) == (13 * 3)
B. not (The currency of Colombia is the Peso.)
C. A day on Earth is 24 hours.
D. (The 1960 Olympics were held in Beijing.) or (((4 ** 2) < (14 * -18)) and ((-8 * -4 - 7 * -7) > (-15 + -12)))
E. ((19 * -17) >= (43 % 5)) and (not ((-14 + -5) != (-5 - 9)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 75801833,
"true_count": 1
},
"question": "Review these logical expressions:\n\nA. (-2 * -1) == (13 * 3)\nB. not (The currency of Colombia is the Peso.)\nC. A day on Earth is 24 hours.\nD. (The 1960 Olympics were held in Beijing.) or (((4 ** 2) < (14 * -18)) and ((-8 * -4 - 7 * -7) > (-15 + -12)))\nE. ((19 * -17) >= (43 % 5)) and (not ((-14 + -5) != (-5 - 9)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 5,
"seed": 75801833,
"true_count": 1
},
"seed": 75801833,
"task_id": 675801833,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. ((((-6 * -3 - -3 * -5) > (-15 - -8)) and (铜的化学符号是Cu。)) or ((not not ((海王星是距离太阳第2近的行星。) or ((-16 + -20) <= (-9 * -8 * -2 * -9) <= (-11 - -4)))) and (((钠的化学符号是Cu。) or ((5 - -9) < (20 - 9))) and (锌的化学符号是Ne。)))) or ((((not not ((14 + 7) == (7 * -3 * 1 * 0))) or (蛇是爬行动物。)) and ((not (泰国位于大洋洲。)) and (not ((2 ** 3) < (-2 * 4))))) and ((not ((海王星是距离太阳第3近的行星。) or (蝴蝶有6条腿。))) and ((((-17 * 11) <= (-16 - -6)) or (地球是距离太阳第3近的行星。)) and ((锰的化学符号是Mn。) and ((8 * -8 * -1 * 7) == (3 ** 3))))))
B. not not (not (not (not (((19 + 10) != (2 ** 1)) or (冰的密度比液态水小。)))))
C. not ((not (((26 % 8) != (3 * 5 + -3 * 8)) or (not ((9 * 10) < (3 ** 3) < (5 ** 2))))) or (not ((((3 * 0) == (-8 * 8 - -3 * -9)) and ((2 ** 2) > (-6 * -9 + -2 * -10))) and (not (地球是距离太阳第3近的行星。)))))
D. ((not not ((1948年奥运会在北京举办。) and (蝴蝶有6条腿。))) or (((((-12 * -10) != (4 * -9)) or (地球绕太阳运转。)) or (植物通过光合作用产生氧气。)) and (((中国位于亚洲。) and (铜在常温下是固体。)) and ((11 + -17) != (-1 * -11))))) or (not (((-13 - -2) <= (1 ** 3) <= (-1 * 4 * 9 * -5)) or ((铀的化学符号是Mn。) or ((-20 - 14) <= (-2 * 5 - 4 * 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,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 97170383,
"true_count": 2
},
"question": "研究以下逻辑语句：\n\nA. ((((-6 * -3 - -3 * -5) > (-15 - -8)) and (铜的化学符号是Cu。)) or ((not not ((海王星是距离太阳第2近的行星。) or ((-16 + -20) <= (-9 * -8 * -2 * -9) <= (-11 - -4)))) and (((钠的化学符号是Cu。) or ((5 - -9) < (20 - 9))) and (锌的化学符号是Ne。)))) or ((((not not ((14 + 7) == (7 * -3 * 1 * 0))) or (蛇是爬行动物。)) and ((not (泰国位于大洋洲。)) and (not ((2 ** 3) < (-2 * 4))))) and ((not ((海王星是距离太阳第3近的行星。) or (蝴蝶有6条腿。))) and ((((-17 * 11) <= (-16 - -6)) or (地球是距离太阳第3近的行星。)) and ((锰的化学符号是Mn。) and ((8 * -8 * -1 * 7) == (3 ** 3))))))\nB. not not (not (not (not (((19 + 10) != (2 ** 1)) or (冰的密度比液态水小。)))))\nC. not ((not (((26 % 8) != (3 * 5 + -3 * 8)) or (not ((9 * 10) < (3 ** 3) < (5 ** 2))))) or (not ((((3 * 0) == (-8 * 8 - -3 * -9)) and ((2 ** 2) > (-6 * -9 + -2 * -10))) and (not (地球是距离太阳第3近的行星。)))))\nD. ((not not ((1948年奥运会在北京举办。) and (蝴蝶有6条腿。))) or (((((-12 * -10) != (4 * -9)) or (地球绕太阳运转。)) or (植物通过光合作用产生氧气。)) and (((中国位于亚洲。) and (铜在常温下是固体。)) and ((11 + -17) != (-1 * -11))))) or (not (((-13 - -2) <= (1 ** 3) <= (-1 * 4 * 9 * -5)) or ((铀的化学符号是Mn。) or ((-20 - 14) <= (-2 * 5 - 4 * 3)))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 97170383,
"true_count": 2
},
"seed": 97170383,
"task_id": 697170383,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (-10 * 1 - 3 * -7) >= (7 - -4)
B. not not (((17 % 7) < (15 % 8)) and (地球是距离太阳第3近的行星。))
C. ((摩洛哥的首都是拉巴特。) and ((-9 - -6) >= (1 - -5))) or (印度尼西亚位于非洲。)
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 68331193,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. (-10 * 1 - 3 * -7) >= (7 - -4)\nB. not not (((17 % 7) < (15 % 8)) and (地球是距离太阳第3近的行星。))\nC. ((摩洛哥的首都是拉巴特。) and ((-9 - -6) >= (1 - -5))) or (印度尼西亚位于非洲。)\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 68331193,
"true_count": 2
},
"seed": 68331193,
"task_id": 668331193,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((21 % 4) > (9 * -1 * 9 * -5)) or (人类有三个肺。)
B. ((7 * -7 * -6 * -8) < (-12 * 7)) or (((五月有31天。) and ((11 + -3) > (4 * 2))) or ((猪是哺乳动物。) or ((5 ** 1) >= (15 % 8))))
C. (((瑞典的货币是克朗。) or ((4 * 7) >= (0 * -19))) and ((14 - -10) > (-12 - 5))) or (荷兰的首都是拉巴特。)
D. (((十二月有29天。) or ((3 * 7 + 7 * -5) >= (3 ** 1))) or (not not (蜘蛛是昆虫。))) or (not ((10 * 2 * -1 * -5) <= (2 * 3 - -7 * 9) <= (-13 + 5)))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 53789454,
"true_count": 3
},
"question": "分析以下逻辑表达式：\n\nA. ((21 % 4) > (9 * -1 * 9 * -5)) or (人类有三个肺。)\nB. ((7 * -7 * -6 * -8) < (-12 * 7)) or (((五月有31天。) and ((11 + -3) > (4 * 2))) or ((猪是哺乳动物。) or ((5 ** 1) >= (15 % 8))))\nC. (((瑞典的货币是克朗。) or ((4 * 7) >= (0 * -19))) and ((14 - -10) > (-12 - 5))) or (荷兰的首都是拉巴特。)\nD. (((十二月有29天。) or ((3 * 7 + 7 * -5) >= (3 ** 1))) or (not not (蜘蛛是昆虫。))) or (not ((10 * 2 * -1 * -5) <= (2 * 3 - -7 * 9) <= (-13 + 5)))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 53789454,
"true_count": 3
},
"seed": 53789454,
"task_id": 653789454,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (((13 % 10) != (6 * 7 * -2 * -7)) and ((-19 * -14) > (-13 * 5))) or (99是偶数。)
B. not (not (氧的化学符号是O。))
C. (not not (古巴的首都是波哥大。)) and (not not (氧的化学符号是O。))
D. (((-15 + 10) <= (-10 + -8)) and (人类有三个肺。)) or (not ((4 ** 2) == (4 * 3 + -7 * -2)))
E. not not (((15 * 9) == (-2 * -9 * 3 * -7)) or (秘鲁位于南美洲。))
F. (not (古巴的首都是堪培拉。)) or (苏联解体发生在1991年。)
G. (not not (铅的化学符号是Pb。)) and (金枪鱼是鱼类。)
H. (((1 ** 2) < (6 * 10 + -10 * 6)) and (越南位于亚洲。)) and (((-8 * -5 + 6 * -8) > (-15 + -18)) or ((11 + 4) <= (-14 * 3) <= (-9 * 19)))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,B,D,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 8818093,
"true_count": 6
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (((13 % 10) != (6 * 7 * -2 * -7)) and ((-19 * -14) > (-13 * 5))) or (99是偶数。)\nB. not (not (氧的化学符号是O。))\nC. (not not (古巴的首都是波哥大。)) and (not not (氧的化学符号是O。))\nD. (((-15 + 10) <= (-10 + -8)) and (人类有三个肺。)) or (not ((4 ** 2) == (4 * 3 + -7 * -2)))\nE. not not (((15 * 9) == (-2 * -9 * 3 * -7)) or (秘鲁位于南美洲。))\nF. (not (古巴的首都是堪培拉。)) or (苏联解体发生在1991年。)\nG. (not not (铅的化学符号是Pb。)) and (金枪鱼是鱼类。)\nH. (((1 ** 2) < (6 * 10 + -10 * 6)) and (越南位于亚洲。)) and (((-8 * -5 + 6 * -8) > (-15 + -18)) or ((11 + 4) <= (-14 * 3) <= (-9 * 19)))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 8,
"seed": 8818093,
"true_count": 6
},
"seed": 8818093,
"task_id": 608818093,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (((not ((-17 + 14) != (-3 + -13))) or (not not (((-5 * 15) <= (18 - -11)) and (西班牙位于欧洲。)))) and ((((-17 - -7) <= (42 % 3)) or ((氖的化学符号是Ne。) or (铜在常温下是固体。))) or (not not ((4 ** 3) < (-8 * 1 * -5 * 2))))) or (((((-11 * 6) >= (4 ** 3)) or ((-14 * -17) == (9 % 9))) or (not not ((-19 + 8) <= (2 ** 3)))) and (86是质数。)) or (not not (not (not ((地球是距离太阳第3近的行星。) or ((18 - 6) >= (-13 - -6))))))
B. not not ((((酒精在常温下是气体。) or (天王星是距离太阳第7近的行星。)) and (伦敦大火发生在1666年。) and (比利时的首都是里斯本。)) and ((((金星是距离太阳第1近的行星。) and (英国位于欧洲。)) and (not not ((10 + -15) != (19 % 2)))) and (((-5 + 3) <= (-13 + -4)) and (沙特阿拉伯位于亚洲。)) and (蝙蝠是瞎的。)))
C. not (not not (((2 ** 3) > (9 * 5 - 0 * -8)) and (not not ((34 % 8) < (-10 * -7 - 10 * -6) < (3 * -10)))))
D. ((not not ((-3 - 9) <= (5 * -5 - 9 * -1))) or (not not (蝙蝠是瞎的。))) and ((((地球上一天是24小时。) and (西班牙位于欧洲。)) or (((1 ** 2) < (4 ** 2) < (4 ** 2)) and (2065年是闰年。)) or (((日本的货币是日元。) or (1992年奥运会在巴塞罗那举办。)) and (金在常温下是固体。))) or (not (not not ((-13 * 4) <= (3 * 0 + 3 * 9)))) or (not (孔雀是鱼类。)))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 4,
"seed": 65868636,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. (((not ((-17 + 14) != (-3 + -13))) or (not not (((-5 * 15) <= (18 - -11)) and (西班牙位于欧洲。)))) and ((((-17 - -7) <= (42 % 3)) or ((氖的化学符号是Ne。) or (铜在常温下是固体。))) or (not not ((4 ** 3) < (-8 * 1 * -5 * 2))))) or (((((-11 * 6) >= (4 ** 3)) or ((-14 * -17) == (9 % 9))) or (not not ((-19 + 8) <= (2 ** 3)))) and (86是质数。)) or (not not (not (not ((地球是距离太阳第3近的行星。) or ((18 - 6) >= (-13 - -6))))))\nB. not not ((((酒精在常温下是气体。) or (天王星是距离太阳第7近的行星。)) and (伦敦大火发生在1666年。) and (比利时的首都是里斯本。)) and ((((金星是距离太阳第1近的行星。) and (英国位于欧洲。)) and (not not ((10 + -15) != (19 % 2)))) and (((-5 + 3) <= (-13 + -4)) and (沙特阿拉伯位于亚洲。)) and (蝙蝠是瞎的。)))\nC. not (not not (((2 ** 3) > (9 * 5 - 0 * -8)) and (not not ((34 % 8) < (-10 * -7 - 10 * -6) < (3 * -10)))))\nD. ((not not ((-3 - 9) <= (5 * -5 - 9 * -1))) or (not not (蝙蝠是瞎的。))) and ((((地球上一天是24小时。) and (西班牙位于欧洲。)) or (((1 ** 2) < (4 ** 2) < (4 ** 2)) and (2065年是闰年。)) or (((日本的货币是日元。) or (1992年奥运会在巴塞罗那举办。)) and (金在常温下是固体。))) or (not (not not ((-13 * 4) <= (3 * 0 + 3 * 9)))) or (not (孔雀是鱼类。)))\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": 4,
"seed": 65868636,
"true_count": 2
},
"seed": 65868636,
"task_id": 665868636,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not ((not not ((The currency of China is the Franc.) and ((20 * -7) > (-10 * 8 * 9 * 2)))) and (((A ladybug is a fish.) or (A cat has 4 legs.)) and (((12 * 16) <= (8 + 4) <= (6 * 12)) and (The 1908 Olympics were held in Montreal.))))
B. (((((12 + -11) == (1 % 1)) and (The chemical symbol for Copper is Ne.)) and ((-5 * -11) < (-5 * -7 + 4 * -9))) and ((A crab has 10 legs.) and (((4 * 10 - -3 * -8) != (16 + 7)) and (Peru is in Antarctica.)))) or (((-14 - 6) <= (17 % 8) <= (-3 * 18)) and ((2 - -18) > (-16 * -9)))
C. (not ((not not (Venus is the 8th planet from the Sun.)) and ((Alcohol is a liquid at room temperature.) and ((1 * -1) < (-10 - -8))))) or ((not ((The capital of Switzerland is Bern.) and ((-13 - -7) <= (2 - 3)))) and (Water boils at 100 degrees Celsius at sea level.))
D. (not not (not (((14 * 14) != (6 - 17)) and ((-12 - -2) > (-15 * -5))))) and (((1 * 9 * 0 * -7) <= (15 + -2)) and (not (Thailand is in North America.)))
E. not (((not not (Brazil is in South America.)) or ((2 - -8) != (-12 - -20))) and (((-6 + -16) != (8 * 7 + -3 * -7)) or (Whales are fish.)) and ((not not (Nitrogen is a gas at room temperature.)) and (((1 ** 2) >= (4 * 1 * 8 * 4)) or (The 1904 Olympics were held in St. Louis.))))
F. (not ((not ((1 * 1 + 7 * 8) <= (3 + -2))) and (((-18 + 16) <= (3 - -19)) and (There are 29 days in July.)))) or (not not (((10 * -1 - -9 * -9) < (-7 * -4 - 7 * -1) < (8 * 19)) or ((5 % 7) < (-6 + -1))))
G. not not ((((There are 29 days in March.) or ((3 * -3 + 4 * 4) != (-16 * -3))) or (((17 + 9) != (7 % 2)) or (Chile is in South America.))) and (not (not ((-8 * 18) >= (4 * -10)))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 11365531,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not not ((not not ((The currency of China is the Franc.) and ((20 * -7) > (-10 * 8 * 9 * 2)))) and (((A ladybug is a fish.) or (A cat has 4 legs.)) and (((12 * 16) <= (8 + 4) <= (6 * 12)) and (The 1908 Olympics were held in Montreal.))))\nB. (((((12 + -11) == (1 % 1)) and (The chemical symbol for Copper is Ne.)) and ((-5 * -11) < (-5 * -7 + 4 * -9))) and ((A crab has 10 legs.) and (((4 * 10 - -3 * -8) != (16 + 7)) and (Peru is in Antarctica.)))) or (((-14 - 6) <= (17 % 8) <= (-3 * 18)) and ((2 - -18) > (-16 * -9)))\nC. (not ((not not (Venus is the 8th planet from the Sun.)) and ((Alcohol is a liquid at room temperature.) and ((1 * -1) < (-10 - -8))))) or ((not ((The capital of Switzerland is Bern.) and ((-13 - -7) <= (2 - 3)))) and (Water boils at 100 degrees Celsius at sea level.))\nD. (not not (not (((14 * 14) != (6 - 17)) and ((-12 - -2) > (-15 * -5))))) and (((1 * 9 * 0 * -7) <= (15 + -2)) and (not (Thailand is in North America.)))\nE. not (((not not (Brazil is in South America.)) or ((2 - -8) != (-12 - -20))) and (((-6 + -16) != (8 * 7 + -3 * -7)) or (Whales are fish.)) and ((not not (Nitrogen is a gas at room temperature.)) and (((1 ** 2) >= (4 * 1 * 8 * 4)) or (The 1904 Olympics were held in St. Louis.))))\nF. (not ((not ((1 * 1 + 7 * 8) <= (3 + -2))) and (((-18 + 16) <= (3 - -19)) and (There are 29 days in July.)))) or (not not (((10 * -1 - -9 * -9) < (-7 * -4 - 7 * -1) < (8 * 19)) or ((5 % 7) < (-6 + -1))))\nG. not not ((((There are 29 days in March.) or ((3 * -3 + 4 * 4) != (-16 * -3))) or (((17 + 9) != (7 % 2)) or (Chile is in South America.))) and (not (not ((-8 * 18) >= (4 * -10)))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 11365531,
"true_count": 3
},
"seed": 11365531,
"task_id": 611365531,
"task_type": "boolean_expressions"
} |
logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. ((-1 + -19) <= (-20 * 11)) or (not not (((-8 * 5 - 5 * -7) != (-19 * -7)) and (泰坦尼克号沉没发生在1912年。)))
B. ((not ((14 % 1) < (12 - -7))) or ((汞的化学符号是Hg。) and (空气在常温下是气体。))) or ((((-13 - 11) >= (8 % 6)) or ((14 * 18) >= (4 * 6 + -10 * 3))) and (((18 + 2) != (47 % 2)) and ((4 ** 2) < (5 ** 2))))
C. ((加拿大位于北美洲。) or (not not (氧气在常温下是气体。))) or ((苏联解体发生在1996年。) and (((10 - -8) >= (3 * 1 * -8 * -8)) and (火星是距离太阳第4近的行星。)))
D. not not ((((-11 * -16) < (44 % 10) < (-8 + 5)) or ((10 - 6) <= (-15 + -4))) or (260是斐波那契数。))
E. (not not (((1 ** 2) < (-10 * 10 + 3 * 2) < (1 ** 2)) and (蛇有6条腿。))) or ((哥伦布到达美洲发生在1492年。) or ((十一月有30天。) and ((9 - 16) < (47 % 7))))
F. not ((4 ** 3) <= (-7 - 5))
G. (地球上一天是24小时。) or ((((-7 - 17) >= (-16 + -18)) or (巴西位于南美洲。)) and ((钻石由碳元素组成。) and (2031年是闰年。)))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "A,B,C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 36180936,
"true_count": 6
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. ((-1 + -19) <= (-20 * 11)) or (not not (((-8 * 5 - 5 * -7) != (-19 * -7)) and (泰坦尼克号沉没发生在1912年。)))\nB. ((not ((14 % 1) < (12 - -7))) or ((汞的化学符号是Hg。) and (空气在常温下是气体。))) or ((((-13 - 11) >= (8 % 6)) or ((14 * 18) >= (4 * 6 + -10 * 3))) and (((18 + 2) != (47 % 2)) and ((4 ** 2) < (5 ** 2))))\nC. ((加拿大位于北美洲。) or (not not (氧气在常温下是气体。))) or ((苏联解体发生在1996年。) and (((10 - -8) >= (3 * 1 * -8 * -8)) and (火星是距离太阳第4近的行星。)))\nD. not not ((((-11 * -16) < (44 % 10) < (-8 + 5)) or ((10 - 6) <= (-15 + -4))) or (260是斐波那契数。))\nE. (not not (((1 ** 2) < (-10 * 10 + 3 * 2) < (1 ** 2)) and (蛇有6条腿。))) or ((哥伦布到达美洲发生在1492年。) or ((十一月有30天。) and ((9 - 16) < (47 % 7))))\nF. not ((4 ** 3) <= (-7 - 5))\nG. (地球上一天是24小时。) or ((((-7 - 17) >= (-16 + -18)) or (巴西位于南美洲。)) and ((钻石由碳元素组成。) and (2031年是闰年。)))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 36180936,
"true_count": 6
},
"seed": 36180936,
"task_id": 636180936,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. ((5 * 6 * -10 * 9) != (19 % 4)) or (not not ((-6 + 10) < (-2 * 9 + -9 * -6)))
B. (not not ((-13 - -5) >= (-14 * -15))) and (The currency of Poland is the Zloty.)
C. ((-12 - 3) <= (-5 - 1) <= (1 * 20)) or ((3 * 15) < (1 ** 1))
D. not ((35 is an even number.) or (Spiders are insects.))
E. (-20 + 0) > (-10 + 16)
F. A owl is a bird.
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 72656234,
"true_count": 4
},
"question": "Evaluate each expression below:\n\nA. ((5 * 6 * -10 * 9) != (19 % 4)) or (not not ((-6 + 10) < (-2 * 9 + -9 * -6)))\nB. (not not ((-13 - -5) >= (-14 * -15))) and (The currency of Poland is the Zloty.)\nC. ((-12 - 3) <= (-5 - 1) <= (1 * 20)) or ((3 * 15) < (1 ** 1))\nD. not ((35 is an even number.) or (Spiders are insects.))\nE. (-20 + 0) > (-10 + 16)\nF. A owl is a bird.\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 72656234,
"true_count": 4
},
"seed": 72656234,
"task_id": 672656234,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (1924年奥运会在巴黎举办。) and (not (西班牙位于欧洲。))
B. not ((钛的化学符号是Ti。) or ((10 * 8) >= (2 * 1)))
C. not not (人体有206块骨头。)
D. ((八月有28天。) or ((5 ** 3) != (5 ** 2))) and (not not (韩国位于北美洲。))
E. ((-13 * -2) < (20 * -2) < (4 * 19)) and (not not (印度尼西亚的货币是欧元。))
F. (not not ((9 - 4) < (1 + -9) < (14 + 2))) and (火星是距离太阳第5近的行星。)
G. not not (日本的首都是东京。)
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,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 81378837,
"true_count": 2
},
"question": "考虑以下布尔表达式：\n\nA. (1924年奥运会在巴黎举办。) and (not (西班牙位于欧洲。))\nB. not ((钛的化学符号是Ti。) or ((10 * 8) >= (2 * 1)))\nC. not not (人体有206块骨头。)\nD. ((八月有28天。) or ((5 ** 3) != (5 ** 2))) and (not not (韩国位于北美洲。))\nE. ((-13 * -2) < (20 * -2) < (4 * 19)) and (not not (印度尼西亚的货币是欧元。))\nF. (not not ((9 - 4) < (1 + -9) < (14 + 2))) and (火星是距离太阳第5近的行星。)\nG. not not (日本的首都是东京。)\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 81378837,
"true_count": 2
},
"seed": 81378837,
"task_id": 681378837,
"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. (((((15 - 5) <= (3 - -3)) and ((not not (天王星是距离太阳第7近的行星。)) or (not not (韩国的首都是首尔。)))) and ((((韩国的货币是韩元。) and (中国位于亚洲。)) or ((人类有0条腿。) or (人体有206块骨头。))) or ((not ((2 * 15) != (4 - 2))) and (not ((-10 * 9 + -10 * -8) <= (29 % 9)))))) or ((not (意大利位于欧洲。)) or ((82是奇数。) and (南极洲是最冷的大陆。)))) and (not not (((((土星是距离太阳第6近的行星。) or ((-3 * 20) < (-20 - 8))) or ((第一次世界大战开始发生在1913年。) or ((-18 - -8) >= (41 % 6)))) or ((-4 * 17) < (10 * -2 + -1 * -4))) or ((闪电不会两次击中同一个地方。) and (not not (not not (十一月有30天。))))))
B. not not (not (not ((((1 ** 1) != (7 * -9 * -5 * -5)) and ((81能被10整除。) and ((9 * 9 - -6 * -1) == (-17 * 19)))) and (((水蒸气在常温下是气体。) or (土星是距离太阳第6近的行星。)) and (木星是距离太阳第5近的行星。)))))
C. (not not (((孔雀是鸟类。) or (not (1912年奥运会在斯德哥尔摩举办。)) or ((法国大革命开始发生在1789年。) or (not not (鲨鱼是哺乳动物。)))) or (not not (((1 ** 2) < (6 + -16)) and ((澳大利亚位于非洲。) and (空气在常温下是液体。)))))) or ((((印度位于亚洲。) or (not (not (四月有30天。)))) or ((((23 % 4) >= (19 * 18)) and (八月有31天。)) or (((33是偶数。) and (50是质数。)) or (not not ((5 ** 1) != (7 * 1 - 7 * -1)))))) or (not not (((9 + -15) < (-20 + -20)) and ((((-4 * 19) <= (37 % 2)) or (金的化学符号是Cl。)) or (二月有28天。)))))
D. not (not (not not ((铁在常温下是固体。) or ((-15 - 16) < (6 * 2 + -3 * 0)) or ((((-16 + -16) >= (-9 + -10)) and ((0 * -6 + 3 * -6) != (2 + 17))) or ((-8 - 7) <= (6 * 8))))))
E. not (((not ((1904年奥运会在罗马举办。) or ((-1 * -2) != (-16 - 10)))) and ((not not (not (变色龙是爬行动物。))) or (水在海平面上的沸点是100摄氏度。) or ((19 + 14) > (-3 * -3 * 0 * 4)))) and (not ((五月有29天。) or ((鳕鱼是爬行动物。) and ((36 % 1) > (-6 * -10 + 2 * -7))) or ((((3 * -14) <= (19 * -12) <= (18 * -10)) and ((-3 * 7 + -4 * 10) < (46 % 4))) or (蜘蛛有8条腿。)))))
F. not not (not (((((5 * 5) >= (9 * 9 * 9 * 9)) or ((1的平方根是1。) and ((3 + 6) < (-20 * -1)))) or ((((9 * -4 * -9 * -7) <= (3 ** 3)) or (新西兰位于亚洲。)) or (not (氮的化学符号是Pt。)))) or ((not not (not not (泰国的货币是比索。))) or (((欧盟的货币是索尔。) and ((10 - 13) >= (34 % 8))) or (((-2 * 0 * 3 * -5) == (-1 * -6 + 4 * -3)) and (巴西的货币是人民币。))))))
G. not not ((not not (not not ((((-7 - 9) != (1 ** 3)) and ((12 * -4) == (1 ** 3))) and ((3 * -5 + -2 * 6) >= (-3 * 5 + 10 * 2))))) or (not not (((银的化学符号是Si。) and ((1 ** 2) < (4 ** 1))) or (((第一次世界大战开始发生在1909年。) and ((13 * 19) != (7 * 5 * -8 * 9))) or (苏联解体发生在1991年。)))))
H. (not (((not (not not ((1 - -13) < (49 % 10) < (13 - 0)))) or ((中国的货币是人民币。) or ((4 ** 1) >= (-6 * -10 + -2 * -3))) or (not not (70是质数。))) or (((0 * -16) < (14 % 3) < (4 ** 3)) or (汞在常温下是液体。)) or (((((0 + 11) >= (15 - -6)) or ((29 % 6) <= (7 - -14))) or (not ((13 - 19) == (14 + 5)))) or (铜的化学符号是Pt。)))) or (not not (not ((not (((-10 + -1) >= (4 + -5)) or ((2 - 7) <= (5 + 8)))) and (乌克兰的首都是基辅。))))
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,D,E,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 27286518,
"true_count": 5
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. (((((15 - 5) <= (3 - -3)) and ((not not (天王星是距离太阳第7近的行星。)) or (not not (韩国的首都是首尔。)))) and ((((韩国的货币是韩元。) and (中国位于亚洲。)) or ((人类有0条腿。) or (人体有206块骨头。))) or ((not ((2 * 15) != (4 - 2))) and (not ((-10 * 9 + -10 * -8) <= (29 % 9)))))) or ((not (意大利位于欧洲。)) or ((82是奇数。) and (南极洲是最冷的大陆。)))) and (not not (((((土星是距离太阳第6近的行星。) or ((-3 * 20) < (-20 - 8))) or ((第一次世界大战开始发生在1913年。) or ((-18 - -8) >= (41 % 6)))) or ((-4 * 17) < (10 * -2 + -1 * -4))) or ((闪电不会两次击中同一个地方。) and (not not (not not (十一月有30天。))))))\nB. not not (not (not ((((1 ** 1) != (7 * -9 * -5 * -5)) and ((81能被10整除。) and ((9 * 9 - -6 * -1) == (-17 * 19)))) and (((水蒸气在常温下是气体。) or (土星是距离太阳第6近的行星。)) and (木星是距离太阳第5近的行星。)))))\nC. (not not (((孔雀是鸟类。) or (not (1912年奥运会在斯德哥尔摩举办。)) or ((法国大革命开始发生在1789年。) or (not not (鲨鱼是哺乳动物。)))) or (not not (((1 ** 2) < (6 + -16)) and ((澳大利亚位于非洲。) and (空气在常温下是液体。)))))) or ((((印度位于亚洲。) or (not (not (四月有30天。)))) or ((((23 % 4) >= (19 * 18)) and (八月有31天。)) or (((33是偶数。) and (50是质数。)) or (not not ((5 ** 1) != (7 * 1 - 7 * -1)))))) or (not not (((9 + -15) < (-20 + -20)) and ((((-4 * 19) <= (37 % 2)) or (金的化学符号是Cl。)) or (二月有28天。)))))\nD. not (not (not not ((铁在常温下是固体。) or ((-15 - 16) < (6 * 2 + -3 * 0)) or ((((-16 + -16) >= (-9 + -10)) and ((0 * -6 + 3 * -6) != (2 + 17))) or ((-8 - 7) <= (6 * 8))))))\nE. not (((not ((1904年奥运会在罗马举办。) or ((-1 * -2) != (-16 - 10)))) and ((not not (not (变色龙是爬行动物。))) or (水在海平面上的沸点是100摄氏度。) or ((19 + 14) > (-3 * -3 * 0 * 4)))) and (not ((五月有29天。) or ((鳕鱼是爬行动物。) and ((36 % 1) > (-6 * -10 + 2 * -7))) or ((((3 * -14) <= (19 * -12) <= (18 * -10)) and ((-3 * 7 + -4 * 10) < (46 % 4))) or (蜘蛛有8条腿。)))))\nF. not not (not (((((5 * 5) >= (9 * 9 * 9 * 9)) or ((1的平方根是1。) and ((3 + 6) < (-20 * -1)))) or ((((9 * -4 * -9 * -7) <= (3 ** 3)) or (新西兰位于亚洲。)) or (not (氮的化学符号是Pt。)))) or ((not not (not not (泰国的货币是比索。))) or (((欧盟的货币是索尔。) and ((10 - 13) >= (34 % 8))) or (((-2 * 0 * 3 * -5) == (-1 * -6 + 4 * -3)) and (巴西的货币是人民币。))))))\nG. not not ((not not (not not ((((-7 - 9) != (1 ** 3)) and ((12 * -4) == (1 ** 3))) and ((3 * -5 + -2 * 6) >= (-3 * 5 + 10 * 2))))) or (not not (((银的化学符号是Si。) and ((1 ** 2) < (4 ** 1))) or (((第一次世界大战开始发生在1909年。) and ((13 * 19) != (7 * 5 * -8 * 9))) or (苏联解体发生在1991年。)))))\nH. (not (((not (not not ((1 - -13) < (49 % 10) < (13 - 0)))) or ((中国的货币是人民币。) or ((4 ** 1) >= (-6 * -10 + -2 * -3))) or (not not (70是质数。))) or (((0 * -16) < (14 % 3) < (4 ** 3)) or (汞在常温下是液体。)) or (((((0 + 11) >= (15 - -6)) or ((29 % 6) <= (7 - -14))) or (not ((13 - 19) == (14 + 5)))) or (铜的化学符号是Pt。)))) or (not not (not ((not (((-10 + -1) >= (4 + -5)) or ((2 - 7) <= (5 + 8)))) and (乌克兰的首都是基辅。))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 27286518,
"true_count": 5
},
"seed": 27286518,
"task_id": 627286518,
"task_type": "boolean_expressions"
} |
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