env stringclasses 1
value | prompt stringlengths 85 3.69k | extra dict |
|---|---|---|
logic-v2 | Here are some boolean expressions to evaluate:
A. not not ((((243 is a perfect square.) and (The 1964 Olympics were held in Moscow.) and ((((4 ** 1) >= (9 * 7)) or (The currency of Saudi Arabia is the Ruble.)) and (The chemical symbol for Iron is Pb.))) or ((not (There are 31 days in October.)) and ((7 - 10) < (-7 + 10)))) and (not not ((((-16 * -3) == (-11 + -17)) and (not not (There are 28 days in March.))) or ((not ((22 % 4) < (-19 - 7) < (4 ** 3))) and (not not (France is in Asia.))))))
B. not (not (((not (Mars is the 4th planet from the Sun.)) and (not not (The currency of Canada is the Riyal.)) and (not (((14 + 9) < (14 % 1)) or (The capital of Philippines is Manila.)))) and ((((2 ** 1) > (-9 - 12)) and ((16 + -13) != (2 ** 1))) or (((9 + 20) == (4 ** 3)) and (A flamingo is a fish.))) and ((((-15 * -4) != (-9 * 10 + 3 * -9)) and (not (Saudi Arabia is in Asia.))) or ((4 * 4 + -2 * 5) <= (-10 * 4 - -7 * -5)))))
C. not not (not not (((not not (The 1996 Olympics were held in Atlanta.)) and (not not ((Humans have five fingers on each hand.) and ((16 * 9) >= (6 * 2 + -9 * 8))))) or ((Australia is in North America.) or (((-18 * 6) > (1 * -4)) and (Indonesia is in Oceania.))) or (not (not not ((5 ** 1) < (-11 * 13))))))
D. (not (not not (not (A ant is a bird.)))) and (not (((Indonesia is in Africa.) or (((Vietnam is in Asia.) and (Morocco is in Antarctica.)) or ((0 * -9 - 9 * 1) == (1 ** 3)))) and ((not (The 2024 Olympics were held in Paris.)) and (((10 % 5) != (-11 - -5)) and ((-4 + -2) <= (7 * 6 + 6 * -1) <= (10 - 7)))) and (not (not ((The capital of Hungary is Budapest.) and ((5 ** 2) <= (-10 * -7 + 8 * 4)))))))
E. not not (((not (The capital of Saudi Arabia is Tokyo.)) and ((not (not ((1 + 11) >= (-1 - -17)))) and (The human body has 150 bones.) and ((not ((9 * -10 * -7 * 1) > (-3 * -10 + -8 * -2))) or (There are 28 days in September.)))) or (not not (not (((A ant has 6 legs.) and ((-2 * 10 - 8 * -10) < (7 * 9))) or (The Soviet Union dissolved occurred in 1991.)))))
F. (not (not not (((not not (There are 29 days in April.)) or (Christopher Columbus reached America occurred in 1492.)) or ((6 + 14) < (4 + -12))))) or (not ((not not ((40 % 7) < (-3 + 12))) or (((The currency of Argentina is the Forint.) and (Plants produce oxygen through photosynthesis.)) or (The capital of Vietnam is Hanoi.)) or ((Germany is in Europe.) or ((-3 + 6) == (4 ** 3)) or (The currency of Egypt is the Dollar.))))
G. not not (not not (not not (not not (The chemical symbol for Potassium is K.))))
H. not not (not not ((((6 + 1) <= (20 - -8)) or (((Mercury is the 1st planet from the Sun.) or ((-15 - 4) <= (5 + 13))) and (((5 ** 1) <= (-6 - 3)) and (A spider has 4 legs.)))) and (((5 ** 3) < (17 * -19)) or (Copper is a solid at room temperature.))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 15506165,
"true_count": 3
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not not ((((243 is a perfect square.) and (The 1964 Olympics were held in Moscow.) and ((((4 ** 1) >= (9 * 7)) or (The currency of Saudi Arabia is the Ruble.)) and (The chemical symbol for Iron is Pb.))) or ((not (There are 31 days in October.)) and ((7 - 10) < (-7 + 10)))) and (not not ((((-16 * -3) == (-11 + -17)) and (not not (There are 28 days in March.))) or ((not ((22 % 4) < (-19 - 7) < (4 ** 3))) and (not not (France is in Asia.))))))\nB. not (not (((not (Mars is the 4th planet from the Sun.)) and (not not (The currency of Canada is the Riyal.)) and (not (((14 + 9) < (14 % 1)) or (The capital of Philippines is Manila.)))) and ((((2 ** 1) > (-9 - 12)) and ((16 + -13) != (2 ** 1))) or (((9 + 20) == (4 ** 3)) and (A flamingo is a fish.))) and ((((-15 * -4) != (-9 * 10 + 3 * -9)) and (not (Saudi Arabia is in Asia.))) or ((4 * 4 + -2 * 5) <= (-10 * 4 - -7 * -5)))))\nC. not not (not not (((not not (The 1996 Olympics were held in Atlanta.)) and (not not ((Humans have five fingers on each hand.) and ((16 * 9) >= (6 * 2 + -9 * 8))))) or ((Australia is in North America.) or (((-18 * 6) > (1 * -4)) and (Indonesia is in Oceania.))) or (not (not not ((5 ** 1) < (-11 * 13))))))\nD. (not (not not (not (A ant is a bird.)))) and (not (((Indonesia is in Africa.) or (((Vietnam is in Asia.) and (Morocco is in Antarctica.)) or ((0 * -9 - 9 * 1) == (1 ** 3)))) and ((not (The 2024 Olympics were held in Paris.)) and (((10 % 5) != (-11 - -5)) and ((-4 + -2) <= (7 * 6 + 6 * -1) <= (10 - 7)))) and (not (not ((The capital of Hungary is Budapest.) and ((5 ** 2) <= (-10 * -7 + 8 * 4)))))))\nE. not not (((not (The capital of Saudi Arabia is Tokyo.)) and ((not (not ((1 + 11) >= (-1 - -17)))) and (The human body has 150 bones.) and ((not ((9 * -10 * -7 * 1) > (-3 * -10 + -8 * -2))) or (There are 28 days in September.)))) or (not not (not (((A ant has 6 legs.) and ((-2 * 10 - 8 * -10) < (7 * 9))) or (The Soviet Union dissolved occurred in 1991.)))))\nF. (not (not not (((not not (There are 29 days in April.)) or (Christopher Columbus reached America occurred in 1492.)) or ((6 + 14) < (4 + -12))))) or (not ((not not ((40 % 7) < (-3 + 12))) or (((The currency of Argentina is the Forint.) and (Plants produce oxygen through photosynthesis.)) or (The capital of Vietnam is Hanoi.)) or ((Germany is in Europe.) or ((-3 + 6) == (4 ** 3)) or (The currency of Egypt is the Dollar.))))\nG. not not (not not (not not (not not (The chemical symbol for Potassium is K.))))\nH. not not (not not ((((6 + 1) <= (20 - -8)) or (((Mercury is the 1st planet from the Sun.) or ((-15 - 4) <= (5 + 13))) and (((5 ** 1) <= (-6 - 3)) and (A spider has 4 legs.)))) and (((5 ** 3) < (17 * -19)) or (Copper is a solid at room temperature.))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 15506165,
"true_count": 3
},
"seed": 15506165,
"task_id": 615506165,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not (The Earth revolves around the Sun.)
B. ((((16 % 9) > (-2 * 9 * 0 * -7)) or ((10 - 14) < (-10 - 4) < (-13 + -12))) or (not ((20 * -6) >= (-18 + 0)))) or (not (((50 % 6) < (2 ** 1)) and (The chemical symbol for Neon is Ne.)))
C. not (not not ((The currency of Colombia is the Peso.) and ((4 ** 3) <= (3 + 11))))
D. (A dog has 0 legs.) or ((((-14 * -7) <= (4 ** 2)) or ((-17 + -5) <= (20 - -9))) or (World War I ended occurred in 1918.))
E. ((-17 * 2) <= (9 * -2 + -3 * -4)) and (((2034 is a leap year.) or (Humans have five fingers on each hand.)) and (((-5 * 6 * -7 * -5) <= (2 + 9)) and ((-20 - 10) > (6 % 4))))
F. not (((-2 - 15) == (9 * 2 + 7 * -6)) or ((Mercury is the 5th planet from the Sun.) or ((3 ** 2) != (8 * -8 * 7 * -1))))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 56284558,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not (The Earth revolves around the Sun.)\nB. ((((16 % 9) > (-2 * 9 * 0 * -7)) or ((10 - 14) < (-10 - 4) < (-13 + -12))) or (not ((20 * -6) >= (-18 + 0)))) or (not (((50 % 6) < (2 ** 1)) and (The chemical symbol for Neon is Ne.)))\nC. not (not not ((The currency of Colombia is the Peso.) and ((4 ** 3) <= (3 + 11))))\nD. (A dog has 0 legs.) or ((((-14 * -7) <= (4 ** 2)) or ((-17 + -5) <= (20 - -9))) or (World War I ended occurred in 1918.))\nE. ((-17 * 2) <= (9 * -2 + -3 * -4)) and (((2034 is a leap year.) or (Humans have five fingers on each hand.)) and (((-5 * 6 * -7 * -5) <= (2 + 9)) and ((-20 - 10) > (6 % 4))))\nF. not (((-2 - 15) == (9 * 2 + 7 * -6)) or ((Mercury is the 5th planet from the Sun.) or ((3 ** 2) != (8 * -8 * 7 * -1))))\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": 56284558,
"true_count": 3
},
"seed": 56284558,
"task_id": 656284558,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (not (not not ((((Japan is in Africa.) and (191 is an even number.)) and ((The Titanic sank occurred in 1912.) or ((2 ** 2) >= (37 % 4)))) or (Penguins can fly.)))) and (not not (not ((Indonesia is in Asia.) or (((5 + -17) == (-16 * 13)) and (21 is less than or equal to 78.)))))
B. not not (not not ((((((-8 * -9 * -7 * -4) > (5 ** 1)) or ((2 ** 2) < (-7 + -1))) and ((14 + 14) < (-20 * -7))) or ((There are 29 days in December.) and (Mercury is the 1st planet from the Sun.)) or (The 1948 Olympics were held in Helsinki.)) or (not ((((17 - -16) != (20 - 5)) or (A human is a mammal.)) or (not ((16 - 14) != (17 - 8)))))))
C. ((not not (not not ((4 + -6) < (17 * -17)))) or (not (not (not ((The 1976 Olympics were held in Beijing.) or ((1 - 0) != (10 * 10 + -10 * -9))))))) or (not (not (not not (not not (not ((2 ** 1) < (-12 - -6) < (42 % 3)))))))
D. not (not (((Mercury is a liquid at room temperature.) or ((The currency of Hungary is the Zloty.) or ((Carbon dioxide is a gas at room temperature.) or (France is in Europe.)))) or (not ((((8 - -8) <= (4 ** 3)) and ((-16 - 8) <= (-16 + 1))) and (not (Steam is a liquid at room temperature.))))))
E. not not (not ((not (not not ((The chemical symbol for Cobalt is Co.) or ((0 + -14) < (1 + 14))))) or (((not ((-2 * -10 * -4 * 7) >= (-7 + -13))) or (((19 - 9) != (4 ** 1)) or (There are 28 days in February.))) or (not not (The currency of Israel is the Shekel.)))))
F. not (not (((((There are 30 days in March.) or (Helium is a gas at room temperature.)) and (A grasshopper is an insect.)) and (not (((6 * -8 * 1 * 7) >= (-13 - -12)) or ((-19 + 3) >= (5 + -2))))) and (Ice is less dense than liquid water.) and (((not not ((16 - -10) < (-4 + 15) < (34 % 1))) or ((Diamonds are made of carbon.) and (The Great Fire of London occurred in 1666.))) and ((-18 - 7) >= (-16 + 12)))))
G. not (not ((((((19 * -1) <= (3 ** 1) <= (4 ** 2)) or (Antarctica is the coldest continent.)) or ((There are 28 days in May.) and (Thailand is in Asia.))) and (The capital of Czech Republic is Santiago.)) or ((A cat has 2 legs.) and ((1 * 1 - 6 * -2) > (-2 * -1 + -4 * -5)))))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 56581571,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. (not (not not ((((Japan is in Africa.) and (191 is an even number.)) and ((The Titanic sank occurred in 1912.) or ((2 ** 2) >= (37 % 4)))) or (Penguins can fly.)))) and (not not (not ((Indonesia is in Asia.) or (((5 + -17) == (-16 * 13)) and (21 is less than or equal to 78.)))))\nB. not not (not not ((((((-8 * -9 * -7 * -4) > (5 ** 1)) or ((2 ** 2) < (-7 + -1))) and ((14 + 14) < (-20 * -7))) or ((There are 29 days in December.) and (Mercury is the 1st planet from the Sun.)) or (The 1948 Olympics were held in Helsinki.)) or (not ((((17 - -16) != (20 - 5)) or (A human is a mammal.)) or (not ((16 - 14) != (17 - 8)))))))\nC. ((not not (not not ((4 + -6) < (17 * -17)))) or (not (not (not ((The 1976 Olympics were held in Beijing.) or ((1 - 0) != (10 * 10 + -10 * -9))))))) or (not (not (not not (not not (not ((2 ** 1) < (-12 - -6) < (42 % 3)))))))\nD. not (not (((Mercury is a liquid at room temperature.) or ((The currency of Hungary is the Zloty.) or ((Carbon dioxide is a gas at room temperature.) or (France is in Europe.)))) or (not ((((8 - -8) <= (4 ** 3)) and ((-16 - 8) <= (-16 + 1))) and (not (Steam is a liquid at room temperature.))))))\nE. not not (not ((not (not not ((The chemical symbol for Cobalt is Co.) or ((0 + -14) < (1 + 14))))) or (((not ((-2 * -10 * -4 * 7) >= (-7 + -13))) or (((19 - 9) != (4 ** 1)) or (There are 28 days in February.))) or (not not (The currency of Israel is the Shekel.)))))\nF. not (not (((((There are 30 days in March.) or (Helium is a gas at room temperature.)) and (A grasshopper is an insect.)) and (not (((6 * -8 * 1 * 7) >= (-13 - -12)) or ((-19 + 3) >= (5 + -2))))) and (Ice is less dense than liquid water.) and (((not not ((16 - -10) < (-4 + 15) < (34 % 1))) or ((Diamonds are made of carbon.) and (The Great Fire of London occurred in 1666.))) and ((-18 - 7) >= (-16 + 12)))))\nG. not (not ((((((19 * -1) <= (3 ** 1) <= (4 ** 2)) or (Antarctica is the coldest continent.)) or ((There are 28 days in May.) and (Thailand is in Asia.))) and (The capital of Czech Republic is Santiago.)) or ((A cat has 2 legs.) and ((1 * 1 - 6 * -2) > (-2 * -1 + -4 * -5)))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 56581571,
"true_count": 3
},
"seed": 56581571,
"task_id": 656581571,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not (not not ((not not (((-5 - 9) == (-17 - -17)) and (not (The currency of India is the Rupee.)))) and (2018 is a leap year.) and ((((A human has 2 legs.) or (There are 30 days in April.)) or ((Alcohol is a liquid at room temperature.) or (India is in Africa.))) and (((73 is a prime number.) or (Alcohol is a solid at room temperature.)) or ((15 - 9) >= (-9 * 20))))))
B. not ((((The chemical symbol for Tin is Ni.) and (Uranus is the 7th planet from the Sun.) and (56 is divisible by 7.)) or (((A carp is a fish.) and (There are 31 days in March.)) or (not ((The chemical symbol for Silicon is Si.) or (Mars is the 1st planet from the Sun.))))) or (not not (not ((Colombia is in Africa.) or (A koala is a mammal.)))))
C. (not not (not not (not not ((-13 - 19) != (11 + 4))))) or ((not (((18 % 2) > (15 * -7)) and ((8 + -13) < (10 * 20) < (13 + 19)))) and (((The chemical symbol for Titanium is Hg.) and (((12 + -15) > (-16 + 13)) or ((The currency of New Zealand is the Dollar.) or (Mercury is a gas at room temperature.)))) or (2068 is a leap year.) or (not (((The Earth revolves around the Sun.) and (Mars is the 3rd planet from the Sun.)) or ((There are 30 days in July.) or (Australia is in Oceania.))))))
D. not not ((not (not (The chemical symbol for Iron is Fe.))) and ((not not ((((4 * 3 - -2 * 6) > (-18 * -10)) or (A frog has 100 legs.)) and ((The currency of China is the Dong.) and (A octopus has 8 legs.)))) or (((-8 * -11) >= (18 * 13)) or (((4 ** 3) <= (11 - 12) <= (2 * -4)) or ((-6 * 8 + -2 * -3) < (-7 + 12))) or (The currency of Poland is the Zloty.))))
E. not (not (not (not ((The currency of Thailand is the Baht.) and ((Lightning never strikes the same place twice.) and (32 is an odd number.))))))
F. not (not not (not (((A elephant has 2 legs.) and (not not (Antarctica is the coldest continent.))) or (66 is an odd number.) or ((The 1908 Olympics were held in London.) or ((Morocco is in Africa.) and (Saudi Arabia is in Asia.))))))
G. not (not (((not not (The French Revolution began occurred in 1789.)) and (not not ((19 - 16) < (7 * 5)))) or (not (not not ((20 + -3) <= (4 - -15))))))
H. not (not (not not ((not (The chemical symbol for Zinc is Hg.)) or (56 is divisible by 11.) or (The capital of Finland is Helsinki.))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,C,D,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 13582550,
"true_count": 6
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not (not not ((not not (((-5 - 9) == (-17 - -17)) and (not (The currency of India is the Rupee.)))) and (2018 is a leap year.) and ((((A human has 2 legs.) or (There are 30 days in April.)) or ((Alcohol is a liquid at room temperature.) or (India is in Africa.))) and (((73 is a prime number.) or (Alcohol is a solid at room temperature.)) or ((15 - 9) >= (-9 * 20))))))\nB. not ((((The chemical symbol for Tin is Ni.) and (Uranus is the 7th planet from the Sun.) and (56 is divisible by 7.)) or (((A carp is a fish.) and (There are 31 days in March.)) or (not ((The chemical symbol for Silicon is Si.) or (Mars is the 1st planet from the Sun.))))) or (not not (not ((Colombia is in Africa.) or (A koala is a mammal.)))))\nC. (not not (not not (not not ((-13 - 19) != (11 + 4))))) or ((not (((18 % 2) > (15 * -7)) and ((8 + -13) < (10 * 20) < (13 + 19)))) and (((The chemical symbol for Titanium is Hg.) and (((12 + -15) > (-16 + 13)) or ((The currency of New Zealand is the Dollar.) or (Mercury is a gas at room temperature.)))) or (2068 is a leap year.) or (not (((The Earth revolves around the Sun.) and (Mars is the 3rd planet from the Sun.)) or ((There are 30 days in July.) or (Australia is in Oceania.))))))\nD. not not ((not (not (The chemical symbol for Iron is Fe.))) and ((not not ((((4 * 3 - -2 * 6) > (-18 * -10)) or (A frog has 100 legs.)) and ((The currency of China is the Dong.) and (A octopus has 8 legs.)))) or (((-8 * -11) >= (18 * 13)) or (((4 ** 3) <= (11 - 12) <= (2 * -4)) or ((-6 * 8 + -2 * -3) < (-7 + 12))) or (The currency of Poland is the Zloty.))))\nE. not (not (not (not ((The currency of Thailand is the Baht.) and ((Lightning never strikes the same place twice.) and (32 is an odd number.))))))\nF. not (not not (not (((A elephant has 2 legs.) and (not not (Antarctica is the coldest continent.))) or (66 is an odd number.) or ((The 1908 Olympics were held in London.) or ((Morocco is in Africa.) and (Saudi Arabia is in Asia.))))))\nG. not (not (((not not (The French Revolution began occurred in 1789.)) and (not not ((19 - 16) < (7 * 5)))) or (not (not not ((20 + -3) <= (4 - -15))))))\nH. not (not (not not ((not (The chemical symbol for Zinc is Hg.)) or (56 is divisible by 11.) or (The capital of Finland is Helsinki.))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 13582550,
"true_count": 6
},
"seed": 13582550,
"task_id": 613582550,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. ((((11 + 10) > (-11 * 18)) or ((19 - 12) == (-18 * -6))) and (not not (not not (The 1968 Olympics were held in Mexico City.)))) or ((not not ((127 is a perfect square.) and (((7 % 10) <= (-13 * 12)) and ((2 ** 3) != (-7 - -6))))) or (not ((((3 * 3 + 0 * 7) == (-1 * -4 - 8 * 10)) and (World War I ended occurred in 1918.)) or (not (Saturn is the 6th planet from the Sun.)))))
B. not not (((not (((3 + -8) != (12 + 9)) or (Air is a solid at room temperature.))) and (not ((17 % 6) != (13 * -8)))) and ((0 * 4 - -8 * -1) <= (-18 + 11)) and (((1 ** 3) < (12 % 10) < (4 * -12)) or ((-18 - -19) != (5 * -11))))
C. (not (((-9 * -4 + 3 * -8) < (34 % 4) < (-9 * -12)) or (not (((6 * 6 + 8 * -7) == (48 % 10)) or ((-13 + 11) < (0 * 5 - 10 * -7) < (-2 + -10)))))) or (not not ((not (130 is an odd number.)) and (not not (307 is a Fibonacci number.)) and ((not not (A kangaroo has 2 legs.)) or (The 2024 Olympics were held in Paris.))))
D. ((not (not not ((150 is an even number.) or ((-5 * -3 - 7 * 8) != (7 * 3 + 4 * 10))))) or (((The Moon orbits the Earth.) or ((The human body has 206 bones.) and (Earth is the 3rd planet from the Sun.))) and ((-12 - 19) != (10 * 3 - -8 * 8)))) and ((not not (not not (The currency of Russia is the Forint.))) or (A ant has 6 legs.)) and (not not ((The first iPhone was released occurred in 2007.) or ((not (A fish has 6 legs.)) and (not not ((-5 - 8) <= (-19 - 1))))))
E. (not not ((((The currency of Peru is the Yen.) or (Morocco is in North America.)) or (((1 ** 1) >= (-20 + -17)) and ((16 - 6) < (-10 - -9)))) or (not (There are 31 days in July.)))) or (not ((The human body has 150 bones.) and ((((1 ** 2) < (20 + 2) < (-2 - 7)) or ((2 % 4) == (-12 * -3))) and (((5 * 1 - 1 * -8) == (1 ** 2)) and ((3 ** 1) >= (7 - 18))))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 85256184,
"true_count": 3
},
"question": "Here are some boolean expressions to evaluate:\n\nA. ((((11 + 10) > (-11 * 18)) or ((19 - 12) == (-18 * -6))) and (not not (not not (The 1968 Olympics were held in Mexico City.)))) or ((not not ((127 is a perfect square.) and (((7 % 10) <= (-13 * 12)) and ((2 ** 3) != (-7 - -6))))) or (not ((((3 * 3 + 0 * 7) == (-1 * -4 - 8 * 10)) and (World War I ended occurred in 1918.)) or (not (Saturn is the 6th planet from the Sun.)))))\nB. not not (((not (((3 + -8) != (12 + 9)) or (Air is a solid at room temperature.))) and (not ((17 % 6) != (13 * -8)))) and ((0 * 4 - -8 * -1) <= (-18 + 11)) and (((1 ** 3) < (12 % 10) < (4 * -12)) or ((-18 - -19) != (5 * -11))))\nC. (not (((-9 * -4 + 3 * -8) < (34 % 4) < (-9 * -12)) or (not (((6 * 6 + 8 * -7) == (48 % 10)) or ((-13 + 11) < (0 * 5 - 10 * -7) < (-2 + -10)))))) or (not not ((not (130 is an odd number.)) and (not not (307 is a Fibonacci number.)) and ((not not (A kangaroo has 2 legs.)) or (The 2024 Olympics were held in Paris.))))\nD. ((not (not not ((150 is an even number.) or ((-5 * -3 - 7 * 8) != (7 * 3 + 4 * 10))))) or (((The Moon orbits the Earth.) or ((The human body has 206 bones.) and (Earth is the 3rd planet from the Sun.))) and ((-12 - 19) != (10 * 3 - -8 * 8)))) and ((not not (not not (The currency of Russia is the Forint.))) or (A ant has 6 legs.)) and (not not ((The first iPhone was released occurred in 2007.) or ((not (A fish has 6 legs.)) and (not not ((-5 - 8) <= (-19 - 1))))))\nE. (not not ((((The currency of Peru is the Yen.) or (Morocco is in North America.)) or (((1 ** 1) >= (-20 + -17)) and ((16 - 6) < (-10 - -9)))) or (not (There are 31 days in July.)))) or (not ((The human body has 150 bones.) and ((((1 ** 2) < (20 + 2) < (-2 - 7)) or ((2 % 4) == (-12 * -3))) and (((5 * 1 - 1 * -8) == (1 ** 2)) and ((3 ** 1) >= (7 - 18))))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 85256184,
"true_count": 3
},
"seed": 85256184,
"task_id": 685256184,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. (not not (not (((尼日利亚位于非洲。) and (金星是距离太阳第2近的行星。)) or (not not ((-12 - 0) != (-1 * 0 * 8 * 8)))))) and ((196的平方根是15。) and ((-20 * -7) <= (6 % 5))) and (((((95是奇数。) or ((-6 - -3) < (-13 * -4) < (5 - 5))) and (马来西亚的首都是莫斯科。)) or ((((-3 * 15) <= (18 + 12)) or ((5 * -8 + -7 * -2) < (9 + 9))) or (((-6 * -2 - -6 * -8) == (9 - 2)) or ((-8 + -16) < (-9 * -12))))) or ((土星是距离太阳第6近的行星。) or ((蝴蝶有8条腿。) or (87是奇数。))) or ((尼日利亚的货币是奈拉。) or (((44 % 5) >= (2 - -1)) or ((声音在真空中传播更快。) and (1972年奥运会在慕尼黑举办。)))))
B. (not ((猫有4条腿。) and (not not (not (智利的首都是华沙。))))) and (not not (((((34 % 10) == (14 % 2)) or (电流比光速更快。)) or (((33 % 4) < (3 * 9 * 10 * -3) < (6 % 9)) and ((-5 * 7 + 1 * 3) <= (2 * 8)))) and (泰坦尼克号沉没发生在1912年。) and (not ((欧盟的货币是欧元。) and (木星是距离太阳第7近的行星。)))))
C. ((not ((not not (蝙蝠是瞎的。)) or (((4 + 6) == (-17 + -19)) or (火星是距离太阳第4近的行星。)))) and (((not not (第一次世界大战结束发生在1918年。)) or (狗有2条腿。)) or (植物通过光合作用产生氧气。))) or (((not not (氦气在常温下是气体。)) and (not not ((第一次世界大战结束发生在1918年。) and ((-17 + 17) <= (-3 * -18))))) or (((29 % 7) >= (16 + 18)) or ((((11 - 6) >= (18 + -4)) and (1948年奥运会在巴黎举办。)) or (not (乌龟是爬行动物。)))))
D. (not not (not (not not ((4 ** 2) > (-10 * 8))))) or ((菲律宾的货币是比索。) or (苏联解体发生在1981年。) or ((4 * -3 + -1 * 8) < (13 + 20) < (13 + -2))) or ((((((-10 + 0) < (2 * 10 - 3 * 5)) or (菲律宾的货币是比索。)) or (not not ((-5 - 15) <= (-14 - 6)))) and (澳大利亚的货币是澳元。)) and ((((-4 * 9 + 2 * 8) < (31 % 1) < (37 % 2)) and (not (尼日利亚位于欧洲。))) and (((2 ** 2) <= (2 + -5)) and (尼日利亚的首都是阿布贾。))))
E. ((((not not ((-5 + 7) != (1 * -13))) and ((肯尼亚位于南极洲。) or (2032年是闰年。))) and (not (((-14 * 10) < (4 ** 1)) or ((-11 * 5) != (14 - -20))))) or (((罗马尼亚的首都是巴西利亚。) or ((第二次世界大战结束发生在1945年。) and (木头在常温下是固体。))) or ((not (肯尼亚的首都是内罗毕。)) or (((-18 * -18) >= (-5 - 19)) and ((20 % 3) >= (4 * 1 + -4 * 6)))))) or ((not (100是完全平方数。)) or ((not ((3 ** 1) <= (-4 + -19) <= (-11 + -2))) and ((委内瑞拉的首都是新德里。) or (not (钛的化学符号是Ti。)))))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
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"difficulty": 1,
"gpt_response": "",
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"question": "评估以下每个表达式：\n\nA. (not not (not (((尼日利亚位于非洲。) and (金星是距离太阳第2近的行星。)) or (not not ((-12 - 0) != (-1 * 0 * 8 * 8)))))) and ((196的平方根是15。) and ((-20 * -7) <= (6 % 5))) and (((((95是奇数。) or ((-6 - -3) < (-13 * -4) < (5 - 5))) and (马来西亚的首都是莫斯科。)) or ((((-3 * 15) <= (18 + 12)) or ((5 * -8 + -7 * -2) < (9 + 9))) or (((-6 * -2 - -6 * -8) == (9 - 2)) or ((-8 + -16) < (-9 * -12))))) or ((土星是距离太阳第6近的行星。) or ((蝴蝶有8条腿。) or (87是奇数。))) or ((尼日利亚的货币是奈拉。) or (((44 % 5) >= (2 - -1)) or ((声音在真空中传播更快。) and (1972年奥运会在慕尼黑举办。)))))\nB. (not ((猫有4条腿。) and (not not (not (智利的首都是华沙。))))) and (not not (((((34 % 10) == (14 % 2)) or (电流比光速更快。)) or (((33 % 4) < (3 * 9 * 10 * -3) < (6 % 9)) and ((-5 * 7 + 1 * 3) <= (2 * 8)))) and (泰坦尼克号沉没发生在1912年。) and (not ((欧盟的货币是欧元。) and (木星是距离太阳第7近的行星。)))))\nC. ((not ((not not (蝙蝠是瞎的。)) or (((4 + 6) == (-17 + -19)) or (火星是距离太阳第4近的行星。)))) and (((not not (第一次世界大战结束发生在1918年。)) or (狗有2条腿。)) or (植物通过光合作用产生氧气。))) or (((not not (氦气在常温下是气体。)) and (not not ((第一次世界大战结束发生在1918年。) and ((-17 + 17) <= (-3 * -18))))) or (((29 % 7) >= (16 + 18)) or ((((11 - 6) >= (18 + -4)) and (1948年奥运会在巴黎举办。)) or (not (乌龟是爬行动物。)))))\nD. (not not (not (not not ((4 ** 2) > (-10 * 8))))) or ((菲律宾的货币是比索。) or (苏联解体发生在1981年。) or ((4 * -3 + -1 * 8) < (13 + 20) < (13 + -2))) or ((((((-10 + 0) < (2 * 10 - 3 * 5)) or (菲律宾的货币是比索。)) or (not not ((-5 - 15) <= (-14 - 6)))) and (澳大利亚的货币是澳元。)) and ((((-4 * 9 + 2 * 8) < (31 % 1) < (37 % 2)) and (not (尼日利亚位于欧洲。))) and (((2 ** 2) <= (2 + -5)) and (尼日利亚的首都是阿布贾。))))\nE. ((((not not ((-5 + 7) != (1 * -13))) and ((肯尼亚位于南极洲。) or (2032年是闰年。))) and (not (((-14 * 10) < (4 ** 1)) or ((-11 * 5) != (14 - -20))))) or (((罗马尼亚的首都是巴西利亚。) or ((第二次世界大战结束发生在1945年。) and (木头在常温下是固体。))) or ((not (肯尼亚的首都是内罗毕。)) or (((-18 * -18) >= (-5 - 19)) and ((20 % 3) >= (4 * 1 + -4 * 6)))))) or ((not (100是完全平方数。)) or ((not ((3 ** 1) <= (-4 + -19) <= (-11 + -2))) and ((委内瑞拉的首都是新德里。) or (not (钛的化学符号是Ti。)))))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
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"language": "cn",
"num_options": 5,
"seed": 69542035,
"true_count": 3
},
"seed": 69542035,
"task_id": 669542035,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. not not ((not ((not not (((14 - -19) >= (11 + 9)) and ((-5 - -12) == (-9 * 6 + 3 * -9)))) or (((17 + -3) > (6 * -8 * -8 * -2)) and (((2 ** 1) < (9 * 0 + 0 * 1)) or ((-1 * 2 * 0 * -5) >= (15 * -19)))))) and (not (not not ((4 % 3) < (-6 * -8) < (6 * 3)))) and (((not not (((4 ** 2) == (0 + 18)) or (印度尼西亚的货币是印尼盾。))) and (火星是距离太阳第4近的行星。)) and ((-10 - 19) <= (22 % 1)) and ((植物通过光合作用产生氧气。) and ((10 * -6 - -9 * 3) >= (20 + -4)))))
B. (not not ((not (1964年奥运会在墨西哥城举办。)) or (not not ((5 - -8) != (4 * 3 * -2 * -7))))) or ((not not (((-5 * -1 + -9 * -10) == (12 - 11)) or (((0 - -19) < (17 + 4)) and ((9 - -16) <= (2 % 2))) or (not (not not (2012年奥运会在东京举办。))))) and (((((50 % 7) < (12 * -15) < (2 * -8 + 9 * 2)) or ((-10 + -4) != (13 * -16))) and ((not not (16是质数。)) and ((秘鲁的首都是墨西哥城。) or ((-11 - -13) < (-18 + 7))))) and (not ((水星是距离太阳第5近的行星。) or (845是斐波那契数。)))))
C. not (not (((not (1915年是闰年。)) or (not ((1953年是闰年。) and (英国位于北美洲。)))) or (((-9 * -8) >= (-15 - -1)) or ((((0 * 5 - -6 * -5) == (46 % 4)) or ((2 + -4) != (-9 + -5))) and (((6 + -10) >= (19 * 1)) or ((2 * 6 - -9 * -10) == (-14 * -5)))))))
D. not not (not not ((((5 ** 2) != (-1 - -15)) or ((哥伦布到达美洲发生在1490年。) and (伦敦大火发生在1665年。)) or (牛有4条腿。)) and (not (not not (not ((-6 + 13) == (-20 * -6)))))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
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"gpt_response": "",
"metadata": {
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"true_count": 2
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"question": "研究以下逻辑语句：\n\nA. not not ((not ((not not (((14 - -19) >= (11 + 9)) and ((-5 - -12) == (-9 * 6 + 3 * -9)))) or (((17 + -3) > (6 * -8 * -8 * -2)) and (((2 ** 1) < (9 * 0 + 0 * 1)) or ((-1 * 2 * 0 * -5) >= (15 * -19)))))) and (not (not not ((4 % 3) < (-6 * -8) < (6 * 3)))) and (((not not (((4 ** 2) == (0 + 18)) or (印度尼西亚的货币是印尼盾。))) and (火星是距离太阳第4近的行星。)) and ((-10 - 19) <= (22 % 1)) and ((植物通过光合作用产生氧气。) and ((10 * -6 - -9 * 3) >= (20 + -4)))))\nB. (not not ((not (1964年奥运会在墨西哥城举办。)) or (not not ((5 - -8) != (4 * 3 * -2 * -7))))) or ((not not (((-5 * -1 + -9 * -10) == (12 - 11)) or (((0 - -19) < (17 + 4)) and ((9 - -16) <= (2 % 2))) or (not (not not (2012年奥运会在东京举办。))))) and (((((50 % 7) < (12 * -15) < (2 * -8 + 9 * 2)) or ((-10 + -4) != (13 * -16))) and ((not not (16是质数。)) and ((秘鲁的首都是墨西哥城。) or ((-11 - -13) < (-18 + 7))))) and (not ((水星是距离太阳第5近的行星。) or (845是斐波那契数。)))))\nC. not (not (((not (1915年是闰年。)) or (not ((1953年是闰年。) and (英国位于北美洲。)))) or (((-9 * -8) >= (-15 - -1)) or ((((0 * 5 - -6 * -5) == (46 % 4)) or ((2 + -4) != (-9 + -5))) and (((6 + -10) >= (19 * 1)) or ((2 * 6 - -9 * -10) == (-14 * -5)))))))\nD. not not (not not ((((5 ** 2) != (-1 - -15)) or ((哥伦布到达美洲发生在1490年。) and (伦敦大火发生在1665年。)) or (牛有4条腿。)) and (not (not not (not ((-6 + 13) == (-20 * -6)))))))\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": {
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"language": "cn",
"num_options": 4,
"seed": 23134166,
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},
"seed": 23134166,
"task_id": 623134166,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not ((A swan is a bird.) and (((2 * 5) < (-8 * -7 + -7 * -2)) or (The square root of 196 is 14.)) and (not ((2061 is a leap year.) or (The chemical symbol for Potassium is K.)))))
B. not not ((((not not ((2 * 4 * 1 * -1) < (-8 * -7 + -4 * -4))) and (((-10 + -9) > (-6 * -6 - -6 * 5)) or ((-18 - 18) < (2 + 11)))) and (not ((36 % 10) != (2 ** 2)))) and ((not not ((The chemical symbol for Iron is Fe.) and ((15 + -20) >= (9 * -5 + 6 * -7)))) or ((-18 - -11) < (-5 * -1 * 3 * -3) < (-16 * 4))))
C. not (not not ((((-17 + -9) <= (-10 - 11) <= (20 - 15)) or ((1983 is a leap year.) or ((13 * 12) != (-15 * 0)))) and ((5 ** 3) == (-8 * 1 - 10 * -2))))
D. not not (((not ((Colombia is in South America.) or ((4 ** 3) != (1 * -4 + -5 * -2)))) and (not (The currency of Australia is the Dollar.)) and ((((14 + 6) <= (2 - 14)) and ((4 * -1 + 3 * 10) > (2 - -5))) or (Saturn is the 6th planet from the Sun.))) and (not not ((-8 * 4 + 6 * -4) < (-2 * -9 + 7 * -10))))
E. (not ((not (((5 - 4) == (-19 + -8)) or (Germany is in South America.))) or ((12 + -4) <= (-1 + -5)))) and ((not not ((4 is a prime number.) and (A snake has 10 legs.))) or (not ((The 2004 Olympics were held in Mexico City.) and (The capital of Finland is Helsinki.)))) and (not (not not ((Kenya is in Africa.) and ((A goldfish is an insect.) and ((39 % 10) > (-19 * 20))))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
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"answer": "C",
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"gpt_response": "",
"metadata": {
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"language": "en",
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"question": "Evaluate each expression below:\n\nA. not (not ((A swan is a bird.) and (((2 * 5) < (-8 * -7 + -7 * -2)) or (The square root of 196 is 14.)) and (not ((2061 is a leap year.) or (The chemical symbol for Potassium is K.)))))\nB. not not ((((not not ((2 * 4 * 1 * -1) < (-8 * -7 + -4 * -4))) and (((-10 + -9) > (-6 * -6 - -6 * 5)) or ((-18 - 18) < (2 + 11)))) and (not ((36 % 10) != (2 ** 2)))) and ((not not ((The chemical symbol for Iron is Fe.) and ((15 + -20) >= (9 * -5 + 6 * -7)))) or ((-18 - -11) < (-5 * -1 * 3 * -3) < (-16 * 4))))\nC. not (not not ((((-17 + -9) <= (-10 - 11) <= (20 - 15)) or ((1983 is a leap year.) or ((13 * 12) != (-15 * 0)))) and ((5 ** 3) == (-8 * 1 - 10 * -2))))\nD. not not (((not ((Colombia is in South America.) or ((4 ** 3) != (1 * -4 + -5 * -2)))) and (not (The currency of Australia is the Dollar.)) and ((((14 + 6) <= (2 - 14)) and ((4 * -1 + 3 * 10) > (2 - -5))) or (Saturn is the 6th planet from the Sun.))) and (not not ((-8 * 4 + 6 * -4) < (-2 * -9 + 7 * -10))))\nE. (not ((not (((5 - 4) == (-19 + -8)) or (Germany is in South America.))) or ((12 + -4) <= (-1 + -5)))) and ((not not ((4 is a prime number.) and (A snake has 10 legs.))) or (not ((The 2004 Olympics were held in Mexico City.) and (The capital of Finland is Helsinki.)))) and (not (not not ((Kenya is in Africa.) and ((A goldfish is an insect.) and ((39 % 10) > (-19 * 20))))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 6738731,
"true_count": 1
},
"seed": 6738731,
"task_id": 606738731,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. not not (not not ((人类只使用了大脑的10%。) or (月球绕地球运转。)))
B. (((15 - -6) != (-18 * 3)) and (((1 ** 2) < (-19 + -18)) or (镁的化学符号是Co。))) or ((((1 ** 3) < (1 ** 2) < (2 * -10)) or (印度尼西亚的首都是哈瓦那。)) and (not not ((4 * 3 + 1 * -3) >= (6 * 8))))
C. ((not not (铜在常温下是气体。)) and (((-5 * -7 - -8 * -5) <= (4 * -19)) and ((-10 * 0 + 0 * 6) < (-7 * 8 * -8 * -10)))) and (((3 + -19) != (12 % 9)) or (水在常温下是气体。)) and ((((5 - -7) <= (19 * 14) <= (3 - -12)) or (海王星是距离太阳第8近的行星。)) and (((7 - 15) != (-14 * -7)) or ((-9 * 5 - -9 * -6) <= (1 - -8) <= (-5 * 20))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
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"answer": "A",
"difficulty": 1,
"gpt_response": "",
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"language": "cn",
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"seed": 50394840,
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"question": "检验这些表达式：\n\nA. not not (not not ((人类只使用了大脑的10%。) or (月球绕地球运转。)))\nB. (((15 - -6) != (-18 * 3)) and (((1 ** 2) < (-19 + -18)) or (镁的化学符号是Co。))) or ((((1 ** 3) < (1 ** 2) < (2 * -10)) or (印度尼西亚的首都是哈瓦那。)) and (not not ((4 * 3 + 1 * -3) >= (6 * 8))))\nC. ((not not (铜在常温下是气体。)) and (((-5 * -7 - -8 * -5) <= (4 * -19)) and ((-10 * 0 + 0 * 6) < (-7 * 8 * -8 * -10)))) and (((3 + -19) != (12 % 9)) or (水在常温下是气体。)) and ((((5 - -7) <= (19 * 14) <= (3 - -12)) or (海王星是距离太阳第8近的行星。)) and (((7 - 15) != (-14 * -7)) or ((-9 * 5 - -9 * -6) <= (1 - -8) <= (-5 * 20))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 3,
"seed": 50394840,
"true_count": 1
},
"seed": 50394840,
"task_id": 650394840,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not (((((The chemical symbol for Hydrogen is Ni.) or ((0 * -9 - 5 * 9) >= (7 * 10 - -9 * -4))) or (not ((11 + 14) != (20 + -13)))) or (((((0 * -4 + -7 * -9) <= (-5 * -9 * -10 * 4) <= (35 % 4)) or ((37 % 4) > (-3 - 17))) and (A octopus has 6 legs.)) and (not not (Earth is the 4th planet from the Sun.)) and (39 is a prime number.))) and (not not ((not not (not not (Brazil is in Europe.))) and (not ((-13 + -2) < (-7 * -10 + -6 * 3))) and (A grasshopper is an insect.))))
B. not (not (not ((((Russia is in North America.) or (The chemical symbol for Platinum is N.)) and ((-8 - -10) > (2 ** 3))) and ((not not ((-12 + 18) != (14 * -18))) or ((4 ** 2) > (1 % 2))))))
C. not ((((There are 29 days in October.) or (not (not (The currency of India is the Naira.)))) or (not (not ((3 ** 1) < (-3 * -5 + 3 * 10)))) or (not not ((1 ** 1) < (13 + 12)))) and ((not not (not not (((7 - 18) < (3 - 5) < (38 % 5)) and (Earth is the 3rd planet from the Sun.)))) or (Mercury is a liquid at room temperature.) or ((The currency of Colombia is the Dong.) or ((-18 * -1) > (-9 + -5)) or ((8 * -4 - -9 * -2) >= (-17 * 17)))))
D. not not (not ((((not (The Berlin Wall fell occurred in 1989.)) or (not ((3 ** 1) > (-11 - -12)))) and (There are 30 days in June.) and ((not (The capital of Malaysia is Kuala Lumpur.)) and ((Earth is the 3rd planet from the Sun.) or ((-7 * -6 + -10 * -3) >= (-14 - -5))))) and (Saturn is the 6th planet from the Sun.) and (not (not (not not ((0 - -4) > (-5 * 3)))))))
E. not not (not (not not (not not (not not (Mercury is the 1st planet from the Sun.)))))
F. not (not (not (((-19 * -1) == (-7 + 20)) and ((not (The chemical symbol for Calcium is Hg.)) and (((14 - -2) > (-7 * 0 * 7 * 9)) or ((5 ** 2) <= (-9 - -12)))))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
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"answer": "A,B,D,F",
"difficulty": 1,
"gpt_response": "",
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"true_count": 4
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not (((((The chemical symbol for Hydrogen is Ni.) or ((0 * -9 - 5 * 9) >= (7 * 10 - -9 * -4))) or (not ((11 + 14) != (20 + -13)))) or (((((0 * -4 + -7 * -9) <= (-5 * -9 * -10 * 4) <= (35 % 4)) or ((37 % 4) > (-3 - 17))) and (A octopus has 6 legs.)) and (not not (Earth is the 4th planet from the Sun.)) and (39 is a prime number.))) and (not not ((not not (not not (Brazil is in Europe.))) and (not ((-13 + -2) < (-7 * -10 + -6 * 3))) and (A grasshopper is an insect.))))\nB. not (not (not ((((Russia is in North America.) or (The chemical symbol for Platinum is N.)) and ((-8 - -10) > (2 ** 3))) and ((not not ((-12 + 18) != (14 * -18))) or ((4 ** 2) > (1 % 2))))))\nC. not ((((There are 29 days in October.) or (not (not (The currency of India is the Naira.)))) or (not (not ((3 ** 1) < (-3 * -5 + 3 * 10)))) or (not not ((1 ** 1) < (13 + 12)))) and ((not not (not not (((7 - 18) < (3 - 5) < (38 % 5)) and (Earth is the 3rd planet from the Sun.)))) or (Mercury is a liquid at room temperature.) or ((The currency of Colombia is the Dong.) or ((-18 * -1) > (-9 + -5)) or ((8 * -4 - -9 * -2) >= (-17 * 17)))))\nD. not not (not ((((not (The Berlin Wall fell occurred in 1989.)) or (not ((3 ** 1) > (-11 - -12)))) and (There are 30 days in June.) and ((not (The capital of Malaysia is Kuala Lumpur.)) and ((Earth is the 3rd planet from the Sun.) or ((-7 * -6 + -10 * -3) >= (-14 - -5))))) and (Saturn is the 6th planet from the Sun.) and (not (not (not not ((0 - -4) > (-5 * 3)))))))\nE. not not (not (not not (not not (not not (Mercury is the 1st planet from the Sun.)))))\nF. not (not (not (((-19 * -1) == (-7 + 20)) and ((not (The chemical symbol for Calcium is Hg.)) and (((14 - -2) > (-7 * 0 * 7 * 9)) or ((5 ** 2) <= (-9 - -12)))))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 6,
"seed": 67582747,
"true_count": 4
},
"seed": 67582747,
"task_id": 667582747,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((-6 * 17) < (19 - 4)) and (not ((2 * -8 * -1 * 6) >= (0 * 5)))
B. 尼日利亚位于非洲。
C. (-8 * 8 + -4 * -3) != (-15 + -16)
D. not not (not (英国的货币是英镑。))
E. (not ((-3 * 1) >= (19 * -5))) and ((10 * -8 + 6 * 10) <= (-19 - -8))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 95601315,
"true_count": 2
},
"question": "下面是几个布尔表达式：\n\nA. ((-6 * 17) < (19 - 4)) and (not ((2 * -8 * -1 * 6) >= (0 * 5)))\nB. 尼日利亚位于非洲。\nC. (-8 * 8 + -4 * -3) != (-15 + -16)\nD. not not (not (英国的货币是英镑。))\nE. (not ((-3 * 1) >= (19 * -5))) and ((10 * -8 + 6 * 10) <= (-19 - -8))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 95601315,
"true_count": 2
},
"seed": 95601315,
"task_id": 695601315,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. ((not (The capital of Denmark is Brasilia.)) or (not (The square root of 196 is 5.))) and (not not (not not ((((-4 + -12) >= (-9 * 10 + -3 * -5)) or ((-6 + -5) < (35 % 10))) and ((Steam is a gas at room temperature.) or (A mouse is an insect.)))))
B. (not not (not not ((There are 28 days in December.) and (((3 ** 2) == (5 + 17)) or (Helium is a gas at room temperature.))))) and ((((The currency of Thailand is the Koruna.) and (not not (The 1968 Olympics were held in Beijing.))) or (The chemical symbol for Carbon is Cu.)) or (not not ((((1 ** 3) < (-8 * 0 - -10 * -5)) and (A alligator is a reptile.)) and (not not ((1 * -2) <= (2 ** 1) <= (3 * -5 - -5 * 10))))))
C. not ((((The currency of United States is the Dollar.) or (not not ((3 ** 2) != (-10 * 1 * -6 * -9)))) and ((3 * 1 + 10 * 10) != (0 - -19))) and (not (not (not not (1938 is a leap year.)))))
D. not ((((24 % 1) > (50 % 6)) and ((not not (The chemical symbol for Oxygen is O.)) or (not (The currency of Switzerland is the Franc.)))) and (((9 + 8) != (6 - 5)) and ((1 + 16) <= (-10 + 3))) and ((Mars is the 6th planet from the Sun.) or (not not ((12 % 1) >= (9 - -3))) or ((((29 % 9) < (10 - 13)) or (The 1980 Olympics were held in Los Angeles.)) and ((2 ** 2) <= (2 * 10 * 9 * 10)))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 12436495,
"true_count": 3
},
"question": "Analyze these boolean expressions:\n\nA. ((not (The capital of Denmark is Brasilia.)) or (not (The square root of 196 is 5.))) and (not not (not not ((((-4 + -12) >= (-9 * 10 + -3 * -5)) or ((-6 + -5) < (35 % 10))) and ((Steam is a gas at room temperature.) or (A mouse is an insect.)))))\nB. (not not (not not ((There are 28 days in December.) and (((3 ** 2) == (5 + 17)) or (Helium is a gas at room temperature.))))) and ((((The currency of Thailand is the Koruna.) and (not not (The 1968 Olympics were held in Beijing.))) or (The chemical symbol for Carbon is Cu.)) or (not not ((((1 ** 3) < (-8 * 0 - -10 * -5)) and (A alligator is a reptile.)) and (not not ((1 * -2) <= (2 ** 1) <= (3 * -5 - -5 * 10))))))\nC. not ((((The currency of United States is the Dollar.) or (not not ((3 ** 2) != (-10 * 1 * -6 * -9)))) and ((3 * 1 + 10 * 10) != (0 - -19))) and (not (not (not not (1938 is a leap year.)))))\nD. not ((((24 % 1) > (50 % 6)) and ((not not (The chemical symbol for Oxygen is O.)) or (not (The currency of Switzerland is the Franc.)))) and (((9 + 8) != (6 - 5)) and ((1 + 16) <= (-10 + 3))) and ((Mars is the 6th planet from the Sun.) or (not not ((12 % 1) >= (9 - -3))) or ((((29 % 9) < (10 - 13)) or (The 1980 Olympics were held in Los Angeles.)) and ((2 ** 2) <= (2 * 10 * 9 * 10)))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 12436495,
"true_count": 3
},
"seed": 12436495,
"task_id": 612436495,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not (not not ((not (A beetle is an insect.)) and ((not not (The Titanic sank occurred in 1912.)) or ((6 * 10) >= (16 * 9)))))
B. not not ((not (not (The 1980 Olympics were held in Los Angeles.))) or (not not (((((-9 * 7 + 9 * -10) < (3 * -1 - -7 * 6)) and ((-12 + -4) <= (2 - 16) <= (-4 * 8 + -6 * -10))) and (Saturn is the 8th planet from the Sun.)) or (((-19 - 14) > (11 % 1)) or (((-8 - -5) < (-11 * 19)) or ((5 % 8) == (-16 - 7)))))))
C. not not (not ((((not not (The capital of Saudi Arabia is Stockholm.)) and (not not ((9 - 1) != (-6 * -10 + -8 * 0)))) and ((A lobster has 10 legs.) and ((18 - 6) <= (-18 + 16)))) and (((((18 * -18) <= (-9 - 9) <= (17 * 7)) and (The chemical symbol for Helium is Ti.)) and ((Vietnam is in Europe.) or ((-18 + -8) < (-4 * -4 * -10 * 10)))) or ((China is in North America.) or ((There are 30 days in November.) and ((10 * -9 * 3 * 3) >= (2 + -2)))))))
D. not (((not not (not (not ((6 - -2) > (-3 - 9))))) or (The capital of Ukraine is Brasilia.) or ((not (32 is divisible by 5.)) or ((((18 % 9) != (20 + -11)) and ((14 * -4) <= (12 * -13) <= (20 - -11))) and (Vietnam is in Asia.)))) and (not not (((-15 + 6) >= (29 % 4)) and (Oil is a solid at room temperature.) and ((Egypt is in Africa.) and (not not ((11 * -1) > (14 * -8)))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 20675056,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. not (not not ((not (A beetle is an insect.)) and ((not not (The Titanic sank occurred in 1912.)) or ((6 * 10) >= (16 * 9)))))\nB. not not ((not (not (The 1980 Olympics were held in Los Angeles.))) or (not not (((((-9 * 7 + 9 * -10) < (3 * -1 - -7 * 6)) and ((-12 + -4) <= (2 - 16) <= (-4 * 8 + -6 * -10))) and (Saturn is the 8th planet from the Sun.)) or (((-19 - 14) > (11 % 1)) or (((-8 - -5) < (-11 * 19)) or ((5 % 8) == (-16 - 7)))))))\nC. not not (not ((((not not (The capital of Saudi Arabia is Stockholm.)) and (not not ((9 - 1) != (-6 * -10 + -8 * 0)))) and ((A lobster has 10 legs.) and ((18 - 6) <= (-18 + 16)))) and (((((18 * -18) <= (-9 - 9) <= (17 * 7)) and (The chemical symbol for Helium is Ti.)) and ((Vietnam is in Europe.) or ((-18 + -8) < (-4 * -4 * -10 * 10)))) or ((China is in North America.) or ((There are 30 days in November.) and ((10 * -9 * 3 * 3) >= (2 + -2)))))))\nD. not (((not not (not (not ((6 - -2) > (-3 - 9))))) or (The capital of Ukraine is Brasilia.) or ((not (32 is divisible by 5.)) or ((((18 % 9) != (20 + -11)) and ((14 * -4) <= (12 * -13) <= (20 - -11))) and (Vietnam is in Asia.)))) and (not not (((-15 + 6) >= (29 % 4)) and (Oil is a solid at room temperature.) and ((Egypt is in Africa.) and (not not ((11 * -1) > (14 * -8)))))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 4,
"seed": 20675056,
"true_count": 3
},
"seed": 20675056,
"task_id": 620675056,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not ((not not (The capital of Japan is Tokyo.)) and (((2001 is a leap year.) and (not ((-12 - -9) > (4 + 2)))) and (((The capital of Nigeria is Abuja.) and (Mexico is in North America.)) and ((-19 * 20) <= (-3 * 10 + -9 * -9) <= (3 + 8)))))
B. not (((not ((7 * 6 - -8 * -7) > (11 - 20))) and (not not (not not ((-3 + -20) >= (-8 - 1))))) or (((not not (South Africa is in Europe.)) and ((Peru is in North America.) or (The 2012 Olympics were held in Los Angeles.))) or ((not (The capital of New Zealand is Wellington.)) and ((The 1896 Olympics were held in Paris.) or ((16 - -8) > (-7 - -18))))))
C. (((not ((The Berlin Wall fell occurred in 1989.) and (The capital of Spain is Warsaw.))) and (((-11 - 8) == (-5 * -6 - -9 * -10)) and ((9 - -2) < (6 % 3))) and ((2 - -16) > (11 % 8))) and (not not (Neptune is the 8th planet from the Sun.))) and (not not (((not (There are 30 days in September.)) or (not not (The chemical symbol for Nitrogen is N.))) and (not (The chemical symbol for Helium is He.)) and (not (((3 - -6) < (3 - 14)) or (Oxygen is a gas at room temperature.)))))
D. ((not not (The capital of Argentina is Ankara.)) and (not not ((((-19 * -20) > (6 * 4 * -9 * 4)) or (Japan is in North America.)) and (((19 % 1) <= (1 * 4 + -6 * -2)) and ((16 % 5) < (-10 * 7 + -4 * -7)))))) and (not ((((16 - 20) != (15 % 9)) or (The capital of Ukraine is Canberra.)) and ((The currency of South Korea is the Peso.) or (South Korea is in Antarctica.)))) and (not not (not not ((((2 ** 1) < (-10 * 2 * -10 * 10)) or ((10 - 2) < (0 * -3 - -5 * -5))) and ((15 % 4) < (-15 * -1)))))
E. not not (not not (not (not not (((-2 * 6 - -8 * 0) != (-2 + 0)) or (The 1924 Olympics were held in Sydney.)))))
F. not not (not not (not ((-1 - 18) != (14 * 14))))
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": 5,
"language": "en",
"num_options": 6,
"seed": 97771590,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not ((not not (The capital of Japan is Tokyo.)) and (((2001 is a leap year.) and (not ((-12 - -9) > (4 + 2)))) and (((The capital of Nigeria is Abuja.) and (Mexico is in North America.)) and ((-19 * 20) <= (-3 * 10 + -9 * -9) <= (3 + 8)))))\nB. not (((not ((7 * 6 - -8 * -7) > (11 - 20))) and (not not (not not ((-3 + -20) >= (-8 - 1))))) or (((not not (South Africa is in Europe.)) and ((Peru is in North America.) or (The 2012 Olympics were held in Los Angeles.))) or ((not (The capital of New Zealand is Wellington.)) and ((The 1896 Olympics were held in Paris.) or ((16 - -8) > (-7 - -18))))))\nC. (((not ((The Berlin Wall fell occurred in 1989.) and (The capital of Spain is Warsaw.))) and (((-11 - 8) == (-5 * -6 - -9 * -10)) and ((9 - -2) < (6 % 3))) and ((2 - -16) > (11 % 8))) and (not not (Neptune is the 8th planet from the Sun.))) and (not not (((not (There are 30 days in September.)) or (not not (The chemical symbol for Nitrogen is N.))) and (not (The chemical symbol for Helium is He.)) and (not (((3 - -6) < (3 - 14)) or (Oxygen is a gas at room temperature.)))))\nD. ((not not (The capital of Argentina is Ankara.)) and (not not ((((-19 * -20) > (6 * 4 * -9 * 4)) or (Japan is in North America.)) and (((19 % 1) <= (1 * 4 + -6 * -2)) and ((16 % 5) < (-10 * 7 + -4 * -7)))))) and (not ((((16 - 20) != (15 % 9)) or (The capital of Ukraine is Canberra.)) and ((The currency of South Korea is the Peso.) or (South Korea is in Antarctica.)))) and (not not (not not ((((2 ** 1) < (-10 * 2 * -10 * 10)) or ((10 - 2) < (0 * -3 - -5 * -5))) and ((15 % 4) < (-15 * -1)))))\nE. not not (not not (not (not not (((-2 * 6 - -8 * 0) != (-2 + 0)) or (The 1924 Olympics were held in Sydney.)))))\nF. not not (not not (not ((-1 - 18) != (14 * 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": 6,
"seed": 97771590,
"true_count": 2
},
"seed": 97771590,
"task_id": 697771590,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. The speed of light is approximately 300,000 km/s.
B. not ((((not not (The 1912 Olympics were held in Los Angeles.)) or (((-13 * -1) > (17 - -10)) and (not ((-20 + -8) <= (31 % 6))))) or ((There are 29 days in November.) and (The capital of Finland is Helsinki.) and (((Oil is a solid at room temperature.) or (The currency of European Union is the Euro.)) or ((Carbon dioxide is a solid at room temperature.) or ((-5 - 16) < (44 % 1) < (-14 + 8)))))) or (not not (not (not not ((Light travels faster than sound.) and ((5 * -8 * 6 * 5) == (4 - -1)))))))
C. not not (not not (not not (not not (((15 * -6) <= (17 * 13) <= (-3 - -1)) and (((31 % 8) <= (-5 + 18) <= (-9 * 3 * -4 * -7)) and (Steam is a solid at room temperature.))))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 8072464,
"true_count": 1
},
"question": "Evaluate each expression below:\n\nA. The speed of light is approximately 300,000 km/s.\nB. not ((((not not (The 1912 Olympics were held in Los Angeles.)) or (((-13 * -1) > (17 - -10)) and (not ((-20 + -8) <= (31 % 6))))) or ((There are 29 days in November.) and (The capital of Finland is Helsinki.) and (((Oil is a solid at room temperature.) or (The currency of European Union is the Euro.)) or ((Carbon dioxide is a solid at room temperature.) or ((-5 - 16) < (44 % 1) < (-14 + 8)))))) or (not not (not (not not ((Light travels faster than sound.) and ((5 * -8 * 6 * 5) == (4 - -1)))))))\nC. not not (not not (not not (not not (((15 * -6) <= (17 * 13) <= (-3 - -1)) and (((31 % 8) <= (-5 + 18) <= (-9 * 3 * -4 * -7)) and (Steam is a solid at room temperature.))))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 3,
"seed": 8072464,
"true_count": 1
},
"seed": 8072464,
"task_id": 608072464,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. ((not not (((36的平方根是6。) or (中国长城是在一年内建成的。)) or ((二月有28天。) and ((-1 + -13) != (-2 - -11))))) or ((智利位于非洲。) or (not ((-14 - -9) >= (-16 + 2))) or ((not not (阿根廷的货币是瑞士法郎。)) or ((美国位于北美洲。) or ((-5 - -14) >= (20 + -19)))))) and (not (((19 - 8) < (20 + 7)) and (((6 + -1) >= (4 * -10 * 3 * 9)) or (镁的化学符号是Mg。)) and (((法国的首都是巴黎。) or (企鹅能飞翔。)) or (not ((10 % 7) > (0 * 10 - -4 * -7))))))
B. (((not not (not (98能被10整除。))) and (not (not ((3 ** 3) > (2 - 10))))) and (((((14 + 6) == (5 % 8)) or ((-2 * 6 * -1 * 1) == (13 * -17))) or (not ((-3 - -15) != (-14 + 7)))) and ((((5 ** 1) >= (2 ** 1)) and (水星是距离太阳第1近的行星。)) and (摩洛哥位于非洲。)))) or (((钠的化学符号是Na。) or (((-2 - -6) <= (-16 * 13)) or (希腊的首都是雅典。))) or (((9 + 20) != (-9 * 10 * -4 * 8)) or (木头在常温下是气体。)) or ((not (氧的化学符号是Cu。)) and ((-16 + -11) < (-10 - 11)))) or (not not ((not not (苏联解体发生在1981年。)) and ((2008年奥运会在洛杉矶举办。) or (澳大利亚的货币是澳元。))))
C. ((not (not (not (铁在常温下是固体。)))) and ((((第一部iPhone发布发生在2007年。) and (镍的化学符号是Ni。)) or ((银在常温下是气体。) or ((-2 * 16) > (-6 * 15)))) and ((-13 * -11) >= (19 + 5)))) and ((((1900年奥运会在巴黎举办。) and (56是质数。)) or ((15 * -9) <= (-8 + 1))) and (1924年奥运会在莫斯科举办。)) and ((not not (铝的化学符号是P。)) and ((not ((1 ** 1) >= (8 * 7 * -5 * -4))) or ((十月有31天。) and ((1 - 14) < (-19 + 11)))) and (not ((蜘蛛有10条腿。) and (2022年是闰年。))))
D. not (not not (not not ((10 * -5 - -5 * 8) > (48 % 8))))
E. (not (((not not (第二次世界大战结束发生在1935年。)) or (五月有28天。)) or (((650是斐波那契数。) or (韩国的货币是韩元。)) or ((20 - 10) == (5 * 1 - 7 * 3))))) and ((not (not ((86大于68。) and (大象有10条腿。)))) and ((((10 * -2 + 6 * 5) == (4 + 10)) and (新西兰的货币是新西兰元。)) or ((伦敦大火发生在1676年。) or ((-2 - -11) > (5 ** 2)))) and (not (((伦敦大火发生在1656年。) and ((-2 * 3 * -2 * 10) < (-9 - 11) < (6 - 6))) and ((青蛙有8条腿。) or (巴西的货币是雷亚尔。)))))
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
"game_data": {
"answer": "B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 57550304,
"true_count": 2
},
"question": "给定以下布尔表达式：\n\nA. ((not not (((36的平方根是6。) or (中国长城是在一年内建成的。)) or ((二月有28天。) and ((-1 + -13) != (-2 - -11))))) or ((智利位于非洲。) or (not ((-14 - -9) >= (-16 + 2))) or ((not not (阿根廷的货币是瑞士法郎。)) or ((美国位于北美洲。) or ((-5 - -14) >= (20 + -19)))))) and (not (((19 - 8) < (20 + 7)) and (((6 + -1) >= (4 * -10 * 3 * 9)) or (镁的化学符号是Mg。)) and (((法国的首都是巴黎。) or (企鹅能飞翔。)) or (not ((10 % 7) > (0 * 10 - -4 * -7))))))\nB. (((not not (not (98能被10整除。))) and (not (not ((3 ** 3) > (2 - 10))))) and (((((14 + 6) == (5 % 8)) or ((-2 * 6 * -1 * 1) == (13 * -17))) or (not ((-3 - -15) != (-14 + 7)))) and ((((5 ** 1) >= (2 ** 1)) and (水星是距离太阳第1近的行星。)) and (摩洛哥位于非洲。)))) or (((钠的化学符号是Na。) or (((-2 - -6) <= (-16 * 13)) or (希腊的首都是雅典。))) or (((9 + 20) != (-9 * 10 * -4 * 8)) or (木头在常温下是气体。)) or ((not (氧的化学符号是Cu。)) and ((-16 + -11) < (-10 - 11)))) or (not not ((not not (苏联解体发生在1981年。)) and ((2008年奥运会在洛杉矶举办。) or (澳大利亚的货币是澳元。))))\nC. ((not (not (not (铁在常温下是固体。)))) and ((((第一部iPhone发布发生在2007年。) and (镍的化学符号是Ni。)) or ((银在常温下是气体。) or ((-2 * 16) > (-6 * 15)))) and ((-13 * -11) >= (19 + 5)))) and ((((1900年奥运会在巴黎举办。) and (56是质数。)) or ((15 * -9) <= (-8 + 1))) and (1924年奥运会在莫斯科举办。)) and ((not not (铝的化学符号是P。)) and ((not ((1 ** 1) >= (8 * 7 * -5 * -4))) or ((十月有31天。) and ((1 - 14) < (-19 + 11)))) and (not ((蜘蛛有10条腿。) and (2022年是闰年。))))\nD. not (not not (not not ((10 * -5 - -5 * 8) > (48 % 8))))\nE. (not (((not not (第二次世界大战结束发生在1935年。)) or (五月有28天。)) or (((650是斐波那契数。) or (韩国的货币是韩元。)) or ((20 - 10) == (5 * 1 - 7 * 3))))) and ((not (not ((86大于68。) and (大象有10条腿。)))) and ((((10 * -2 + 6 * 5) == (4 + 10)) and (新西兰的货币是新西兰元。)) or ((伦敦大火发生在1676年。) or ((-2 - -11) > (5 ** 2)))) and (not (((伦敦大火发生在1656年。) and ((-2 * 3 * -2 * 10) < (-9 - 11) < (6 - 6))) and ((青蛙有8条腿。) or (巴西的货币是雷亚尔。)))))\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": 5,
"seed": 57550304,
"true_count": 2
},
"seed": 57550304,
"task_id": 657550304,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. not not (not not ((not (A human has 0 legs.)) and ((((A bat is a mammal.) and ((43 % 7) <= (4 * -5) <= (7 % 5))) and (90 is a prime number.)) or ((((-5 * 1 * 1 * -2) == (6 * 8)) or (India is in Oceania.)) and (not not ((-4 * 0 * 5 * -2) == (19 * -1)))))))
B. not (not not (((not ((The capital of South Korea is Beijing.) or ((4 * 12) >= (2 * -14)))) or (not ((1 ** 2) >= (27 % 10))) or (A flamingo is a reptile.)) or (not not (not not (The chemical symbol for Magnesium is Ne.)))))
C. not (((not (The capital of South Korea is Seoul.)) and ((not not (The capital of Japan is Tokyo.)) and (((There are 30 days in April.) or (The Sun revolves around the Earth.)) and (((3 ** 3) > (19 - 9)) or (Gold is a gas at room temperature.))))) and (not not (((9 + -13) <= (3 - 12) <= (13 % 1)) or ((not not (A turtle is a reptile.)) and (not not ((-7 + -17) <= (-10 - 20) <= (-1 * -2)))))))
D. not not ((not not ((not not (not not ((48 % 8) != (12 - -3)))) and ((-2 * 1 + 3 * -7) == (2 ** 3)))) or (((((0 + 1) > (8 * 0 - 9 * -2)) and ((-14 * -8) < (-5 - 16))) and (((9 % 8) >= (7 * -16)) or (The human body has 150 bones.))) and (((15 + 0) > (20 - -17)) and ((4 - -1) <= (-1 * 18))) and ((4 * -9 * 3 * -4) > (4 - 20))) or (not not ((((There are 29 days in November.) or (Carbon dioxide is a solid at room temperature.)) and ((27 % 7) > (12 * -4))) and (The capital of Hungary is Budapest.))))
E. not (not (not not ((1972 is a leap year.) or (((A alligator is a reptile.) and (Carbon dioxide is a gas at room temperature.)) and (((-1 * 4 * 5 * -7) == (4 ** 1)) or ((-17 + -1) == (-14 * 13)))))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 15035444,
"true_count": 2
},
"question": "Here are some boolean expressions to evaluate:\n\nA. not not (not not ((not (A human has 0 legs.)) and ((((A bat is a mammal.) and ((43 % 7) <= (4 * -5) <= (7 % 5))) and (90 is a prime number.)) or ((((-5 * 1 * 1 * -2) == (6 * 8)) or (India is in Oceania.)) and (not not ((-4 * 0 * 5 * -2) == (19 * -1)))))))\nB. not (not not (((not ((The capital of South Korea is Beijing.) or ((4 * 12) >= (2 * -14)))) or (not ((1 ** 2) >= (27 % 10))) or (A flamingo is a reptile.)) or (not not (not not (The chemical symbol for Magnesium is Ne.)))))\nC. not (((not (The capital of South Korea is Seoul.)) and ((not not (The capital of Japan is Tokyo.)) and (((There are 30 days in April.) or (The Sun revolves around the Earth.)) and (((3 ** 3) > (19 - 9)) or (Gold is a gas at room temperature.))))) and (not not (((9 + -13) <= (3 - 12) <= (13 % 1)) or ((not not (A turtle is a reptile.)) and (not not ((-7 + -17) <= (-10 - 20) <= (-1 * -2)))))))\nD. not not ((not not ((not not (not not ((48 % 8) != (12 - -3)))) and ((-2 * 1 + 3 * -7) == (2 ** 3)))) or (((((0 + 1) > (8 * 0 - 9 * -2)) and ((-14 * -8) < (-5 - 16))) and (((9 % 8) >= (7 * -16)) or (The human body has 150 bones.))) and (((15 + 0) > (20 - -17)) and ((4 - -1) <= (-1 * 18))) and ((4 * -9 * 3 * -4) > (4 - 20))) or (not not ((((There are 29 days in November.) or (Carbon dioxide is a solid at room temperature.)) and ((27 % 7) > (12 * -4))) and (The capital of Hungary is Budapest.))))\nE. not (not (not not ((1972 is a leap year.) or (((A alligator is a reptile.) and (Carbon dioxide is a gas at room temperature.)) and (((-1 * 4 * 5 * -7) == (4 ** 1)) or ((-17 + -1) == (-14 * 13)))))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 15035444,
"true_count": 2
},
"seed": 15035444,
"task_id": 615035444,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. (((not ((中国位于亚洲。) and ((3 * -5 * -5 * 9) != (-3 + 5)))) and (莱特兄弟首次飞行发生在1903年。)) and (not not (not not (((4 * 4) <= (2 ** 1)) and (十二月有31天。))))) or ((not not (火星是距离太阳最近的行星。)) and ((6 * 8 + -8 * 1) <= (12 + 0))) or ((((-8 * -1 * 3 * -2) < (-5 + 18)) or (哥伦布到达美洲发生在1502年。) or (not not (((16 * 5) <= (4 ** 2) <= (-14 * -18)) and (螃蟹有8条腿。)))) and (((271是斐波那契数。) and ((汞在常温下是液体。) and (二月有30天。))) or (乌鸦是哺乳动物。) or (not not (钴的化学符号是Ag。))))
B. (not (((not (第一次世界大战开始发生在1909年。)) or ((西班牙的首都是柏林。) or (1992年奥运会在巴塞罗那举办。))) and (385是斐波那契数。) and ((1980年奥运会在墨西哥城举办。) or (金在常温下是气体。)))) or (not not ((蝴蝶有6条腿。) and ((巴西的货币是新西兰元。) or ((-14 + -3) < (-1 * -6 + 10 * 10))))) or ((not not (地球绕太阳运转。)) or (((2 ** 1) == (-2 * -6)) or ((((9 % 2) >= (19 * 11)) and ((19 - -15) > (12 - -8))) or (((16 * -4) > (17 * -5)) and (现代奥运会首届举办发生在1896年。)))))
C. not not ((((not ((-8 - -14) == (15 + -11))) or (not not (2068年是闰年。))) or ((4 * 4 + 3 * 10) != (15 - 8))) or ((十二月有29天。) or ((铂的化学符号是Pt。) or ((6 + -11) > (44 % 7))) or ((((44 % 2) >= (21 % 8)) and (铜在常温下是液体。)) and ((捷克的货币是克朗。) and (土星是距离太阳第6近的行星。)))))
D. (not (not not (not (not not (哥伦比亚的货币是泰铢。))))) or (((not not (铁的化学符号是Fe。)) or (((瑞典的货币是克朗。) and (菲律宾的首都是马尼拉。)) and (not (鸭子是昆虫。)))) and ((not not (氧的化学符号是K。)) and (not not ((20 * 19) == (1 ** 2)))) and ((((丹麦的首都是北京。) and (印度位于亚洲。)) and (光速约为每秒30万公里。)) and ((45 % 1) != (-12 + -11))))
E. not ((not not ((not not (氮气在常温下是气体。)) and ((摩洛哥位于非洲。) or ((-11 + -15) <= (2 * 20))))) and ((((0 * 16) == (-18 + 10)) and ((-3 * -5 - -6 * 10) == (18 * 13))) and ((not not ((-5 * 9 * -10 * -10) != (1 % 5))) or (阿根廷的货币是韩元。))))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 5,
"seed": 94301255,
"true_count": 3
},
"question": "分析以下逻辑表达式：\n\nA. (((not ((中国位于亚洲。) and ((3 * -5 * -5 * 9) != (-3 + 5)))) and (莱特兄弟首次飞行发生在1903年。)) and (not not (not not (((4 * 4) <= (2 ** 1)) and (十二月有31天。))))) or ((not not (火星是距离太阳最近的行星。)) and ((6 * 8 + -8 * 1) <= (12 + 0))) or ((((-8 * -1 * 3 * -2) < (-5 + 18)) or (哥伦布到达美洲发生在1502年。) or (not not (((16 * 5) <= (4 ** 2) <= (-14 * -18)) and (螃蟹有8条腿。)))) and (((271是斐波那契数。) and ((汞在常温下是液体。) and (二月有30天。))) or (乌鸦是哺乳动物。) or (not not (钴的化学符号是Ag。))))\nB. (not (((not (第一次世界大战开始发生在1909年。)) or ((西班牙的首都是柏林。) or (1992年奥运会在巴塞罗那举办。))) and (385是斐波那契数。) and ((1980年奥运会在墨西哥城举办。) or (金在常温下是气体。)))) or (not not ((蝴蝶有6条腿。) and ((巴西的货币是新西兰元。) or ((-14 + -3) < (-1 * -6 + 10 * 10))))) or ((not not (地球绕太阳运转。)) or (((2 ** 1) == (-2 * -6)) or ((((9 % 2) >= (19 * 11)) and ((19 - -15) > (12 - -8))) or (((16 * -4) > (17 * -5)) and (现代奥运会首届举办发生在1896年。)))))\nC. not not ((((not ((-8 - -14) == (15 + -11))) or (not not (2068年是闰年。))) or ((4 * 4 + 3 * 10) != (15 - 8))) or ((十二月有29天。) or ((铂的化学符号是Pt。) or ((6 + -11) > (44 % 7))) or ((((44 % 2) >= (21 % 8)) and (铜在常温下是液体。)) and ((捷克的货币是克朗。) and (土星是距离太阳第6近的行星。)))))\nD. (not (not not (not (not not (哥伦比亚的货币是泰铢。))))) or (((not not (铁的化学符号是Fe。)) or (((瑞典的货币是克朗。) and (菲律宾的首都是马尼拉。)) and (not (鸭子是昆虫。)))) and ((not not (氧的化学符号是K。)) and (not not ((20 * 19) == (1 ** 2)))) and ((((丹麦的首都是北京。) and (印度位于亚洲。)) and (光速约为每秒30万公里。)) and ((45 % 1) != (-12 + -11))))\nE. not ((not not ((not not (氮气在常温下是气体。)) and ((摩洛哥位于非洲。) or ((-11 + -15) <= (2 * 20))))) and ((((0 * 16) == (-18 + 10)) and ((-3 * -5 - -6 * 10) == (18 * 13))) and ((not not ((-5 * 9 * -10 * -10) != (1 % 5))) or (阿根廷的货币是韩元。))))\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": 5,
"seed": 94301255,
"true_count": 3
},
"seed": 94301255,
"task_id": 694301255,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. (not not (((铜在常温下是液体。) or (阿根廷位于南美洲。)) or ((1908年奥运会在巴黎举办。) and (1932年奥运会在洛杉矶举办。)))) or (not not (not ((-16 * -8) == (0 * 1 - -1 * -9)))) or (not (锰的化学符号是Cl。))
B. (((摩洛哥位于非洲。) or (鲸鱼是鱼类。)) or (((马来西亚的货币是越南盾。) or (24小于等于65。)) and (((-5 * -1 - 9 * -6) > (4 * -9 - 4 * -9)) or ((-16 * 3) <= (0 - 14))))) and (not not ((not not ((-3 - -8) >= (1 + -3))) or (一月有31天。)))
C. (not (not not (((39 % 9) < (0 + 2) < (6 * -3 * 10 * 10)) or (麻雀是鸟类。)))) and (not not ((1 ** 2) <= (13 % 6))) and ((120是完全平方数。) and ((8 * -13) >= (-13 * 14)))
D. not (((not not (金星是距离太阳第2近的行星。)) and ((5 * 16) == (-3 * -2 * -1 * -8))) and ((法国大革命开始发生在1789年。) and ((-11 - -6) <= (-14 * 4))))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 72780437,
"true_count": 3
},
"question": "考虑以下布尔表达式：\n\nA. (not not (((铜在常温下是液体。) or (阿根廷位于南美洲。)) or ((1908年奥运会在巴黎举办。) and (1932年奥运会在洛杉矶举办。)))) or (not not (not ((-16 * -8) == (0 * 1 - -1 * -9)))) or (not (锰的化学符号是Cl。))\nB. (((摩洛哥位于非洲。) or (鲸鱼是鱼类。)) or (((马来西亚的货币是越南盾。) or (24小于等于65。)) and (((-5 * -1 - 9 * -6) > (4 * -9 - 4 * -9)) or ((-16 * 3) <= (0 - 14))))) and (not not ((not not ((-3 - -8) >= (1 + -3))) or (一月有31天。)))\nC. (not (not not (((39 % 9) < (0 + 2) < (6 * -3 * 10 * 10)) or (麻雀是鸟类。)))) and (not not ((1 ** 2) <= (13 % 6))) and ((120是完全平方数。) and ((8 * -13) >= (-13 * 14)))\nD. not (((not not (金星是距离太阳第2近的行星。)) and ((5 * 16) == (-3 * -2 * -1 * -8))) and ((法国大革命开始发生在1789年。) and ((-11 - -6) <= (-14 * 4))))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 4,
"seed": 72780437,
"true_count": 3
},
"seed": 72780437,
"task_id": 672780437,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. 埃及的货币是人民币。
B. (((0 * 6 * -3 * 0) < (-5 * 16)) and ((4 ** 2) != (19 + 7))) or (not ((4 ** 3) <= (9 * 3 + -1 * 3)))
C. ((372是完全平方数。) and (1972年奥运会在慕尼黑举办。)) and ((氢的化学符号是O。) or (太阳绕地球运转。))
D. (2 * 6 - 2 * -8) == (-4 * 10 * 8 * 7)
E. (((-8 * 4) < (-5 * 10 * 9 * 7)) or ((-4 - 0) <= (9 * -8 - -3 * 2))) and (柏林墙倒塌发生在1987年。)
F. ((-13 - 15) >= (-20 - -3)) and (not (蜘蛛是昆虫。))
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": 6,
"seed": 39620308,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. 埃及的货币是人民币。\nB. (((0 * 6 * -3 * 0) < (-5 * 16)) and ((4 ** 2) != (19 + 7))) or (not ((4 ** 3) <= (9 * 3 + -1 * 3)))\nC. ((372是完全平方数。) and (1972年奥运会在慕尼黑举办。)) and ((氢的化学符号是O。) or (太阳绕地球运转。))\nD. (2 * 6 - 2 * -8) == (-4 * 10 * 8 * 7)\nE. (((-8 * 4) < (-5 * 10 * 9 * 7)) or ((-4 - 0) <= (9 * -8 - -3 * 2))) and (柏林墙倒塌发生在1987年。)\nF. ((-13 - 15) >= (-20 - -3)) and (not (蜘蛛是昆虫。))\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": 6,
"seed": 39620308,
"true_count": 1
},
"seed": 39620308,
"task_id": 639620308,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (-20 * -11) < (-19 - -2)
B. not (Uranus is the 7th planet from the Sun.)
C. The currency of United States is the Dollar.
D. ((United States is in Europe.) or (The capital of Ireland is Vienna.)) or (((6 * -1 + -4 * 3) == (-1 * -1 * -10 * 10)) and (The 1952 Olympics were held in London.))
E. There are 29 days in September.
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": 2,
"language": "en",
"num_options": 5,
"seed": 95421655,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (-20 * -11) < (-19 - -2)\nB. not (Uranus is the 7th planet from the Sun.)\nC. The currency of United States is the Dollar.\nD. ((United States is in Europe.) or (The capital of Ireland is Vienna.)) or (((6 * -1 + -4 * 3) == (-1 * -1 * -10 * 10)) and (The 1952 Olympics were held in London.))\nE. There are 29 days in September.\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": 95421655,
"true_count": 1
},
"seed": 95421655,
"task_id": 695421655,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (not ((World War I began occurred in 1914.) and (India is in North America.)))
B. (not not (The human body has 150 bones.)) and (((15 is a prime number.) or ((20 % 9) == (-20 - -16))) or (not not ((-11 - -8) != (-16 + -11))))
C. (not not (The capital of Colombia is Bogota.)) or (((189 is an even number.) or ((-10 * -9 * -8 * 3) >= (-1 - -4))) or (The 1964 Olympics were held in Tokyo.))
D. (The capital of Nigeria is Brasilia.) or ((((2 ** 2) <= (4 + -20) <= (-13 - 17)) and (Neptune is the 8th planet from the Sun.)) and (Saturn is the 2nd planet from the Sun.))
E. not not ((The chemical symbol for Nickel is Ni.) or (((3 % 8) == (16 - -13)) or (The currency of Chile is the Krone.)))
F. (not (not not (325 is a perfect square.))) or (not (The 1904 Olympics were held in St. Louis.)) or ((not not (2097 is a leap year.)) and ((44 % 10) < (-12 + -4)))
G. (((-12 - 0) == (4 - 18)) and (((11 + -19) < (4 * -1 - -4 * -7) < (13 * -19)) or (The capital of Norway is Oslo.))) or (not ((8 * -2 + 7 * -7) > (3 * 20)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 74352785,
"true_count": 5
},
"question": "Examine these expressions:\n\nA. not not (not ((World War I began occurred in 1914.) and (India is in North America.)))\nB. (not not (The human body has 150 bones.)) and (((15 is a prime number.) or ((20 % 9) == (-20 - -16))) or (not not ((-11 - -8) != (-16 + -11))))\nC. (not not (The capital of Colombia is Bogota.)) or (((189 is an even number.) or ((-10 * -9 * -8 * 3) >= (-1 - -4))) or (The 1964 Olympics were held in Tokyo.))\nD. (The capital of Nigeria is Brasilia.) or ((((2 ** 2) <= (4 + -20) <= (-13 - 17)) and (Neptune is the 8th planet from the Sun.)) and (Saturn is the 2nd planet from the Sun.))\nE. not not ((The chemical symbol for Nickel is Ni.) or (((3 % 8) == (16 - -13)) or (The currency of Chile is the Krone.)))\nF. (not (not not (325 is a perfect square.))) or (not (The 1904 Olympics were held in St. Louis.)) or ((not not (2097 is a leap year.)) and ((44 % 10) < (-12 + -4)))\nG. (((-12 - 0) == (4 - 18)) and (((11 + -19) < (4 * -1 - -4 * -7) < (13 * -19)) or (The capital of Norway is Oslo.))) or (not ((8 * -2 + 7 * -7) > (3 * 20)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 74352785,
"true_count": 5
},
"seed": 74352785,
"task_id": 674352785,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. ((The chemical symbol for Potassium is K.) or ((5 - 0) >= (2 * -4 + -6 * 4))) and (not not ((16 * 18) < (13 - -18)))
B. (((-11 + -1) > (-1 * 3 + -3 * 8)) and ((4 * 11) <= (-16 + -16) <= (-1 + -2))) or ((The currency of Israel is the Pound.) and ((4 * 6 - -3 * -10) < (-3 * -3) < (3 * 12)))
C. ((The capital of Australia is Rome.) or ((0 * 4 * 2 * 4) > (5 ** 3))) or (not not ((-18 - -11) <= (11 + -8) <= (5 * 4 - -1 * -2)))
D. ((Mercury is a liquid at room temperature.) and (Water is a liquid at room temperature.)) and (not ((4 ** 1) != (19 % 7)))
E. not (not not (The currency of Czech Republic is the Koruna.))
F. 585 is a Fibonacci number.
G. (not not (A trout is a mammal.)) and (not not (The capital of Brazil is Brasilia.))
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": 2,
"language": "en",
"num_options": 7,
"seed": 80996344,
"true_count": 1
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. ((The chemical symbol for Potassium is K.) or ((5 - 0) >= (2 * -4 + -6 * 4))) and (not not ((16 * 18) < (13 - -18)))\nB. (((-11 + -1) > (-1 * 3 + -3 * 8)) and ((4 * 11) <= (-16 + -16) <= (-1 + -2))) or ((The currency of Israel is the Pound.) and ((4 * 6 - -3 * -10) < (-3 * -3) < (3 * 12)))\nC. ((The capital of Australia is Rome.) or ((0 * 4 * 2 * 4) > (5 ** 3))) or (not not ((-18 - -11) <= (11 + -8) <= (5 * 4 - -1 * -2)))\nD. ((Mercury is a liquid at room temperature.) and (Water is a liquid at room temperature.)) and (not ((4 ** 1) != (19 % 7)))\nE. not (not not (The currency of Czech Republic is the Koruna.))\nF. 585 is a Fibonacci number.\nG. (not not (A trout is a mammal.)) and (not not (The capital of Brazil is Brasilia.))\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": 80996344,
"true_count": 1
},
"seed": 80996344,
"task_id": 680996344,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (Earth is the 4th planet from the Sun.) or (A ant has 6 legs.) or ((not (Venus is the 2nd planet from the Sun.)) and (Thailand is in Europe.))
B. (((5 * 7 * -10 * 0) < (17 - -8)) and (The chemical symbol for Silver is P.)) and ((Diamonds are made of carbon.) or ((3 * -10 + 10 * -3) < (9 + -13))) and (Steam is a gas at room temperature.)
C. (((There are 29 days in February.) and ((19 * 19) > (0 * 9))) or ((Oil is a liquid at room temperature.) or (The 1972 Olympics were held in Munich.))) or (((8 + 7) < (-2 + 17) < (-10 - -15)) and (South Africa is in Africa.)) or ((The Moon orbits the Earth.) or ((The 1924 Olympics were held in Amsterdam.) and ((2 ** 2) < (30 % 4) < (4 ** 1))))
D. ((0 * -8 * 10 * 0) >= (-14 * 3)) or (not ((16 % 7) == (9 - 13))) or (not ((Whales are fish.) and ((-5 * 4 - 7 * -5) < (-13 + 4) < (15 % 2))))
E. (((There are 29 days in May.) and ((-20 + -4) < (-6 + 14) < (-18 * 4))) and (((-9 * 10 * 2 * 2) != (6 * -3 - 9 * -4)) and ((3 + -16) != (4 - 4)))) and ((15 - 5) == (6 - 17))
F. ((-1 - 0) <= (17 * 2)) and (not not (not (Neptune is the 8th planet from the Sun.)))
G. not not ((not not (The capital of Poland is Warsaw.)) and (not (The currency of Denmark is the Krone.)))
H. (not ((Ice is less dense than liquid water.) and (Earth is the 3rd planet from the Sun.))) or (((The capital of Philippines is Ankara.) and (Whales are fish.)) and ((Uranus is the 3rd planet from the Sun.) or (The 1896 Olympics were held in Athens.)))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 86010155,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. (Earth is the 4th planet from the Sun.) or (A ant has 6 legs.) or ((not (Venus is the 2nd planet from the Sun.)) and (Thailand is in Europe.))\nB. (((5 * 7 * -10 * 0) < (17 - -8)) and (The chemical symbol for Silver is P.)) and ((Diamonds are made of carbon.) or ((3 * -10 + 10 * -3) < (9 + -13))) and (Steam is a gas at room temperature.)\nC. (((There are 29 days in February.) and ((19 * 19) > (0 * 9))) or ((Oil is a liquid at room temperature.) or (The 1972 Olympics were held in Munich.))) or (((8 + 7) < (-2 + 17) < (-10 - -15)) and (South Africa is in Africa.)) or ((The Moon orbits the Earth.) or ((The 1924 Olympics were held in Amsterdam.) and ((2 ** 2) < (30 % 4) < (4 ** 1))))\nD. ((0 * -8 * 10 * 0) >= (-14 * 3)) or (not ((16 % 7) == (9 - 13))) or (not ((Whales are fish.) and ((-5 * 4 - 7 * -5) < (-13 + 4) < (15 % 2))))\nE. (((There are 29 days in May.) and ((-20 + -4) < (-6 + 14) < (-18 * 4))) and (((-9 * 10 * 2 * 2) != (6 * -3 - 9 * -4)) and ((3 + -16) != (4 - 4)))) and ((15 - 5) == (6 - 17))\nF. ((-1 - 0) <= (17 * 2)) and (not not (not (Neptune is the 8th planet from the Sun.)))\nG. not not ((not not (The capital of Poland is Warsaw.)) and (not (The currency of Denmark is the Krone.)))\nH. (not ((Ice is less dense than liquid water.) and (Earth is the 3rd planet from the Sun.))) or (((The capital of Philippines is Ankara.) and (Whales are fish.)) and ((Uranus is the 3rd planet from the Sun.) or (The 1896 Olympics were held in Athens.)))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 8,
"seed": 86010155,
"true_count": 3
},
"seed": 86010155,
"task_id": 686010155,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. not (not (((-12 - -19) <= (-11 - -16) <= (-4 * 8 * -2 * -1)) or ((The 2008 Olympics were held in Beijing.) and ((20 * -7) >= (2 + -20)))))
B. ((((16 * 8) <= (-10 * -1 * -5 * 10)) or (((-7 - 11) < (-14 * 17)) and (Venus is the 2nd planet from the Sun.))) and ((((1 ** 1) <= (-7 * 8 - 3 * 2) <= (38 % 4)) or (66 is an even number.)) and (not (There are 30 days in September.)))) and (not not (((-4 * -4 + -3 * -2) < (9 * -9 - -4 * 10)) or ((The chemical symbol for Neon is Ag.) or ((-12 - -18) != (16 * 9)))))
C. (not (There are 30 days in June.)) and (The currency of Philippines is the Peso.) and ((Christopher Columbus reached America occurred in 1492.) or ((not not ((-8 * 12) <= (4 + -15))) or (((5 ** 1) >= (-7 * 2)) or (A spider has 8 legs.))))
D. (not ((not (3 is a perfect square.)) or ((2020 is a leap year.) and (The chemical symbol for Tin is Cl.)))) and ((not not ((The capital of Belgium is Moscow.) and ((50 % 5) < (9 - -16)))) and (A snake has 0 legs.) and (((10 - -5) < (9 - 6)) or ((Diamonds are made of carbon.) or ((3 ** 2) <= (-2 - 19) <= (-14 - -9)))))
E. not not (not not (not ((The capital of India is Cairo.) or (The chemical symbol for Magnesium is Mg.))))
F. (((not not ((5 ** 1) <= (3 ** 2))) or (((-5 * 1 - -4 * 0) < (5 * -3 - 8 * 10) < (49 % 6)) or ((14 * -8) <= (19 * -15) <= (3 * -7 * -9 * 6)))) or ((18 * -2) == (-8 - -19))) or (not not (not (The capital of Nigeria is Lisbon.))) or (not ((2 ** 3) < (-10 + 6)))
G. (((-18 * 8) <= (13 * 7)) or ((4 - 7) >= (1 ** 3))) or ((((Ice is a liquid at room temperature.) or (Japan is in Africa.)) or ((90 is an odd number.) or (There are 30 days in November.))) and (((Lightning never strikes the same place twice.) and (Uranus is the 4th planet from the Sun.)) and (not not ((2 - -3) == (20 % 2)))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 89680501,
"true_count": 2
},
"question": "Review these logical expressions:\n\nA. not (not (((-12 - -19) <= (-11 - -16) <= (-4 * 8 * -2 * -1)) or ((The 2008 Olympics were held in Beijing.) and ((20 * -7) >= (2 + -20)))))\nB. ((((16 * 8) <= (-10 * -1 * -5 * 10)) or (((-7 - 11) < (-14 * 17)) and (Venus is the 2nd planet from the Sun.))) and ((((1 ** 1) <= (-7 * 8 - 3 * 2) <= (38 % 4)) or (66 is an even number.)) and (not (There are 30 days in September.)))) and (not not (((-4 * -4 + -3 * -2) < (9 * -9 - -4 * 10)) or ((The chemical symbol for Neon is Ag.) or ((-12 - -18) != (16 * 9)))))\nC. (not (There are 30 days in June.)) and (The currency of Philippines is the Peso.) and ((Christopher Columbus reached America occurred in 1492.) or ((not not ((-8 * 12) <= (4 + -15))) or (((5 ** 1) >= (-7 * 2)) or (A spider has 8 legs.))))\nD. (not ((not (3 is a perfect square.)) or ((2020 is a leap year.) and (The chemical symbol for Tin is Cl.)))) and ((not not ((The capital of Belgium is Moscow.) and ((50 % 5) < (9 - -16)))) and (A snake has 0 legs.) and (((10 - -5) < (9 - 6)) or ((Diamonds are made of carbon.) or ((3 ** 2) <= (-2 - 19) <= (-14 - -9)))))\nE. not not (not not (not ((The capital of India is Cairo.) or (The chemical symbol for Magnesium is Mg.))))\nF. (((not not ((5 ** 1) <= (3 ** 2))) or (((-5 * 1 - -4 * 0) < (5 * -3 - 8 * 10) < (49 % 6)) or ((14 * -8) <= (19 * -15) <= (3 * -7 * -9 * 6)))) or ((18 * -2) == (-8 - -19))) or (not not (not (The capital of Nigeria is Lisbon.))) or (not ((2 ** 3) < (-10 + 6)))\nG. (((-18 * 8) <= (13 * 7)) or ((4 - 7) >= (1 ** 3))) or ((((Ice is a liquid at room temperature.) or (Japan is in Africa.)) or ((90 is an odd number.) or (There are 30 days in November.))) and (((Lightning never strikes the same place twice.) and (Uranus is the 4th planet from the Sun.)) and (not not ((2 - -3) == (20 % 2)))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 89680501,
"true_count": 2
},
"seed": 89680501,
"task_id": 689680501,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. not not ((((not (not not ((-3 - -7) > (46 % 2)))) or (羊是哺乳动物。)) or ((not ((五月有31天。) or (法国的首都是巴黎。))) or ((-16 - -5) <= (7 * -12)))) or (((not (74能被11整除。)) and (not not (not ((8 * 6 + 1 * 1) < (-8 * 15) < (12 + -1))))) and ((not not (地球是距离太阳第3近的行星。)) and ((not (现代奥运会首届举办发生在1896年。)) and (第一次世界大战开始发生在1924年。)))))
B. not not (not ((not not ((1 * 2 + 8 * 8) <= (-4 * -6 * -7 * -2) <= (2 ** 2))) and (((not (284是完全平方数。)) and ((19 + -14) <= (9 - -10))) or (not ((鹦鹉是鸟类。) and ((-5 + 11) != (15 + -6)))))))
C. not (not not (not ((not not (((2 % 6) < (2 ** 3)) and (韩国的首都是首尔。))) or (not ((-14 * -10) <= (13 + -9) <= (3 ** 2))))))
D. not not (((not ((((10 * -1 * -2 * 5) < (5 * -18)) and ((-4 + -17) < (20 * -19))) and (not (瑞士的首都是伯尔尼。)))) and ((((35 % 6) <= (-14 + 19) <= (-4 * 11)) and (越南的首都是河内。)) or ((鲱鱼是鱼类。) and ((16 * -16) <= (7 * 3)))) and (not not (((4 ** 1) > (3 ** 2)) and ((19 + 11) < (14 * -5))))) and ((not ((-14 - -16) == (8 - 17))) or ((伦敦大火发生在1666年。) or ((-6 * 7 + 7 * 8) <= (-15 + -3)) or (((钙的化学符号是Ca。) or (阿根廷位于南美洲。)) and (not not ((17 - -13) > (12 - 1)))))))
E. not not ((not not ((((42 % 1) >= (-12 * 5)) and (((5 + -4) != (28 % 2)) and (南极洲是最冷的大陆。))) and (空气在常温下是液体。) and (not (not (老鼠是哺乳动物。))))) or ((not (not (((-16 * 12) < (13 % 5)) and (水在常温下是液体。)))) or (not not (((2 ** 3) != (4 ** 3)) and (秘鲁的首都是阿布贾。)))))
F. not (not ((((((13 + 8) == (2 * -4 * -3 * -2)) and ((2 ** 2) < (-4 * 7 + 2 * 2))) or (((11 - -8) > (5 - -20)) and ((13 * -2) <= (-12 * 13)))) and (((-11 * -19) < (10 - 0) < (5 ** 2)) and ((汞在常温下是气体。) and (十月有30天。)))) and ((not ((2 ** 2) >= (2 ** 2))) or ((2004年奥运会在巴塞罗那举办。) and (蚂蚁是昆虫。))) and (not (not not (((-12 * 2) >= (11 - 3)) and (铁的化学符号是Si。))))))
G. not not (((not not (2008年奥运会在巴黎举办。)) and ((0 + 5) <= (3 ** 3) <= (-3 + 17)) and (((not not (硫的化学符号是S。)) and ((大象有4条腿。) and ((-3 * 0 + -9 * -4) <= (-2 - 14)))) or (蜘蛛是昆虫。))) and (((not (((3 ** 1) < (-5 + 15)) or (六月有29天。))) and ((10 * -7) < (-4 * -9) < (-20 - 8))) or (not (not (354是完全平方数。)))))
H. not ((not not ((not ((荷兰的首都是北京。) and ((-20 + 13) <= (-17 * -9)))) and (not not (not (伦敦大火发生在1666年。))))) and ((not not (not not (((2 ** 2) < (6 * -10 * -3 * -8) < (-4 * -2)) and ((15 + 11) == (-3 + 5))))) and ((not (((7 + -7) >= (44 % 4)) or ((-9 * -4 * 3 * -5) <= (-1 - 8)))) or ((鸟有2条腿。) and (第二次世界大战结束发生在1945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,E,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 83418421,
"true_count": 5
},
"question": "给定以下布尔表达式：\n\nA. not not ((((not (not not ((-3 - -7) > (46 % 2)))) or (羊是哺乳动物。)) or ((not ((五月有31天。) or (法国的首都是巴黎。))) or ((-16 - -5) <= (7 * -12)))) or (((not (74能被11整除。)) and (not not (not ((8 * 6 + 1 * 1) < (-8 * 15) < (12 + -1))))) and ((not not (地球是距离太阳第3近的行星。)) and ((not (现代奥运会首届举办发生在1896年。)) and (第一次世界大战开始发生在1924年。)))))\nB. not not (not ((not not ((1 * 2 + 8 * 8) <= (-4 * -6 * -7 * -2) <= (2 ** 2))) and (((not (284是完全平方数。)) and ((19 + -14) <= (9 - -10))) or (not ((鹦鹉是鸟类。) and ((-5 + 11) != (15 + -6)))))))\nC. not (not not (not ((not not (((2 % 6) < (2 ** 3)) and (韩国的首都是首尔。))) or (not ((-14 * -10) <= (13 + -9) <= (3 ** 2))))))\nD. not not (((not ((((10 * -1 * -2 * 5) < (5 * -18)) and ((-4 + -17) < (20 * -19))) and (not (瑞士的首都是伯尔尼。)))) and ((((35 % 6) <= (-14 + 19) <= (-4 * 11)) and (越南的首都是河内。)) or ((鲱鱼是鱼类。) and ((16 * -16) <= (7 * 3)))) and (not not (((4 ** 1) > (3 ** 2)) and ((19 + 11) < (14 * -5))))) and ((not ((-14 - -16) == (8 - 17))) or ((伦敦大火发生在1666年。) or ((-6 * 7 + 7 * 8) <= (-15 + -3)) or (((钙的化学符号是Ca。) or (阿根廷位于南美洲。)) and (not not ((17 - -13) > (12 - 1)))))))\nE. not not ((not not ((((42 % 1) >= (-12 * 5)) and (((5 + -4) != (28 % 2)) and (南极洲是最冷的大陆。))) and (空气在常温下是液体。) and (not (not (老鼠是哺乳动物。))))) or ((not (not (((-16 * 12) < (13 % 5)) and (水在常温下是液体。)))) or (not not (((2 ** 3) != (4 ** 3)) and (秘鲁的首都是阿布贾。)))))\nF. not (not ((((((13 + 8) == (2 * -4 * -3 * -2)) and ((2 ** 2) < (-4 * 7 + 2 * 2))) or (((11 - -8) > (5 - -20)) and ((13 * -2) <= (-12 * 13)))) and (((-11 * -19) < (10 - 0) < (5 ** 2)) and ((汞在常温下是气体。) and (十月有30天。)))) and ((not ((2 ** 2) >= (2 ** 2))) or ((2004年奥运会在巴塞罗那举办。) and (蚂蚁是昆虫。))) and (not (not not (((-12 * 2) >= (11 - 3)) and (铁的化学符号是Si。))))))\nG. not not (((not not (2008年奥运会在巴黎举办。)) and ((0 + 5) <= (3 ** 3) <= (-3 + 17)) and (((not not (硫的化学符号是S。)) and ((大象有4条腿。) and ((-3 * 0 + -9 * -4) <= (-2 - 14)))) or (蜘蛛是昆虫。))) and (((not (((3 ** 1) < (-5 + 15)) or (六月有29天。))) and ((10 * -7) < (-4 * -9) < (-20 - 8))) or (not (not (354是完全平方数。)))))\nH. not ((not not ((not ((荷兰的首都是北京。) and ((-20 + 13) <= (-17 * -9)))) and (not not (not (伦敦大火发生在1666年。))))) and ((not not (not not (((2 ** 2) < (6 * -10 * -3 * -8) < (-4 * -2)) and ((15 + 11) == (-3 + 5))))) and ((not (((7 + -7) >= (44 % 4)) or ((-9 * -4 * 3 * -5) <= (-1 - 8)))) or ((鸟有2条腿。) and (第二次世界大战结束发生在1945年。)))))\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 8,
"seed": 83418421,
"true_count": 5
},
"seed": 83418421,
"task_id": 683418421,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (The Pacific Ocean is the largest ocean.) or ((3 ** 3) == (7 * 6 + 2 * -9)) or (30 is a prime number.)
B. ((not not (The chemical symbol for Tin is Sn.)) or ((-14 - 13) != (-2 * 5))) or (A lobster has 10 legs.)
C. not ((3 * 6) >= (10 * 7 * 7 * -5))
D. (not ((World War I ended occurred in 1918.) or ((1 ** 1) != (4 - -6)))) or ((((-9 - 6) < (7 - -12)) and (Humans have three lungs.)) and ((The capital of Egypt is New Delhi.) or (Wood is a solid at room temperature.)))
E. (not not (((30 % 3) <= (-3 * -7 + 7 * 6)) or (The first airplane flight by the Wright Brothers occurred in 1903.))) and ((A salmon is a fish.) and ((South Africa is in Antarctica.) and (The Berlin Wall fell occurred in 1989.)))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 93853679,
"true_count": 2
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (The Pacific Ocean is the largest ocean.) or ((3 ** 3) == (7 * 6 + 2 * -9)) or (30 is a prime number.)\nB. ((not not (The chemical symbol for Tin is Sn.)) or ((-14 - 13) != (-2 * 5))) or (A lobster has 10 legs.)\nC. not ((3 * 6) >= (10 * 7 * 7 * -5))\nD. (not ((World War I ended occurred in 1918.) or ((1 ** 1) != (4 - -6)))) or ((((-9 - 6) < (7 - -12)) and (Humans have three lungs.)) and ((The capital of Egypt is New Delhi.) or (Wood is a solid at room temperature.)))\nE. (not not (((30 % 3) <= (-3 * -7 + 7 * 6)) or (The first airplane flight by the Wright Brothers occurred in 1903.))) and ((A salmon is a fish.) and ((South Africa is in Antarctica.) and (The Berlin Wall fell occurred in 1989.)))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 5,
"seed": 93853679,
"true_count": 2
},
"seed": 93853679,
"task_id": 693853679,
"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 ((新加坡的首都是新加坡。) or (考拉是鱼类。))
B. (1932年奥运会在洛杉矶举办。) and (not not ((1900年奥运会在墨西哥城举办。) or (钻石在常温下是固体。)))
C. (金在常温下是液体。) and (月球自己发光。)
D. not (not not (not ((-11 + -7) >= (-3 * 2 + -10 * -1))))
E. not (not (not not ((20 * -5) == (-14 + -11))))
F. not (((-12 * 10) != (8 * -2)) and (美国宣布独立发生在1775年。))
G. not (肯尼亚位于北美洲。)
H. (((地球上一天是24小时。) or ((12 * -19) <= (1 - 10))) or (10大于91。)) and (((5 * -5 * -3 * -7) >= (-8 * 4 * -4 * -3)) and ((-17 - -16) <= (14 + 7) <= (48 % 8))) and ((((-7 * -10 + -4 * 9) >= (-13 - 7)) or ((12 + -12) < (-2 * 2 - 10 * 1) < (-17 - -4))) or ((六月有28天。) or (水蒸气在常温下是气体。)))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "B,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 8,
"seed": 56686258,
"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 ((新加坡的首都是新加坡。) or (考拉是鱼类。))\nB. (1932年奥运会在洛杉矶举办。) and (not not ((1900年奥运会在墨西哥城举办。) or (钻石在常温下是固体。)))\nC. (金在常温下是液体。) and (月球自己发光。)\nD. not (not not (not ((-11 + -7) >= (-3 * 2 + -10 * -1))))\nE. not (not (not not ((20 * -5) == (-14 + -11))))\nF. not (((-12 * 10) != (8 * -2)) and (美国宣布独立发生在1775年。))\nG. not (肯尼亚位于北美洲。)\nH. (((地球上一天是24小时。) or ((12 * -19) <= (1 - 10))) or (10大于91。)) and (((5 * -5 * -3 * -7) >= (-8 * 4 * -4 * -3)) and ((-17 - -16) <= (14 + 7) <= (48 % 8))) and ((((-7 * -10 + -4 * 9) >= (-13 - 7)) or ((12 + -12) < (-2 * 2 - 10 * 1) < (-17 - -4))) or ((六月有28天。) or (水蒸气在常温下是气体。)))\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": 56686258,
"true_count": 3
},
"seed": 56686258,
"task_id": 656686258,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not (not (((20 * -19) == (20 - 16)) and ((10 + 1) == (-9 + 5))))
B. (not (not (Gold is a solid at room temperature.))) or ((((-20 - -7) < (2 ** 1) < (15 * -5)) and (Gold is a solid at room temperature.)) or (The capital of Russia is Madrid.))
C. not not (not (not not (Neptune is the 6th planet from the Sun.)))
D. ((The 1980 Olympics were held in Moscow.) or (((-15 - -17) <= (8 * 7 * 2 * -8) <= (3 * 5)) and (Brazil is in Europe.))) or ((((-7 * -10 + -9 * -3) > (15 + 11)) and (The square root of 16 is 4.)) or (Helium is a gas at room temperature.))
E. ((((16 + -17) <= (11 - -11)) and ((15 * 7) >= (-17 * 0))) and (((5 ** 3) < (5 + -17)) or ((-3 * 2 + -1 * 2) <= (13 % 1) <= (-3 - 5)))) and ((((8 - -17) < (9 * 2)) or ((-20 + -1) < (-11 + 0))) and ((Humans only use 10% of their brain.) or (A butterfly has 6 legs.)))
F. not (not not (The speed of light is approximately 300,000 km/s.))
G. (not not (((8 * 3 - -1 * 0) > (7 + -7)) and (Antarctica is the coldest continent.))) or (((7 - -17) > (17 - 1)) or (The currency of Israel is the Dollar.)) or (((24 % 10) < (-7 + 6) < (3 + -12)) or ((South Korea is in Asia.) or ((9 * 9 - 7 * -5) > (11 % 9))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,C,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 6491085,
"true_count": 4
},
"question": "Study the following logical statements:\n\nA. not (not (((20 * -19) == (20 - 16)) and ((10 + 1) == (-9 + 5))))\nB. (not (not (Gold is a solid at room temperature.))) or ((((-20 - -7) < (2 ** 1) < (15 * -5)) and (Gold is a solid at room temperature.)) or (The capital of Russia is Madrid.))\nC. not not (not (not not (Neptune is the 6th planet from the Sun.)))\nD. ((The 1980 Olympics were held in Moscow.) or (((-15 - -17) <= (8 * 7 * 2 * -8) <= (3 * 5)) and (Brazil is in Europe.))) or ((((-7 * -10 + -9 * -3) > (15 + 11)) and (The square root of 16 is 4.)) or (Helium is a gas at room temperature.))\nE. ((((16 + -17) <= (11 - -11)) and ((15 * 7) >= (-17 * 0))) and (((5 ** 3) < (5 + -17)) or ((-3 * 2 + -1 * 2) <= (13 % 1) <= (-3 - 5)))) and ((((8 - -17) < (9 * 2)) or ((-20 + -1) < (-11 + 0))) and ((Humans only use 10% of their brain.) or (A butterfly has 6 legs.)))\nF. not (not not (The speed of light is approximately 300,000 km/s.))\nG. (not not (((8 * 3 - -1 * 0) > (7 + -7)) and (Antarctica is the coldest continent.))) or (((7 - -17) > (17 - 1)) or (The currency of Israel is the Dollar.)) or (((24 % 10) < (-7 + 6) < (3 + -12)) or ((South Korea is in Asia.) or ((9 * 9 - 7 * -5) > (11 % 9))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 6491085,
"true_count": 4
},
"seed": 6491085,
"task_id": 606491085,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not not ((not not ((Earth is the 3rd planet from the Sun.) or ((The 1904 Olympics were held in Paris.) or (78 is a prime number.)) or ((((0 * 6 * 4 * -9) < (47 % 6)) or ((-11 * 5) == (1 ** 2))) or (not not ((15 + -13) == (-15 * -12)))))) and ((Humans have five fingers on each hand.) and (The capital of Nigeria is Paris.)) and ((not ((-8 * -4) < (20 % 3))) or (not (The capital of Portugal is Lisbon.))))
B. not ((not (not (not (not not ((-10 * 1 - 4 * -8) == (1 + -7)))))) or (not not (not not (((-6 * 8 - 10 * 0) <= (-2 + 13)) and ((A sheep is a mammal.) or ((5 ** 3) != (-5 * -9 + -10 * 8)))))))
C. not (not not (not (not (902 is a Fibonacci number.))))
D. not ((not not (((9 - -4) < (-11 - -16)) or (not (not not (The currency of Singapore is the Real.))))) and (((not not (The 1988 Olympics were held in Seoul.)) and ((The currency of Saudi Arabia is the Riyal.) or (The chemical symbol for Carbon is C.))) or (((not (There are 30 days in May.)) and ((Water boils at 100 degrees Celsius at sea level.) and ((3 * 1 + -5 * -9) != (17 * 10)))) and ((6 - 5) != (-16 + -19)))))
E. not ((not not (((-1 * -2 - 5 * 9) < (8 * -8)) and (The 1900 Olympics were held in Berlin.) and ((not ((19 * 14) <= (4 * -3 + -1 * 9))) and ((A octopus has 8 legs.) or ((-5 * 3 - 5 * -6) < (4 ** 1)))))) or ((not not ((not not ((9 * 3) >= (-2 * -4 - 2 * -6))) and (((14 % 2) != (3 + -11)) or ((16 * 6) >= (-9 + 19))))) or (not not ((1 * 13) > (-8 + -4)))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 52511847,
"true_count": 1
},
"question": "Given the following boolean expressions:\n\nA. not not ((not not ((Earth is the 3rd planet from the Sun.) or ((The 1904 Olympics were held in Paris.) or (78 is a prime number.)) or ((((0 * 6 * 4 * -9) < (47 % 6)) or ((-11 * 5) == (1 ** 2))) or (not not ((15 + -13) == (-15 * -12)))))) and ((Humans have five fingers on each hand.) and (The capital of Nigeria is Paris.)) and ((not ((-8 * -4) < (20 % 3))) or (not (The capital of Portugal is Lisbon.))))\nB. not ((not (not (not (not not ((-10 * 1 - 4 * -8) == (1 + -7)))))) or (not not (not not (((-6 * 8 - 10 * 0) <= (-2 + 13)) and ((A sheep is a mammal.) or ((5 ** 3) != (-5 * -9 + -10 * 8)))))))\nC. not (not not (not (not (902 is a Fibonacci number.))))\nD. not ((not not (((9 - -4) < (-11 - -16)) or (not (not not (The currency of Singapore is the Real.))))) and (((not not (The 1988 Olympics were held in Seoul.)) and ((The currency of Saudi Arabia is the Riyal.) or (The chemical symbol for Carbon is C.))) or (((not (There are 30 days in May.)) and ((Water boils at 100 degrees Celsius at sea level.) and ((3 * 1 + -5 * -9) != (17 * 10)))) and ((6 - 5) != (-16 + -19)))))\nE. not ((not not (((-1 * -2 - 5 * 9) < (8 * -8)) and (The 1900 Olympics were held in Berlin.) and ((not ((19 * 14) <= (4 * -3 + -1 * 9))) and ((A octopus has 8 legs.) or ((-5 * 3 - 5 * -6) < (4 ** 1)))))) or ((not not ((not not ((9 * 3) >= (-2 * -4 - 2 * -6))) and (((14 % 2) != (3 + -11)) or ((16 * 6) >= (-9 + 19))))) or (not not ((1 * 13) > (-8 + -4)))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 5,
"seed": 52511847,
"true_count": 1
},
"seed": 52511847,
"task_id": 652511847,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not ((not (not not (((2073 is a leap year.) and ((0 + 7) < (6 * -5 - 2 * 7))) and ((15 - -20) == (4 - -6))))) or (not not (((((-18 + 18) <= (5 ** 1) <= (1 * 10 + 5 * -10)) and (The currency of Japan is the Ringgit.)) and (The currency of Nigeria is the Rupiah.)) or ((not not (The speed of light is approximately 300,000 km/s.)) and (((5 - -5) >= (0 * -2 + -6 * 8)) and (Saturn is the 3rd planet from the Sun.))))))
B. (not (((not ((1 * 20) < (5 ** 1))) or ((The 2012 Olympics were held in London.) and (not not ((1 ** 1) <= (-15 * -6))))) and (not not ((not not (A chicken has 2 legs.)) and (not not (Plants produce oxygen through photosynthesis.)))))) and (not (not ((not (not (The 1920 Olympics were held in Antwerp.))) or (((The currency of United Kingdom is the Zloty.) and ((7 * 9) > (13 * 19))) or ((The currency of Brazil is the Dollar.) and (Japan is in North America.))))))
C. not (not not (not not ((((The Sun revolves around the Earth.) or (World War I ended occurred in 1918.)) and ((The first airplane flight by the Wright Brothers occurred in 1903.) and ((-1 - 18) <= (15 - 2)))) and (not (((11 - 9) <= (3 + -11) <= (-6 + 5)) or ((41 % 10) < (3 - -15)))))))
D. not (not not ((((-18 - -14) == (1 ** 2)) or (The first iPhone was released occurred in 2007.) or (not (((-6 + 2) < (3 ** 1) < (5 * 0 * -8 * -8)) or (Uranus is the 1st planet from the Sun.)))) and ((There are 30 days in September.) and (((1968 is a leap year.) and ((5 ** 2) <= (-1 * -8))) or ((The square root of 121 is 11.) or ((11 - -20) != (2 ** 2)))))))
E. not (not not (not not (not not ((not ((-1 * 9 - -10 * -5) < (-3 + -15))) or (Argentina is in South America.)))))
F. not (((not not ((The capital of Ireland is Dublin.) or ((18 * -11) == (3 ** 1)))) and (not (Uranus is the 7th planet from the Sun.))) or (not not (not ((((-3 - 18) != (4 ** 1)) or (The chemical symbol for Chromium is Ni.)) or (There are 30 days in April.)))))
G. not not (not (not not (((((-14 + -1) <= (4 ** 2)) and (Venus is the 8th planet from the Sun.)) and (not not (Ice is a liquid at room temperature.))) or ((not ((6 % 7) != (-2 * 20))) and (not not (There are 29 days in June.))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "C,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 78606477,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. not ((not (not not (((2073 is a leap year.) and ((0 + 7) < (6 * -5 - 2 * 7))) and ((15 - -20) == (4 - -6))))) or (not not (((((-18 + 18) <= (5 ** 1) <= (1 * 10 + 5 * -10)) and (The currency of Japan is the Ringgit.)) and (The currency of Nigeria is the Rupiah.)) or ((not not (The speed of light is approximately 300,000 km/s.)) and (((5 - -5) >= (0 * -2 + -6 * 8)) and (Saturn is the 3rd planet from the Sun.))))))\nB. (not (((not ((1 * 20) < (5 ** 1))) or ((The 2012 Olympics were held in London.) and (not not ((1 ** 1) <= (-15 * -6))))) and (not not ((not not (A chicken has 2 legs.)) and (not not (Plants produce oxygen through photosynthesis.)))))) and (not (not ((not (not (The 1920 Olympics were held in Antwerp.))) or (((The currency of United Kingdom is the Zloty.) and ((7 * 9) > (13 * 19))) or ((The currency of Brazil is the Dollar.) and (Japan is in North America.))))))\nC. not (not not (not not ((((The Sun revolves around the Earth.) or (World War I ended occurred in 1918.)) and ((The first airplane flight by the Wright Brothers occurred in 1903.) and ((-1 - 18) <= (15 - 2)))) and (not (((11 - 9) <= (3 + -11) <= (-6 + 5)) or ((41 % 10) < (3 - -15)))))))\nD. not (not not ((((-18 - -14) == (1 ** 2)) or (The first iPhone was released occurred in 2007.) or (not (((-6 + 2) < (3 ** 1) < (5 * 0 * -8 * -8)) or (Uranus is the 1st planet from the Sun.)))) and ((There are 30 days in September.) and (((1968 is a leap year.) and ((5 ** 2) <= (-1 * -8))) or ((The square root of 121 is 11.) or ((11 - -20) != (2 ** 2)))))))\nE. not (not not (not not (not not ((not ((-1 * 9 - -10 * -5) < (-3 + -15))) or (Argentina is in South America.)))))\nF. not (((not not ((The capital of Ireland is Dublin.) or ((18 * -11) == (3 ** 1)))) and (not (Uranus is the 7th planet from the Sun.))) or (not not (not ((((-3 - 18) != (4 ** 1)) or (The chemical symbol for Chromium is Ni.)) or (There are 30 days in April.)))))\nG. not not (not (not not (((((-14 + -1) <= (4 ** 2)) and (Venus is the 8th planet from the Sun.)) and (not not (Ice is a liquid at room temperature.))) or ((not ((6 % 7) != (-2 * 20))) and (not not (There are 29 days in June.))))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 78606477,
"true_count": 3
},
"seed": 78606477,
"task_id": 678606477,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (银在常温下是液体。) or ((土耳其的货币是谢克尔。) and ((8 - 4) == (-4 * -2 * -3 * -7)))
B. (((19 * 13) == (10 - 17)) and (((7 + 4) >= (6 * -9 + -3 * 8)) and (蜘蛛有8条腿。))) or ((尼日利亚的首都是阿布贾。) and (人体有206块骨头。)) or (not ((1980年奥运会在蒙特利尔举办。) and (一月有31天。)))
C. ((地球是距离太阳第3近的行星。) or ((土耳其的首都是曼谷。) or ((-8 - 9) < (-14 + 14) < (-4 * 7 + -10 * -4)))) or (not (水蒸气在常温下是气体。)) or ((((15 + -2) > (-3 * 15)) and ((3 + -5) == (-13 * -1))) and ((水星是距离太阳第3近的行星。) and (八月有31天。)))
D. not not (not not (((0 * 5 - 0 * -3) == (-9 * 2)) or (一月有31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,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 80832916,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. (银在常温下是液体。) or ((土耳其的货币是谢克尔。) and ((8 - 4) == (-4 * -2 * -3 * -7)))\nB. (((19 * 13) == (10 - 17)) and (((7 + 4) >= (6 * -9 + -3 * 8)) and (蜘蛛有8条腿。))) or ((尼日利亚的首都是阿布贾。) and (人体有206块骨头。)) or (not ((1980年奥运会在蒙特利尔举办。) and (一月有31天。)))\nC. ((地球是距离太阳第3近的行星。) or ((土耳其的首都是曼谷。) or ((-8 - 9) < (-14 + 14) < (-4 * 7 + -10 * -4)))) or (not (水蒸气在常温下是气体。)) or ((((15 + -2) > (-3 * 15)) and ((3 + -5) == (-13 * -1))) and ((水星是距离太阳第3近的行星。) and (八月有31天。)))\nD. not not (not not (((0 * 5 - 0 * -3) == (-9 * 2)) or (一月有31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": 4,
"seed": 80832916,
"true_count": 3
},
"seed": 80832916,
"task_id": 680832916,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not (The capital of Indonesia is Jakarta.))
B. (not ((A turtle is a reptile.) or (((-2 * 0 - 9 * -4) <= (20 % 3)) and (Helium is a gas at room temperature.)))) and (((8 * 5 - 4 * 5) < (10 * -9) < (1 % 2)) and ((not ((10 * 7 - -9 * -1) > (16 * 11))) or (The capital of Turkey is Ankara.)))
C. (not (not not (not (There are 29 days in October.)))) and (not not (not ((-1 - -9) <= (0 * 10 + 0 * -5))))
D. (not (The 1928 Olympics were held in Amsterdam.)) and (not not ((4 + 20) <= (3 ** 2)))
E. not (not not (not not (not not (Neptune is the 8th planet from the Sun.))))
F. ((((24 % 10) != (-6 * -5 + -9 * -3)) or (not (Vietnam is in Asia.))) and (not (not ((-9 * 0 + 7 * -3) == (11 * -6))))) or ((1944 is a leap year.) or ((9 % 4) >= (1 * 5 + -7 * 6)) or ((((14 * -18) <= (0 + -11)) or ((-2 * 15) <= (11 * 3))) and ((1969 is a leap year.) or ((7 * -8 - -10 * -5) > (13 + -8)))))
G. (not not (((The Titanic sank occurred in 1912.) and (The currency of New Zealand is the Rand.)) or ((-1 - -2) <= (-10 * 0 * 7 * -5)))) and ((not (not ((2 + 5) < (5 * -5 * -2 * 3)))) and ((-12 * 7) <= (-14 - -11) <= (-14 + -17)))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 76711671,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. not (not (The capital of Indonesia is Jakarta.))\nB. (not ((A turtle is a reptile.) or (((-2 * 0 - 9 * -4) <= (20 % 3)) and (Helium is a gas at room temperature.)))) and (((8 * 5 - 4 * 5) < (10 * -9) < (1 % 2)) and ((not ((10 * 7 - -9 * -1) > (16 * 11))) or (The capital of Turkey is Ankara.)))\nC. (not (not not (not (There are 29 days in October.)))) and (not not (not ((-1 - -9) <= (0 * 10 + 0 * -5))))\nD. (not (The 1928 Olympics were held in Amsterdam.)) and (not not ((4 + 20) <= (3 ** 2)))\nE. not (not not (not not (not not (Neptune is the 8th planet from the Sun.))))\nF. ((((24 % 10) != (-6 * -5 + -9 * -3)) or (not (Vietnam is in Asia.))) and (not (not ((-9 * 0 + 7 * -3) == (11 * -6))))) or ((1944 is a leap year.) or ((9 % 4) >= (1 * 5 + -7 * 6)) or ((((14 * -18) <= (0 + -11)) or ((-2 * 15) <= (11 * 3))) and ((1969 is a leap year.) or ((7 * -8 - -10 * -5) > (13 + -8)))))\nG. (not not (((The Titanic sank occurred in 1912.) and (The currency of New Zealand is the Rand.)) or ((-1 - -2) <= (-10 * 0 * 7 * -5)))) and ((not (not ((2 + 5) < (5 * -5 * -2 * 3)))) and ((-12 * 7) <= (-14 - -11) <= (-14 + -17)))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 76711671,
"true_count": 2
},
"seed": 76711671,
"task_id": 676711671,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. ((not not (Oil is a solid at room temperature.)) or ((not not (A kangaroo has 2 legs.)) or ((The chemical symbol for Phosphorus is P.) and ((-12 * -17) != (-3 - 3))))) or (not ((((6 + -14) == (35 % 3)) and ((10 * 19) <= (-6 * 20))) or (not ((2 * 9) <= (15 + 5)))))
B. (not ((-2 * 2 - 3 * 10) >= (6 * 1 + -5 * -9))) or (not ((not not ((7 - 13) > (1 + -1))) and (A elephant has 6 legs.)))
C. not not (((-19 - 13) <= (0 - -14)) or (not (The 1904 Olympics were held in St. Louis.)) or (not not (((-18 + -11) != (5 + -19)) or (Nitrogen is a gas at room temperature.))))
D. (((((1 + -11) <= (-15 * 15)) or ((7 - 18) != (-5 * 5 + 3 * 10))) or (((-5 * 5 + -3 * 6) <= (5 ** 3)) or (The currency of Singapore is the Dollar.))) or (The chemical symbol for Magnesium is Fe.)) or (((not (30 is less than or equal to 67.)) or (not not (The 1908 Olympics were held in Paris.))) or ((((19 - -14) < (-14 - -16) < (4 + -8)) and ((2 ** 2) != (4 * 2 + -4 * -4))) and (((10 % 9) == (-20 + -10)) or ((9 * 1) < (15 + -11) < (20 * 15)))))
E. (not ((not not ((-20 - 17) < (7 * -10))) or ((-7 + -18) <= (-20 - -19) <= (12 + -3)))) or (((((5 * -5) > (-8 * 13)) and (A turtle is a fish.)) or ((3 + -3) > (-10 - -10))) and ((not ((8 + 1) == (1 ** 1))) or ((Iron is a solid at room temperature.) or ((-17 - -20) <= (-18 - 0) <= (-14 - 14)))))
F. not not (((((10 * 20) != (-10 * -9 * -1 * 6)) and (A fish has 0 legs.)) or (not not (73 is a prime number.))) or ((not not ((-11 - -8) < (9 * 1 + 2 * -10))) and ((The currency of Hungary is the Forint.) and ((-4 * -1) <= (20 + 13)))))
G. not not ((103 is an even number.) and ((Ice is a liquid at room temperature.) or (The chemical symbol for Sulfur is Ag.)) and (((27 % 7) < (6 * -5 - -10 * -6) < (-20 * 6)) and (((-19 * 9) == (1 + -12)) or (The capital of Netherlands is New Delhi.))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "A,B,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 7,
"seed": 25031304,
"true_count": 5
},
"question": "Here are some boolean expressions to evaluate:\n\nA. ((not not (Oil is a solid at room temperature.)) or ((not not (A kangaroo has 2 legs.)) or ((The chemical symbol for Phosphorus is P.) and ((-12 * -17) != (-3 - 3))))) or (not ((((6 + -14) == (35 % 3)) and ((10 * 19) <= (-6 * 20))) or (not ((2 * 9) <= (15 + 5)))))\nB. (not ((-2 * 2 - 3 * 10) >= (6 * 1 + -5 * -9))) or (not ((not not ((7 - 13) > (1 + -1))) and (A elephant has 6 legs.)))\nC. not not (((-19 - 13) <= (0 - -14)) or (not (The 1904 Olympics were held in St. Louis.)) or (not not (((-18 + -11) != (5 + -19)) or (Nitrogen is a gas at room temperature.))))\nD. (((((1 + -11) <= (-15 * 15)) or ((7 - 18) != (-5 * 5 + 3 * 10))) or (((-5 * 5 + -3 * 6) <= (5 ** 3)) or (The currency of Singapore is the Dollar.))) or (The chemical symbol for Magnesium is Fe.)) or (((not (30 is less than or equal to 67.)) or (not not (The 1908 Olympics were held in Paris.))) or ((((19 - -14) < (-14 - -16) < (4 + -8)) and ((2 ** 2) != (4 * 2 + -4 * -4))) and (((10 % 9) == (-20 + -10)) or ((9 * 1) < (15 + -11) < (20 * 15)))))\nE. (not ((not not ((-20 - 17) < (7 * -10))) or ((-7 + -18) <= (-20 - -19) <= (12 + -3)))) or (((((5 * -5) > (-8 * 13)) and (A turtle is a fish.)) or ((3 + -3) > (-10 - -10))) and ((not ((8 + 1) == (1 ** 1))) or ((Iron is a solid at room temperature.) or ((-17 - -20) <= (-18 - 0) <= (-14 - 14)))))\nF. not not (((((10 * 20) != (-10 * -9 * -1 * 6)) and (A fish has 0 legs.)) or (not not (73 is a prime number.))) or ((not not ((-11 - -8) < (9 * 1 + 2 * -10))) and ((The currency of Hungary is the Forint.) and ((-4 * -1) <= (20 + 13)))))\nG. not not ((103 is an even number.) and ((Ice is a liquid at room temperature.) or (The chemical symbol for Sulfur is Ag.)) and (((27 % 7) < (6 * -5 - -10 * -6) < (-20 * 6)) and (((-19 * 9) == (1 + -12)) or (The capital of Netherlands is New Delhi.))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
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"language": "en",
"num_options": 7,
"seed": 25031304,
"true_count": 5
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"seed": 25031304,
"task_id": 625031304,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. ((((((2 * 10 + -9 * -6) == (4 ** 3)) and (Earth is the 2nd planet from the Sun.)) and (Whales are fish.)) or (2083 is a leap year.)) or ((not ((-18 + -11) >= (-11 * 8))) or (((United Kingdom is in Europe.) and (A fish has 0 legs.)) or ((United States is in North America.) or ((-7 + -15) >= (-1 + 12)))))) and ((not not ((5 ** 2) >= (-2 + 5))) or (((17 - 10) < (15 * -8)) or ((18 + 4) > (-6 * 8 + 10 * 0)) or (1909 is a leap year.)))
B. (not ((((8 * -3 - 7 * 9) == (-4 + 11)) and (not (Mars is the closest planet to the Sun.))) or (((2 - 14) > (2 - 7)) or ((A cow has 4 legs.) or (Mexico is in North America.))))) or ((((7 - 15) == (1 * 16)) or (not (Jupiter is the 4th planet from the Sun.)) or ((29 % 8) <= (-6 * 5 - -6 * 8))) or ((A snake has 0 legs.) or ((not (The capital of Finland is Lima.)) and (not not (There are 29 days in July.)))))
C. not (not (not not (((The French Revolution began occurred in 1789.) or (52 is divisible by 9.)) and ((The square root of 4 is 2.) or ((17 - 16) >= (-2 * -12))))))
D. not (not (not not ((The Earth revolves around the Sun.) and (((-16 + 16) == (11 + 5)) and (The capital of Japan is Tokyo.)))))
E. (((There are 28 days in December.) or ((14 is a prime number.) and (not (40 is a prime number.)))) or (((-2 - 15) > (42 % 8)) or (Mars is the 4th planet from the Sun.))) or (not (((There are 28 days in December.) or (not not ((-2 * 2) == (1 * 5 * -3 * -6)))) and (((The capital of Egypt is Berlin.) and (The 1964 Olympics were held in Tokyo.)) and (((-12 - 3) < (1 ** 2)) and ((5 ** 3) > (-3 * -9 - 2 * 7))))))
F. ((not ((((18 * 5) < (15 * 17) < (1 % 8)) and (The capital of Chile is Santiago.)) or (The square root of 100 is 10.))) and (not not ((10 - -14) != (-6 - -4)))) and (not not ((The chemical symbol for Mercury is Hg.) or (The chemical symbol for Manganese is Mn.)))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
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"seed": 417569,
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"question": "Given the following boolean expressions:\n\nA. ((((((2 * 10 + -9 * -6) == (4 ** 3)) and (Earth is the 2nd planet from the Sun.)) and (Whales are fish.)) or (2083 is a leap year.)) or ((not ((-18 + -11) >= (-11 * 8))) or (((United Kingdom is in Europe.) and (A fish has 0 legs.)) or ((United States is in North America.) or ((-7 + -15) >= (-1 + 12)))))) and ((not not ((5 ** 2) >= (-2 + 5))) or (((17 - 10) < (15 * -8)) or ((18 + 4) > (-6 * 8 + 10 * 0)) or (1909 is a leap year.)))\nB. (not ((((8 * -3 - 7 * 9) == (-4 + 11)) and (not (Mars is the closest planet to the Sun.))) or (((2 - 14) > (2 - 7)) or ((A cow has 4 legs.) or (Mexico is in North America.))))) or ((((7 - 15) == (1 * 16)) or (not (Jupiter is the 4th planet from the Sun.)) or ((29 % 8) <= (-6 * 5 - -6 * 8))) or ((A snake has 0 legs.) or ((not (The capital of Finland is Lima.)) and (not not (There are 29 days in July.)))))\nC. not (not (not not (((The French Revolution began occurred in 1789.) or (52 is divisible by 9.)) and ((The square root of 4 is 2.) or ((17 - 16) >= (-2 * -12))))))\nD. not (not (not not ((The Earth revolves around the Sun.) and (((-16 + 16) == (11 + 5)) and (The capital of Japan is Tokyo.)))))\nE. (((There are 28 days in December.) or ((14 is a prime number.) and (not (40 is a prime number.)))) or (((-2 - 15) > (42 % 8)) or (Mars is the 4th planet from the Sun.))) or (not (((There are 28 days in December.) or (not not ((-2 * 2) == (1 * 5 * -3 * -6)))) and (((The capital of Egypt is Berlin.) and (The 1964 Olympics were held in Tokyo.)) and (((-12 - 3) < (1 ** 2)) and ((5 ** 3) > (-3 * -9 - 2 * 7))))))\nF. ((not ((((18 * 5) < (15 * 17) < (1 % 8)) and (The capital of Chile is Santiago.)) or (The square root of 100 is 10.))) and (not not ((10 - -14) != (-6 - -4)))) and (not not ((The chemical symbol for Mercury is Hg.) or (The chemical symbol for Manganese is Mn.)))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
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"seed": 417569,
"true_count": 4
},
"seed": 417569,
"task_id": 600417569,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not not ((not (14 is divisible by 10.)) or (not (The capital of Germany is Bucharest.)))) and (not not (((The currency of Switzerland is the Peso.) or ((5 + -1) >= (-13 * 20))) and (Electricity flows faster than light.)))
B. not not ((not (not (The capital of Colombia is Canberra.))) and ((5 * -9) < (-3 - -18) < (20 * -7)) and (not (not (The chemical symbol for Helium is Co.))))
C. ((((A lizard is a reptile.) and (The 1948 Olympics were held in London.)) or ((15 + 17) < (19 * -1))) or (not ((The chemical symbol for Aluminum is N.) or (The 1904 Olympics were held in Paris.)))) or (((745 is a Fibonacci number.) or (((16 * 0) < (-15 + -20)) and (120 is a Fibonacci number.))) and (((4 ** 2) != (15 - -9)) or (not (The capital of Poland is Warsaw.))))
D. (not (((-12 + 16) < (3 % 1) < (-6 * 2 + 9 * 0)) and (((39 % 2) > (-14 - -2)) and (Silver is a solid at room temperature.)))) or (not not ((((28 % 2) >= (2 + -1)) and ((2 * 8 - 1 * -6) < (46 % 8))) or (not ((-2 - -12) != (19 + -13)))))
E. not (not not (Saturn is the 6th planet from the Sun.))
F. not not (not ((not ((-19 * 3) != (-11 * -16))) and (The capital of Colombia is Bogota.)))
G. ((not not ((-14 - 4) != (-15 + -20))) and (((9 + 14) >= (13 - 3)) or (Mercury is the 1st planet from the Sun.))) or (not ((24 % 6) < (-8 - -4)))
H. (not not (The currency of Norway is the Krone.)) and (((-17 * -2) > (-7 * 5)) and (not not ((1 * 1 + -4 * 9) <= (48 % 4)))) and ((74 is a Fibonacci number.) or (((Light travels faster than sound.) and (The currency of Sweden is the Krona.)) or (((13 - 15) < (5 ** 3)) and ((12 + 5) != (11 * 2)))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C,D,F,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 64039869,
"true_count": 5
},
"question": "Here are some boolean expressions to evaluate:\n\nA. (not not ((not (14 is divisible by 10.)) or (not (The capital of Germany is Bucharest.)))) and (not not (((The currency of Switzerland is the Peso.) or ((5 + -1) >= (-13 * 20))) and (Electricity flows faster than light.)))\nB. not not ((not (not (The capital of Colombia is Canberra.))) and ((5 * -9) < (-3 - -18) < (20 * -7)) and (not (not (The chemical symbol for Helium is Co.))))\nC. ((((A lizard is a reptile.) and (The 1948 Olympics were held in London.)) or ((15 + 17) < (19 * -1))) or (not ((The chemical symbol for Aluminum is N.) or (The 1904 Olympics were held in Paris.)))) or (((745 is a Fibonacci number.) or (((16 * 0) < (-15 + -20)) and (120 is a Fibonacci number.))) and (((4 ** 2) != (15 - -9)) or (not (The capital of Poland is Warsaw.))))\nD. (not (((-12 + 16) < (3 % 1) < (-6 * 2 + 9 * 0)) and (((39 % 2) > (-14 - -2)) and (Silver is a solid at room temperature.)))) or (not not ((((28 % 2) >= (2 + -1)) and ((2 * 8 - 1 * -6) < (46 % 8))) or (not ((-2 - -12) != (19 + -13)))))\nE. not (not not (Saturn is the 6th planet from the Sun.))\nF. not not (not ((not ((-19 * 3) != (-11 * -16))) and (The capital of Colombia is Bogota.)))\nG. ((not not ((-14 - 4) != (-15 + -20))) and (((9 + 14) >= (13 - 3)) or (Mercury is the 1st planet from the Sun.))) or (not ((24 % 6) < (-8 - -4)))\nH. (not not (The currency of Norway is the Krone.)) and (((-17 * -2) > (-7 * 5)) and (not not ((1 * 1 + -4 * 9) <= (48 % 4)))) and ((74 is a Fibonacci number.) or (((Light travels faster than sound.) and (The currency of Sweden is the Krona.)) or (((13 - 15) < (5 ** 3)) and ((12 + 5) != (11 * 2)))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 64039869,
"true_count": 5
},
"seed": 64039869,
"task_id": 664039869,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. ((二月有31天。) and (土耳其的首都是里斯本。) and (((菲律宾的货币是比索。) or ((4 ** 3) != (1 + 12))) and ((大象有4条腿。) and (电流比光速更快。)))) or (not not (not (not not (俄罗斯的货币是卢布。))))
B. (not (尼日利亚的货币是兹罗提。)) and ((((鸵鸟是鸟类。) or (81的平方根是9。)) or (not ((20 * -4) <= (2 ** 1) <= (-6 + 13)))) or (not (秘鲁位于欧洲。)) or (袋鼠是爬行动物。))
C. not ((not (((-4 * -5 - 7 * 4) <= (2 * 4 + -7 * 6) <= (20 + 0)) and (镍的化学符号是Ni。))) or ((地球是距离太阳第3近的行星。) or ((4 * 20) > (20 + -8))) or (not not ((8 * -3 * 10 * -9) < (5 * 6))))
D. not not (((3 ** 3) == (-15 - 0)) or (((0 * -10 * 7 * 3) <= (-10 + -6)) and (氧的化学符号是O。)))
E. ((not not (not not (金鱼是鸟类。))) or ((挪威的货币是卢布。) or (2020年奥运会在东京举办。)) or ((((7 * -12) == (-3 * -5 * 6 * -1)) or (第一次世界大战结束发生在1918年。)) and ((法国大革命开始发生在1791年。) or ((3 - -16) >= (-4 * -14))))) or ((((7 % 8) < (6 * 6 + -5 * -10)) and (not (欧盟的货币是埃及镑。))) or ((97大于39。) and ((13 * -1) >= (7 % 5))) or (not not (人体有150块骨头。)))
F. ((not not ((-13 + -19) <= (5 * -17))) and ((-12 * 5) <= (4 * 1) <= (13 - 4)) and (((印度位于南极洲。) or ((-16 * -8) != (5 * 3 - 8 * 4))) and (((15 + 2) <= (7 - -11) <= (1 + -17)) and ((-17 + 17) < (17 - 5))))) or (((10 * -15) < (-17 + -16) < (7 * -7)) or (1912年奥运会在斯德哥尔摩举办。))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "B,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 32564901,
"true_count": 3
},
"question": "下面是几个布尔表达式：\n\nA. ((二月有31天。) and (土耳其的首都是里斯本。) and (((菲律宾的货币是比索。) or ((4 ** 3) != (1 + 12))) and ((大象有4条腿。) and (电流比光速更快。)))) or (not not (not (not not (俄罗斯的货币是卢布。))))\nB. (not (尼日利亚的货币是兹罗提。)) and ((((鸵鸟是鸟类。) or (81的平方根是9。)) or (not ((20 * -4) <= (2 ** 1) <= (-6 + 13)))) or (not (秘鲁位于欧洲。)) or (袋鼠是爬行动物。))\nC. not ((not (((-4 * -5 - 7 * 4) <= (2 * 4 + -7 * 6) <= (20 + 0)) and (镍的化学符号是Ni。))) or ((地球是距离太阳第3近的行星。) or ((4 * 20) > (20 + -8))) or (not not ((8 * -3 * 10 * -9) < (5 * 6))))\nD. not not (((3 ** 3) == (-15 - 0)) or (((0 * -10 * 7 * 3) <= (-10 + -6)) and (氧的化学符号是O。)))\nE. ((not not (not not (金鱼是鸟类。))) or ((挪威的货币是卢布。) or (2020年奥运会在东京举办。)) or ((((7 * -12) == (-3 * -5 * 6 * -1)) or (第一次世界大战结束发生在1918年。)) and ((法国大革命开始发生在1791年。) or ((3 - -16) >= (-4 * -14))))) or ((((7 % 8) < (6 * 6 + -5 * -10)) and (not (欧盟的货币是埃及镑。))) or ((97大于39。) and ((13 * -1) >= (7 % 5))) or (not not (人体有150块骨头。)))\nF. ((not not ((-13 + -19) <= (5 * -17))) and ((-12 * 5) <= (4 * 1) <= (13 - 4)) and (((印度位于南极洲。) or ((-16 * -8) != (5 * 3 - 8 * 4))) and (((15 + 2) <= (7 - -11) <= (1 + -17)) and ((-17 + 17) < (17 - 5))))) or (((10 * -15) < (-17 + -16) < (7 * -7)) or (1912年奥运会在斯德哥尔摩举办。))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 6,
"seed": 32564901,
"true_count": 3
},
"seed": 32564901,
"task_id": 632564901,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (not (not not (((7 * 4 + 4 * -6) != (3 ** 3)) and ((7 * -2 * 2 * 6) >= (9 * 13))))) and ((((-1 - -8) != (-2 * -9 - -7 * -6)) or ((There are 31 days in September.) and (((-9 * 5 + -6 * 5) == (-1 * 8 * -3 * -2)) or ((1 ** 2) < (11 * -3) < (3 * 2 - -3 * -10))))) and ((Wood is a solid at room temperature.) and (The capital of Poland is Warsaw.)))
B. not not ((((not ((-8 + -13) <= (4 ** 3))) or (The capital of Peru is Kyiv.)) and (not ((The capital of Venezuela is Bogota.) and ((33 % 2) > (-5 * -1))))) and (not not (not (not (The Soviet Union dissolved occurred in 1991.)))))
C. not (not not (not not (A gecko is a reptile.)))
D. (not not (((not (The capital of Colombia is Ottawa.)) and (not not ((5 - -6) < (-10 * -3 - -5 * -1)))) or (not ((A chameleon is a reptile.) or (Mars is the 5th planet from the Sun.))))) or ((not (not (not ((14 - 1) <= (9 + 3))))) and ((not (((5 - 5) >= (-2 * 2)) and ((1 ** 1) > (2 * 4 - -7 * -5)))) or ((The 1932 Olympics were held in Los Angeles.) or ((-8 * 7 * -7 * 0) == (5 ** 1)))))
E. not not (((not ((Diamond is a solid at room temperature.) or (The United States declared independence occurred in 1776.))) and ((13 + 12) <= (4 * -1 * -4 * 4) <= (7 * -6 * -10 * -8))) or (not not (Penguins can fly.)))
F. not not ((((not not ((-7 * 8 - 5 * -6) <= (3 * -5))) and ((Air is a gas at room temperature.) or (There are 29 days in February.))) and (not not ((The capital of France is Paris.) or ((19 - -17) < (4 ** 3))))) and (not not ((The currency of South Korea is the Lira.) and (not not (The chemical symbol for Cobalt is Co.)))))
G. not (not not ((not not (not not ((-9 - 5) >= (-4 * 6)))) and (not not (The Moon orbits the Earth.)) and ((9 * 17) < (5 + 4) < (-10 - 14))))
H. ((not not (A chameleon is a mammal.)) or ((Penguins can fly.) and ((The Great Fire of London occurred in 1666.) and (India is in Oceania.)) and ((not not (The Great Fire of London occurred in 1666.)) or (((43 % 3) > (-17 + -17)) or ((-8 - -14) >= (4 ** 3)))))) or (not ((((The capital of India is New Delhi.) or (60 is a prime number.)) and ((Uranus is the 3rd planet from the Sun.) or ((-1 + -5) == (12 + 13)))) or (not (12 is less than or equal to 35.))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "A,D,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "en",
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"question": "Review these logical expressions:\n\nA. (not (not not (((7 * 4 + 4 * -6) != (3 ** 3)) and ((7 * -2 * 2 * 6) >= (9 * 13))))) and ((((-1 - -8) != (-2 * -9 - -7 * -6)) or ((There are 31 days in September.) and (((-9 * 5 + -6 * 5) == (-1 * 8 * -3 * -2)) or ((1 ** 2) < (11 * -3) < (3 * 2 - -3 * -10))))) and ((Wood is a solid at room temperature.) and (The capital of Poland is Warsaw.)))\nB. not not ((((not ((-8 + -13) <= (4 ** 3))) or (The capital of Peru is Kyiv.)) and (not ((The capital of Venezuela is Bogota.) and ((33 % 2) > (-5 * -1))))) and (not not (not (not (The Soviet Union dissolved occurred in 1991.)))))\nC. not (not not (not not (A gecko is a reptile.)))\nD. (not not (((not (The capital of Colombia is Ottawa.)) and (not not ((5 - -6) < (-10 * -3 - -5 * -1)))) or (not ((A chameleon is a reptile.) or (Mars is the 5th planet from the Sun.))))) or ((not (not (not ((14 - 1) <= (9 + 3))))) and ((not (((5 - 5) >= (-2 * 2)) and ((1 ** 1) > (2 * 4 - -7 * -5)))) or ((The 1932 Olympics were held in Los Angeles.) or ((-8 * 7 * -7 * 0) == (5 ** 1)))))\nE. not not (((not ((Diamond is a solid at room temperature.) or (The United States declared independence occurred in 1776.))) and ((13 + 12) <= (4 * -1 * -4 * 4) <= (7 * -6 * -10 * -8))) or (not not (Penguins can fly.)))\nF. not not ((((not not ((-7 * 8 - 5 * -6) <= (3 * -5))) and ((Air is a gas at room temperature.) or (There are 29 days in February.))) and (not not ((The capital of France is Paris.) or ((19 - -17) < (4 ** 3))))) and (not not ((The currency of South Korea is the Lira.) and (not not (The chemical symbol for Cobalt is Co.)))))\nG. not (not not ((not not (not not ((-9 - 5) >= (-4 * 6)))) and (not not (The Moon orbits the Earth.)) and ((9 * 17) < (5 + 4) < (-10 - 14))))\nH. ((not not (A chameleon is a mammal.)) or ((Penguins can fly.) and ((The Great Fire of London occurred in 1666.) and (India is in Oceania.)) and ((not not (The Great Fire of London occurred in 1666.)) or (((43 % 3) > (-17 + -17)) or ((-8 - -14) >= (4 ** 3)))))) or (not ((((The capital of India is New Delhi.) or (60 is a prime number.)) and ((Uranus is the 3rd planet from the Sun.) or ((-1 + -5) == (12 + 13)))) or (not (12 is less than or equal to 35.))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
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"language": "en",
"num_options": 8,
"seed": 55885796,
"true_count": 4
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"seed": 55885796,
"task_id": 655885796,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not (((not not (Ice is less dense than liquid water.)) and ((Silver is a gas at room temperature.) and ((-12 * 0) >= (14 + -17)))) and (not ((49 % 7) < (13 * -20))))) or (not not ((-11 * 1) <= (-10 * 7 * 10 * -8))) or (not ((South Korea is in Oceania.) or (((7 + 3) > (-18 * -20)) or (not not ((-11 - 8) <= (-2 + -20))))))
B. not ((((((36 % 4) <= (9 * -9 + 4 * -4) <= (6 + -2)) and (78 is divisible by 12.)) and (not ((-12 + 16) != (-12 * 12)))) and ((Russia is in Europe.) or (((-16 + -2) == (-9 - 10)) or ((19 - 1) >= (-10 - 19))))) or ((10 - -3) >= (4 ** 3)) or ((not (((-4 * -6 * 3 * 1) < (28 % 8) < (3 ** 3)) and (Japan is in Asia.))) and (((5 ** 2) <= (16 * -9)) and ((-17 * 11) <= (14 - -20) <= (8 - 10))) and (The currency of Russia is the Baht.)))
C. not ((not not (not not (The Pacific Ocean is the largest ocean.))) and (not not (not (The 1976 Olympics were held in Montreal.))) and ((The capital of Morocco is Rabat.) or ((((4 ** 2) >= (-4 * -7 * -5 * 6)) or ((-10 * -11) <= (18 * -7) <= (-16 - -4))) and (((3 + -9) <= (-2 - -17) <= (25 % 6)) and (Canada is in Europe.)))))
D. not not (((not not ((Jupiter is the 7th planet from the Sun.) and ((-8 - 0) < (14 + 19)))) and (Oxygen is necessary for human survival.)) and ((The currency of Thailand is the Baht.) and ((There are 29 days in August.) and (The chemical symbol for Tin is S.)) and (Gold is a solid at room temperature.)))
E. (not not (not not ((((-20 - 1) < (11 * 10) < (10 * -10 + 8 * 6)) or ((3 ** 1) != (-5 * 8 * -4 * -10))) and (Alcohol is a solid at room temperature.)))) or (not not (not (not ((217 is a perfect square.) or (The capital of Netherlands is Amsterdam.)))))
F. not not (not ((Venus is the 2nd planet from the Sun.) and ((((-10 * -6 * 4 * -10) < (12 + -12) < (4 + -5)) and (Uranus is the 7th planet from the Sun.)) and (((34 % 7) == (3 - -13)) or ((-6 * 1 + 1 * 1) <= (-9 + 18))))))
G. not not (((The Great Fire of London occurred in 1666.) and (((19 + 13) < (9 * 2 + -10 * -4) < (-18 - 15)) and ((-7 * 7) == (-14 * 15)))) or (((2 * -4 - -1 * -3) != (-7 * -5 - 8 * 4)) and (The chemical symbol for Nickel is C.)))
H. (not (not ((((-10 * 6 * -10 * 7) >= (-11 + 13)) or (Air is a liquid at room temperature.)) and ((The Titanic sank occurred in 1912.) or (Iron is a solid at room temperature.))))) or (not not (not ((not (There are 29 days in November.)) and (((3 * -8 + 3 * -5) <= (34 % 5)) or ((-7 * -5) == (0 - -16))))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,E,F,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
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"seed": 73540416,
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"question": "Analyze these boolean expressions:\n\nA. (not (((not not (Ice is less dense than liquid water.)) and ((Silver is a gas at room temperature.) and ((-12 * 0) >= (14 + -17)))) and (not ((49 % 7) < (13 * -20))))) or (not not ((-11 * 1) <= (-10 * 7 * 10 * -8))) or (not ((South Korea is in Oceania.) or (((7 + 3) > (-18 * -20)) or (not not ((-11 - 8) <= (-2 + -20))))))\nB. not ((((((36 % 4) <= (9 * -9 + 4 * -4) <= (6 + -2)) and (78 is divisible by 12.)) and (not ((-12 + 16) != (-12 * 12)))) and ((Russia is in Europe.) or (((-16 + -2) == (-9 - 10)) or ((19 - 1) >= (-10 - 19))))) or ((10 - -3) >= (4 ** 3)) or ((not (((-4 * -6 * 3 * 1) < (28 % 8) < (3 ** 3)) and (Japan is in Asia.))) and (((5 ** 2) <= (16 * -9)) and ((-17 * 11) <= (14 - -20) <= (8 - 10))) and (The currency of Russia is the Baht.)))\nC. not ((not not (not not (The Pacific Ocean is the largest ocean.))) and (not not (not (The 1976 Olympics were held in Montreal.))) and ((The capital of Morocco is Rabat.) or ((((4 ** 2) >= (-4 * -7 * -5 * 6)) or ((-10 * -11) <= (18 * -7) <= (-16 - -4))) and (((3 + -9) <= (-2 - -17) <= (25 % 6)) and (Canada is in Europe.)))))\nD. not not (((not not ((Jupiter is the 7th planet from the Sun.) and ((-8 - 0) < (14 + 19)))) and (Oxygen is necessary for human survival.)) and ((The currency of Thailand is the Baht.) and ((There are 29 days in August.) and (The chemical symbol for Tin is S.)) and (Gold is a solid at room temperature.)))\nE. (not not (not not ((((-20 - 1) < (11 * 10) < (10 * -10 + 8 * 6)) or ((3 ** 1) != (-5 * 8 * -4 * -10))) and (Alcohol is a solid at room temperature.)))) or (not not (not (not ((217 is a perfect square.) or (The capital of Netherlands is Amsterdam.)))))\nF. not not (not ((Venus is the 2nd planet from the Sun.) and ((((-10 * -6 * 4 * -10) < (12 + -12) < (4 + -5)) and (Uranus is the 7th planet from the Sun.)) and (((34 % 7) == (3 - -13)) or ((-6 * 1 + 1 * 1) <= (-9 + 18))))))\nG. not not (((The Great Fire of London occurred in 1666.) and (((19 + 13) < (9 * 2 + -10 * -4) < (-18 - 15)) and ((-7 * 7) == (-14 * 15)))) or (((2 * -4 - -1 * -3) != (-7 * -5 - 8 * 4)) and (The chemical symbol for Nickel is C.)))\nH. (not (not ((((-10 * 6 * -10 * 7) >= (-11 + 13)) or (Air is a liquid at room temperature.)) and ((The Titanic sank occurred in 1912.) or (Iron is a solid at room temperature.))))) or (not not (not ((not (There are 29 days in November.)) and (((3 * -8 + 3 * -5) <= (34 % 5)) or ((-7 * -5) == (0 - -16))))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
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"language": "en",
"num_options": 8,
"seed": 73540416,
"true_count": 6
},
"seed": 73540416,
"task_id": 673540416,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (not (not (The chemical symbol for Manganese is Mn.))) and ((not not ((19 - -3) <= (-7 * -2 - 5 * 7))) or (not not (not (Gold is a solid at room temperature.))))
B. not ((((-10 * 3 + -8 * 7) >= (-18 + -9)) or (((9 - 9) <= (2 ** 1) <= (-6 * 0 * -10 * -10)) or ((8 * -9 * -10 * 7) != (-4 - 20))) or (There are 31 days in January.)) and (((-19 * 12) >= (4 * -6 - 9 * 8)) and (((2 + -2) < (-9 * 8) < (-16 - 7)) and (A crab has 8 legs.)) and ((not not ((-16 * -9) > (-12 * 12))) and ((12 - -13) != (5 ** 1)))))
C. not not ((not not (((9 * 0) <= (10 + -3)) or (The chemical symbol for Nitrogen is Ti.))) and (((Electricity flows faster than light.) and ((The chemical symbol for Neon is Ne.) and ((-16 + 5) != (-14 + 7)))) and ((not not (The capital of Romania is Bucharest.)) or (Venus is the 2nd planet from the Sun.))))
D. not ((not not (not not (not ((-20 * 5) == (19 + -15))))) and (not not ((not (The chemical symbol for Uranium is U.)) or (((-14 * -2) == (6 + 16)) or (The capital of Colombia is Moscow.)))))
E. not not ((not (((A spider has 2 legs.) and ((1 - -20) < (8 + -3))) or (((49 % 8) == (18 - -8)) or (Sharks are mammals.)))) or ((There are 29 days in January.) and (not not ((A alligator is a reptile.) or (The capital of Indonesia is Jakarta.)))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
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"seed": 86024358,
"true_count": 3
},
"question": "Study the following logical statements:\n\nA. (not (not (The chemical symbol for Manganese is Mn.))) and ((not not ((19 - -3) <= (-7 * -2 - 5 * 7))) or (not not (not (Gold is a solid at room temperature.))))\nB. not ((((-10 * 3 + -8 * 7) >= (-18 + -9)) or (((9 - 9) <= (2 ** 1) <= (-6 * 0 * -10 * -10)) or ((8 * -9 * -10 * 7) != (-4 - 20))) or (There are 31 days in January.)) and (((-19 * 12) >= (4 * -6 - 9 * 8)) and (((2 + -2) < (-9 * 8) < (-16 - 7)) and (A crab has 8 legs.)) and ((not not ((-16 * -9) > (-12 * 12))) and ((12 - -13) != (5 ** 1)))))\nC. not not ((not not (((9 * 0) <= (10 + -3)) or (The chemical symbol for Nitrogen is Ti.))) and (((Electricity flows faster than light.) and ((The chemical symbol for Neon is Ne.) and ((-16 + 5) != (-14 + 7)))) and ((not not (The capital of Romania is Bucharest.)) or (Venus is the 2nd planet from the Sun.))))\nD. not ((not not (not not (not ((-20 * 5) == (19 + -15))))) and (not not ((not (The chemical symbol for Uranium is U.)) or (((-14 * -2) == (6 + 16)) or (The capital of Colombia is Moscow.)))))\nE. not not ((not (((A spider has 2 legs.) and ((1 - -20) < (8 + -3))) or (((49 % 8) == (18 - -8)) or (Sharks are mammals.)))) or ((There are 29 days in January.) and (not not ((A alligator is a reptile.) or (The capital of Indonesia is Jakarta.)))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
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"language": "en",
"num_options": 5,
"seed": 86024358,
"true_count": 3
},
"seed": 86024358,
"task_id": 686024358,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. ((((1 - 19) < (-4 * -11)) and (not not (226 is a Fibonacci number.)) and (not not ((41 % 7) != (-19 + -12)))) or (((18 - 17) < (-15 * -16)) and ((not not (2009 is a leap year.)) and ((Vietnam is in North America.) or ((15 * -5) != (-13 + 13)))))) and (not not (not not ((Sound travels faster in a vacuum.) and ((14 + -10) >= (14 - -7))))) and (not not ((not (((7 % 6) <= (-18 + 14)) or ((-1 + 16) > (10 - 5)))) or (not not ((The capital of China is Beijing.) and (There are 30 days in June.)))))
B. not not (((((The first moon landing occurred in 1969.) or (The chemical symbol for Cobalt is Au.)) or (Water is a liquid at room temperature.)) or (((5 * -10 * -10 * 5) < (-8 * 7 * -3 * 6)) and (2072 is a leap year.)) or (((1 * -10) < (5 * -10 + -9 * -3) < (12 + -7)) or (((3 ** 1) != (-14 - -6)) and (Japan is in Asia.)))) and (not (not not (Copper is a solid at room temperature.))))
C. ((((The currency of United States is the Krona.) or ((5 % 10) == (-7 * -13))) or ((-18 - -15) >= (-20 - -15))) or (((not ((3 ** 1) <= (15 - 10))) and ((A butterfly has 6 legs.) and ((-14 - -10) >= (14 - 1)))) or ((3 - 20) > (-1 * 1 - -3 * -5)) or ((8 * -6 - -8 * 7) != (-5 + -18)))) or (not not (not not ((The chemical symbol for Manganese is Ti.) or ((-17 + 0) > (1 ** 2)))))
D. not ((not (not (not ((3 + 14) <= (2 ** 3) <= (-4 * 2))))) or (The speed of light is approximately 300,000 km/s.) or (((((19 % 9) == (2 ** 1)) or (India is in Asia.)) or ((Diamond is a solid at room temperature.) and ((5 ** 1) >= (17 - -5)))) and ((-11 + -8) >= (9 + 8)) and (((-14 * 7) < (-4 * 3)) and ((-7 + 18) <= (15 * 15)))))
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": 5,
"language": "en",
"num_options": 4,
"seed": 53635614,
"true_count": 1
},
"question": "Below are several boolean expressions:\n\nA. ((((1 - 19) < (-4 * -11)) and (not not (226 is a Fibonacci number.)) and (not not ((41 % 7) != (-19 + -12)))) or (((18 - 17) < (-15 * -16)) and ((not not (2009 is a leap year.)) and ((Vietnam is in North America.) or ((15 * -5) != (-13 + 13)))))) and (not not (not not ((Sound travels faster in a vacuum.) and ((14 + -10) >= (14 - -7))))) and (not not ((not (((7 % 6) <= (-18 + 14)) or ((-1 + 16) > (10 - 5)))) or (not not ((The capital of China is Beijing.) and (There are 30 days in June.)))))\nB. not not (((((The first moon landing occurred in 1969.) or (The chemical symbol for Cobalt is Au.)) or (Water is a liquid at room temperature.)) or (((5 * -10 * -10 * 5) < (-8 * 7 * -3 * 6)) and (2072 is a leap year.)) or (((1 * -10) < (5 * -10 + -9 * -3) < (12 + -7)) or (((3 ** 1) != (-14 - -6)) and (Japan is in Asia.)))) and (not (not not (Copper is a solid at room temperature.))))\nC. ((((The currency of United States is the Krona.) or ((5 % 10) == (-7 * -13))) or ((-18 - -15) >= (-20 - -15))) or (((not ((3 ** 1) <= (15 - 10))) and ((A butterfly has 6 legs.) and ((-14 - -10) >= (14 - 1)))) or ((3 - 20) > (-1 * 1 - -3 * -5)) or ((8 * -6 - -8 * 7) != (-5 + -18)))) or (not not (not not ((The chemical symbol for Manganese is Ti.) or ((-17 + 0) > (1 ** 2)))))\nD. not ((not (not (not ((3 + 14) <= (2 ** 3) <= (-4 * 2))))) or (The speed of light is approximately 300,000 km/s.) or (((((19 % 9) == (2 ** 1)) or (India is in Asia.)) or ((Diamond is a solid at room temperature.) and ((5 ** 1) >= (17 - -5)))) and ((-11 + -8) >= (9 + 8)) and (((-14 * 7) < (-4 * 3)) and ((-7 + 18) <= (15 * 15)))))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 4,
"seed": 53635614,
"true_count": 1
},
"seed": 53635614,
"task_id": 653635614,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. ((((World War II began occurred in 1939.) and ((10 - 16) == (6 - -10))) or (not (The currency of Colombia is the Shekel.))) and ((A carp is an insect.) or ((Humans have three lungs.) and ((3 + 20) <= (15 * -8))))) and ((not not ((23 % 4) <= (-7 * -4 + -2 * -10))) or (not ((9 + 8) < (4 * 0 * 9 * 4))) or ((Peru is in North America.) or ((Mars is the 4th planet from the Sun.) and ((-2 * -1 - 0 * 10) >= (-1 * 9 * 1 * 10)))))
B. ((The 1984 Olympics were held in Los Angeles.) and ((10 * -11) < (-19 * 12))) and (not not ((The capital of Italy is Riyadh.) or (Iron is a solid at room temperature.))) and ((not (The capital of Belgium is Mexico City.)) and (not (The chemical symbol for Gold is Au.)))
C. ((not not (World War II ended occurred in 1945.)) and (not not ((The capital of Australia is Canberra.) or ((-8 * 0) <= (2 * -20))))) or ((((6 * -12) != (-6 * 4 + 8 * -4)) or ((The currency of Poland is the Zloty.) or ((-6 + -15) == (22 % 5)))) or ((not ((10 - -10) > (1 * 7 + 6 * 7))) or ((1962 is a leap year.) or (The chemical symbol for Chromium is Cr.))))
D. not not (not (not not (not ((0 * -5 + 10 * 1) < (6 + 1) < (-20 + -7)))))
E. (((5 + 11) == (20 * -9)) or ((Argentina is in Africa.) and (There are 31 days in March.))) and (((The chemical symbol for Carbon is U.) or (The capital of Spain is Madrid.)) or (not (Light travels faster than sound.))) and (not (not (not (A frog has 4 legs.))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 5,
"seed": 94819502,
"true_count": 1
},
"question": "Here are some boolean expressions to evaluate:\n\nA. ((((World War II began occurred in 1939.) and ((10 - 16) == (6 - -10))) or (not (The currency of Colombia is the Shekel.))) and ((A carp is an insect.) or ((Humans have three lungs.) and ((3 + 20) <= (15 * -8))))) and ((not not ((23 % 4) <= (-7 * -4 + -2 * -10))) or (not ((9 + 8) < (4 * 0 * 9 * 4))) or ((Peru is in North America.) or ((Mars is the 4th planet from the Sun.) and ((-2 * -1 - 0 * 10) >= (-1 * 9 * 1 * 10)))))\nB. ((The 1984 Olympics were held in Los Angeles.) and ((10 * -11) < (-19 * 12))) and (not not ((The capital of Italy is Riyadh.) or (Iron is a solid at room temperature.))) and ((not (The capital of Belgium is Mexico City.)) and (not (The chemical symbol for Gold is Au.)))\nC. ((not not (World War II ended occurred in 1945.)) and (not not ((The capital of Australia is Canberra.) or ((-8 * 0) <= (2 * -20))))) or ((((6 * -12) != (-6 * 4 + 8 * -4)) or ((The currency of Poland is the Zloty.) or ((-6 + -15) == (22 % 5)))) or ((not ((10 - -10) > (1 * 7 + 6 * 7))) or ((1962 is a leap year.) or (The chemical symbol for Chromium is Cr.))))\nD. not not (not (not not (not ((0 * -5 + 10 * 1) < (6 + 1) < (-20 + -7)))))\nE. (((5 + 11) == (20 * -9)) or ((Argentina is in Africa.) and (There are 31 days in March.))) and (((The chemical symbol for Carbon is U.) or (The capital of Spain is Madrid.)) or (not (Light travels faster than sound.))) and (not (not (not (A frog has 4 legs.))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
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"language": "en",
"num_options": 5,
"seed": 94819502,
"true_count": 1
},
"seed": 94819502,
"task_id": 694819502,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. (not (not (not not ((Italy is in Europe.) and (There are 30 days in February.))))) and (not ((62 is divisible by 2.) or (((-12 * 3) < (19 * 1)) and (Steam is a liquid at room temperature.)) or (Sound cannot travel through a vacuum.)))
B. not ((((A duck has 2 legs.) or ((Spain is in Europe.) and ((1 ** 1) < (-9 * 2) < (2 - 18)))) or ((not (There are 30 days in November.)) and ((Earth is the 6th planet from the Sun.) and ((-8 + -6) < (3 ** 2))))) or ((((The capital of Switzerland is Stockholm.) and (A chameleon is a reptile.)) and (((4 * -9) == (4 * 9 - -5 * -9)) or ((-11 - -18) <= (-1 - 19) <= (1 ** 1)))) or (not (Christopher Columbus reached America occurred in 1492.))))
C. ((not not ((-1 - -2) == (-1 + 20))) or ((((5 ** 2) == (-8 - 14)) and (A duck has 4 legs.)) or (not not (New Zealand is in North America.))) or (((-5 + 20) >= (2 ** 2)) or (A chameleon is an insect.))) and ((not ((6 - -8) <= (11 - -4))) or ((16 + 17) > (-8 + 9)) or ((((3 - -14) <= (19 - 8)) and ((A day on Earth is 24 hours.) or (A snake is a reptile.))) and ((Penguins can fly.) or (((0 + -16) != (-2 * 3 - 3 * 6)) and (The 1968 Olympics were held in Los Angeles.)))))
D. (not ((not not (A bat is a mammal.)) or (not not (not (The capital of Peru is Lima.))))) and (not not (((not not ((2 ** 2) <= (-8 + 12) <= (19 + 18))) and (((12 + -8) < (2 - 12)) or ((19 * 8) > (-7 - -9)))) and ((((18 - -19) < (-9 * 1) < (14 - 15)) or (Uranus is the 1st planet from the Sun.)) and (not (There are 31 days in June.)))))
E. ((not not (((Iron is a solid at room temperature.) and (The chemical symbol for Chlorine is Mg.)) and (not not (Uranus is the 6th planet from the Sun.)))) or ((The chemical symbol for Silver is Cr.) and ((Uranus is the 4th planet from the Sun.) and (84 is a prime number.)))) and (not not ((The 1904 Olympics were held in St. Louis.) and ((((3 ** 3) >= (-8 - -9)) and ((-12 + -6) <= (-11 + 10) <= (-12 - -12))) or ((-6 - 0) <= (-13 + -11)))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 5,
"seed": 10088507,
"true_count": 1
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"question": "Consider the following logical expressions:\n\nA. (not (not (not not ((Italy is in Europe.) and (There are 30 days in February.))))) and (not ((62 is divisible by 2.) or (((-12 * 3) < (19 * 1)) and (Steam is a liquid at room temperature.)) or (Sound cannot travel through a vacuum.)))\nB. not ((((A duck has 2 legs.) or ((Spain is in Europe.) and ((1 ** 1) < (-9 * 2) < (2 - 18)))) or ((not (There are 30 days in November.)) and ((Earth is the 6th planet from the Sun.) and ((-8 + -6) < (3 ** 2))))) or ((((The capital of Switzerland is Stockholm.) and (A chameleon is a reptile.)) and (((4 * -9) == (4 * 9 - -5 * -9)) or ((-11 - -18) <= (-1 - 19) <= (1 ** 1)))) or (not (Christopher Columbus reached America occurred in 1492.))))\nC. ((not not ((-1 - -2) == (-1 + 20))) or ((((5 ** 2) == (-8 - 14)) and (A duck has 4 legs.)) or (not not (New Zealand is in North America.))) or (((-5 + 20) >= (2 ** 2)) or (A chameleon is an insect.))) and ((not ((6 - -8) <= (11 - -4))) or ((16 + 17) > (-8 + 9)) or ((((3 - -14) <= (19 - 8)) and ((A day on Earth is 24 hours.) or (A snake is a reptile.))) and ((Penguins can fly.) or (((0 + -16) != (-2 * 3 - 3 * 6)) and (The 1968 Olympics were held in Los Angeles.)))))\nD. (not ((not not (A bat is a mammal.)) or (not not (not (The capital of Peru is Lima.))))) and (not not (((not not ((2 ** 2) <= (-8 + 12) <= (19 + 18))) and (((12 + -8) < (2 - 12)) or ((19 * 8) > (-7 - -9)))) and ((((18 - -19) < (-9 * 1) < (14 - 15)) or (Uranus is the 1st planet from the Sun.)) and (not (There are 31 days in June.)))))\nE. ((not not (((Iron is a solid at room temperature.) and (The chemical symbol for Chlorine is Mg.)) and (not not (Uranus is the 6th planet from the Sun.)))) or ((The chemical symbol for Silver is Cr.) and ((Uranus is the 4th planet from the Sun.) and (84 is a prime number.)))) and (not not ((The 1904 Olympics were held in St. Louis.) and ((((3 ** 3) >= (-8 - -9)) and ((-12 + -6) <= (-11 + 10) <= (-12 - -12))) or ((-6 - 0) <= (-13 + -11)))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
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"language": "en",
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"seed": 10088507,
"true_count": 1
},
"seed": 10088507,
"task_id": 610088507,
"task_type": "boolean_expressions"
} |
logic-v2 | 请评估以下布尔表达式，选择其中为真的选项：
A. (not (not not ((not not (金星是距离太阳第2近的行星。)) or (not not ((17 - 5) >= (14 + -17)))))) and (not not ((((14 * 9) <= (-10 * -6 * -3 * 4)) and (((-12 * 18) != (-15 - 9)) or (狗有6条腿。))) or ((尼日利亚位于非洲。) and ((43 % 4) <= (-4 - -17))) or ((((-14 - 17) > (-3 * -5)) or (法国大革命开始发生在1789年。)) or (not not (泰国的首都是曼谷。)))))
B. not not ((((日本位于欧洲。) or (not (人类有2条腿。))) or (((-16 * -3) <= (-8 * 3 + -1 * -10)) and ((-18 - 3) < (-2 * 9 * 6 * -3))) or ((not not ((13 - 12) < (-9 - 15))) or ((土星是距离太阳第5近的行星。) and ((-2 * 19) != (-17 - 3))))) or (not (not (((5 * 3 - -8 * 5) == (10 * -3 - -6 * 4)) or (人类只使用了大脑的10%。)))))
C. (((氮气在常温下是气体。) and (((18 + -5) < (-3 * -9 * -1 * -2) < (4 * -9)) and ((-19 + 14) >= (2 - -18)))) and (((1 ** 2) > (0 - 10)) and ((20是完全平方数。) or (3是质数。)) and (2是完全平方数。))) and (not ((not ((铁的化学符号是U。) or ((1 ** 2) == (-19 - -14)))) or (((第二次世界大战开始发生在1938年。) and ((-3 - -20) != (2 % 2))) and ((-13 - -17) == (-17 + 5)))))
D. (((((德国位于非洲。) or (1952年奥运会在雅典举办。)) or ((越南的货币是比索。) or (1964年奥运会在东京举办。))) and ((20 - 20) <= (-9 - -7))) and (((20 + -9) < (-1 + 0) < (10 * -2 * 6 * 5)) and ((水在常温下是气体。) and (爱尔兰的首都是里斯本。))) and (not not (not (地球是距离太阳第1近的行星。)))) or (not not (not not ((57是奇数。) or ((-5 + -19) <= (-8 * 5 * -9 * 9) <= (16 * -4))))) or (((((1968年是闰年。) and (瑞典的首都是莫斯科。)) and ((4 - -5) < (-19 + -6))) or (not ((埃及的货币是卢比。) or (芬兰的首都是莫斯科。)))) or (not (越南的货币是克朗。)))
E. not ((not ((((20 - -8) <= (-9 + 14)) or (木头在常温下是固体。)) or ((人类只使用了大脑的10%。) or ((7 + 5) > (20 - -1))))) or (not not (古巴的首都是墨西哥城。)))
F. (((水在常温下是液体。) and ((((-9 * -6 + 0 * -5) > (-2 * 0 * -9 * 9)) or (氖的化学符号是Fe。)) and (not not ((11 * -20) > (20 % 1))))) or (not not (马来西亚的货币是福林。))) or (not ((not not (((-13 - 8) != (-6 * 3 + 8 * -6)) and (82是偶数。))) and (((第二次世界大战开始发生在1939年。) or (英国位于欧洲。)) or (not not (苏联解体发生在1981年。)))))
G. (((((4 * 4) <= (3 * 1 - 10 * 1) <= (14 + -12)) and (天王星是距离太阳第7近的行星。)) or ((29 % 6) < (20 * 15) < (6 * -2))) or ((not not (钠的化学符号是Na。)) or (鳄鱼是爬行动物。)) or ((((17 + -13) > (3 + 2)) or (水星是距离太阳第1近的行星。)) and ((((11 * 20) > (11 * -11)) or ((19 - -10) > (-7 * -7))) and (((-18 + 2) == (20 * 7)) and (第二次世界大战结束发生在1945年。))))) and (not (((9 * -4 + 9 * -4) < (11 * -11) < (21 % 9)) and ((2065年是闰年。) or (英国位于欧洲。)))) and (not (not (((油在常温下是液体。) or ((0 - 9) < (0 + 18))) and (8小于等于10。))))
哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \boxed{} 中。 | {
"game_data": {
"answer": "D,E,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 79359989,
"true_count": 3
},
"question": "请评估以下布尔表达式，选择其中为真的选项：\n\nA. (not (not not ((not not (金星是距离太阳第2近的行星。)) or (not not ((17 - 5) >= (14 + -17)))))) and (not not ((((14 * 9) <= (-10 * -6 * -3 * 4)) and (((-12 * 18) != (-15 - 9)) or (狗有6条腿。))) or ((尼日利亚位于非洲。) and ((43 % 4) <= (-4 - -17))) or ((((-14 - 17) > (-3 * -5)) or (法国大革命开始发生在1789年。)) or (not not (泰国的首都是曼谷。)))))\nB. not not ((((日本位于欧洲。) or (not (人类有2条腿。))) or (((-16 * -3) <= (-8 * 3 + -1 * -10)) and ((-18 - 3) < (-2 * 9 * 6 * -3))) or ((not not ((13 - 12) < (-9 - 15))) or ((土星是距离太阳第5近的行星。) and ((-2 * 19) != (-17 - 3))))) or (not (not (((5 * 3 - -8 * 5) == (10 * -3 - -6 * 4)) or (人类只使用了大脑的10%。)))))\nC. (((氮气在常温下是气体。) and (((18 + -5) < (-3 * -9 * -1 * -2) < (4 * -9)) and ((-19 + 14) >= (2 - -18)))) and (((1 ** 2) > (0 - 10)) and ((20是完全平方数。) or (3是质数。)) and (2是完全平方数。))) and (not ((not ((铁的化学符号是U。) or ((1 ** 2) == (-19 - -14)))) or (((第二次世界大战开始发生在1938年。) and ((-3 - -20) != (2 % 2))) and ((-13 - -17) == (-17 + 5)))))\nD. (((((德国位于非洲。) or (1952年奥运会在雅典举办。)) or ((越南的货币是比索。) or (1964年奥运会在东京举办。))) and ((20 - 20) <= (-9 - -7))) and (((20 + -9) < (-1 + 0) < (10 * -2 * 6 * 5)) and ((水在常温下是气体。) and (爱尔兰的首都是里斯本。))) and (not not (not (地球是距离太阳第1近的行星。)))) or (not not (not not ((57是奇数。) or ((-5 + -19) <= (-8 * 5 * -9 * 9) <= (16 * -4))))) or (((((1968年是闰年。) and (瑞典的首都是莫斯科。)) and ((4 - -5) < (-19 + -6))) or (not ((埃及的货币是卢比。) or (芬兰的首都是莫斯科。)))) or (not (越南的货币是克朗。)))\nE. not ((not ((((20 - -8) <= (-9 + 14)) or (木头在常温下是固体。)) or ((人类只使用了大脑的10%。) or ((7 + 5) > (20 - -1))))) or (not not (古巴的首都是墨西哥城。)))\nF. (((水在常温下是液体。) and ((((-9 * -6 + 0 * -5) > (-2 * 0 * -9 * 9)) or (氖的化学符号是Fe。)) and (not not ((11 * -20) > (20 % 1))))) or (not not (马来西亚的货币是福林。))) or (not ((not not (((-13 - 8) != (-6 * 3 + 8 * -6)) and (82是偶数。))) and (((第二次世界大战开始发生在1939年。) or (英国位于欧洲。)) or (not not (苏联解体发生在1981年。)))))\nG. (((((4 * 4) <= (3 * 1 - 10 * 1) <= (14 + -12)) and (天王星是距离太阳第7近的行星。)) or ((29 % 6) < (20 * 15) < (6 * -2))) or ((not not (钠的化学符号是Na。)) or (鳄鱼是爬行动物。)) or ((((17 + -13) > (3 + 2)) or (水星是距离太阳第1近的行星。)) and ((((11 * 20) > (11 * -11)) or ((19 - -10) > (-7 * -7))) and (((-18 + 2) == (20 * 7)) and (第二次世界大战结束发生在1945年。))))) and (not (((9 * -4 + 9 * -4) < (11 * -11) < (21 % 9)) and ((2065年是闰年。) or (英国位于欧洲。)))) and (not (not (((油在常温下是液体。) or ((0 - 9) < (0 + 18))) and (8小于等于10。))))\n\n哪些选项的值为真？请列出所有为真的选项标识，用逗号分隔，填入 \\boxed{} 中。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 79359989,
"true_count": 3
},
"seed": 79359989,
"task_id": 679359989,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. not (((92是斐波那契数。) and (79能被6整除。)) and ((铁的化学符号是Ag。) and (铀的化学符号是U。)))
B. ((-2 - 14) <= (0 - 1)) and ((2059年是闰年。) or (((-7 * -5 * 1 * -2) >= (-11 - -11)) or (加拿大的货币是加元。)))
C. (217是斐波那契数。) and ((not (2013年是闰年。)) or ((九月有28天。) and (蜥蜴是爬行动物。)))
D. (not not (1968年奥运会在伦敦举办。)) and (((日本的货币是美元。) or ((17 - 10) > (2 ** 3))) or ((第二次世界大战结束发生在1946年。) or ((0 * -4 * -10 * 2) <= (7 - 8))))
E. not not ((not (法国位于欧洲。)) or (((-12 + 2) > (16 - 4)) and ((43 % 3) >= (3 ** 2))))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 56338588,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. not (((92是斐波那契数。) and (79能被6整除。)) and ((铁的化学符号是Ag。) and (铀的化学符号是U。)))\nB. ((-2 - 14) <= (0 - 1)) and ((2059年是闰年。) or (((-7 * -5 * 1 * -2) >= (-11 - -11)) or (加拿大的货币是加元。)))\nC. (217是斐波那契数。) and ((not (2013年是闰年。)) or ((九月有28天。) and (蜥蜴是爬行动物。)))\nD. (not not (1968年奥运会在伦敦举办。)) and (((日本的货币是美元。) or ((17 - 10) > (2 ** 3))) or ((第二次世界大战结束发生在1946年。) or ((0 * -4 * -10 * 2) <= (7 - 8))))\nE. not not ((not (法国位于欧洲。)) or (((-12 + 2) > (16 - 4)) and ((43 % 3) >= (3 ** 2))))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 56338588,
"true_count": 2
},
"seed": 56338588,
"task_id": 656338588,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. (((not ((7 * -1) >= (33 % 1))) or ((4 + -15) == (3 * -4 + 8 * -5))) and (not not (冰的密度比液态水小。)) and (not (not (not not (光速比声速快。))))) and (((((1904年奥运会在圣路易斯举办。) or ((3 ** 3) == (3 + 1))) and (2039年是闰年。)) and ((美国位于北美洲。) or (金星是距离太阳第2近的行星。)) and (氮气在常温下是气体。)) or (((((46 % 6) > (7 * 5 - 6 * 4)) and (爱尔兰的首都是都柏林。)) or ((43 % 6) < (-19 - -7))) or ((蝙蝠是瞎的。) and ((6 + -18) <= (5 ** 2) <= (13 + -13))) or (((水在海平面上的沸点是100摄氏度。) and ((1 ** 3) <= (2 ** 3))) and ((三月有31天。) and (870是斐波那契数。)))))
B. (not ((((-14 * 17) != (20 - 7)) and ((-1 * 3 * -6 * 4) < (2 ** 2))) or ((鸭子是鱼类。) and ((0 * -1 * -6 * 7) <= (-2 * 20))) or ((天王星是距离太阳第7近的行星。) and (not not (俄罗斯的货币是英镑。))))) or (not not ((蜥蜴是爬行动物。) or (((-19 * -15) <= (-7 * -7)) or ((13 - 19) == (9 * 16))))) or ((not ((59大于68。) or (木星是距离太阳第2近的行星。))) or (((银的化学符号是Ag。) or ((18 * 4) > (4 ** 2))) or (章鱼有4条腿。)))
C. ((not (67大于8。)) and ((not not (not (水星是距离太阳第1近的行星。))) or (铜在常温下是固体。))) or ((not not (钻石由碳元素组成。)) or ((not not (((2 ** 2) >= (8 * 13)) and (哥伦比亚的货币是人民币。))) and (鲨鱼是哺乳动物。)))
D. (((62能被2整除。) or (金星是距离太阳第2近的行星。)) or (not (人体有150块骨头。))) and (not not (91能被7整除。)) and (not ((not not (苏联解体发生在1990年。)) or (((鲸鱼是鱼类。) or ((2 + -6) > (3 + 18))) or (月球绕地球运转。))))
E. not (not not (((((-13 * -18) < (-7 * -8 * 6 * -6)) or ((9 * 6 * 7 * 1) < (16 + 10))) or (((6 * 6 * -9 * 4) != (-3 * -14)) and (铬的化学符号是S。))) and ((波兰的首都是华沙。) and (179是斐波那契数。))))
F. not (not not (((-19 + -17) == (-6 * -7 + -1 * -8)) and (莱特兄弟首次飞行发生在1903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,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 17091040,
"true_count": 4
},
"question": "研究以下逻辑语句：\n\nA. (((not ((7 * -1) >= (33 % 1))) or ((4 + -15) == (3 * -4 + 8 * -5))) and (not not (冰的密度比液态水小。)) and (not (not (not not (光速比声速快。))))) and (((((1904年奥运会在圣路易斯举办。) or ((3 ** 3) == (3 + 1))) and (2039年是闰年。)) and ((美国位于北美洲。) or (金星是距离太阳第2近的行星。)) and (氮气在常温下是气体。)) or (((((46 % 6) > (7 * 5 - 6 * 4)) and (爱尔兰的首都是都柏林。)) or ((43 % 6) < (-19 - -7))) or ((蝙蝠是瞎的。) and ((6 + -18) <= (5 ** 2) <= (13 + -13))) or (((水在海平面上的沸点是100摄氏度。) and ((1 ** 3) <= (2 ** 3))) and ((三月有31天。) and (870是斐波那契数。)))))\nB. (not ((((-14 * 17) != (20 - 7)) and ((-1 * 3 * -6 * 4) < (2 ** 2))) or ((鸭子是鱼类。) and ((0 * -1 * -6 * 7) <= (-2 * 20))) or ((天王星是距离太阳第7近的行星。) and (not not (俄罗斯的货币是英镑。))))) or (not not ((蜥蜴是爬行动物。) or (((-19 * -15) <= (-7 * -7)) or ((13 - 19) == (9 * 16))))) or ((not ((59大于68。) or (木星是距离太阳第2近的行星。))) or (((银的化学符号是Ag。) or ((18 * 4) > (4 ** 2))) or (章鱼有4条腿。)))\nC. ((not (67大于8。)) and ((not not (not (水星是距离太阳第1近的行星。))) or (铜在常温下是固体。))) or ((not not (钻石由碳元素组成。)) or ((not not (((2 ** 2) >= (8 * 13)) and (哥伦比亚的货币是人民币。))) and (鲨鱼是哺乳动物。)))\nD. (((62能被2整除。) or (金星是距离太阳第2近的行星。)) or (not (人体有150块骨头。))) and (not not (91能被7整除。)) and (not ((not not (苏联解体发生在1990年。)) or (((鲸鱼是鱼类。) or ((2 + -6) > (3 + 18))) or (月球绕地球运转。))))\nE. not (not not (((((-13 * -18) < (-7 * -8 * 6 * -6)) or ((9 * 6 * 7 * 1) < (16 + 10))) or (((6 * 6 * -9 * 4) != (-3 * -14)) and (铬的化学符号是S。))) and ((波兰的首都是华沙。) and (179是斐波那契数。))))\nF. not (not not (((-19 + -17) == (-6 * -7 + -1 * -8)) and (莱特兄弟首次飞行发生在1903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": 5,
"language": "cn",
"num_options": 6,
"seed": 17091040,
"true_count": 4
},
"seed": 17091040,
"task_id": 617091040,
"task_type": "boolean_expressions"
} |
logic-v2 | 评估以下每个表达式：
A. ((-10 * 9 - 4 * -1) <= (2 * -8)) and (((15 - 15) < (8 * -1 * 2 * 1)) and (265是完全平方数。))
B. 海王星是距离太阳第4近的行星。
C. (4 ** 1) == (1 * -6 * 2 * -7)
D. (((-5 * 7) < (9 - 7) < (-10 * -10 + -1 * -8)) or ((16 - 14) > (-9 * 7 * -4 * 7))) and ((0 * -6 * -8 * 6) > (-10 - 7))
E. (-20 - 17) <= (2 ** 3) <= (-7 - -14)
F. ((-20 - -8) != (4 * 7 * -6 * -6)) and (not not (加拿大的首都是马德里。))
列出所有值为 True 的选项，在 \boxed{} 中用逗号分隔。 | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 58091225,
"true_count": 1
},
"question": "评估以下每个表达式：\n\nA. ((-10 * 9 - 4 * -1) <= (2 * -8)) and (((15 - 15) < (8 * -1 * 2 * 1)) and (265是完全平方数。))\nB. 海王星是距离太阳第4近的行星。\nC. (4 ** 1) == (1 * -6 * 2 * -7)\nD. (((-5 * 7) < (9 - 7) < (-10 * -10 + -1 * -8)) or ((16 - 14) > (-9 * 7 * -4 * 7))) and ((0 * -6 * -8 * 6) > (-10 - 7))\nE. (-20 - 17) <= (2 ** 3) <= (-7 - -14)\nF. ((-20 - -8) != (4 * 7 * -6 * -6)) and (not not (加拿大的首都是马德里。))\n\n列出所有值为 True 的选项，在 \\boxed{} 中用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 58091225,
"true_count": 1
},
"seed": 58091225,
"task_id": 658091225,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. 埃及位于欧洲。
B. not ((10 - 0) > (18 - 4))
C. (39 % 4) > (-4 - -12)
D. (3 ** 1) == (-11 * 14)
E. 希腊的首都是雅典。
F. ((第二次世界大战开始发生在1934年。) or (土星是距离太阳第1近的行星。)) or ((-20 - -7) == (10 * 7 + -4 * -6))
G. not not (铜的化学符号是P。)
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 89785380,
"true_count": 2
},
"question": "下面是几个布尔表达式：\n\nA. 埃及位于欧洲。\nB. not ((10 - 0) > (18 - 4))\nC. (39 % 4) > (-4 - -12)\nD. (3 ** 1) == (-11 * 14)\nE. 希腊的首都是雅典。\nF. ((第二次世界大战开始发生在1934年。) or (土星是距离太阳第1近的行星。)) or ((-20 - -7) == (10 * 7 + -4 * -6))\nG. not not (铜的化学符号是P。)\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 89785380,
"true_count": 2
},
"seed": 89785380,
"task_id": 689785380,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not (not (The currency of Switzerland is the Naira.))
B. ((Uranus is the 7th planet from the Sun.) and (((-12 * -6) <= (16 + -3) <= (16 - 14)) or (not not (Oxygen is necessary for human survival.)))) or ((There are 28 days in September.) or (not not (((13 - -8) == (5 - 6)) and (The capital of Japan is Tokyo.))))
C. not ((not not (((44 % 8) == (18 * 7)) and ((2 ** 3) < (24 % 8)))) and ((The capital of Romania is Seoul.) and ((8 - 3) <= (5 - 16))))
D. not not (((((0 * 6 - 0 * 5) != (10 * 6 * -5 * 0)) or (The currency of United States is the Lira.)) or (The 1896 Olympics were held in Athens.)) and (The capital of Norway is Berlin.))
E. ((((1 + -20) < (32 % 3)) or ((-6 * -7) > (5 ** 1))) and (((Brazil is in North America.) and ((-8 * -4 + -4 * 9) < (-16 * 10) < (17 + 5))) and (not ((4 * 9) < (3 * 12) < (-17 + -18))))) and (((not not ((-16 * -7) <= (-4 * 9 + 9 * 2))) or ((World War II ended occurred in 1945.) or ((25 % 9) >= (4 ** 3)))) or ((((7 * -3 * 1 * -2) >= (-14 * 17)) or ((33 % 7) < (9 * -4 - -9 * 7))) and ((The 1920 Olympics were held in Montreal.) and (There are 31 days in January.))))
F. (not not (not not (((5 ** 3) <= (6 * 2 + 6 * -1)) and (World War II ended occurred in 1945.)))) or ((-2 * -10) != (19 + -20)) or ((not (((4 * 5 + -4 * -10) <= (21 % 6)) or (The chemical symbol for Tin is Au.))) or ((The 1972 Olympics were held in Munich.) and (83 is divisible by 7.)) or (not (((26 % 4) != (39 % 2)) or (Mercury is a liquid at room temperature.))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,B,C,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 46813411,
"true_count": 4
},
"question": "Evaluate each expression below:\n\nA. not not (not (The currency of Switzerland is the Naira.))\nB. ((Uranus is the 7th planet from the Sun.) and (((-12 * -6) <= (16 + -3) <= (16 - 14)) or (not not (Oxygen is necessary for human survival.)))) or ((There are 28 days in September.) or (not not (((13 - -8) == (5 - 6)) and (The capital of Japan is Tokyo.))))\nC. not ((not not (((44 % 8) == (18 * 7)) and ((2 ** 3) < (24 % 8)))) and ((The capital of Romania is Seoul.) and ((8 - 3) <= (5 - 16))))\nD. not not (((((0 * 6 - 0 * 5) != (10 * 6 * -5 * 0)) or (The currency of United States is the Lira.)) or (The 1896 Olympics were held in Athens.)) and (The capital of Norway is Berlin.))\nE. ((((1 + -20) < (32 % 3)) or ((-6 * -7) > (5 ** 1))) and (((Brazil is in North America.) and ((-8 * -4 + -4 * 9) < (-16 * 10) < (17 + 5))) and (not ((4 * 9) < (3 * 12) < (-17 + -18))))) and (((not not ((-16 * -7) <= (-4 * 9 + 9 * 2))) or ((World War II ended occurred in 1945.) or ((25 % 9) >= (4 ** 3)))) or ((((7 * -3 * 1 * -2) >= (-14 * 17)) or ((33 % 7) < (9 * -4 - -9 * 7))) and ((The 1920 Olympics were held in Montreal.) and (There are 31 days in January.))))\nF. (not not (not not (((5 ** 3) <= (6 * 2 + 6 * -1)) and (World War II ended occurred in 1945.)))) or ((-2 * -10) != (19 + -20)) or ((not (((4 * 5 + -4 * -10) <= (21 % 6)) or (The chemical symbol for Tin is Au.))) or ((The 1972 Olympics were held in Munich.) and (83 is divisible by 7.)) or (not (((26 % 4) != (39 % 2)) or (Mercury is a liquid at room temperature.))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 46813411,
"true_count": 4
},
"seed": 46813411,
"task_id": 646813411,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not not (The 2004 Olympics were held in Antwerp.)
B. (not ((4 + -20) > (27 % 10))) and ((85 is less than or equal to 71.) or ((-1 + 9) > (-16 - -7)))
C. (not not (1933 is a leap year.)) or ((35 % 10) < (4 * -3 + -3 * 2))
D. (not (2094 is a leap year.)) and ((1 ** 3) >= (-5 + 16))
E. ((A duck has 2 legs.) and (The square root of 100 is 10.)) or (((-14 - 1) > (13 - -9)) or (The capital of Spain is Budapest.))
F. not not (not ((37 % 4) < (3 ** 2)))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 71483346,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not not (The 2004 Olympics were held in Antwerp.)\nB. (not ((4 + -20) > (27 % 10))) and ((85 is less than or equal to 71.) or ((-1 + 9) > (-16 - -7)))\nC. (not not (1933 is a leap year.)) or ((35 % 10) < (4 * -3 + -3 * 2))\nD. (not (2094 is a leap year.)) and ((1 ** 3) >= (-5 + 16))\nE. ((A duck has 2 legs.) and (The square root of 100 is 10.)) or (((-14 - 1) > (13 - -9)) or (The capital of Spain is Budapest.))\nF. not not (not ((37 % 4) < (3 ** 2)))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 71483346,
"true_count": 2
},
"seed": 71483346,
"task_id": 671483346,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. (-1 * 17) <= (19 % 10)
B. not not (((-16 + 12) != (10 * -1 + 0 * 9)) and (Alcohol is a liquid at room temperature.))
C. (-18 * -20) <= (4 ** 2)
D. ((2003 is a leap year.) and ((6 * 8 - 4 * 9) < (16 + -12))) and (not (16 is divisible by 8.))
E. The 1932 Olympics were held in Los Angeles.
F. (((-15 * -13) <= (-3 - 20)) and (China is in Asia.)) or (not not ((2 * -5 + 0 * 0) >= (15 + 12)))
G. ((Japan is in Asia.) and (218 is a perfect square.)) or ((The square root of 225 is 15.) and (The chemical symbol for Hydrogen is Pt.))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
"game_data": {
"answer": "A,B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 11895766,
"true_count": 3
},
"question": "Given the following boolean expressions:\n\nA. (-1 * 17) <= (19 % 10)\nB. not not (((-16 + 12) != (10 * -1 + 0 * 9)) and (Alcohol is a liquid at room temperature.))\nC. (-18 * -20) <= (4 ** 2)\nD. ((2003 is a leap year.) and ((6 * 8 - 4 * 9) < (16 + -12))) and (not (16 is divisible by 8.))\nE. The 1932 Olympics were held in Los Angeles.\nF. (((-15 * -13) <= (-3 - 20)) and (China is in Asia.)) or (not not ((2 * -5 + 0 * 0) >= (15 + 12)))\nG. ((Japan is in Asia.) and (218 is a perfect square.)) or ((The square root of 225 is 15.) and (The chemical symbol for Hydrogen is Pt.))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 11895766,
"true_count": 3
},
"seed": 11895766,
"task_id": 611895766,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((五月有31天。) and (俄罗斯的货币是英镑。)) and ((1933年是闰年。) or (第一次世界大战开始发生在1915年。))
B. not ((19 * -5) <= (4 * -9) <= (18 * -14))
C. (1997年是闰年。) and ((2 ** 3) >= (-12 * -9))
D. (8 * 8 + -6 * -3) > (8 * 15)
E. (not not ((-10 * -8 - 6 * 9) <= (6 * 6 - -5 * 7))) and ((289是完全平方数。) and (马来西亚的首都是吉隆坡。))
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,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 5,
"seed": 77619015,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. ((五月有31天。) and (俄罗斯的货币是英镑。)) and ((1933年是闰年。) or (第一次世界大战开始发生在1915年。))\nB. not ((19 * -5) <= (4 * -9) <= (18 * -14))\nC. (1997年是闰年。) and ((2 ** 3) >= (-12 * -9))\nD. (8 * 8 + -6 * -3) > (8 * 15)\nE. (not not ((-10 * -8 - 6 * 9) <= (6 * 6 - -5 * 7))) and ((289是完全平方数。) and (马来西亚的首都是吉隆坡。))\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": 5,
"seed": 77619015,
"true_count": 2
},
"seed": 77619015,
"task_id": 677619015,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. The 1936 Olympics were held in Berlin.
B. not not (There are 30 days in January.)
C. The capital of Indonesia is Manila.
D. (-13 - -20) > (5 * 4 + 3 * -7)
E. (-10 * 0) < (9 + -5) < (5 * 4)
F. The chemical symbol for Chromium is Fe.
G. ((The 1972 Olympics were held in Rio de Janeiro.) and (The square root of 9 is 2.)) or (not (Oil is a liquid at room temperature.))
H. not (((-2 * -6 - -5 * -2) == (-13 + -18)) or ((18 - -10) >= (6 - 14)))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 79101951,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. The 1936 Olympics were held in Berlin.\nB. not not (There are 30 days in January.)\nC. The capital of Indonesia is Manila.\nD. (-13 - -20) > (5 * 4 + 3 * -7)\nE. (-10 * 0) < (9 + -5) < (5 * 4)\nF. The chemical symbol for Chromium is Fe.\nG. ((The 1972 Olympics were held in Rio de Janeiro.) and (The square root of 9 is 2.)) or (not (Oil is a liquid at room temperature.))\nH. not (((-2 * -6 - -5 * -2) == (-13 + -18)) or ((18 - -10) >= (6 - 14)))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 79101951,
"true_count": 3
},
"seed": 79101951,
"task_id": 679101951,
"task_type": "boolean_expressions"
} |
logic-v2 | Below are several boolean expressions:
A. (10 * 0) < (11 - 1)
B. (((5 ** 3) < (10 - -16) < (-15 + 11)) or (The capital of Norway is Rome.)) and ((The capital of Brazil is Brasilia.) or (The capital of Saudi Arabia is Madrid.))
C. The 2000 Olympics were held in Sydney.
D. not ((The 1908 Olympics were held in Seoul.) and (The 1984 Olympics were held in Athens.))
E. (not not (212 is a perfect square.)) or (((20 * -14) < (-5 * -5 * 8 * 6) < (-3 * 2 - 10 * -6)) and (A lobster has 10 legs.))
F. not ((Uranus is the 3rd planet from the Sun.) or ((9 % 9) != (18 * 17)))
Identify all expressions that are true. Answer with the option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 24135783,
"true_count": 3
},
"question": "Below are several boolean expressions:\n\nA. (10 * 0) < (11 - 1)\nB. (((5 ** 3) < (10 - -16) < (-15 + 11)) or (The capital of Norway is Rome.)) and ((The capital of Brazil is Brasilia.) or (The capital of Saudi Arabia is Madrid.))\nC. The 2000 Olympics were held in Sydney.\nD. not ((The 1908 Olympics were held in Seoul.) and (The 1984 Olympics were held in Athens.))\nE. (not not (212 is a perfect square.)) or (((20 * -14) < (-5 * -5 * 8 * 6) < (-3 * 2 - 10 * -6)) and (A lobster has 10 legs.))\nF. not ((Uranus is the 3rd planet from the Sun.) or ((9 % 9) != (18 * 17)))\n\nIdentify all expressions that are true. Answer with the option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 6,
"seed": 24135783,
"true_count": 3
},
"seed": 24135783,
"task_id": 624135783,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (2077年是闰年。) or ((2070年是闰年。) and (瑞典的首都是斯德哥尔摩。)) or (not not (((5 ** 3) != (-4 - 0)) or (人类首次登月发生在1969年。)))
B. ((鲨鱼是哺乳动物。) and ((第二次世界大战开始发生在1939年。) and ((6 + -1) <= (14 + 14)))) or (50是质数。) or (摩洛哥位于非洲。)
C. ((not ((20 + 8) <= (12 - -12))) or (((34 % 3) >= (6 - 3)) or ((13 - -17) < (-6 * 7 + 5 * -3) < (4 % 6)))) or (((7 * 0 * 2 * -5) < (17 - -11)) or (not not (巴西的货币是雷亚尔。)))
D. (((八月有31天。) or (十二月有31天。)) and (1908年奥运会在洛杉矶举办。)) or (((9 * 6) < (-4 + -5)) or ((1 + 6) <= (-11 - 17) <= (-3 * -7 * -3 * -6))) or ((铂的化学符号是Pt。) or (not (98小于等于29。)))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
"game_data": {
"answer": "A,B,C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 37187955,
"true_count": 4
},
"question": "下面是几个布尔表达式：\n\nA. (2077年是闰年。) or ((2070年是闰年。) and (瑞典的首都是斯德哥尔摩。)) or (not not (((5 ** 3) != (-4 - 0)) or (人类首次登月发生在1969年。)))\nB. ((鲨鱼是哺乳动物。) and ((第二次世界大战开始发生在1939年。) and ((6 + -1) <= (14 + 14)))) or (50是质数。) or (摩洛哥位于非洲。)\nC. ((not ((20 + 8) <= (12 - -12))) or (((34 % 3) >= (6 - 3)) or ((13 - -17) < (-6 * 7 + 5 * -3) < (4 % 6)))) or (((7 * 0 * 2 * -5) < (17 - -11)) or (not not (巴西的货币是雷亚尔。)))\nD. (((八月有31天。) or (十二月有31天。)) and (1908年奥运会在洛杉矶举办。)) or (((9 * 6) < (-4 + -5)) or ((1 + 6) <= (-11 - 17) <= (-3 * -7 * -3 * -6))) or ((铂的化学符号是Pt。) or (not (98小于等于29。)))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 4,
"seed": 37187955,
"true_count": 4
},
"seed": 37187955,
"task_id": 637187955,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. 1949 is a leap year.
B. ((-8 * -4 + -3 * -3) > (-7 * 8 * -1 * -8)) or (not not ((17 * 15) > (-9 - 7)))
C. not ((-20 + 0) < (7 + 1))
D. ((7 + 13) <= (-6 * -6 - 3 * 6)) or (((-15 - 5) == (-8 * -2 * 4 * -9)) and (The square root of 1 is 1.))
E. The currency of India is the Krone.
F. not ((6 * 9) == (3 ** 2))
G. (-5 * -3 * 7 * 5) <= (7 + -12)
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "B,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 13421706,
"true_count": 2
},
"question": "Evaluate each expression below:\n\nA. 1949 is a leap year.\nB. ((-8 * -4 + -3 * -3) > (-7 * 8 * -1 * -8)) or (not not ((17 * 15) > (-9 - 7)))\nC. not ((-20 + 0) < (7 + 1))\nD. ((7 + 13) <= (-6 * -6 - 3 * 6)) or (((-15 - 5) == (-8 * -2 * 4 * -9)) and (The square root of 1 is 1.))\nE. The currency of India is the Krone.\nF. not ((6 * 9) == (3 ** 2))\nG. (-5 * -3 * 7 * 5) <= (7 + -12)\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 13421706,
"true_count": 2
},
"seed": 13421706,
"task_id": 613421706,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. 2089 is a leap year.
B. (Oil is a solid at room temperature.) or ((3 % 7) == (10 * 8 + -4 * 4))
C. ((A lobster has 10 legs.) and ((47 % 10) <= (1 * 0 * -5 * -7) <= (-6 * -3 * 4 * -1))) or (((1 ** 1) != (-8 * -9)) and (There are 30 days in April.))
D. ((4 * 10 * 1 * -8) >= (-11 + -19)) and ((The capital of China is Beijing.) and ((13 + 17) < (7 + -18)))
E. ((A koala is a mammal.) and (Mercury is the 4th planet from the Sun.)) or ((The currency of China is the Pound.) or ((-14 - 1) != (1 ** 3)))
F. not not ((5 + -17) != (3 - 17))
G. (-8 * 4 * 3 * 3) < (-10 * -6 * 4 * 10) < (1 * -10 * -7 * -1)
H. (There are 28 days in April.) and (not (The Pacific Ocean is the largest ocean.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 8,
"seed": 34585068,
"true_count": 3
},
"question": "Examine these expressions:\n\nA. 2089 is a leap year.\nB. (Oil is a solid at room temperature.) or ((3 % 7) == (10 * 8 + -4 * 4))\nC. ((A lobster has 10 legs.) and ((47 % 10) <= (1 * 0 * -5 * -7) <= (-6 * -3 * 4 * -1))) or (((1 ** 1) != (-8 * -9)) and (There are 30 days in April.))\nD. ((4 * 10 * 1 * -8) >= (-11 + -19)) and ((The capital of China is Beijing.) and ((13 + 17) < (7 + -18)))\nE. ((A koala is a mammal.) and (Mercury is the 4th planet from the Sun.)) or ((The currency of China is the Pound.) or ((-14 - 1) != (1 ** 3)))\nF. not not ((5 + -17) != (3 - 17))\nG. (-8 * 4 * 3 * 3) < (-10 * -6 * 4 * 10) < (1 * -10 * -7 * -1)\nH. (There are 28 days in April.) and (not (The Pacific Ocean is the largest ocean.))\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": 34585068,
"true_count": 3
},
"seed": 34585068,
"task_id": 634585068,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. not not ((((1 ** 3) == (6 * -12)) or (1972年奥运会在慕尼黑举办。)) and ((-2 * -13) > (16 - -6)))
B. (not ((4 ** 2) != (15 * -18))) and ((10 + 10) <= (-8 * 7) <= (-19 - -13))
C. (钻石在常温下是固体。) or ((((17 * 8) > (0 - 3)) or (人体有206块骨头。)) and ((鸡是鸟类。) and (波兰的首都是华沙。)))
D. not ((-4 - 20) >= (1 - 15))
E. ((not (85是斐波那契数。)) and ((-13 - -3) <= (8 - 9))) or (((二氧化碳在常温下是固体。) and (新加坡的货币是新加坡元。)) or (((-19 * -19) > (-7 * 4 + -4 * 1)) or ((-4 * -2 - -5 * -6) <= (-20 + 7))))
哪些语句为真？在 \boxed{} 中填入所有为真的选项标识，用逗号分隔。 | {
"game_data": {
"answer": "A,C,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 14192137,
"true_count": 4
},
"question": "研究以下逻辑语句：\n\nA. not not ((((1 ** 3) == (6 * -12)) or (1972年奥运会在慕尼黑举办。)) and ((-2 * -13) > (16 - -6)))\nB. (not ((4 ** 2) != (15 * -18))) and ((10 + 10) <= (-8 * 7) <= (-19 - -13))\nC. (钻石在常温下是固体。) or ((((17 * 8) > (0 - 3)) or (人体有206块骨头。)) and ((鸡是鸟类。) and (波兰的首都是华沙。)))\nD. not ((-4 - 20) >= (1 - 15))\nE. ((not (85是斐波那契数。)) and ((-13 - -3) <= (8 - 9))) or (((二氧化碳在常温下是固体。) and (新加坡的货币是新加坡元。)) or (((-19 * -19) > (-7 * 4 + -4 * 1)) or ((-4 * -2 - -5 * -6) <= (-20 + 7))))\n\n哪些语句为真？在 \\boxed{} 中填入所有为真的选项标识，用逗号分隔。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 5,
"seed": 14192137,
"true_count": 4
},
"seed": 14192137,
"task_id": 614192137,
"task_type": "boolean_expressions"
} |
logic-v2 | 给定以下布尔表达式：
A. 阿根廷的货币是克朗。
B. (((4 ** 2) <= (5 ** 1)) or (海王星是距离太阳第3近的行星。)) and ((1 * -2 - 7 * 5) < (10 * -7 * -6 * -5))
C. not (not not ((45 % 1) < (-20 - 19) < (-7 * -10 - 5 * 6)))
D. 水星是距离太阳第1近的行星。
E. (not not (土星是距离太阳第6近的行星。)) and ((1912年奥运会在斯德哥尔摩举办。) or (铜在常温下是固体。))
F. (0 * 1 * 10 * 2) <= (20 - -12)
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,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 6,
"seed": 23915113,
"true_count": 4
},
"question": "给定以下布尔表达式：\n\nA. 阿根廷的货币是克朗。\nB. (((4 ** 2) <= (5 ** 1)) or (海王星是距离太阳第3近的行星。)) and ((1 * -2 - 7 * 5) < (10 * -7 * -6 * -5))\nC. not (not not ((45 % 1) < (-20 - 19) < (-7 * -10 - 5 * 6)))\nD. 水星是距离太阳第1近的行星。\nE. (not not (土星是距离太阳第6近的行星。)) and ((1912年奥运会在斯德哥尔摩举办。) or (铜在常温下是固体。))\nF. (0 * 1 * 10 * 2) <= (20 - -12)\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": 6,
"seed": 23915113,
"true_count": 4
},
"seed": 23915113,
"task_id": 623915113,
"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. (-7 * -10 * -8 * 9) < (19 + -7) < (10 * 3 - 4 * 2)
B. not not (((32 % 10) < (17 * 17) < (3 ** 2)) or (There are 30 days in July.))
C. (Alcohol is a liquid at room temperature.) and (not not (113 is a perfect square.))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 20691398,
"true_count": 1
},
"question": "Study the following logical statements:\n\nA. (-7 * -10 * -8 * 9) < (19 + -7) < (10 * 3 - 4 * 2)\nB. not not (((32 % 10) < (17 * 17) < (3 ** 2)) or (There are 30 days in July.))\nC. (Alcohol is a liquid at room temperature.) and (not not (113 is a perfect square.))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 3,
"seed": 20691398,
"true_count": 1
},
"seed": 20691398,
"task_id": 620691398,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not (not not (not not (not not ((not not (The capital of Russia is Moscow.)) or (The first Olympic Games of modern era occurred in 1896.)))))
B. not not (not (not not ((((3 * 16) > (-8 + -12)) or ((The 1960 Olympics were held in Beijing.) and (65 is an even number.))) and (((-9 * -7) >= (-17 + 10)) or (The chemical symbol for Chromium is Cr.)) and ((Earth is the 3rd planet from the Sun.) or (((18 - -9) > (20 * 6)) and (Uranus is the 5th planet from the Sun.))))))
C. not ((not not ((The 1984 Olympics were held in Los Angeles.) and (not not ((204 is a Fibonacci number.) or (The chemical symbol for Potassium is K.))))) or (((not (not (India is in South America.))) and ((((-18 - -17) == (2 ** 3)) or (Helium is a gas at room temperature.)) and ((2 * -3 * -4 * 0) >= (15 * -12)))) and (((16 * 20) <= (16 + 14)) and (Saturn is the 6th planet from the Sun.))))
D. not not (((((not ((-10 * 8 * 2 * 1) >= (9 - -12))) and ((The currency of Argentina is the Peso.) and ((5 - 12) >= (3 * -5 + 8 * -5)))) and (The 1912 Olympics were held in Munich.)) or (((not not ((1 ** 3) >= (3 ** 2))) and ((11 * -6) < (-2 * 6 + -4 * 8) < (-3 + 8))) and ((-7 * 9 * 6 * 1) < (14 * 9)))) and (not not (((851 is a Fibonacci number.) and ((-19 - -17) == (5 % 2))) and (Gold is a liquid at room temperature.))))
E. ((not not ((not not ((2 + -13) < (-1 - -15))) and (not (not (The Berlin Wall fell occurred in 1989.))))) and (not not (not (not not (((4 ** 2) >= (24 % 1)) or ((-5 * 10) > (-11 + -11))))))) and (not not (not not (not not (not ((-15 - -15) >= (5 + -17))))))
F. not (not (((Jupiter is the 6th planet from the Sun.) or ((((7 % 8) < (41 % 10)) or (The chemical symbol for Hydrogen is H.)) or ((The chemical symbol for Hydrogen is Ag.) or ((-5 + 7) > (35 % 5))))) and ((((World War II began occurred in 1939.) and (The capital of Italy is Rome.)) and ((Humans only use 10% of their brain.) or (A snake has 8 legs.))) and (The currency of Singapore is the Dong.) and (((7 - 9) < (16 - -5)) and ((A cat has 4 legs.) or ((-15 * -5) == (-11 - 17)))))))
G. (not (not not (((-8 - 1) < (14 - 4) < (1 ** 1)) or (not ((Steam is a gas at room temperature.) or (The chemical symbol for Chlorine is S.)))))) and (not (not not (A frog has 100 legs.))) and (not ((not (not (The currency of United States is the Dollar.))) or (((not not ((2 * 1 * 4 * -9) > (-2 * -9 * -4 * -5))) or (963 is a Fibonacci number.)) or (((1 ** 1) < (10 * 0) < (-3 - 8)) and ((The chemical symbol for Gold is Au.) and (The currency of Sweden is the Krona.))))))
H. not (not ((((((19 + 10) > (1 ** 1)) or (The Great Wall of China was built in one year.)) or ((The currency of Philippines is the Peso.) and (A butterfly has 6 legs.))) and (not (not ((-5 * -7 - 10 * 8) <= (33 % 9))))) or ((not (not ((26 % 8) <= (48 % 4) <= (7 + 19)))) or ((not (The chemical symbol for Platinum is Pt.)) and ((-3 * 15) <= (3 + -7))))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 2696887,
"true_count": 1
},
"question": "Evaluate each expression below:\n\nA. not (not not (not not (not not ((not not (The capital of Russia is Moscow.)) or (The first Olympic Games of modern era occurred in 1896.)))))\nB. not not (not (not not ((((3 * 16) > (-8 + -12)) or ((The 1960 Olympics were held in Beijing.) and (65 is an even number.))) and (((-9 * -7) >= (-17 + 10)) or (The chemical symbol for Chromium is Cr.)) and ((Earth is the 3rd planet from the Sun.) or (((18 - -9) > (20 * 6)) and (Uranus is the 5th planet from the Sun.))))))\nC. not ((not not ((The 1984 Olympics were held in Los Angeles.) and (not not ((204 is a Fibonacci number.) or (The chemical symbol for Potassium is K.))))) or (((not (not (India is in South America.))) and ((((-18 - -17) == (2 ** 3)) or (Helium is a gas at room temperature.)) and ((2 * -3 * -4 * 0) >= (15 * -12)))) and (((16 * 20) <= (16 + 14)) and (Saturn is the 6th planet from the Sun.))))\nD. not not (((((not ((-10 * 8 * 2 * 1) >= (9 - -12))) and ((The currency of Argentina is the Peso.) and ((5 - 12) >= (3 * -5 + 8 * -5)))) and (The 1912 Olympics were held in Munich.)) or (((not not ((1 ** 3) >= (3 ** 2))) and ((11 * -6) < (-2 * 6 + -4 * 8) < (-3 + 8))) and ((-7 * 9 * 6 * 1) < (14 * 9)))) and (not not (((851 is a Fibonacci number.) and ((-19 - -17) == (5 % 2))) and (Gold is a liquid at room temperature.))))\nE. ((not not ((not not ((2 + -13) < (-1 - -15))) and (not (not (The Berlin Wall fell occurred in 1989.))))) and (not not (not (not not (((4 ** 2) >= (24 % 1)) or ((-5 * 10) > (-11 + -11))))))) and (not not (not not (not not (not ((-15 - -15) >= (5 + -17))))))\nF. not (not (((Jupiter is the 6th planet from the Sun.) or ((((7 % 8) < (41 % 10)) or (The chemical symbol for Hydrogen is H.)) or ((The chemical symbol for Hydrogen is Ag.) or ((-5 + 7) > (35 % 5))))) and ((((World War II began occurred in 1939.) and (The capital of Italy is Rome.)) and ((Humans only use 10% of their brain.) or (A snake has 8 legs.))) and (The currency of Singapore is the Dong.) and (((7 - 9) < (16 - -5)) and ((A cat has 4 legs.) or ((-15 * -5) == (-11 - 17)))))))\nG. (not (not not (((-8 - 1) < (14 - 4) < (1 ** 1)) or (not ((Steam is a gas at room temperature.) or (The chemical symbol for Chlorine is S.)))))) and (not (not not (A frog has 100 legs.))) and (not ((not (not (The currency of United States is the Dollar.))) or (((not not ((2 * 1 * 4 * -9) > (-2 * -9 * -4 * -5))) or (963 is a Fibonacci number.)) or (((1 ** 1) < (10 * 0) < (-3 - 8)) and ((The chemical symbol for Gold is Au.) and (The currency of Sweden is the Krona.))))))\nH. not (not ((((((19 + 10) > (1 ** 1)) or (The Great Wall of China was built in one year.)) or ((The currency of Philippines is the Peso.) and (A butterfly has 6 legs.))) and (not (not ((-5 * -7 - 10 * 8) <= (33 % 9))))) or ((not (not ((26 % 8) <= (48 % 4) <= (7 + 19)))) or ((not (The chemical symbol for Platinum is Pt.)) and ((-3 * 15) <= (3 + -7))))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 8,
"seed": 2696887,
"true_count": 1
},
"seed": 2696887,
"task_id": 602696887,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. (2 * 0 + 2 * -1) <= (4 * 14)
B. (not not (165是完全平方数。)) and (not not ((-9 * 9 + 2 * -7) > (-12 - -6)))
C. (9 * -3 + -1 * 6) > (2 - -5)
D. (((9 + 10) != (42 % 5)) and (木星是距离太阳第1近的行星。)) or ((蝴蝶是昆虫。) and (莱特兄弟首次飞行发生在1902年。))
E. ((2014年是闰年。) or ((4 - 6) == (-6 - 20))) or (巴西位于欧洲。)
F. (((4 ** 3) <= (11 * 4)) and (金的化学符号是Na。)) or (蝴蝶有6条腿。)
G. 第一部iPhone发布发生在2012年。
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
"game_data": {
"answer": "A,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 75879338,
"true_count": 2
},
"question": "这里有一些需要评估的布尔表达式：\n\nA. (2 * 0 + 2 * -1) <= (4 * 14)\nB. (not not (165是完全平方数。)) and (not not ((-9 * 9 + 2 * -7) > (-12 - -6)))\nC. (9 * -3 + -1 * 6) > (2 - -5)\nD. (((9 + 10) != (42 % 5)) and (木星是距离太阳第1近的行星。)) or ((蝴蝶是昆虫。) and (莱特兄弟首次飞行发生在1902年。))\nE. ((2014年是闰年。) or ((4 - 6) == (-6 - 20))) or (巴西位于欧洲。)\nF. (((4 ** 3) <= (11 * 4)) and (金的化学符号是Na。)) or (蝴蝶有6条腿。)\nG. 第一部iPhone发布发生在2012年。\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 7,
"seed": 75879338,
"true_count": 2
},
"seed": 75879338,
"task_id": 675879338,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. (((The chemical symbol for Oxygen is Ni.) or (The Pacific Ocean is the largest ocean.) or ((4 + -17) != (-3 + 9))) or (not (not (not not (297 is a perfect square.))))) and ((((2 ** 1) <= (9 * 8 * 7 * -2)) and (not (5 is an odd number.)) and (((-8 * 3) != (-1 - 2)) and ((16 * 5) >= (3 + 9)))) and (not not ((((1 * 7 * -6 * 7) < (18 - -1) < (-5 + -3)) and (Mercury is the 1st planet from the Sun.)) or ((A sparrow is a bird.) or ((2 ** 3) != (-6 * 20))))))
B. (not not (not not ((((-13 + -11) < (0 - 3)) and (Silver is a liquid at room temperature.)) and (The currency of Denmark is the Naira.)))) or (not (not not ((not not (The 1948 Olympics were held in Rome.)) or (not ((15 - -17) != (35 % 1))))))
C. ((not not (The chemical symbol for Calcium is Ca.)) or ((((-4 * 4 + -2 * 1) > (-7 * -1 - 4 * -4)) or ((-16 * -1) > (49 % 2))) and (not not (The chemical symbol for Lead is Pb.))) or (((1 ** 1) < (4 % 5)) and (Alcohol is a gas at room temperature.))) or (not not (((not not ((-15 * 15) <= (-8 - 10) <= (16 % 9))) and (The 2016 Olympics were held in Rio de Janeiro.)) and (not ((4 * -10 - -5 * -3) != (9 - -16)))))
D. not (not (((11 + -20) == (7 + -8)) and (The capital of Czech Republic is Amsterdam.)))
E. not not (not not (not ((((1 ** 3) != (20 - 1)) or ((4 * -10 + 5 * 3) != (19 + 19))) and (((9 * 6 - -3 * -8) < (-18 - 11)) and (The chemical symbol for Chlorine is Cl.)))))
F. ((((-13 * -5) < (-20 * -14) < (46 % 1)) or (not ((-2 - -5) == (2 * -8 - -8 * 5))) or ((((16 - -3) == (-1 * 5 + -2 * 1)) or ((3 - -12) >= (17 * -14))) and (Venus is the 2nd planet from the Sun.))) or (((((-10 - -7) != (4 + 11)) and ((-11 * 18) != (15 * 3))) or (not not (Humans have five fingers on each hand.))) and (((22 % 1) <= (2 * 9 + 3 * 9)) or (not ((20 + 15) < (-2 * 0 * 9 * -3)))))) and (not not (not not (The currency of Poland is the Zloty.)))
G. (((18 is greater than 12.) or (The 2000 Olympics were held in Sydney.) or ((-14 * 9) < (7 * -9 * 9 * -1))) or (not not (not (((4 ** 3) != (5 ** 2)) or (110 is an odd number.))))) or (not ((not not (not not ((6 - 17) != (-2 * 4 * -8 * -10)))) or (Water is a liquid at room temperature.)))
H. (not (not (((152 is a perfect square.) and (A cow has 4 legs.)) or (not ((10 * -9 - -9 * 3) >= (19 + -3)))))) and (((The United States declared independence occurred in 1776.) and ((Neptune is the 8th planet from the Sun.) and (171 is a perfect square.))) and (The capital of Hungary is Nairobi.)) and (not not (not ((not not (Mars is the 4th planet from the Sun.)) and (((5 ** 1) > (1 ** 2)) or (The Sun revolves around the Earth.)))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
"game_data": {
"answer": "B,C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 78877742,
"true_count": 5
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. (((The chemical symbol for Oxygen is Ni.) or (The Pacific Ocean is the largest ocean.) or ((4 + -17) != (-3 + 9))) or (not (not (not not (297 is a perfect square.))))) and ((((2 ** 1) <= (9 * 8 * 7 * -2)) and (not (5 is an odd number.)) and (((-8 * 3) != (-1 - 2)) and ((16 * 5) >= (3 + 9)))) and (not not ((((1 * 7 * -6 * 7) < (18 - -1) < (-5 + -3)) and (Mercury is the 1st planet from the Sun.)) or ((A sparrow is a bird.) or ((2 ** 3) != (-6 * 20))))))\nB. (not not (not not ((((-13 + -11) < (0 - 3)) and (Silver is a liquid at room temperature.)) and (The currency of Denmark is the Naira.)))) or (not (not not ((not not (The 1948 Olympics were held in Rome.)) or (not ((15 - -17) != (35 % 1))))))\nC. ((not not (The chemical symbol for Calcium is Ca.)) or ((((-4 * 4 + -2 * 1) > (-7 * -1 - 4 * -4)) or ((-16 * -1) > (49 % 2))) and (not not (The chemical symbol for Lead is Pb.))) or (((1 ** 1) < (4 % 5)) and (Alcohol is a gas at room temperature.))) or (not not (((not not ((-15 * 15) <= (-8 - 10) <= (16 % 9))) and (The 2016 Olympics were held in Rio de Janeiro.)) and (not ((4 * -10 - -5 * -3) != (9 - -16)))))\nD. not (not (((11 + -20) == (7 + -8)) and (The capital of Czech Republic is Amsterdam.)))\nE. not not (not not (not ((((1 ** 3) != (20 - 1)) or ((4 * -10 + 5 * 3) != (19 + 19))) and (((9 * 6 - -3 * -8) < (-18 - 11)) and (The chemical symbol for Chlorine is Cl.)))))\nF. ((((-13 * -5) < (-20 * -14) < (46 % 1)) or (not ((-2 - -5) == (2 * -8 - -8 * 5))) or ((((16 - -3) == (-1 * 5 + -2 * 1)) or ((3 - -12) >= (17 * -14))) and (Venus is the 2nd planet from the Sun.))) or (((((-10 - -7) != (4 + 11)) and ((-11 * 18) != (15 * 3))) or (not not (Humans have five fingers on each hand.))) and (((22 % 1) <= (2 * 9 + 3 * 9)) or (not ((20 + 15) < (-2 * 0 * 9 * -3)))))) and (not not (not not (The currency of Poland is the Zloty.)))\nG. (((18 is greater than 12.) or (The 2000 Olympics were held in Sydney.) or ((-14 * 9) < (7 * -9 * 9 * -1))) or (not not (not (((4 ** 3) != (5 ** 2)) or (110 is an odd number.))))) or (not ((not not (not not ((6 - 17) != (-2 * 4 * -8 * -10)))) or (Water is a liquid at room temperature.)))\nH. (not (not (((152 is a perfect square.) and (A cow has 4 legs.)) or (not ((10 * -9 - -9 * 3) >= (19 + -3)))))) and (((The United States declared independence occurred in 1776.) and ((Neptune is the 8th planet from the Sun.) and (171 is a perfect square.))) and (The capital of Hungary is Nairobi.)) and (not not (not ((not not (Mars is the 4th planet from the Sun.)) and (((5 ** 1) > (1 ** 2)) or (The Sun revolves around the Earth.)))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 78877742,
"true_count": 5
},
"seed": 78877742,
"task_id": 678877742,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not not (not not (Iron is a liquid at room temperature.))) or ((6 + 20) > (1 ** 2)) or (not not (There are 31 days in March.))
B. not not ((not (not ((5 ** 1) == (-3 - 10)))) and (not not (not (The capital of Nigeria is Seoul.))))
C. ((not not (not not ((-9 + 7) > (6 + 3)))) or ((not not ((-7 + 12) > (-18 * -11))) or ((Colombia is in South America.) and (Russia is in Europe.)))) or (((((-5 - 7) > (-5 + -13)) and ((49 % 6) >= (5 * -8))) or (not not (Silver is a liquid at room temperature.))) and (not ((5 * -5 + 9 * 8) != (34 % 9))))
D. (not not ((The currency of Peru is the Sol.) or ((A butterfly has 6 legs.) and ((-12 - 12) < (1 ** 2))))) or (The 1964 Olympics were held in Tokyo.) or (((8 * -2) != (0 * 20)) or (((0 - -14) != (20 % 5)) or (Kenya is in Africa.)) or (not not (((4 * 2) >= (-7 * 4 - -6 * -1)) or (Diamond is a solid at room temperature.))))
E. ((not ((1963 is a leap year.) or (A spider has 8 legs.))) and ((17 * 17) < (-3 + 13))) or ((6 * 7) > (5 ** 2)) or (((-7 + 18) < (8 * -1)) and (not ((60 is divisible by 4.) or (82 is an even number.))))
F. ((not (((15 * 12) != (4 ** 2)) or ((1 * -18) != (13 + 0)))) or (not not (94 is a prime number.)) or ((not ((1 ** 1) >= (-7 + 15))) and (not (1939 is a leap year.)))) and (((8 - 13) != (-18 * 0)) or (not ((3 * 15) > (9 * -9 + 8 * -7))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 64281709,
"true_count": 5
},
"question": "Analyze these boolean expressions:\n\nA. (not not (not not (Iron is a liquid at room temperature.))) or ((6 + 20) > (1 ** 2)) or (not not (There are 31 days in March.))\nB. not not ((not (not ((5 ** 1) == (-3 - 10)))) and (not not (not (The capital of Nigeria is Seoul.))))\nC. ((not not (not not ((-9 + 7) > (6 + 3)))) or ((not not ((-7 + 12) > (-18 * -11))) or ((Colombia is in South America.) and (Russia is in Europe.)))) or (((((-5 - 7) > (-5 + -13)) and ((49 % 6) >= (5 * -8))) or (not not (Silver is a liquid at room temperature.))) and (not ((5 * -5 + 9 * 8) != (34 % 9))))\nD. (not not ((The currency of Peru is the Sol.) or ((A butterfly has 6 legs.) and ((-12 - 12) < (1 ** 2))))) or (The 1964 Olympics were held in Tokyo.) or (((8 * -2) != (0 * 20)) or (((0 - -14) != (20 % 5)) or (Kenya is in Africa.)) or (not not (((4 * 2) >= (-7 * 4 - -6 * -1)) or (Diamond is a solid at room temperature.))))\nE. ((not ((1963 is a leap year.) or (A spider has 8 legs.))) and ((17 * 17) < (-3 + 13))) or ((6 * 7) > (5 ** 2)) or (((-7 + 18) < (8 * -1)) and (not ((60 is divisible by 4.) or (82 is an even number.))))\nF. ((not (((15 * 12) != (4 ** 2)) or ((1 * -18) != (13 + 0)))) or (not not (94 is a prime number.)) or ((not ((1 ** 1) >= (-7 + 15))) and (not (1939 is a leap year.)))) and (((8 - 13) != (-18 * 0)) or (not ((3 * 15) > (9 * -9 + 8 * -7))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 64281709,
"true_count": 5
},
"seed": 64281709,
"task_id": 664281709,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not (not not (not not (((1 * 10 * 3 * -4) <= (-4 + -11)) and (not (not (Silver is a solid at room temperature.))))))
B. not not (not ((not not (The chemical symbol for Silicon is S.)) or (not not ((2065 is a leap year.) and (Uranus is the 2nd planet from the Sun.))) or (((The capital of Germany is Berlin.) or (((2 ** 3) < (15 % 5)) and (The capital of New Zealand is Bogota.))) and ((((14 % 3) != (7 - 2)) and ((-18 * -9) > (-2 + 8))) and (not ((10 + -18) > (13 % 7)))))))
C. not (not (not (not (not not ((Christopher Columbus reached America occurred in 1492.) or (The Titanic sank occurred in 1912.))))))
D. not (not not (not (not not ((40 % 7) == (-7 - 6)))))
E. ((not ((((The currency of United Kingdom is the Pound.) or (360 is a perfect square.)) and (not not ((-6 * -5 - -1 * 1) <= (-8 * 3 - 6 * 0)))) and ((5 ** 2) <= (2 ** 3)))) or ((not not (not not (((14 * -3) <= (2 ** 2)) or (Mercury is the 1st planet from the Sun.)))) and ((not (((1 ** 2) >= (4 + -8)) or (The capital of Peru is Lima.))) and (not (The human body has 206 bones.))))) or (not not (not not (not not (((22 % 7) <= (-9 + -7)) or ((1 ** 2) >= (2 % 9))))))
F. not (not ((((not ((38 % 9) > (18 * -14))) or (((16 % 6) < (1 ** 3) < (5 - 5)) and (The 1948 Olympics were held in London.))) and ((((5 * -11) >= (-11 * 2)) or (Light travels faster than sound.)) or (not ((9 - -17) >= (0 * 9 + 5 * 5))))) and ((9 * 4 + -5 * 5) == (3 ** 2)) and (((4 ** 1) > (10 * -10 - -1 * 2)) or ((6 * -8 - -8 * 2) < (14 * 14)))))
G. not not (not (not (not (A tiger is a mammal.))))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 16268645,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not (not not (not not (((1 * 10 * 3 * -4) <= (-4 + -11)) and (not (not (Silver is a solid at room temperature.))))))\nB. not not (not ((not not (The chemical symbol for Silicon is S.)) or (not not ((2065 is a leap year.) and (Uranus is the 2nd planet from the Sun.))) or (((The capital of Germany is Berlin.) or (((2 ** 3) < (15 % 5)) and (The capital of New Zealand is Bogota.))) and ((((14 % 3) != (7 - 2)) and ((-18 * -9) > (-2 + 8))) and (not ((10 + -18) > (13 % 7)))))))\nC. not (not (not (not (not not ((Christopher Columbus reached America occurred in 1492.) or (The Titanic sank occurred in 1912.))))))\nD. not (not not (not (not not ((40 % 7) == (-7 - 6)))))\nE. ((not ((((The currency of United Kingdom is the Pound.) or (360 is a perfect square.)) and (not not ((-6 * -5 - -1 * 1) <= (-8 * 3 - 6 * 0)))) and ((5 ** 2) <= (2 ** 3)))) or ((not not (not not (((14 * -3) <= (2 ** 2)) or (Mercury is the 1st planet from the Sun.)))) and ((not (((1 ** 2) >= (4 + -8)) or (The capital of Peru is Lima.))) and (not (The human body has 206 bones.))))) or (not not (not not (not not (((22 % 7) <= (-9 + -7)) or ((1 ** 2) >= (2 % 9))))))\nF. not (not ((((not ((38 % 9) > (18 * -14))) or (((16 % 6) < (1 ** 3) < (5 - 5)) and (The 1948 Olympics were held in London.))) and ((((5 * -11) >= (-11 * 2)) or (Light travels faster than sound.)) or (not ((9 - -17) >= (0 * 9 + 5 * 5))))) and ((9 * 4 + -5 * 5) == (3 ** 2)) and (((4 ** 1) > (10 * -10 - -1 * 2)) or ((6 * -8 - -8 * 2) < (14 * 14)))))\nG. not not (not (not (not (A tiger is a mammal.))))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 16268645,
"true_count": 2
},
"seed": 16268645,
"task_id": 616268645,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not ((not not ((The currency of Norway is the Krone.) and (not (The Sun revolves around the Earth.)) and (((There are 31 days in January.) or ((-3 + 4) == (-2 - 7))) or (not ((-20 + 20) >= (-1 * -2 - 7 * -6)))))) and (not not (((11 % 7) != (-10 * -4 + 8 * 2)) and (The currency of Australia is the Dollar.))))
B. not (not not ((((-4 - -17) != (1 - 11)) and (Light travels faster than sound.)) and ((((28 % 10) <= (47 % 3)) or ((17 - -18) == (0 - 19))) or (not ((2 * -3) < (1 ** 1) < (8 * -8 * 9 * 7)))) and ((Morocco is in Africa.) and (not (((6 * -4 + -9 * 2) < (14 + 4)) or (The 1936 Olympics were held in Berlin.))))))
C. (not ((not ((((1 ** 2) <= (-19 + -6)) or ((-12 + -1) < (2 + 2))) or (not ((-6 * 10 * -2 * 4) >= (-6 * -3 - -4 * 8))))) and (not ((14 * 5) >= (18 % 6))))) and (not not (not (not (63 is a prime number.))))
D. not ((((The capital of Portugal is Singapore.) and (((-14 * -6) != (4 ** 1)) or (((5 * 2 * -4 * 6) <= (10 * 3 - 3 * -6) <= (-3 + -12)) or ((-1 - -14) <= (-5 + 4))))) and (not not (not not (((-10 + -4) < (-3 + -18)) or ((15 * 19) == (4 ** 2)))))) and (((The 1912 Olympics were held in Stockholm.) or (66 is an even number.)) and (not not (((-7 - 5) < (5 ** 1)) or ((The 1956 Olympics were held in Montreal.) or ((-20 * -3) < (4 * 2)))))))
E. not (not (((not not (not not ((-20 + 5) > (-16 + 1)))) or (not not ((22 % 2) <= (-9 * 7) <= (0 * -1 * 9 * -9))) or (not (((11 % 1) <= (-3 * -8 - -8 * -10) <= (-7 * 15)) or (132 is a perfect square.)))) and (not ((4 * 7) != (-2 - -6)))))
F. (not not (((1991 is a leap year.) or (The 1964 Olympics were held in Tokyo.)) or (not not ((12 * -19) < (13 + 4))))) or ((not not (not not ((The Soviet Union dissolved occurred in 1991.) or ((Light travels faster than sound.) or (The 1924 Olympics were held in Paris.))))) and (not (not not (not ((-11 - -2) < (1 ** 2) < (8 * 3 * -7 * -4))))))
G. (not (not (not ((-15 * 3) >= (4 ** 3))))) and ((not not ((29 % 5) < (-2 - 18))) and ((((-14 * -15) == (-4 + 16)) or ((-18 * -9) >= (-1 * 14))) or (not not (Ice is less dense than liquid water.)))) and (((((not (The chemical symbol for Cobalt is Au.)) or (((6 - 20) < (-10 * -7)) or (There are 30 days in June.))) or (Thailand is in Asia.)) or (not not (not (((-4 * -8 + 2 * 2) >= (-19 * -10)) and ((13 * 19) < (1 ** 1)))))) or (not not (not not (not not (not not (340 is a Fibonacci number.))))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
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"answer": "B,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
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"seed": 52342614,
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},
"question": "Consider the following logical expressions:\n\nA. not ((not not ((The currency of Norway is the Krone.) and (not (The Sun revolves around the Earth.)) and (((There are 31 days in January.) or ((-3 + 4) == (-2 - 7))) or (not ((-20 + 20) >= (-1 * -2 - 7 * -6)))))) and (not not (((11 % 7) != (-10 * -4 + 8 * 2)) and (The currency of Australia is the Dollar.))))\nB. not (not not ((((-4 - -17) != (1 - 11)) and (Light travels faster than sound.)) and ((((28 % 10) <= (47 % 3)) or ((17 - -18) == (0 - 19))) or (not ((2 * -3) < (1 ** 1) < (8 * -8 * 9 * 7)))) and ((Morocco is in Africa.) and (not (((6 * -4 + -9 * 2) < (14 + 4)) or (The 1936 Olympics were held in Berlin.))))))\nC. (not ((not ((((1 ** 2) <= (-19 + -6)) or ((-12 + -1) < (2 + 2))) or (not ((-6 * 10 * -2 * 4) >= (-6 * -3 - -4 * 8))))) and (not ((14 * 5) >= (18 % 6))))) and (not not (not (not (63 is a prime number.))))\nD. not ((((The capital of Portugal is Singapore.) and (((-14 * -6) != (4 ** 1)) or (((5 * 2 * -4 * 6) <= (10 * 3 - 3 * -6) <= (-3 + -12)) or ((-1 - -14) <= (-5 + 4))))) and (not not (not not (((-10 + -4) < (-3 + -18)) or ((15 * 19) == (4 ** 2)))))) and (((The 1912 Olympics were held in Stockholm.) or (66 is an even number.)) and (not not (((-7 - 5) < (5 ** 1)) or ((The 1956 Olympics were held in Montreal.) or ((-20 * -3) < (4 * 2)))))))\nE. not (not (((not not (not not ((-20 + 5) > (-16 + 1)))) or (not not ((22 % 2) <= (-9 * 7) <= (0 * -1 * 9 * -9))) or (not (((11 % 1) <= (-3 * -8 - -8 * -10) <= (-7 * 15)) or (132 is a perfect square.)))) and (not ((4 * 7) != (-2 - -6)))))\nF. (not not (((1991 is a leap year.) or (The 1964 Olympics were held in Tokyo.)) or (not not ((12 * -19) < (13 + 4))))) or ((not not (not not ((The Soviet Union dissolved occurred in 1991.) or ((Light travels faster than sound.) or (The 1924 Olympics were held in Paris.))))) and (not (not not (not ((-11 - -2) < (1 ** 2) < (8 * 3 * -7 * -4))))))\nG. (not (not (not ((-15 * 3) >= (4 ** 3))))) and ((not not ((29 % 5) < (-2 - 18))) and ((((-14 * -15) == (-4 + 16)) or ((-18 * -9) >= (-1 * 14))) or (not not (Ice is less dense than liquid water.)))) and (((((not (The chemical symbol for Cobalt is Au.)) or (((6 - 20) < (-10 * -7)) or (There are 30 days in June.))) or (Thailand is in Asia.)) or (not not (not (((-4 * -8 + 2 * 2) >= (-19 * -10)) and ((13 * 19) < (1 ** 1)))))) or (not not (not not (not not (not not (340 is a Fibonacci number.))))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
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"language": "en",
"num_options": 7,
"seed": 52342614,
"true_count": 3
},
"seed": 52342614,
"task_id": 652342614,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate the following boolean expressions and select the ones that are true:
A. not not ((not ((not not (Indonesia is in Asia.)) and (not not ((4 ** 1) > (43 % 6))) and (not (not not (Venus is the 4th planet from the Sun.))))) and (((not (not (The Pacific Ocean is the largest ocean.))) or (not not (Bats are blind.))) or ((((Mercury is the 5th planet from the Sun.) or ((2 - 6) == (-8 * -4 - 5 * -6))) and ((-20 + 4) == (16 + -20))) or (not ((Morocco is in Oceania.) or ((-1 * 6 * 5 * -1) == (14 + -5)))))))
B. not ((not (not not (not (not (Uranus is the 7th planet from the Sun.))))) or ((not not (((Helium is a liquid at room temperature.) or (The currency of Vietnam is the Dong.)) or ((The 1912 Olympics were held in Stockholm.) or (Venus is the 4th planet from the Sun.)))) or ((The capital of Switzerland is Bern.) and ((-5 - -12) >= (49 % 7)))))
C. (not not (not (not not ((1 ** 1) < (9 * -7 * 9 * -4) < (7 * -3 * 5 * 1))))) and ((not ((The capital of Austria is Vienna.) or ((0 * -2 + -1 * 4) >= (0 + -5)))) or ((not not (((Wood is a gas at room temperature.) and (The capital of Indonesia is Jakarta.)) and (The 1988 Olympics were held in Seoul.))) or (not ((((26 % 1) == (4 ** 2)) or (The capital of Japan is Tokyo.)) and (not ((-11 * 1) >= (-18 * 16)))))))
D. not ((((not ((-4 * 18) >= (22 % 5))) or ((-14 * 0) != (-9 * -16)) or (((Lightning never strikes the same place twice.) and (United Kingdom is in Europe.)) and (157 is an even number.))) or (((4 * 16) != (17 - -9)) and ((not ((-13 * 7) < (17 + -5) < (5 + 5))) and (not ((-1 * -12) <= (31 % 2)))))) and (not not (not (The currency of Singapore is the Dollar.))))
E. not not (not (((not ((19 - 11) <= (13 + 6) <= (5 + -7))) and ((((-4 + -6) > (3 ** 1)) and (There are 31 days in January.)) and ((The chemical symbol for Nickel is Ni.) and (The 2024 Olympics were held in Athens.)))) or ((not not ((The 2012 Olympics were held in Los Angeles.) or (The capital of Portugal is Lisbon.))) and ((((-7 + -19) < (-1 + 9)) or (1999 is a leap year.)) or (not (China is in Oceania.))))))
F. not not ((not not (not not ((3 ** 1) >= (14 + -13)))) and (not (Earth is the 3rd planet from the Sun.)) and (((((-6 - -2) != (11 + 16)) or (Water boils at 100 degrees Celsius at sea level.)) and ((5 ** 2) == (-18 - -9))) and ((Mercury is a liquid at room temperature.) or ((2 * -11) == (-10 * -5 - -7 * -4)))))
G. not (not (((The chemical symbol for Mercury is Cr.) or ((2 * -5 - -10 * -8) != (5 - -17))) or ((2073 is a leap year.) and ((-2 * -5 + 2 * -5) < (3 * 5) < (-1 + -9))) or (not ((Penguins can fly.) or ((19 * -17) < (45 % 10))))))
Which options evaluate to True? List all true option labels separated by commas. Put your final answer in \boxed{}. | {
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"answer": "C,D,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 13665316,
"true_count": 3
},
"question": "Evaluate the following boolean expressions and select the ones that are true:\n\nA. not not ((not ((not not (Indonesia is in Asia.)) and (not not ((4 ** 1) > (43 % 6))) and (not (not not (Venus is the 4th planet from the Sun.))))) and (((not (not (The Pacific Ocean is the largest ocean.))) or (not not (Bats are blind.))) or ((((Mercury is the 5th planet from the Sun.) or ((2 - 6) == (-8 * -4 - 5 * -6))) and ((-20 + 4) == (16 + -20))) or (not ((Morocco is in Oceania.) or ((-1 * 6 * 5 * -1) == (14 + -5)))))))\nB. not ((not (not not (not (not (Uranus is the 7th planet from the Sun.))))) or ((not not (((Helium is a liquid at room temperature.) or (The currency of Vietnam is the Dong.)) or ((The 1912 Olympics were held in Stockholm.) or (Venus is the 4th planet from the Sun.)))) or ((The capital of Switzerland is Bern.) and ((-5 - -12) >= (49 % 7)))))\nC. (not not (not (not not ((1 ** 1) < (9 * -7 * 9 * -4) < (7 * -3 * 5 * 1))))) and ((not ((The capital of Austria is Vienna.) or ((0 * -2 + -1 * 4) >= (0 + -5)))) or ((not not (((Wood is a gas at room temperature.) and (The capital of Indonesia is Jakarta.)) and (The 1988 Olympics were held in Seoul.))) or (not ((((26 % 1) == (4 ** 2)) or (The capital of Japan is Tokyo.)) and (not ((-11 * 1) >= (-18 * 16)))))))\nD. not ((((not ((-4 * 18) >= (22 % 5))) or ((-14 * 0) != (-9 * -16)) or (((Lightning never strikes the same place twice.) and (United Kingdom is in Europe.)) and (157 is an even number.))) or (((4 * 16) != (17 - -9)) and ((not ((-13 * 7) < (17 + -5) < (5 + 5))) and (not ((-1 * -12) <= (31 % 2)))))) and (not not (not (The currency of Singapore is the Dollar.))))\nE. not not (not (((not ((19 - 11) <= (13 + 6) <= (5 + -7))) and ((((-4 + -6) > (3 ** 1)) and (There are 31 days in January.)) and ((The chemical symbol for Nickel is Ni.) and (The 2024 Olympics were held in Athens.)))) or ((not not ((The 2012 Olympics were held in Los Angeles.) or (The capital of Portugal is Lisbon.))) and ((((-7 + -19) < (-1 + 9)) or (1999 is a leap year.)) or (not (China is in Oceania.))))))\nF. not not ((not not (not not ((3 ** 1) >= (14 + -13)))) and (not (Earth is the 3rd planet from the Sun.)) and (((((-6 - -2) != (11 + 16)) or (Water boils at 100 degrees Celsius at sea level.)) and ((5 ** 2) == (-18 - -9))) and ((Mercury is a liquid at room temperature.) or ((2 * -11) == (-10 * -5 - -7 * -4)))))\nG. not (not (((The chemical symbol for Mercury is Cr.) or ((2 * -5 - -10 * -8) != (5 - -17))) or ((2073 is a leap year.) and ((-2 * -5 + 2 * -5) < (3 * 5) < (-1 + -9))) or (not ((Penguins can fly.) or ((19 * -17) < (45 % 10))))))\n\nWhich options evaluate to True? List all true option labels separated by commas. Put your final answer in \\boxed{}."
},
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"language": "en",
"num_options": 7,
"seed": 13665316,
"true_count": 3
},
"seed": 13665316,
"task_id": 613665316,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not ((not (not (not not ((The chemical symbol for Helium is H.) and ((-3 + 2) <= (-8 * -7 * -6 * -8)))))) or ((not not ((-8 * -1 - 7 * -5) > (-10 * 2 - 10 * 9))) and (not ((The currency of Switzerland is the Koruna.) and ((86 is a prime number.) or (A whale is a mammal.))))))
B. not ((not ((not (((19 * 4) >= (21 % 3)) or (The capital of Saudi Arabia is Riyadh.))) and (((Japan is in Oceania.) or (Ice is a solid at room temperature.)) and (((-6 + 6) < (19 + -7)) and ((8 * 9 - 7 * 5) >= (19 - -17)))))) or (not ((not (((3 * -12) < (16 % 6) < (15 * 16)) and ((12 - -16) < (6 - 17)))) or (not (not ((5 % 4) == (11 + -10)))))))
C. not not (not (not not (not (not (not not ((3 ** 2) < (1 ** 1)))))))
D. not not (not not ((not not ((not ((3 + 2) == (-18 * -7))) and ((The chemical symbol for Phosphorus is Pt.) or (299 is a perfect square.)))) and (not ((not not ((1 + 18) > (-3 * 9 * 2 * -2))) and (1997 is a leap year.)))))
E. not not (not (not not (not not (194 is an odd number.))))
F. not ((not (((((5 ** 2) > (9 + -15)) and (The 1956 Olympics were held in Melbourne.)) or (not ((18 * -1) < (9 % 2) < (6 * 6 * 8 * -7)))) or (not not ((The 2016 Olympics were held in Stockholm.) and ((8 - -17) < (15 - -17)))))) and (not not (not (((15 + -16) == (9 + -7)) or (Chile is in South America.)))) and ((not not ((The 1968 Olympics were held in Montreal.) or (not ((16 * -7) != (-8 + -17))))) and (Nitrogen is a gas at room temperature.) and (not (The 1988 Olympics were held in Seoul.))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,C,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 6,
"seed": 16077170,
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},
"question": "Evaluate each expression below:\n\nA. not not ((not (not (not not ((The chemical symbol for Helium is H.) and ((-3 + 2) <= (-8 * -7 * -6 * -8)))))) or ((not not ((-8 * -1 - 7 * -5) > (-10 * 2 - 10 * 9))) and (not ((The currency of Switzerland is the Koruna.) and ((86 is a prime number.) or (A whale is a mammal.))))))\nB. not ((not ((not (((19 * 4) >= (21 % 3)) or (The capital of Saudi Arabia is Riyadh.))) and (((Japan is in Oceania.) or (Ice is a solid at room temperature.)) and (((-6 + 6) < (19 + -7)) and ((8 * 9 - 7 * 5) >= (19 - -17)))))) or (not ((not (((3 * -12) < (16 % 6) < (15 * 16)) and ((12 - -16) < (6 - 17)))) or (not (not ((5 % 4) == (11 + -10)))))))\nC. not not (not (not not (not (not (not not ((3 ** 2) < (1 ** 1)))))))\nD. not not (not not ((not not ((not ((3 + 2) == (-18 * -7))) and ((The chemical symbol for Phosphorus is Pt.) or (299 is a perfect square.)))) and (not ((not not ((1 + 18) > (-3 * 9 * 2 * -2))) and (1997 is a leap year.)))))\nE. not not (not (not not (not not (194 is an odd number.))))\nF. not ((not (((((5 ** 2) > (9 + -15)) and (The 1956 Olympics were held in Melbourne.)) or (not ((18 * -1) < (9 % 2) < (6 * 6 * 8 * -7)))) or (not not ((The 2016 Olympics were held in Stockholm.) and ((8 - -17) < (15 - -17)))))) and (not not (not (((15 + -16) == (9 + -7)) or (Chile is in South America.)))) and ((not not ((The 1968 Olympics were held in Montreal.) or (not ((16 * -7) != (-8 + -17))))) and (Nitrogen is a gas at room temperature.) and (not (The 1988 Olympics were held in Seoul.))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
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"language": "en",
"num_options": 6,
"seed": 16077170,
"true_count": 4
},
"seed": 16077170,
"task_id": 616077170,
"task_type": "boolean_expressions"
} |
logic-v2 | Given the following boolean expressions:
A. not not (not ((not (Chile is in South America.)) and (not (((6 * -2 + -8 * 7) < (-7 * 3 + -7 * 9) < (27 % 2)) and ((-16 - 8) != (1 % 1)))) and (not not ((((-7 * 1) > (0 * -8)) and (The capital of Greece is Athens.)) and (not ((4 ** 3) <= (2 ** 2)))))))
B. not (not ((((((-5 * 0 - -7 * 7) == (10 % 2)) or (214 is a perfect square.)) or (not not (Morocco is in Asia.))) and ((-13 * 16) <= (4 ** 2))) and (((((3 - 10) == (3 * 6 * 2 * 0)) or (The Sun revolves around the Earth.)) or (((9 * 2 + -7 * 4) == (-3 * 0 + 0 * -3)) and (The chemical symbol for Magnesium is Mg.))) and ((10 * 3 + 3 * -3) >= (22 % 5)) and (((Argentina is in South America.) or ((-4 * -17) > (-2 * -10))) or (A crocodile is a reptile.)))))
C. not not (not ((((((-13 + -18) != (-1 + 1)) and ((0 * 5) < (4 * 4 + 4 * 6))) or (not not (Argentina is in South America.))) and ((Water boils at 100 degrees Celsius at sea level.) and ((-8 - 16) > (1 ** 2))) and (not not ((25 is an odd number.) or ((17 % 7) == (0 * -3 + -2 * -3))))) or ((((4 ** 3) != (13 % 6)) and ((4 ** 2) <= (16 + -13))) and (Jupiter is the 3rd planet from the Sun.) and ((-6 * -2 - -6 * 10) == (26 % 8)))))
D. not not (((not not (1928 is a leap year.)) and (((not not ((1 - 17) > (2 % 4))) and (The capital of New Zealand is Bucharest.)) and ((-12 * 5) < (21 % 8)))) and (((((-19 - -14) > (0 + 8)) and (((-19 * -11) < (13 - -10) < (-5 + 14)) or (The 1976 Olympics were held in Montreal.))) or ((The currency of Colombia is the Peso.) or ((5 * -1 * 8 * -8) >= (8 - -13)))) or ((Nitrogen is a gas at room temperature.) or (not not ((Uranus is the 7th planet from the Sun.) or ((13 % 7) == (10 % 3)))))))
Select all that evaluate to True. Put your answer in \boxed{} as comma-separated labels. | {
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"answer": "A,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"language": "en",
"num_options": 4,
"seed": 97997694,
"true_count": 2
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"question": "Given the following boolean expressions:\n\nA. not not (not ((not (Chile is in South America.)) and (not (((6 * -2 + -8 * 7) < (-7 * 3 + -7 * 9) < (27 % 2)) and ((-16 - 8) != (1 % 1)))) and (not not ((((-7 * 1) > (0 * -8)) and (The capital of Greece is Athens.)) and (not ((4 ** 3) <= (2 ** 2)))))))\nB. not (not ((((((-5 * 0 - -7 * 7) == (10 % 2)) or (214 is a perfect square.)) or (not not (Morocco is in Asia.))) and ((-13 * 16) <= (4 ** 2))) and (((((3 - 10) == (3 * 6 * 2 * 0)) or (The Sun revolves around the Earth.)) or (((9 * 2 + -7 * 4) == (-3 * 0 + 0 * -3)) and (The chemical symbol for Magnesium is Mg.))) and ((10 * 3 + 3 * -3) >= (22 % 5)) and (((Argentina is in South America.) or ((-4 * -17) > (-2 * -10))) or (A crocodile is a reptile.)))))\nC. not not (not ((((((-13 + -18) != (-1 + 1)) and ((0 * 5) < (4 * 4 + 4 * 6))) or (not not (Argentina is in South America.))) and ((Water boils at 100 degrees Celsius at sea level.) and ((-8 - 16) > (1 ** 2))) and (not not ((25 is an odd number.) or ((17 % 7) == (0 * -3 + -2 * -3))))) or ((((4 ** 3) != (13 % 6)) and ((4 ** 2) <= (16 + -13))) and (Jupiter is the 3rd planet from the Sun.) and ((-6 * -2 - -6 * 10) == (26 % 8)))))\nD. not not (((not not (1928 is a leap year.)) and (((not not ((1 - 17) > (2 % 4))) and (The capital of New Zealand is Bucharest.)) and ((-12 * 5) < (21 % 8)))) and (((((-19 - -14) > (0 + 8)) and (((-19 * -11) < (13 - -10) < (-5 + 14)) or (The 1976 Olympics were held in Montreal.))) or ((The currency of Colombia is the Peso.) or ((5 * -1 * 8 * -8) >= (8 - -13)))) or ((Nitrogen is a gas at room temperature.) or (not not ((Uranus is the 7th planet from the Sun.) or ((13 % 7) == (10 % 3)))))))\n\nSelect all that evaluate to True. Put your answer in \\boxed{} as comma-separated labels."
},
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"seed": 97997694,
"true_count": 2
},
"seed": 97997694,
"task_id": 697997694,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (not not (not (not (not not ((-19 + -8) >= (3 - -12)))))) or (not not ((Indonesia is in North America.) or ((-2 * -9 * -1 * -7) <= (-17 + -1)))) or (not not ((not not (not not ((World War II ended occurred in 1945.) or (27 is divisible by 6.)))) or ((((Mars is the 4th planet from the Sun.) or (The speed of light is approximately 300,000 km/s.)) and (Humans have three lungs.)) or (not ((-8 * -7 - 4 * -6) < (-10 + 0))) or (The currency of Australia is the Dollar.))))
B. not (not (not (not (not not (((-19 - -4) != (37 % 5)) or ((-14 * -17) < (19 + 0) < (-16 * 10)))))))
C. not not (not not (not not (not ((not not ((27 % 1) == (-5 - -9))) or ((The 1904 Olympics were held in Paris.) and (The capital of Vietnam is Buenos Aires.))))))
D. not ((not not (not not ((-11 + -20) == (3 ** 2)))) and (((((20 * 11) != (6 - -2)) and ((Electricity flows faster than light.) and ((49 % 5) != (5 ** 2)))) and (not (The 2004 Olympics were held in Athens.)) and ((not not ((-13 + -2) > (-1 - 5))) or (not (100 is divisible by 7.)))) and (not not (not ((The currency of Denmark is the Krone.) or (The chemical symbol for Potassium is K.))))))
E. not not ((not (not ((The chemical symbol for Chromium is Cr.) and (The currency of New Zealand is the Dollar.)))) or (((Humans have five fingers on each hand.) or (The currency of Mexico is the Peso.)) and (((((3 ** 1) >= (7 - -1)) or (Uranus is the 6th planet from the Sun.)) or ((Helium is a gas at room temperature.) and (Mercury is the 7th planet from the Sun.))) and ((not not ((-9 - 5) == (20 + 17))) or ((-18 - -10) > (10 * 10 - 8 * -7))))))
F. not not (((((not not (Oil is a liquid at room temperature.)) and ((The capital of Turkey is Seoul.) or (A grasshopper is a bird.))) and (not not (The capital of Italy is Rome.))) or (not (not not ((The capital of Turkey is Ankara.) or (Mexico is in North America.))))) and (not not (((-7 - -16) <= (-7 * 9 * -3 * 4)) and (Mexico is in Oceania.))))
G. not not ((not not (((17 + -6) <= (14 * 19)) and ((19 * -4) < (4 * -6 * 7 * 10) < (-19 + 5)))) or (not not ((not not ((7 % 8) != (43 % 10))) or (Mars is the closest planet to the Sun.))))
H. not not (not not ((not not (not ((The capital of Egypt is Cairo.) and (The 1908 Olympics were held in London.)))) or (((The currency of Colombia is the Peso.) and ((18 % 8) <= (5 % 1))) or ((Wood is a solid at room temperature.) or ((14 * -14) < (-20 - 20)))) or (((-6 - 18) <= (20 - 20)) or ((24 % 6) == (-4 * -13)))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"answer": "A,B,C,D,E,G,H",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"true_count": 7
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"question": "Review these logical expressions:\n\nA. (not not (not (not (not not ((-19 + -8) >= (3 - -12)))))) or (not not ((Indonesia is in North America.) or ((-2 * -9 * -1 * -7) <= (-17 + -1)))) or (not not ((not not (not not ((World War II ended occurred in 1945.) or (27 is divisible by 6.)))) or ((((Mars is the 4th planet from the Sun.) or (The speed of light is approximately 300,000 km/s.)) and (Humans have three lungs.)) or (not ((-8 * -7 - 4 * -6) < (-10 + 0))) or (The currency of Australia is the Dollar.))))\nB. not (not (not (not (not not (((-19 - -4) != (37 % 5)) or ((-14 * -17) < (19 + 0) < (-16 * 10)))))))\nC. not not (not not (not not (not ((not not ((27 % 1) == (-5 - -9))) or ((The 1904 Olympics were held in Paris.) and (The capital of Vietnam is Buenos Aires.))))))\nD. not ((not not (not not ((-11 + -20) == (3 ** 2)))) and (((((20 * 11) != (6 - -2)) and ((Electricity flows faster than light.) and ((49 % 5) != (5 ** 2)))) and (not (The 2004 Olympics were held in Athens.)) and ((not not ((-13 + -2) > (-1 - 5))) or (not (100 is divisible by 7.)))) and (not not (not ((The currency of Denmark is the Krone.) or (The chemical symbol for Potassium is K.))))))\nE. not not ((not (not ((The chemical symbol for Chromium is Cr.) and (The currency of New Zealand is the Dollar.)))) or (((Humans have five fingers on each hand.) or (The currency of Mexico is the Peso.)) and (((((3 ** 1) >= (7 - -1)) or (Uranus is the 6th planet from the Sun.)) or ((Helium is a gas at room temperature.) and (Mercury is the 7th planet from the Sun.))) and ((not not ((-9 - 5) == (20 + 17))) or ((-18 - -10) > (10 * 10 - 8 * -7))))))\nF. not not (((((not not (Oil is a liquid at room temperature.)) and ((The capital of Turkey is Seoul.) or (A grasshopper is a bird.))) and (not not (The capital of Italy is Rome.))) or (not (not not ((The capital of Turkey is Ankara.) or (Mexico is in North America.))))) and (not not (((-7 - -16) <= (-7 * 9 * -3 * 4)) and (Mexico is in Oceania.))))\nG. not not ((not not (((17 + -6) <= (14 * 19)) and ((19 * -4) < (4 * -6 * 7 * 10) < (-19 + 5)))) or (not not ((not not ((7 % 8) != (43 % 10))) or (Mars is the closest planet to the Sun.))))\nH. not not (not not ((not not (not ((The capital of Egypt is Cairo.) and (The 1908 Olympics were held in London.)))) or (((The currency of Colombia is the Peso.) and ((18 % 8) <= (5 % 1))) or ((Wood is a solid at room temperature.) or ((14 * -14) < (-20 - 20)))) or (((-6 - 18) <= (20 - 20)) or ((24 % 6) == (-4 * -13)))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
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"seed": 84679932,
"true_count": 7
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"seed": 84679932,
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"task_type": "boolean_expressions"
} |
logic-v2 | Study the following logical statements:
A. not ((((not not (not (The capital of Romania is Brussels.))) and (((Humans have three lungs.) or (The chemical symbol for Chlorine is Cl.)) or ((The currency of India is the Rupee.) and (115 is an odd number.)))) and (not ((not ((-15 * 16) >= (7 * -13))) and ((4 - -13) > (-15 + -6))))) or (not not (not not (not ((The 2024 Olympics were held in Paris.) or (The currency of Argentina is the Peso.))))))
B. not (((((The currency of Russia is the Dollar.) or (not ((15 - -15) < (20 * -17)))) or (A cow has 4 legs.)) and ((not not (The capital of South Korea is Seoul.)) and (Helium is a solid at room temperature.))) or ((not not (687 is a Fibonacci number.)) or ((Humans have three lungs.) and (not not ((Canada is in North America.) and (The human body has 150 bones.))))))
C. not (not (not (((not (Sharks are mammals.)) and ((There are 29 days in June.) or (The chemical symbol for Platinum is Pt.))) and ((-4 * 7) == (1 + 0)) and ((not not ((-8 * 5 - -7 * 3) < (20 - -12))) or ((Mercury is the 1st planet from the Sun.) or ((34 % 10) < (15 * -20)))))))
D. (not not (not not (not (((Copper is a solid at room temperature.) and (434 is a Fibonacci number.)) or ((6 % 1) < (-3 + 19)))))) or (not (not (not (The 1964 Olympics were held in Tokyo.))))
E. not not (not (not not (not ((Alcohol is a liquid at room temperature.) and ((10 - -8) < (4 * 2 + 8 * -4))))))
Which statements are true? Put all true option labels in \boxed{}, separated by commas. | {
"game_data": {
"answer": "A,B,C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
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"true_count": 3
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"question": "Study the following logical statements:\n\nA. not ((((not not (not (The capital of Romania is Brussels.))) and (((Humans have three lungs.) or (The chemical symbol for Chlorine is Cl.)) or ((The currency of India is the Rupee.) and (115 is an odd number.)))) and (not ((not ((-15 * 16) >= (7 * -13))) and ((4 - -13) > (-15 + -6))))) or (not not (not not (not ((The 2024 Olympics were held in Paris.) or (The currency of Argentina is the Peso.))))))\nB. not (((((The currency of Russia is the Dollar.) or (not ((15 - -15) < (20 * -17)))) or (A cow has 4 legs.)) and ((not not (The capital of South Korea is Seoul.)) and (Helium is a solid at room temperature.))) or ((not not (687 is a Fibonacci number.)) or ((Humans have three lungs.) and (not not ((Canada is in North America.) and (The human body has 150 bones.))))))\nC. not (not (not (((not (Sharks are mammals.)) and ((There are 29 days in June.) or (The chemical symbol for Platinum is Pt.))) and ((-4 * 7) == (1 + 0)) and ((not not ((-8 * 5 - -7 * 3) < (20 - -12))) or ((Mercury is the 1st planet from the Sun.) or ((34 % 10) < (15 * -20)))))))\nD. (not not (not not (not (((Copper is a solid at room temperature.) and (434 is a Fibonacci number.)) or ((6 % 1) < (-3 + 19)))))) or (not (not (not (The 1964 Olympics were held in Tokyo.))))\nE. not not (not (not not (not ((Alcohol is a liquid at room temperature.) and ((10 - -8) < (4 * 2 + 8 * -4))))))\n\nWhich statements are true? Put all true option labels in \\boxed{}, separated by commas."
},
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"seed": 34428040,
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"seed": 34428040,
"task_id": 634428040,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not (not ((not (There are 30 days in October.)) or ((((-7 * 10 * 10 * -1) < (3 ** 1)) or (The currency of Mexico is the Peso.)) or ((87 is a perfect square.) and (The currency of Egypt is the Pound.))) or (not not (not ((The capital of Ireland is Wellington.) or (The capital of Italy is Rome.))))))
B. not ((not not (((The chemical symbol for Magnesium is N.) or (((-8 - -15) >= (7 * -10 + -3 * 0)) and ((5 ** 2) == (-15 * 19)))) or ((not (A cat has 4 legs.)) and ((Humans have three lungs.) and (The chemical symbol for Cobalt is Co.))))) or (((Carbon dioxide is a gas at room temperature.) or (not not (Oxygen is a gas at room temperature.))) and ((((14 + 20) < (-9 - 3)) and (not (A cow has 4 legs.))) or (The chemical symbol for Silver is Cl.))))
C. not ((not (((3 ** 3) <= (1 * 3 + 5 * -4)) and (34 is a Fibonacci number.) and (((Mexico is in North America.) and ((11 - -12) != (5 * -10 + 3 * -7))) or (Oil is a gas at room temperature.)))) or (not not ((not (not (Spain is in Europe.))) or (Humans only use 10% of their brain.))))
D. not (not (((((15 % 2) == (4 - -2)) and ((The 1996 Olympics were held in Mexico City.) and ((17 + 9) < (-19 * -10)))) and ((Antarctica is the coldest continent.) or (not not (14 is divisible by 8.)))) and (((14 * -19) >= (2 ** 2)) or (not ((-2 * -10 + -9 * -8) == (14 % 3)))) and (((((-18 * 9) == (13 - 14)) or (The chemical symbol for Oxygen is Si.)) and ((World War II began occurred in 1939.) and (A horse has 4 legs.))) or ((10 * 6) <= (9 + 12)))))
E. not not (((not ((-7 * 0 + 0 * 2) > (13 % 10))) and (not (The chemical symbol for Magnesium is Cl.))) and ((not (not (((2 ** 2) != (11 - 5)) or ((3 * -10 + -9 * 9) <= (15 - -3))))) and ((((The currency of Vietnam is the Rupee.) or ((11 + -3) <= (6 * 18) <= (-1 * -7 - 6 * -3))) or (((3 * 12) < (6 * -2) < (-2 * -2 - 8 * 1)) and ((4 * -20) > (-19 - 12)))) and (not not (not not (1972 is a leap year.))))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "B",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
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"seed": 51984707,
"true_count": 1
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"question": "Evaluate each expression below:\n\nA. not not (not ((not (There are 30 days in October.)) or ((((-7 * 10 * 10 * -1) < (3 ** 1)) or (The currency of Mexico is the Peso.)) or ((87 is a perfect square.) and (The currency of Egypt is the Pound.))) or (not not (not ((The capital of Ireland is Wellington.) or (The capital of Italy is Rome.))))))\nB. not ((not not (((The chemical symbol for Magnesium is N.) or (((-8 - -15) >= (7 * -10 + -3 * 0)) and ((5 ** 2) == (-15 * 19)))) or ((not (A cat has 4 legs.)) and ((Humans have three lungs.) and (The chemical symbol for Cobalt is Co.))))) or (((Carbon dioxide is a gas at room temperature.) or (not not (Oxygen is a gas at room temperature.))) and ((((14 + 20) < (-9 - 3)) and (not (A cow has 4 legs.))) or (The chemical symbol for Silver is Cl.))))\nC. not ((not (((3 ** 3) <= (1 * 3 + 5 * -4)) and (34 is a Fibonacci number.) and (((Mexico is in North America.) and ((11 - -12) != (5 * -10 + 3 * -7))) or (Oil is a gas at room temperature.)))) or (not not ((not (not (Spain is in Europe.))) or (Humans only use 10% of their brain.))))\nD. not (not (((((15 % 2) == (4 - -2)) and ((The 1996 Olympics were held in Mexico City.) and ((17 + 9) < (-19 * -10)))) and ((Antarctica is the coldest continent.) or (not not (14 is divisible by 8.)))) and (((14 * -19) >= (2 ** 2)) or (not ((-2 * -10 + -9 * -8) == (14 % 3)))) and (((((-18 * 9) == (13 - 14)) or (The chemical symbol for Oxygen is Si.)) and ((World War II began occurred in 1939.) and (A horse has 4 legs.))) or ((10 * 6) <= (9 + 12)))))\nE. not not (((not ((-7 * 0 + 0 * 2) > (13 % 10))) and (not (The chemical symbol for Magnesium is Cl.))) and ((not (not (((2 ** 2) != (11 - 5)) or ((3 * -10 + -9 * 9) <= (15 - -3))))) and ((((The currency of Vietnam is the Rupee.) or ((11 + -3) <= (6 * 18) <= (-1 * -7 - 6 * -3))) or (((3 * 12) < (6 * -2) < (-2 * -2 - 8 * 1)) and ((4 * -20) > (-19 - 12)))) and (not not (not not (1972 is a leap year.))))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
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"seed": 51984707,
"true_count": 1
},
"seed": 51984707,
"task_id": 651984707,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not ((not (not not (The currency of United Kingdom is the Peso.))) or (((not ((The 2016 Olympics were held in Melbourne.) or ((18 * -14) != (-8 * 6)))) or (not ((10 + 7) <= (-2 - 12)))) or (not not (((4 ** 3) > (0 + 20)) or ((18 * -13) < (7 + -3)))) or ((((Diamonds are made of carbon.) or (Neptune is the 8th planet from the Sun.)) or (Oxygen is a liquid at room temperature.)) or (((-9 + -3) > (-2 + 19)) and ((13 * -6) < (4 * 8 + 4 * 3))) or (2063 is a leap year.))))
B. not (not ((((5 * 10 + 9 * -6) <= (10 % 2)) or ((((-5 * -5 * 10 * -3) < (-11 - -1)) or (The 1964 Olympics were held in Paris.)) and (The French Revolution began occurred in 1789.))) or ((((The chemical symbol for Sulfur is S.) or ((-7 * 10 * 4 * 7) == (19 + 14))) or (((15 + -11) <= (10 * -1 * 7 * 2)) or ((-12 + 0) <= (19 + -3) <= (-4 * 7 + 8 * 6)))) and ((The capital of Ukraine is Kyiv.) or ((Sharks are mammals.) and ((-1 * 4 - -10 * -2) != (-5 * -9)))))))
C. (not not ((not not ((((-7 * 3 * -8 * -1) >= (-3 * -8)) and (A elephant has 4 legs.)) and (not not (Earth is the 1st planet from the Sun.)))) and (not not ((585 is a Fibonacci number.) or (not not ((-10 * -10 + -7 * -3) <= (12 - 3) <= (-11 * -15))))))) and (not ((not (((The chemical symbol for Aluminum is Ne.) and (Diamond is a solid at room temperature.)) and (not not ((10 * -4 + 2 * 6) != (3 + 15))))) and (not not (((-20 * 5) <= (3 * 6 * 8 * 3) <= (1 ** 2)) or ((-20 - -13) <= (-16 * -8))))))
D. not not (not not (not (((not not ((12 * -13) != (-19 * 2))) and (The 1928 Olympics were held in Amsterdam.)) or (not ((-7 * 3) < (5 * -4 + -5 * 8))) or (not (Japan is in Asia.)))))
E. not not (((not (not not (Antarctica is the coldest continent.))) and (((not not (The capital of Argentina is Paris.)) and ((37 % 2) <= (19 + -5) <= (5 % 6))) or ((((-11 * -11) != (10 * -10 - -6 * -4)) or (Air is a solid at room temperature.)) and (((10 - -13) < (15 + 18) < (16 * -16)) or (1983 is a leap year.))))) and (not (((not (1909 is a leap year.)) and ((-3 - -1) <= (-12 - 4))) or ((4 ** 1) < (11 - 16)))))
F. not not (not not (not not ((((The 2012 Olympics were held in London.) or ((11 - 7) < (-11 + 15) < (1 % 3))) and (not (The Sun revolves around the Earth.))) and ((((-17 * -1) >= (4 - -13)) or (2017 is a leap year.)) and (Gold is a solid at room temperature.)))))
G. not (((((((-13 * -1) <= (7 - -9)) or ((18 * -10) != (14 + 3))) and (((-10 + -3) <= (-3 * 15)) and (The human body has 150 bones.))) or ((10 + 5) == (-3 - -14))) and ((not ((1919 is a leap year.) or (Nigeria is in Asia.))) and (((8 - -11) >= (-2 + 10)) or (1974 is a leap year.)))) and (not (((not (Christopher Columbus reached America occurred in 1492.)) and ((-17 - 12) <= (7 + 17))) and (The currency of Thailand is the Baht.))))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "B,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "en",
"num_options": 7,
"seed": 95073632,
"true_count": 3
},
"question": "Consider the following logical expressions:\n\nA. not ((not (not not (The currency of United Kingdom is the Peso.))) or (((not ((The 2016 Olympics were held in Melbourne.) or ((18 * -14) != (-8 * 6)))) or (not ((10 + 7) <= (-2 - 12)))) or (not not (((4 ** 3) > (0 + 20)) or ((18 * -13) < (7 + -3)))) or ((((Diamonds are made of carbon.) or (Neptune is the 8th planet from the Sun.)) or (Oxygen is a liquid at room temperature.)) or (((-9 + -3) > (-2 + 19)) and ((13 * -6) < (4 * 8 + 4 * 3))) or (2063 is a leap year.))))\nB. not (not ((((5 * 10 + 9 * -6) <= (10 % 2)) or ((((-5 * -5 * 10 * -3) < (-11 - -1)) or (The 1964 Olympics were held in Paris.)) and (The French Revolution began occurred in 1789.))) or ((((The chemical symbol for Sulfur is S.) or ((-7 * 10 * 4 * 7) == (19 + 14))) or (((15 + -11) <= (10 * -1 * 7 * 2)) or ((-12 + 0) <= (19 + -3) <= (-4 * 7 + 8 * 6)))) and ((The capital of Ukraine is Kyiv.) or ((Sharks are mammals.) and ((-1 * 4 - -10 * -2) != (-5 * -9)))))))\nC. (not not ((not not ((((-7 * 3 * -8 * -1) >= (-3 * -8)) and (A elephant has 4 legs.)) and (not not (Earth is the 1st planet from the Sun.)))) and (not not ((585 is a Fibonacci number.) or (not not ((-10 * -10 + -7 * -3) <= (12 - 3) <= (-11 * -15))))))) and (not ((not (((The chemical symbol for Aluminum is Ne.) and (Diamond is a solid at room temperature.)) and (not not ((10 * -4 + 2 * 6) != (3 + 15))))) and (not not (((-20 * 5) <= (3 * 6 * 8 * 3) <= (1 ** 2)) or ((-20 - -13) <= (-16 * -8))))))\nD. not not (not not (not (((not not ((12 * -13) != (-19 * 2))) and (The 1928 Olympics were held in Amsterdam.)) or (not ((-7 * 3) < (5 * -4 + -5 * 8))) or (not (Japan is in Asia.)))))\nE. not not (((not (not not (Antarctica is the coldest continent.))) and (((not not (The capital of Argentina is Paris.)) and ((37 % 2) <= (19 + -5) <= (5 % 6))) or ((((-11 * -11) != (10 * -10 - -6 * -4)) or (Air is a solid at room temperature.)) and (((10 - -13) < (15 + 18) < (16 * -16)) or (1983 is a leap year.))))) and (not (((not (1909 is a leap year.)) and ((-3 - -1) <= (-12 - 4))) or ((4 ** 1) < (11 - 16)))))\nF. not not (not not (not not ((((The 2012 Olympics were held in London.) or ((11 - 7) < (-11 + 15) < (1 % 3))) and (not (The Sun revolves around the Earth.))) and ((((-17 * -1) >= (4 - -13)) or (2017 is a leap year.)) and (Gold is a solid at room temperature.)))))\nG. not (((((((-13 * -1) <= (7 - -9)) or ((18 * -10) != (14 + 3))) and (((-10 + -3) <= (-3 * 15)) and (The human body has 150 bones.))) or ((10 + 5) == (-3 - -14))) and ((not ((1919 is a leap year.) or (Nigeria is in Asia.))) and (((8 - -11) >= (-2 + 10)) or (1974 is a leap year.)))) and (not (((not (Christopher Columbus reached America occurred in 1492.)) and ((-17 - 12) <= (7 + 17))) and (The currency of Thailand is the Baht.))))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
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"language": "en",
"num_options": 7,
"seed": 95073632,
"true_count": 3
},
"seed": 95073632,
"task_id": 695073632,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not not (((人类只使用了大脑的10%。) and (汞在常温下是液体。)) and (((-12 + 11) < (-16 + -13) < (-2 + -1)) or (2045年是闰年。)))
B. ((not ((3 ** 3) <= (17 - -7))) and ((-16 + 12) <= (-13 + 17))) or (((欧盟的货币是比索。) or ((19 - 5) != (14 - -3))) or (not (第二次世界大战开始发生在1939年。)))
C. (not (7大于12。)) or (not not (((-4 - -8) <= (30 % 4)) or ((7 + 12) < (-9 * -7 - 10 * 2) < (-5 - 17))))
D. (1928年奥运会在悉尼举办。) and (((美国宣布独立发生在1766年。) or (美国宣布独立发生在1781年。)) and (((-12 - 3) == (-18 + 6)) and (铬的化学符号是Cr。)))
E. (not ((银在常温下是气体。) and ((9 - -6) >= (10 % 4)))) or ((火星是距离太阳第7近的行星。) or ((汞在常温下是液体。) and (水在常温下是液体。)))
F. not (not (((1 ** 3) <= (5 * 4 * -10 * -1) <= (15 % 5)) or ((2 ** 3) != (9 + -8))))
G. ((((-1 + 3) <= (19 * 10) <= (10 + 20)) and ((-1 * -10) < (-18 + -11) < (40 % 5))) and (((1 ** 1) >= (4 ** 3)) or (八月有31天。))) or ((not not ((4 - -5) >= (12 * -2))) and (((4 * 5) == (-14 + 2)) and (锌的化学符号是O。)))
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,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 7,
"seed": 88024858,
"true_count": 4
},
"question": "审视以下逻辑表达式：\n\nA. not not (((人类只使用了大脑的10%。) and (汞在常温下是液体。)) and (((-12 + 11) < (-16 + -13) < (-2 + -1)) or (2045年是闰年。)))\nB. ((not ((3 ** 3) <= (17 - -7))) and ((-16 + 12) <= (-13 + 17))) or (((欧盟的货币是比索。) or ((19 - 5) != (14 - -3))) or (not (第二次世界大战开始发生在1939年。)))\nC. (not (7大于12。)) or (not not (((-4 - -8) <= (30 % 4)) or ((7 + 12) < (-9 * -7 - 10 * 2) < (-5 - 17))))\nD. (1928年奥运会在悉尼举办。) and (((美国宣布独立发生在1766年。) or (美国宣布独立发生在1781年。)) and (((-12 - 3) == (-18 + 6)) and (铬的化学符号是Cr。)))\nE. (not ((银在常温下是气体。) and ((9 - -6) >= (10 % 4)))) or ((火星是距离太阳第7近的行星。) or ((汞在常温下是液体。) and (水在常温下是液体。)))\nF. not (not (((1 ** 3) <= (5 * 4 * -10 * -1) <= (15 % 5)) or ((2 ** 3) != (9 + -8))))\nG. ((((-1 + 3) <= (19 * 10) <= (10 + 20)) and ((-1 * -10) < (-18 + -11) < (40 % 5))) and (((1 ** 1) >= (4 ** 3)) or (八月有31天。))) or ((not not ((4 - -5) >= (12 * -2))) and (((4 * 5) == (-14 + 2)) and (锌的化学符号是O。)))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
},
"metadata": {
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"language": "cn",
"num_options": 7,
"seed": 88024858,
"true_count": 4
},
"seed": 88024858,
"task_id": 688024858,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not (Ice is a solid at room temperature.)
B. (not (((-6 * 6 + -10 * -10) >= (5 - -5)) or (The capital of Portugal is Lisbon.))) or ((Uranus is the 8th planet from the Sun.) and ((-1 - 12) <= (16 + 6)))
C. ((3 ** 2) < (-2 * -2 + -2 * -7) < (5 ** 1)) and ((((13 * 13) == (0 * 4 - -1 * -4)) and (1963 is a leap year.)) and ((10 * 10 + -7 * 8) <= (-4 * -6 - 1 * 2) <= (5 - -9)))
D. The speed of light is approximately 300,000 km/s.
E. (not not (The chemical symbol for Helium is He.)) and ((New Zealand is in Oceania.) or (The capital of Czech Republic is Singapore.)) and ((Oil is a liquid at room temperature.) and ((-11 * -8) <= (-12 - -1)))
F. (not not (((4 - 17) <= (-4 * -4 - -10 * 9) <= (11 * 7)) or (The chemical symbol for Cobalt is P.))) and ((Sound cannot travel through a vacuum.) and (United States is in North America.))
Which ones are true? List the labels of all true options in \boxed{}, separated by commas. | {
"game_data": {
"answer": "D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
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"seed": 88912424,
"true_count": 1
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"question": "Examine these expressions:\n\nA. not (Ice is a solid at room temperature.)\nB. (not (((-6 * 6 + -10 * -10) >= (5 - -5)) or (The capital of Portugal is Lisbon.))) or ((Uranus is the 8th planet from the Sun.) and ((-1 - 12) <= (16 + 6)))\nC. ((3 ** 2) < (-2 * -2 + -2 * -7) < (5 ** 1)) and ((((13 * 13) == (0 * 4 - -1 * -4)) and (1963 is a leap year.)) and ((10 * 10 + -7 * 8) <= (-4 * -6 - 1 * 2) <= (5 - -9)))\nD. The speed of light is approximately 300,000 km/s.\nE. (not not (The chemical symbol for Helium is He.)) and ((New Zealand is in Oceania.) or (The capital of Czech Republic is Singapore.)) and ((Oil is a liquid at room temperature.) and ((-11 * -8) <= (-12 - -1)))\nF. (not not (((4 - 17) <= (-4 * -4 - -10 * 9) <= (11 * 7)) or (The chemical symbol for Cobalt is P.))) and ((Sound cannot travel through a vacuum.) and (United States is in North America.))\n\nWhich ones are true? List the labels of all true options in \\boxed{}, separated by commas."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 6,
"seed": 88912424,
"true_count": 1
},
"seed": 88912424,
"task_id": 688912424,
"task_type": "boolean_expressions"
} |
logic-v2 | 审视以下逻辑表达式：
A. not ((not (((-12 - 16) < (2 * 0 + 3 * 6) < (0 * 2 - 5 * -4)) and (not not (not not (太阳绕地球运转。))))) or (not not (not (not ((38是质数。) or (泰国的首都是曼谷。))))))
B. (not not (not (not not (((-4 * 4) == (6 - 11)) and (((4 ** 3) >= (11 + -5)) or ((1 ** 1) < (7 + -14))))))) or (not (not (not not (三月有29天。))))
C. not (not not ((((2 ** 1) >= (8 * 12)) or (not not ((20 % 2) <= (27 % 1) <= (-9 + -2)))) or (not (not (1917年是闰年。))) or (((24 % 5) >= (0 * 6 * -5 * 6)) and (((50 % 4) != (5 * -10 * 8 * 3)) or (摩洛哥的首都是巴西利亚。)) and (((1984年奥运会在亚特兰大举办。) and (西班牙位于欧洲。)) or ((土星是距离太阳第7近的行星。) or ((1 ** 3) >= (-11 - 13)))))))
D. not not (((not not (not not (901是斐波那契数。))) and (((((-13 * -1) > (2 - 5)) or (巴西的货币是克朗。)) or (not ((-5 * -8) < (40 % 6)))) and ((((-6 * 0 * 0 * 7) > (-5 * 10 * -2 * 10)) or (瑞士的首都是伯尔尼。)) and ((5 ** 3) >= (8 % 9))))) or (not not (not (一月有31天。))))
E. ((not not ((((98大于33。) and (龙虾有4条腿。)) and (地球是距离太阳第3近的行星。)) and (((1954年是闰年。) or (闪电不会两次击中同一个地方。)) or (((42 % 10) <= (12 - -3) <= (-5 * -6 + 5 * -3)) or (94能被12整除。))))) or (not (not (not not (((1 ** 2) > (10 * -7 - -3 * -8)) and (铜在常温下是气体。)))))) or (not (not (((日本的首都是东京。) and (not not (企鹅是鸟类。))) and (((0 * 1 - 1 * -8) < (-6 - 12)) or (氢的化学符号是Pb。)) and ((((10 % 9) <= (10 * -3 - 6 * 1)) or (闪电不会两次击中同一个地方。)) or ((4 ** 2) > (-13 + 6))))))
F. not not (not not ((((巴西的货币是雷亚尔。) and (not (硅的化学符号是Si。))) or (not not (马来西亚的首都是华沙。)) or ((((3 - 17) == (1 * 12)) and (1920年奥运会在圣路易斯举办。)) or (((-20 * -15) <= (45 % 5)) and (加拿大位于北美洲。)))) or ((中国长城是在一年内建成的。) and ((8 * 6 * 3 * 8) != (16 * -11))) or ((蛇有0条腿。) and ((印度尼西亚的首都是雅加达。) and ((-18 - -9) == (0 + 8))) and ((19 % 10) < (-10 * 6 - -5 * 8) < (-9 * -7 - -6 * 5)))))
G. (not not ((not not ((1 * 3 - -3 * 6) >= (8 * -4 * -3 * -3))) and ((铂的化学符号是Zn。) and ((4 - 12) <= (12 - 2) <= (14 * 12))))) or ((((not not (75能被5整除。)) or (狗有6条腿。) or (((144的平方根是12。) and (越南的货币是越南盾。)) or (not not (第一次世界大战结束发生在1917年。)))) and ((not not ((菲律宾的货币是瑞士法郎。) or ((49 % 7) <= (9 * 9 - 1 * 2)))) and (2069年是闰年。) and ((兔子是哺乳动物。) or ((五月有31天。) and (1976年奥运会在蒙特利尔举办。))))) and (not ((not not (((20 + 5) != (1 * 2)) or ((-13 * -1) >= (4 ** 3)))) or ((钾的化学符号是K。) and (1908年奥运会在伦敦举办。)) or (猪有6条腿。))))
哪些表达式为真？在 \boxed{} 中用逗号分隔给出答案。 | {
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"question": "审视以下逻辑表达式：\n\nA. not ((not (((-12 - 16) < (2 * 0 + 3 * 6) < (0 * 2 - 5 * -4)) and (not not (not not (太阳绕地球运转。))))) or (not not (not (not ((38是质数。) or (泰国的首都是曼谷。))))))\nB. (not not (not (not not (((-4 * 4) == (6 - 11)) and (((4 ** 3) >= (11 + -5)) or ((1 ** 1) < (7 + -14))))))) or (not (not (not not (三月有29天。))))\nC. not (not not ((((2 ** 1) >= (8 * 12)) or (not not ((20 % 2) <= (27 % 1) <= (-9 + -2)))) or (not (not (1917年是闰年。))) or (((24 % 5) >= (0 * 6 * -5 * 6)) and (((50 % 4) != (5 * -10 * 8 * 3)) or (摩洛哥的首都是巴西利亚。)) and (((1984年奥运会在亚特兰大举办。) and (西班牙位于欧洲。)) or ((土星是距离太阳第7近的行星。) or ((1 ** 3) >= (-11 - 13)))))))\nD. not not (((not not (not not (901是斐波那契数。))) and (((((-13 * -1) > (2 - 5)) or (巴西的货币是克朗。)) or (not ((-5 * -8) < (40 % 6)))) and ((((-6 * 0 * 0 * 7) > (-5 * 10 * -2 * 10)) or (瑞士的首都是伯尔尼。)) and ((5 ** 3) >= (8 % 9))))) or (not not (not (一月有31天。))))\nE. ((not not ((((98大于33。) and (龙虾有4条腿。)) and (地球是距离太阳第3近的行星。)) and (((1954年是闰年。) or (闪电不会两次击中同一个地方。)) or (((42 % 10) <= (12 - -3) <= (-5 * -6 + 5 * -3)) or (94能被12整除。))))) or (not (not (not not (((1 ** 2) > (10 * -7 - -3 * -8)) and (铜在常温下是气体。)))))) or (not (not (((日本的首都是东京。) and (not not (企鹅是鸟类。))) and (((0 * 1 - 1 * -8) < (-6 - 12)) or (氢的化学符号是Pb。)) and ((((10 % 9) <= (10 * -3 - 6 * 1)) or (闪电不会两次击中同一个地方。)) or ((4 ** 2) > (-13 + 6))))))\nF. not not (not not ((((巴西的货币是雷亚尔。) and (not (硅的化学符号是Si。))) or (not not (马来西亚的首都是华沙。)) or ((((3 - 17) == (1 * 12)) and (1920年奥运会在圣路易斯举办。)) or (((-20 * -15) <= (45 % 5)) and (加拿大位于北美洲。)))) or ((中国长城是在一年内建成的。) and ((8 * 6 * 3 * 8) != (16 * -11))) or ((蛇有0条腿。) and ((印度尼西亚的首都是雅加达。) and ((-18 - -9) == (0 + 8))) and ((19 % 10) < (-10 * 6 - -5 * 8) < (-9 * -7 - -6 * 5)))))\nG. (not not ((not not ((1 * 3 - -3 * 6) >= (8 * -4 * -3 * -3))) and ((铂的化学符号是Zn。) and ((4 - 12) <= (12 - 2) <= (14 * 12))))) or ((((not not (75能被5整除。)) or (狗有6条腿。) or (((144的平方根是12。) and (越南的货币是越南盾。)) or (not not (第一次世界大战结束发生在1917年。)))) and ((not not ((菲律宾的货币是瑞士法郎。) or ((49 % 7) <= (9 * 9 - 1 * 2)))) and (2069年是闰年。) and ((兔子是哺乳动物。) or ((五月有31天。) and (1976年奥运会在蒙特利尔举办。))))) and (not ((not not (((20 + 5) != (1 * 2)) or ((-13 * -1) >= (4 ** 3)))) or ((钾的化学符号是K。) and (1908年奥运会在伦敦举办。)) or (猪有6条腿。))))\n\n哪些表达式为真？在 \\boxed{} 中用逗号分隔给出答案。"
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logic-v2 | Review these logical expressions:
A. not not (not ((((-16 + 14) <= (-5 + 14) <= (36 % 10)) or ((not not ((-20 + -12) == (0 * 4 + 7 * -2))) or (not not (67 is divisible by 2.)))) and ((10 * 7 * 1 * -2) > (-7 * 6 + -1 * -3)) and ((not not ((Earth is the 4th planet from the Sun.) or ((-10 * 10 * -1 * -10) == (20 - 16)))) and ((The currency of Switzerland is the Franc.) and (The chemical symbol for Mercury is Ne.)) and ((16 is greater than 82.) and (A iguana is a bird.)))))
B. not not (((not (not not (There are 29 days in September.))) and (not not (not not (Penguins can fly.)))) and (not ((Antarctica is the coldest continent.) or ((((26 % 1) < (16 % 7) < (6 * -4 - 6 * -8)) and (Saudi Arabia is in Africa.)) and (not not ((13 * -18) > (8 * -1 - -3 * 2)))))))
C. not not (not not (not not (((((2 ** 2) == (-5 * 7)) and ((-2 * -10 - -3 * 0) <= (-9 + 16))) or (((7 - 4) <= (-14 + 20)) and ((5 * 0 + 2 * 8) <= (2 ** 3)))) and (not not (not not ((4 * 15) < (-17 - 19)))))))
D. not (not ((not (not not (((-20 - 2) == (10 + 8)) or (Diamond is a solid at room temperature.)))) or ((37 % 8) < (-2 * 13)) or (((((-7 + -8) == (-4 + -18)) or (Uranus is the 7th planet from the Sun.)) or ((There are 30 days in March.) and (The 1912 Olympics were held in Stockholm.))) and ((3 * 7 + 2 * 2) >= (5 ** 3)))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"question": "Review these logical expressions:\n\nA. not not (not ((((-16 + 14) <= (-5 + 14) <= (36 % 10)) or ((not not ((-20 + -12) == (0 * 4 + 7 * -2))) or (not not (67 is divisible by 2.)))) and ((10 * 7 * 1 * -2) > (-7 * 6 + -1 * -3)) and ((not not ((Earth is the 4th planet from the Sun.) or ((-10 * 10 * -1 * -10) == (20 - 16)))) and ((The currency of Switzerland is the Franc.) and (The chemical symbol for Mercury is Ne.)) and ((16 is greater than 82.) and (A iguana is a bird.)))))\nB. not not (((not (not not (There are 29 days in September.))) and (not not (not not (Penguins can fly.)))) and (not ((Antarctica is the coldest continent.) or ((((26 % 1) < (16 % 7) < (6 * -4 - 6 * -8)) and (Saudi Arabia is in Africa.)) and (not not ((13 * -18) > (8 * -1 - -3 * 2)))))))\nC. not not (not not (not not (((((2 ** 2) == (-5 * 7)) and ((-2 * -10 - -3 * 0) <= (-9 + 16))) or (((7 - 4) <= (-14 + 20)) and ((5 * 0 + 2 * 8) <= (2 ** 3)))) and (not not (not not ((4 * 15) < (-17 - 19)))))))\nD. not (not ((not (not not (((-20 - 2) == (10 + 8)) or (Diamond is a solid at room temperature.)))) or ((37 % 8) < (-2 * 13)) or (((((-7 + -8) == (-4 + -18)) or (Uranus is the 7th planet from the Sun.)) or ((There are 30 days in March.) and (The 1912 Olympics were held in Stockholm.))) and ((3 * 7 + 2 * 2) >= (5 ** 3)))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
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logic-v2 | Review these logical expressions:
A. not not (not not (not (((27 % 4) < (-15 + -3)) and (((United States is in North America.) or (China is in Asia.)) or ((France is in Africa.) or ((13 - 0) != (-3 * 7 * -2 * -3)))))))
B. not not (not ((not (((2074 is a leap year.) and ((19 + -7) >= (-5 * 7 - -10 * 5))) and ((The Titanic sank occurred in 1912.) or (World War II began occurred in 1939.)))) or ((not ((The currency of Vietnam is the Zloty.) and (269 is a perfect square.))) or ((Morocco is in Africa.) or (Gold is a liquid at room temperature.)))))
C. (not ((((((-10 * 6 + 6 * -5) < (20 + 11)) or ((2 - -17) != (15 % 10))) or (not ((-4 + -18) <= (8 * 0 + 4 * -4)))) and ((8 + 5) != (15 - 20))) and ((((Copper is a liquid at room temperature.) and ((-6 * 5 + -9 * 3) > (23 % 3))) and (not ((-6 * -18) == (3 * 9 * 6 * 1)))) or (((-11 + 14) < (44 % 9)) or ((The chemical symbol for Titanium is Ti.) and ((-10 + -19) <= (-13 * 20))))))) or (not not (not not (not ((-5 * -4 + 5 * 8) >= (17 + -12)))))
D. not (not (((Diamonds are made of carbon.) and (((There are 30 days in November.) and ((25 % 6) >= (9 * 6 + -3 * -9))) or (not not (The currency of India is the Rupee.)))) and (not not (Argentina is in South America.))))
E. not not (not (((Neptune is the 8th planet from the Sun.) and ((13 % 7) < (24 % 1))) or ((Colombia is in South America.) and ((The capital of Cuba is Havana.) and ((-7 * -2 * -2 * 2) == (10 * -4 - 3 * 5))) and (A day on Earth is 24 hours.))))
F. not ((not ((((5 ** 1) <= (0 * 18)) or (not not (The currency of United Kingdom is the Dollar.))) or (((20 * 6) > (12 - -13)) or (((-1 - 4) > (-10 * -9 * 10 * -4)) and (39 is greater than 67.))))) or (not (not ((-9 * 3 * 10 * -10) != (-14 + 2)))))
G. not not (not not ((((2 ** 1) >= (-7 + -3)) or (not (((-1 * -5) <= (1 ** 1)) or (There are 31 days in December.)))) and ((Ice is a gas at room temperature.) and ((10 + -15) != (11 + -11)))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"question": "Review these logical expressions:\n\nA. not not (not not (not (((27 % 4) < (-15 + -3)) and (((United States is in North America.) or (China is in Asia.)) or ((France is in Africa.) or ((13 - 0) != (-3 * 7 * -2 * -3)))))))\nB. not not (not ((not (((2074 is a leap year.) and ((19 + -7) >= (-5 * 7 - -10 * 5))) and ((The Titanic sank occurred in 1912.) or (World War II began occurred in 1939.)))) or ((not ((The currency of Vietnam is the Zloty.) and (269 is a perfect square.))) or ((Morocco is in Africa.) or (Gold is a liquid at room temperature.)))))\nC. (not ((((((-10 * 6 + 6 * -5) < (20 + 11)) or ((2 - -17) != (15 % 10))) or (not ((-4 + -18) <= (8 * 0 + 4 * -4)))) and ((8 + 5) != (15 - 20))) and ((((Copper is a liquid at room temperature.) and ((-6 * 5 + -9 * 3) > (23 % 3))) and (not ((-6 * -18) == (3 * 9 * 6 * 1)))) or (((-11 + 14) < (44 % 9)) or ((The chemical symbol for Titanium is Ti.) and ((-10 + -19) <= (-13 * 20))))))) or (not not (not not (not ((-5 * -4 + 5 * 8) >= (17 + -12)))))\nD. not (not (((Diamonds are made of carbon.) and (((There are 30 days in November.) and ((25 % 6) >= (9 * 6 + -3 * -9))) or (not not (The currency of India is the Rupee.)))) and (not not (Argentina is in South America.))))\nE. not not (not (((Neptune is the 8th planet from the Sun.) and ((13 % 7) < (24 % 1))) or ((Colombia is in South America.) and ((The capital of Cuba is Havana.) and ((-7 * -2 * -2 * 2) == (10 * -4 - 3 * 5))) and (A day on Earth is 24 hours.))))\nF. not ((not ((((5 ** 1) <= (0 * 18)) or (not not (The currency of United Kingdom is the Dollar.))) or (((20 * 6) > (12 - -13)) or (((-1 - 4) > (-10 * -9 * 10 * -4)) and (39 is greater than 67.))))) or (not (not ((-9 * 3 * 10 * -10) != (-14 + 2)))))\nG. not not (not not ((((2 ** 1) >= (-7 + -3)) or (not (((-1 * -5) <= (1 ** 1)) or (There are 31 days in December.)))) and ((Ice is a gas at room temperature.) and ((10 + -15) != (11 + -11)))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
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logic-v2 | Evaluate each expression below:
A. not not (not not (not (((not ((2 ** 2) != (-10 + 18))) or (not not ((-1 * 5 + 8 * 0) < (5 % 9) < (-2 * -8)))) and (((A snake is a fish.) and ((-20 + 19) == (18 - 0))) or ((3 - -4) <= (-10 + -18))))))
B. not (not (((not not (not not ((16 * 9) < (5 ** 2)))) and (The capital of France is Oslo.)) or (not (The 1960 Olympics were held in London.))))
C. not not ((not not (((((8 * 5 - -1 * -6) == (2 ** 3)) and (The currency of Chile is the Peso.)) or ((9 + 11) > (-8 * -13))) or ((not (A beetle is an insect.)) and (not not (The 1980 Olympics were held in Paris.))))) or (((((1 ** 2) != (20 + -3)) or ((1 + 7) != (8 * 8 + -4 * 6))) and (Neptune is the 2nd planet from the Sun.)) or (not (not (The 2008 Olympics were held in Seoul.)))) or (not not (not not (((8 % 1) != (-3 + -1)) and (not not (Steam is a solid at room temperature.))))))
D. (not ((not not (not ((A butterfly is an insect.) or (Egypt is in Africa.)))) and ((((The capital of Singapore is Singapore.) or (Venus is the 2nd planet from the Sun.)) and (Alcohol is a liquid at room temperature.)) and (((-19 + 20) <= (-17 - -3)) and ((The chemical symbol for Sulfur is Pb.) and ((13 * -20) >= (-7 * 8 + 2 * -5))))))) or (not (not (not not ((-19 + -3) >= (6 % 6)))))
E. not (not (((There are 30 days in March.) or ((not (The chemical symbol for Chlorine is Au.)) and ((3 ** 1) >= (5 ** 3)))) or (not (The capital of Kenya is Hanoi.))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
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"question": "Evaluate each expression below:\n\nA. not not (not not (not (((not ((2 ** 2) != (-10 + 18))) or (not not ((-1 * 5 + 8 * 0) < (5 % 9) < (-2 * -8)))) and (((A snake is a fish.) and ((-20 + 19) == (18 - 0))) or ((3 - -4) <= (-10 + -18))))))\nB. not (not (((not not (not not ((16 * 9) < (5 ** 2)))) and (The capital of France is Oslo.)) or (not (The 1960 Olympics were held in London.))))\nC. not not ((not not (((((8 * 5 - -1 * -6) == (2 ** 3)) and (The currency of Chile is the Peso.)) or ((9 + 11) > (-8 * -13))) or ((not (A beetle is an insect.)) and (not not (The 1980 Olympics were held in Paris.))))) or (((((1 ** 2) != (20 + -3)) or ((1 + 7) != (8 * 8 + -4 * 6))) and (Neptune is the 2nd planet from the Sun.)) or (not (not (The 2008 Olympics were held in Seoul.)))) or (not not (not not (((8 % 1) != (-3 + -1)) and (not not (Steam is a solid at room temperature.))))))\nD. (not ((not not (not ((A butterfly is an insect.) or (Egypt is in Africa.)))) and ((((The capital of Singapore is Singapore.) or (Venus is the 2nd planet from the Sun.)) and (Alcohol is a liquid at room temperature.)) and (((-19 + 20) <= (-17 - -3)) and ((The chemical symbol for Sulfur is Pb.) and ((13 * -20) >= (-7 * 8 + 2 * -5))))))) or (not (not (not not ((-19 + -3) >= (6 % 6)))))\nE. not (not (((There are 30 days in March.) or ((not (The chemical symbol for Chlorine is Au.)) and ((3 ** 1) >= (5 ** 3)))) or (not (The capital of Kenya is Hanoi.))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
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logic-v2 | 分析以下逻辑表达式：
A. not ((not not ((((龙虾有0条腿。) or ((10 + 11) >= (19 + 0))) and ((哥伦比亚的首都是波哥大。) and ((1 ** 2) == (9 * 3 + 2 * 3)))) and ((10 + -14) == (9 + 1)))) and ((not (((14 * 19) < (8 * 1 - -8 * 10)) or (钙的化学符号是Ca。))) and (新西兰的货币是新西兰元。)) and ((((49 % 5) > (-8 - -2)) or (六月有30天。)) or (not (油在常温下是液体。))))
B. not (not not ((((((49 % 2) >= (-16 - -1)) and ((4 ** 2) == (4 + 20))) or ((十一月有30天。) and ((12 + 13) == (-17 - -2)))) or ((-1 - 14) < (2 * 1 - -5 * -4))) and (((not not (三月有29天。)) or (not ((-2 * 8 - 8 * -5) == (19 + -16)))) and ((10 * 8 - 8 * 5) > (-2 * 8 + 6 * 4)))))
C. not not ((((锌的化学符号是Zn。) and ((4 + -11) != (18 - 12)) and ((-9 - -12) == (1 * 17))) and (not (not ((6 - 17) != (19 + 12))))) or (((not (((1 ** 3) <= (-13 * 1)) and (2012年奥运会在悉尼举办。))) or ((6 + 6) != (-5 + -12))) or (not (七月有31天。))))
D. not (not not ((((4 * -10) != (-18 - 15)) and ((not ((13 * -1) > (24 % 5))) and ((蝙蝠是瞎的。) or ((9 * 4) <= (-4 * 2 * 3 * 8))))) and (汞在常温下是固体。) and ((not not (((5 + -12) >= (6 + 9)) or (1908年奥运会在伦敦举办。))) or (1912年奥运会在斯德哥尔摩举办。))))
E. not not (not (not not ((((-10 * 0 + 6 * 2) < (-12 - 8)) and ((1 % 8) <= (-10 + 9))) or ((not (阿根廷的货币是人民币。)) or (((2 + 1) < (2 * -9 - 6 * -4)) and (652是斐波那契数。))))))
F. not not (not (not not ((水星是距离太阳第1近的行星。) and ((((-10 * 10 * -6 * -10) <= (-7 + 1)) or ((1 ** 2) < (-13 * -5))) and (1988年奥运会在伦敦举办。)))))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
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"question": "分析以下逻辑表达式：\n\nA. not ((not not ((((龙虾有0条腿。) or ((10 + 11) >= (19 + 0))) and ((哥伦比亚的首都是波哥大。) and ((1 ** 2) == (9 * 3 + 2 * 3)))) and ((10 + -14) == (9 + 1)))) and ((not (((14 * 19) < (8 * 1 - -8 * 10)) or (钙的化学符号是Ca。))) and (新西兰的货币是新西兰元。)) and ((((49 % 5) > (-8 - -2)) or (六月有30天。)) or (not (油在常温下是液体。))))\nB. not (not not ((((((49 % 2) >= (-16 - -1)) and ((4 ** 2) == (4 + 20))) or ((十一月有30天。) and ((12 + 13) == (-17 - -2)))) or ((-1 - 14) < (2 * 1 - -5 * -4))) and (((not not (三月有29天。)) or (not ((-2 * 8 - 8 * -5) == (19 + -16)))) and ((10 * 8 - 8 * 5) > (-2 * 8 + 6 * 4)))))\nC. not not ((((锌的化学符号是Zn。) and ((4 + -11) != (18 - 12)) and ((-9 - -12) == (1 * 17))) and (not (not ((6 - 17) != (19 + 12))))) or (((not (((1 ** 3) <= (-13 * 1)) and (2012年奥运会在悉尼举办。))) or ((6 + 6) != (-5 + -12))) or (not (七月有31天。))))\nD. not (not not ((((4 * -10) != (-18 - 15)) and ((not ((13 * -1) > (24 % 5))) and ((蝙蝠是瞎的。) or ((9 * 4) <= (-4 * 2 * 3 * 8))))) and (汞在常温下是固体。) and ((not not (((5 + -12) >= (6 + 9)) or (1908年奥运会在伦敦举办。))) or (1912年奥运会在斯德哥尔摩举办。))))\nE. not not (not (not not ((((-10 * 0 + 6 * 2) < (-12 - 8)) and ((1 % 8) <= (-10 + 9))) or ((not (阿根廷的货币是人民币。)) or (((2 + 1) < (2 * -9 - 6 * -4)) and (652是斐波那契数。))))))\nF. not not (not (not not ((水星是距离太阳第1近的行星。) and ((((-10 * 10 * -6 * -10) <= (-7 + 1)) or ((1 ** 2) < (-13 * -5))) and (1988年奥运会在伦敦举办。)))))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
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logic-v2 | 检验这些表达式：
A. ((((not ((-1 * -2 + 0 * 9) >= (-3 + 14))) and ((4小于等于96。) and (日本的货币是韩元。))) or ((3 * 2 * -5 * 6) == (1 ** 3)) or ((((4 ** 2) == (13 % 1)) and (菲律宾的货币是卢比。)) and (not ((-3 * 1 - 0 * 10) != (-6 - 13))))) and ((15 * 13) > (-9 * 10 - -5 * 1)) and (not not ((-8 * 9) < (9 + -9)))) and ((((1 % 2) == (6 * 6)) or (土星是距离太阳第5近的行星。)) and (not not (((4 + 12) < (8 % 7) < (-4 * 2)) and (not ((20 * 12) <= (1 ** 2))))))
B. (not ((((冰在常温下是液体。) or (第二次世界大战结束发生在1946年。)) or (((14 + 17) != (6 * 2 - 4 * -3)) and (1900年奥运会在东京举办。))) or (((-3 * 6 * -1 * 5) > (10 - 1)) or ((-16 + -19) <= (-10 * 3 + 1 * -1))) or (((英国的货币是雷亚尔。) and (1915年是闰年。)) and (not not (中国位于欧洲。))))) or (((金在常温下是固体。) and ((2 * 9 + -8 * 10) != (4 % 1))) or (((not not ((27 % 5) >= (-10 * -6 - -6 * -2))) and (not not ((3 * -5 + -2 * -9) != (-9 * 5 * 3 * -5)))) and ((not ((-13 * 9) >= (-16 * -15))) and ((氢的化学符号是H。) and (82是质数。)))))
C. (not (((not (第二次世界大战开始发生在1939年。)) and (((19 - -20) < (-16 - -13)) or (以色列的货币是谢克尔。))) or ((((-13 - 0) <= (8 + 11) <= (4 ** 2)) and ((13 * 4) < (-9 + -17))) and ((202是完全平方数。) and (1904年奥运会在雅典举办。))))) and ((not not (not ((889是斐波那契数。) or ((-7 - 8) <= (0 * 10 * 7 * -7))))) or (((-9 * -5 - -7 * 9) >= (16 + -19)) or ((14 + -2) > (44 % 5))))
D. (not not ((((新西兰位于大洋洲。) and (智利的货币是比索。)) or ((猪有4条腿。) and (土星是距离太阳第4近的行星。))) and ((1 ** 1) <= (0 - -16)) and (((氮气在常温下是气体。) and (2000年奥运会在东京举办。)) and (not not (秘鲁位于南美洲。))))) and (not (((-4 * 6 + 7 * 4) <= (-7 * 18)) or (not not (现代奥运会首届举办发生在1886年。)))) and (not ((not (not not (太阳绕地球运转。))) and ((5 * -8 + 0 * 8) != (12 + -5))))
E. (not ((not (((-1 * 4 - 10 * -4) < (5 ** 2) < (20 * 16)) or (镁的化学符号是Mg。))) or (not not (((17 % 6) >= (-5 * 9 + 9 * -4)) or ((6 * 15) < (-1 * 5 * -3 * 7)))))) or (not not (not ((古巴的首都是惠灵顿。) or (蝙蝠是瞎的。)))) or (not not (not ((((19 + -7) < (20 % 2) < (37 % 1)) or ((-14 + 0) <= (10 - -17) <= (5 + 2))) or (((-20 + 10) <= (19 * 13) <= (17 + 3)) and ((-4 + 0) <= (-17 * 15))))))
F. not (((((第一次世界大战结束发生在1923年。) or (木星是距离太阳第2近的行星。)) or ((硫的化学符号是Hg。) and (铁的化学符号是Fe。))) or (((44能被3整除。) or ((2 * -7 + 2 * -6) == (-14 * -8))) or ((1924年奥运会在雅典举办。) or ((4 * 6 * -8 * 1) < (-8 + -10) < (6 * 10 - 0 * 7))))) and (not not ((not not (印度尼西亚的货币是兹罗提。)) or (((4 * 4) >= (5 + 18)) and (氮气在常温下是气体。)))))
G. not (not (((((-13 - -10) == (8 % 1)) and ((-2 + 20) > (-3 - -17))) and ((84能被12整除。) and ((1 - 8) == (-9 - -13)))) and (天王星是距离太阳第1近的行星。) and ((美国宣布独立发生在1776年。) and (((5 - 12) < (22 % 3)) and ((-12 + 17) < (8 * 11))))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
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"question": "检验这些表达式：\n\nA. ((((not ((-1 * -2 + 0 * 9) >= (-3 + 14))) and ((4小于等于96。) and (日本的货币是韩元。))) or ((3 * 2 * -5 * 6) == (1 ** 3)) or ((((4 ** 2) == (13 % 1)) and (菲律宾的货币是卢比。)) and (not ((-3 * 1 - 0 * 10) != (-6 - 13))))) and ((15 * 13) > (-9 * 10 - -5 * 1)) and (not not ((-8 * 9) < (9 + -9)))) and ((((1 % 2) == (6 * 6)) or (土星是距离太阳第5近的行星。)) and (not not (((4 + 12) < (8 % 7) < (-4 * 2)) and (not ((20 * 12) <= (1 ** 2))))))\nB. (not ((((冰在常温下是液体。) or (第二次世界大战结束发生在1946年。)) or (((14 + 17) != (6 * 2 - 4 * -3)) and (1900年奥运会在东京举办。))) or (((-3 * 6 * -1 * 5) > (10 - 1)) or ((-16 + -19) <= (-10 * 3 + 1 * -1))) or (((英国的货币是雷亚尔。) and (1915年是闰年。)) and (not not (中国位于欧洲。))))) or (((金在常温下是固体。) and ((2 * 9 + -8 * 10) != (4 % 1))) or (((not not ((27 % 5) >= (-10 * -6 - -6 * -2))) and (not not ((3 * -5 + -2 * -9) != (-9 * 5 * 3 * -5)))) and ((not ((-13 * 9) >= (-16 * -15))) and ((氢的化学符号是H。) and (82是质数。)))))\nC. (not (((not (第二次世界大战开始发生在1939年。)) and (((19 - -20) < (-16 - -13)) or (以色列的货币是谢克尔。))) or ((((-13 - 0) <= (8 + 11) <= (4 ** 2)) and ((13 * 4) < (-9 + -17))) and ((202是完全平方数。) and (1904年奥运会在雅典举办。))))) and ((not not (not ((889是斐波那契数。) or ((-7 - 8) <= (0 * 10 * 7 * -7))))) or (((-9 * -5 - -7 * 9) >= (16 + -19)) or ((14 + -2) > (44 % 5))))\nD. (not not ((((新西兰位于大洋洲。) and (智利的货币是比索。)) or ((猪有4条腿。) and (土星是距离太阳第4近的行星。))) and ((1 ** 1) <= (0 - -16)) and (((氮气在常温下是气体。) and (2000年奥运会在东京举办。)) and (not not (秘鲁位于南美洲。))))) and (not (((-4 * 6 + 7 * 4) <= (-7 * 18)) or (not not (现代奥运会首届举办发生在1886年。)))) and (not ((not (not not (太阳绕地球运转。))) and ((5 * -8 + 0 * 8) != (12 + -5))))\nE. (not ((not (((-1 * 4 - 10 * -4) < (5 ** 2) < (20 * 16)) or (镁的化学符号是Mg。))) or (not not (((17 % 6) >= (-5 * 9 + 9 * -4)) or ((6 * 15) < (-1 * 5 * -3 * 7)))))) or (not not (not ((古巴的首都是惠灵顿。) or (蝙蝠是瞎的。)))) or (not not (not ((((19 + -7) < (20 % 2) < (37 % 1)) or ((-14 + 0) <= (10 - -17) <= (5 + 2))) or (((-20 + 10) <= (19 * 13) <= (17 + 3)) and ((-4 + 0) <= (-17 * 15))))))\nF. not (((((第一次世界大战结束发生在1923年。) or (木星是距离太阳第2近的行星。)) or ((硫的化学符号是Hg。) and (铁的化学符号是Fe。))) or (((44能被3整除。) or ((2 * -7 + 2 * -6) == (-14 * -8))) or ((1924年奥运会在雅典举办。) or ((4 * 6 * -8 * 1) < (-8 + -10) < (6 * 10 - 0 * 7))))) and (not not ((not not (印度尼西亚的货币是兹罗提。)) or (((4 * 4) >= (5 + 18)) and (氮气在常温下是气体。)))))\nG. not (not (((((-13 - -10) == (8 % 1)) and ((-2 + 20) > (-3 - -17))) and ((84能被12整除。) and ((1 - 8) == (-9 - -13)))) and (天王星是距离太阳第1近的行星。) and ((美国宣布独立发生在1776年。) and (((5 - 12) < (22 % 3)) and ((-12 + 17) < (8 * 11))))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
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logic-v2 | Review these logical expressions:
A. ((not (((((-11 + 12) <= (2 * -4 - -4 * 2)) or ((1 - -13) <= (0 + -3))) and ((20 is a prime number.) or (Peru is in South America.))) or (South Africa is in Africa.))) or (not (not (((There are 31 days in October.) and (1927 is a leap year.)) and (The chemical symbol for Titanium is Ti.))))) or (not (not not ((not not (((-15 - 5) <= (-11 * 17) <= (13 * -4)) or (Mars is the closest planet to the Sun.))) or (not not (The currency of Colombia is the Peso.)))))
B. not (not not (((((Saturn is the 6th planet from the Sun.) or ((2 % 2) > (4 ** 3))) or (((20 % 4) >= (8 - 2)) or (The chemical symbol for Lead is Pb.))) or ((Nitrogen is a gas at room temperature.) and ((5 + 19) <= (8 * 6 + -5 * -1)))) and (The square root of 64 is 8.) and (((not not ((5 - 15) < (2 * 8) < (-20 * 4))) or (The human body has 206 bones.)) and (Humans only use 10% of their brain.))))
C. not not (not not ((((1 ** 1) < (-13 * -18) < (9 * 5 * -9 * -1)) and (not ((1 ** 1) == (18 + 6)))) or ((There are 30 days in March.) or (((33 % 3) != (12 + 2)) or (A tuna is a mammal.)) or (not not ((1 - -3) >= (9 * 4 + 8 * -8))))))
D. not not (not (not not (not not ((The 1984 Olympics were held in Mexico City.) or (((18 * -6) >= (-1 + 15)) or (There are 30 days in August.))))))
E. (not (not ((not (((18 % 9) <= (7 * -6 + -5 * 1)) and ((7 * 3) <= (12 - 8) <= (16 + 18)))) or ((A butterfly has 0 legs.) or (Saturn is the 5th planet from the Sun.)) or ((3 % 8) == (-12 + -14))))) or (not (not (not ((2 % 8) <= (0 + -1) <= (8 + 5)))))
F. not (not not (((not not ((There are 29 days in January.) or ((-12 + -13) != (-9 + -18)))) or (not (((4 + 7) < (13 - 19)) or ((3 * 10 * 7 * -8) < (-17 + 4))))) or ((((12 - 0) > (14 * -12)) and (not not (Alcohol is a liquid at room temperature.))) or (A elephant has 4 legs.) or (not (((10 % 1) != (5 - -15)) and ((3 * 18) <= (-11 - -18)))))))
G. not not ((not (((((-18 + 14) <= (10 * -8 * 4 * -5)) and ((-7 * 1 - -5 * 8) <= (4 * -10 + -9 * -1) <= (8 - 16))) and (((-8 - -15) > (-7 - 19)) and ((-9 + 4) <= (11 - -8)))) and ((not not ((3 ** 1) > (-3 * -3 - 9 * -10))) or ((-11 * 20) <= (3 - -8) <= (-11 + -20))))) or ((not (not (((-8 * 4 + -6 * -8) > (-4 + 0)) and ((-13 * -5) >= (-8 + 4))))) or (not not (A frog has 4 legs.))))
H. not not (not not ((not not ((Russia is in Europe.) or ((The square root of 64 is 8.) and (Silver is a solid at room temperature.)))) or (((not (China is in Asia.)) and (not not (1916 is a leap year.))) and (South Africa is in Africa.) and (not (((-6 + 6) > (4 + 13)) or (The capital of Venezuela is Caracas.))))))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
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"question": "Review these logical expressions:\n\nA. ((not (((((-11 + 12) <= (2 * -4 - -4 * 2)) or ((1 - -13) <= (0 + -3))) and ((20 is a prime number.) or (Peru is in South America.))) or (South Africa is in Africa.))) or (not (not (((There are 31 days in October.) and (1927 is a leap year.)) and (The chemical symbol for Titanium is Ti.))))) or (not (not not ((not not (((-15 - 5) <= (-11 * 17) <= (13 * -4)) or (Mars is the closest planet to the Sun.))) or (not not (The currency of Colombia is the Peso.)))))\nB. not (not not (((((Saturn is the 6th planet from the Sun.) or ((2 % 2) > (4 ** 3))) or (((20 % 4) >= (8 - 2)) or (The chemical symbol for Lead is Pb.))) or ((Nitrogen is a gas at room temperature.) and ((5 + 19) <= (8 * 6 + -5 * -1)))) and (The square root of 64 is 8.) and (((not not ((5 - 15) < (2 * 8) < (-20 * 4))) or (The human body has 206 bones.)) and (Humans only use 10% of their brain.))))\nC. not not (not not ((((1 ** 1) < (-13 * -18) < (9 * 5 * -9 * -1)) and (not ((1 ** 1) == (18 + 6)))) or ((There are 30 days in March.) or (((33 % 3) != (12 + 2)) or (A tuna is a mammal.)) or (not not ((1 - -3) >= (9 * 4 + 8 * -8))))))\nD. not not (not (not not (not not ((The 1984 Olympics were held in Mexico City.) or (((18 * -6) >= (-1 + 15)) or (There are 30 days in August.))))))\nE. (not (not ((not (((18 % 9) <= (7 * -6 + -5 * 1)) and ((7 * 3) <= (12 - 8) <= (16 + 18)))) or ((A butterfly has 0 legs.) or (Saturn is the 5th planet from the Sun.)) or ((3 % 8) == (-12 + -14))))) or (not (not (not ((2 % 8) <= (0 + -1) <= (8 + 5)))))\nF. not (not not (((not not ((There are 29 days in January.) or ((-12 + -13) != (-9 + -18)))) or (not (((4 + 7) < (13 - 19)) or ((3 * 10 * 7 * -8) < (-17 + 4))))) or ((((12 - 0) > (14 * -12)) and (not not (Alcohol is a liquid at room temperature.))) or (A elephant has 4 legs.) or (not (((10 % 1) != (5 - -15)) and ((3 * 18) <= (-11 - -18)))))))\nG. not not ((not (((((-18 + 14) <= (10 * -8 * 4 * -5)) and ((-7 * 1 - -5 * 8) <= (4 * -10 + -9 * -1) <= (8 - 16))) and (((-8 - -15) > (-7 - 19)) and ((-9 + 4) <= (11 - -8)))) and ((not not ((3 ** 1) > (-3 * -3 - 9 * -10))) or ((-11 * 20) <= (3 - -8) <= (-11 + -20))))) or ((not (not (((-8 * 4 + -6 * -8) > (-4 + 0)) and ((-13 * -5) >= (-8 + 4))))) or (not not (A frog has 4 legs.))))\nH. not not (not not ((not not ((Russia is in Europe.) or ((The square root of 64 is 8.) and (Silver is a solid at room temperature.)))) or (((not (China is in Asia.)) and (not not (1916 is a leap year.))) and (South Africa is in Africa.) and (not (((-6 + 6) > (4 + 13)) or (The capital of Venezuela is Caracas.))))))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
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"seed": 55530218,
"true_count": 6
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logic-v2 | 给定以下布尔表达式：
A. 海王星是距离太阳第8近的行星。
B. (8 + -4) < (-16 * 1)
C. (1 ** 3) < (0 - 3)
D. 银在常温下是固体。
E. (八月有31天。) or (九月有30天。)
F. ((空气在常温下是固体。) and ((-7 * -6 * 4 * 5) >= (-6 - -12))) or (not (火星是距离太阳第4近的行星。))
G. (not not (莱特兄弟首次飞行发生在1893年。)) or (not not ((0 * 10 - 8 * -7) <= (11 * -14)))
H. (not ((8 + 10) == (11 - 17))) and (钠的化学符号是U。)
选出所有值为 True 的选项。在 \boxed{} 中以逗号分隔的形式给出答案。 | {
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"question": "给定以下布尔表达式：\n\nA. 海王星是距离太阳第8近的行星。\nB. (8 + -4) < (-16 * 1)\nC. (1 ** 3) < (0 - 3)\nD. 银在常温下是固体。\nE. (八月有31天。) or (九月有30天。)\nF. ((空气在常温下是固体。) and ((-7 * -6 * 4 * 5) >= (-6 - -12))) or (not (火星是距离太阳第4近的行星。))\nG. (not not (莱特兄弟首次飞行发生在1893年。)) or (not not ((0 * 10 - 8 * -7) <= (11 * -14)))\nH. (not ((8 + 10) == (11 - 17))) and (钠的化学符号是U。)\n\n选出所有值为 True 的选项。在 \\boxed{} 中以逗号分隔的形式给出答案。"
},
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"language": "cn",
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"seed": 67668974,
"true_count": 3
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"seed": 67668974,
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logic-v2 | 检验这些表达式：
A. not not (not not ((not (not (((-1 + -9) >= (13 - 9)) and (章鱼有100条腿。)))) and (not not (猪有0条腿。))))
B. not not (not ((not not (((鲨鱼是哺乳动物。) or (第二次世界大战开始发生在1938年。)) or ((8 + -20) == (-8 * 2 - -5 * -8)))) and ((1996年奥运会在北京举办。) or (not not (((12 + 15) < (-1 * -3 - -1 * 6)) and (35大于41。))))))
C. (not (not ((((4 - -4) == (1 ** 2)) and (((39 % 5) < (-15 + -3)) and (1912年奥运会在洛杉矶举办。))) or ((((23 % 10) != (42 % 9)) or ((-3 * -4) == (20 % 5))) or (((2 * -15) <= (1 ** 3)) and (韩国位于大洋洲。)))))) or ((not ((氢的化学符号是H。) and (((6 * -20) > (2 * -4)) or (((9 * -8 * 0 * -3) > (-5 - -2)) and ((3 + -14) == (19 + -7)))))) and (((钻石在常温下是固体。) and ((49 % 7) >= (32 % 10))) and ((氦的化学符号是He。) or ((((2 ** 3) <= (16 - 7) <= (29 % 7)) or (八月有31天。)) or (not not (氧的化学符号是O。))))))
D. not not (((not (((80小于等于18。) or (鲸鱼是鱼类。)) and (not not ((25 % 3) < (6 + -9))))) or ((((6 * -1 - 1 * 9) <= (31 % 1) <= (3 + 20)) and (声音在真空中传播更快。)) and (((22 % 5) == (2 ** 2)) or ((南非的货币是兰特。) or ((3 ** 2) != (-1 * -10)))))) and (not (not (((-8 * -10 - -5 * -6) < (-18 - 13) < (4 * -4 + -9 * -3)) or (not not (马来西亚的首都是吉隆坡。))))))
E. ((not not ((((火星是距离太阳最近的行星。) or (钠的化学符号是Cl。)) or ((氮的化学符号是N。) or (铜在常温下是固体。))) or (7是质数。) or (not not (油在常温下是液体。)))) or (not not (not not (西班牙的首都是首尔。)))) and ((not not (not (埃及的首都是马德里。))) or ((((2099年是闰年。) and (七月有31天。)) or (((7 + 14) < (6 * 8)) or ((-18 - 9) == (5 * -3 * 2 * -8)))) or ((牛有6条腿。) or (八月有31天。)) or (((7 * 9 - 5 * 6) >= (-19 * 18)) or (not ((4 % 9) < (-11 - 7)))))) and (not not ((not ((14 % 6) != (10 - 0))) and (not not (not not (((2 ** 1) != (-5 - 20)) and (猫有10条腿。))))))
F. not not ((((((金在常温下是固体。) and (蛇有0条腿。)) or (not not (氮气在常温下是气体。))) or ((氧气在常温下是液体。) or (((6 * -12) == (-15 - -18)) or ((2 ** 1) < (15 + -10) < (4 - 10))))) or ((not not ((792是斐波那契数。) or (83是质数。))) and ((not not ((18 * 20) < (17 - 17))) and (德国的首都是堪培拉。)))) or (not (not not (((十月有31天。) or (2003年是闰年。)) or (水星是距离太阳第1近的行星。)))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "B,C,D,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 68351124,
"true_count": 4
},
"question": "检验这些表达式：\n\nA. not not (not not ((not (not (((-1 + -9) >= (13 - 9)) and (章鱼有100条腿。)))) and (not not (猪有0条腿。))))\nB. not not (not ((not not (((鲨鱼是哺乳动物。) or (第二次世界大战开始发生在1938年。)) or ((8 + -20) == (-8 * 2 - -5 * -8)))) and ((1996年奥运会在北京举办。) or (not not (((12 + 15) < (-1 * -3 - -1 * 6)) and (35大于41。))))))\nC. (not (not ((((4 - -4) == (1 ** 2)) and (((39 % 5) < (-15 + -3)) and (1912年奥运会在洛杉矶举办。))) or ((((23 % 10) != (42 % 9)) or ((-3 * -4) == (20 % 5))) or (((2 * -15) <= (1 ** 3)) and (韩国位于大洋洲。)))))) or ((not ((氢的化学符号是H。) and (((6 * -20) > (2 * -4)) or (((9 * -8 * 0 * -3) > (-5 - -2)) and ((3 + -14) == (19 + -7)))))) and (((钻石在常温下是固体。) and ((49 % 7) >= (32 % 10))) and ((氦的化学符号是He。) or ((((2 ** 3) <= (16 - 7) <= (29 % 7)) or (八月有31天。)) or (not not (氧的化学符号是O。))))))\nD. not not (((not (((80小于等于18。) or (鲸鱼是鱼类。)) and (not not ((25 % 3) < (6 + -9))))) or ((((6 * -1 - 1 * 9) <= (31 % 1) <= (3 + 20)) and (声音在真空中传播更快。)) and (((22 % 5) == (2 ** 2)) or ((南非的货币是兰特。) or ((3 ** 2) != (-1 * -10)))))) and (not (not (((-8 * -10 - -5 * -6) < (-18 - 13) < (4 * -4 + -9 * -3)) or (not not (马来西亚的首都是吉隆坡。))))))\nE. ((not not ((((火星是距离太阳最近的行星。) or (钠的化学符号是Cl。)) or ((氮的化学符号是N。) or (铜在常温下是固体。))) or (7是质数。) or (not not (油在常温下是液体。)))) or (not not (not not (西班牙的首都是首尔。)))) and ((not not (not (埃及的首都是马德里。))) or ((((2099年是闰年。) and (七月有31天。)) or (((7 + 14) < (6 * 8)) or ((-18 - 9) == (5 * -3 * 2 * -8)))) or ((牛有6条腿。) or (八月有31天。)) or (((7 * 9 - 5 * 6) >= (-19 * 18)) or (not ((4 % 9) < (-11 - 7)))))) and (not not ((not ((14 % 6) != (10 - 0))) and (not not (not not (((2 ** 1) != (-5 - 20)) and (猫有10条腿。))))))\nF. not not ((((((金在常温下是固体。) and (蛇有0条腿。)) or (not not (氮气在常温下是气体。))) or ((氧气在常温下是液体。) or (((6 * -12) == (-15 - -18)) or ((2 ** 1) < (15 + -10) < (4 - 10))))) or ((not not ((792是斐波那契数。) or (83是质数。))) and ((not not ((18 * 20) < (17 - 17))) and (德国的首都是堪培拉。)))) or (not (not not (((十月有31天。) or (2003年是闰年。)) or (水星是距离太阳第1近的行星。)))))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 6,
"language": "cn",
"num_options": 6,
"seed": 68351124,
"true_count": 4
},
"seed": 68351124,
"task_id": 668351124,
"task_type": "boolean_expressions"
} |
logic-v2 | 研究以下逻辑语句：
A. ((((not (火星是距离太阳第4近的行星。)) or (钴的化学符号是Co。)) and ((8 + 9) <= (27 % 5)) and (((1924年奥运会在赫尔辛基举办。) or ((-10 + 1) <= (9 * -19))) and (not (土耳其的首都是雅加达。)))) or ((委内瑞拉的首都是加拉加斯。) and ((-20 + -4) == (0 * 8)))) and ((埃及的货币是欧元。) and (not ((蚂蚁有6条腿。) and ((-12 * -6) <= (-18 - 3))))) and ((not not ((not not (氮气在常温下是固体。)) or (第一次世界大战结束发生在1918年。))) and ((海王星是距离太阳第8近的行星。) and (((-10 - 9) >= (34 % 10)) and (锡的化学符号是Sn。))))
B. ((not not ((((0 - 17) > (-6 * -2 - -6 * 7)) and (猫有4条腿。)) and (not not ((-15 * -12) >= (-17 + 14))))) and (((4 - -10) <= (13 * 0)) and (57是质数。))) and ((not not ((46是质数。) or ((-7 - -14) != (12 + 12)))) and (((丹麦的货币是克朗。) and (not not ((3 ** 1) >= (3 ** 3)))) and ((7 * -10) >= (-5 - 10))))
C. not ((((((18 * 2) != (20 + -17)) and ((-11 * 14) == (-6 * 6))) and ((312是斐波那契数。) or (苏联解体发生在1986年。))) and ((not (尼日利亚位于非洲。)) or (((-16 + 4) > (6 * 17)) or (170是奇数。)))) or (((not ((1 * 9 + -8 * -5) == (-20 * -19))) or (((-16 * -6) > (-16 + -18)) and ((8 * -8 * 3 * 3) < (43 % 6)))) and ((((-10 * -5 - -7 * 7) >= (40 % 10)) or (2004年奥运会在赫尔辛基举办。)) and (((19 % 7) < (-17 * -6)) and (121的平方根是11。)))))
D. ((((14 * -7) >= (12 - 13)) or (法国位于欧洲。)) and (钠的化学符号是Au。) and ((((地球是距离太阳第3近的行星。) and (巴西的首都是首尔。)) or ((10 * 3 * -7 * -2) < (-12 - 0))) and (((14 + -4) >= (4 ** 1)) or (21大于8。)) and ((41 % 7) < (-3 * 6 + 5 * 10)))) and (not not ((((10 * 3 - -2 * 1) < (-6 * -18)) or (((-2 * 13) < (6 - 13) < (-3 * 4 - 5 * 2)) or ((7 + -19) >= (17 + -1)))) or (((1 ** 3) >= (16 * -11)) or (人类只使用了大脑的10%。)) or (((声音无法在真空中传播。) and (18是质数。)) and (((46 % 8) == (19 * -19)) and ((4 * 14) != (2 ** 2))))))
E. not not (not not ((not (2016年奥运会在墨尔本举办。)) and (not not ((20 + -19) < (6 * 5 * 9 * 1)))))
F. (not not ((((匈牙利的货币是福林。) or ((-11 + 20) != (4 - -20))) or ((6 - -11) != (-2 * -2))) or (((丹麦的货币是克朗。) or ((-14 + -14) != (-15 + -13))) and ((钴的化学符号是Co。) or (英国的货币是卢比。))))) and ((not not ((-6 - -20) <= (-4 * 10 * 10 * -3) <= (9 * 5 + 9 * 4))) and (((100的平方根是4。) and (121的平方根是11。)) or ((蜘蛛是昆虫。) and (月球自己发光。))) and ((not not (龙虾有10条腿。)) and ((((0 * 2) == (-7 * -19)) or ((-1 * -7 - -10 * -3) >= (-16 - -13))) and (not (第二次世界大战开始发生在1940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": "E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 53971869,
"true_count": 1
},
"question": "研究以下逻辑语句：\n\nA. ((((not (火星是距离太阳第4近的行星。)) or (钴的化学符号是Co。)) and ((8 + 9) <= (27 % 5)) and (((1924年奥运会在赫尔辛基举办。) or ((-10 + 1) <= (9 * -19))) and (not (土耳其的首都是雅加达。)))) or ((委内瑞拉的首都是加拉加斯。) and ((-20 + -4) == (0 * 8)))) and ((埃及的货币是欧元。) and (not ((蚂蚁有6条腿。) and ((-12 * -6) <= (-18 - 3))))) and ((not not ((not not (氮气在常温下是固体。)) or (第一次世界大战结束发生在1918年。))) and ((海王星是距离太阳第8近的行星。) and (((-10 - 9) >= (34 % 10)) and (锡的化学符号是Sn。))))\nB. ((not not ((((0 - 17) > (-6 * -2 - -6 * 7)) and (猫有4条腿。)) and (not not ((-15 * -12) >= (-17 + 14))))) and (((4 - -10) <= (13 * 0)) and (57是质数。))) and ((not not ((46是质数。) or ((-7 - -14) != (12 + 12)))) and (((丹麦的货币是克朗。) and (not not ((3 ** 1) >= (3 ** 3)))) and ((7 * -10) >= (-5 - 10))))\nC. not ((((((18 * 2) != (20 + -17)) and ((-11 * 14) == (-6 * 6))) and ((312是斐波那契数。) or (苏联解体发生在1986年。))) and ((not (尼日利亚位于非洲。)) or (((-16 + 4) > (6 * 17)) or (170是奇数。)))) or (((not ((1 * 9 + -8 * -5) == (-20 * -19))) or (((-16 * -6) > (-16 + -18)) and ((8 * -8 * 3 * 3) < (43 % 6)))) and ((((-10 * -5 - -7 * 7) >= (40 % 10)) or (2004年奥运会在赫尔辛基举办。)) and (((19 % 7) < (-17 * -6)) and (121的平方根是11。)))))\nD. ((((14 * -7) >= (12 - 13)) or (法国位于欧洲。)) and (钠的化学符号是Au。) and ((((地球是距离太阳第3近的行星。) and (巴西的首都是首尔。)) or ((10 * 3 * -7 * -2) < (-12 - 0))) and (((14 + -4) >= (4 ** 1)) or (21大于8。)) and ((41 % 7) < (-3 * 6 + 5 * 10)))) and (not not ((((10 * 3 - -2 * 1) < (-6 * -18)) or (((-2 * 13) < (6 - 13) < (-3 * 4 - 5 * 2)) or ((7 + -19) >= (17 + -1)))) or (((1 ** 3) >= (16 * -11)) or (人类只使用了大脑的10%。)) or (((声音无法在真空中传播。) and (18是质数。)) and (((46 % 8) == (19 * -19)) and ((4 * 14) != (2 ** 2))))))\nE. not not (not not ((not (2016年奥运会在墨尔本举办。)) and (not not ((20 + -19) < (6 * 5 * 9 * 1)))))\nF. (not not ((((匈牙利的货币是福林。) or ((-11 + 20) != (4 - -20))) or ((6 - -11) != (-2 * -2))) or (((丹麦的货币是克朗。) or ((-14 + -14) != (-15 + -13))) and ((钴的化学符号是Co。) or (英国的货币是卢比。))))) and ((not not ((-6 - -20) <= (-4 * 10 * 10 * -3) <= (9 * 5 + 9 * 4))) and (((100的平方根是4。) and (121的平方根是11。)) or ((蜘蛛是昆虫。) and (月球自己发光。))) and ((not not (龙虾有10条腿。)) and ((((0 * 2) == (-7 * -19)) or ((-1 * -7 - -10 * -3) >= (-16 - -13))) and (not (第二次世界大战开始发生在1940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": 5,
"language": "cn",
"num_options": 6,
"seed": 53971869,
"true_count": 1
},
"seed": 53971869,
"task_id": 653971869,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (((not (冰的密度比液态水小。)) or (((20 + 20) >= (5 * -4 + -4 * 10)) and (智利的货币是人民币。))) and (not not (not not (太阳绕地球运转。)))) and (not not ((2 * 0 + 5 * 3) > (19 + -10)))
B. (not not ((((1 - -18) <= (-17 + -3)) or (第一次世界大战结束发生在1923年。)) and (((7 * -10) == (9 + 0)) or ((8 * 5 * -7 * -5) < (27 % 6) < (17 - -3))))) or ((not ((人类是哺乳动物。) and ((12 * -5) != (-16 + -14)))) and ((韩国的首都是加拉加斯。) or (牛有4条腿。)) and (not (((14 * 7) <= (10 * -5 + 1 * -10) <= (-16 * 7)) and (二氧化碳在常温下是气体。))))
C. ((氦气在常温下是气体。) and (not (not ((-6 - 12) != (-20 + 8))))) and (not (not (((26 % 6) == (-10 - -16)) or (铝的化学符号是Al。))))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "C",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "cn",
"num_options": 3,
"seed": 48070339,
"true_count": 1
},
"question": "检验这些表达式：\n\nA. (((not (冰的密度比液态水小。)) or (((20 + 20) >= (5 * -4 + -4 * 10)) and (智利的货币是人民币。))) and (not not (not not (太阳绕地球运转。)))) and (not not ((2 * 0 + 5 * 3) > (19 + -10)))\nB. (not not ((((1 - -18) <= (-17 + -3)) or (第一次世界大战结束发生在1923年。)) and (((7 * -10) == (9 + 0)) or ((8 * 5 * -7 * -5) < (27 % 6) < (17 - -3))))) or ((not ((人类是哺乳动物。) and ((12 * -5) != (-16 + -14)))) and ((韩国的首都是加拉加斯。) or (牛有4条腿。)) and (not (((14 * 7) <= (10 * -5 + 1 * -10) <= (-16 * 7)) and (二氧化碳在常温下是气体。))))\nC. ((氦气在常温下是气体。) and (not (not ((-6 - 12) != (-20 + 8))))) and (not (not (((26 % 6) == (-10 - -16)) or (铝的化学符号是Al。))))\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": 3,
"seed": 48070339,
"true_count": 1
},
"seed": 48070339,
"task_id": 648070339,
"task_type": "boolean_expressions"
} |
logic-v2 | Analyze these boolean expressions:
A. (not (not not (not ((The capital of Hungary is Budapest.) and ((9 + 0) < (-20 + -1) < (2 * 0 + -8 * 7)))))) or (((The Moon orbits the Earth.) or ((((6 - -12) == (20 * 10)) or (Lightning never strikes the same place twice.)) and ((3 * -5) >= (2 * -4 + -5 * -3)))) or (not ((((-3 * 12) > (-4 * 2 * 4 * -5)) or ((2 ** 1) <= (-8 * -4 - 1 * -3))) and (Water is a liquid at room temperature.))))
B. (not (not (not (not not ((19 * -10) >= (3 ** 1)))))) or (((not (Diamond is a solid at room temperature.)) or ((not ((10 + -11) <= (-15 * 1))) or (((6 * 10) != (-9 * -4 + -7 * 4)) or ((-16 * -2) <= (-17 * 10))))) and ((((The capital of Czech Republic is Prague.) or ((-3 - 15) == (-17 - 18))) and ((960 is a Fibonacci number.) or ((9 * 5 - -6 * -2) > (-16 * 18)))) and (((11 + 7) < (12 % 5)) and ((24 % 4) > (-8 - -16))) and ((9 * 0) >= (-12 + 6))))
C. not (((123 is an odd number.) or ((7 + 9) <= (6 - 17))) and (not (((2 ** 2) >= (11 * 9)) or (The currency of Sweden is the Krona.))) and (not not (The chemical symbol for Iron is S.)))
D. not not (((World War I ended occurred in 1918.) or ((-1 * -17) > (-2 - 19))) and (((The currency of India is the Rupiah.) or (The chemical symbol for Mercury is H.)) and ((The capital of Thailand is Bangkok.) and ((4 - -11) < (23 % 1) < (-11 + 4)))) and (not not (((The 1932 Olympics were held in Montreal.) and (The speed of light is approximately 300,000 km/s.)) or ((The chemical symbol for Potassium is K.) and ((4 ** 3) >= (-1 * -3))))))
E. (not (((Jupiter is the 7th planet from the Sun.) or (Mars is the 7th planet from the Sun.)) and (((13 * -18) > (3 ** 2)) and ((-5 * -7 * 3 * -8) >= (-5 * 1 * -4 * 9))) and (not (Sound travels faster in a vacuum.)))) or ((((50 % 5) != (-9 * -2 - -3 * -2)) and ((The capital of Mexico is Mexico City.) and ((-18 + -7) <= (14 * -20))) and ((not ((10 + 6) <= (12 * -5))) or (not not (A spider has 8 legs.)))) or ((The capital of Cuba is Hanoi.) and ((-19 + -4) <= (10 + 6) <= (-4 * 16))))
F. not (not ((((The capital of Nigeria is Bangkok.) or (Nigeria is in Africa.)) and (((-19 * 0) == (19 + -5)) and (France is in South America.))) or (Vietnam is in Asia.)))
G. not (((not not (not ((10 * -3 - -1 * -10) < (9 * -17)))) and ((((16 - 9) != (42 % 2)) or (24 is less than or equal to 8.)) or (((15 + 12) == (24 % 1)) and ((43 % 1) >= (5 % 1))))) and (not (The capital of Ukraine is Cairo.)) and (((((8 * 16) < (-4 - -3)) or ((-12 - -11) == (4 ** 1))) or ((2 - -12) < (-1 * 10 - 2 * 1) < (-16 + -5))) and ((6 * 4 + 2 * 5) != (6 * 9))))
H. ((not not (There are 29 days in May.)) or (not (The capital of Canada is Ottawa.))) and (not (Sound travels faster in a vacuum.)) and ((((not not (Chile is in South America.)) and (((16 - 17) != (7 * -6 - 1 * -1)) or ((-1 * -17) >= (43 % 8)))) and (Russia is in South America.)) and (not not (not ((A spider has 10 legs.) or (Earth is the 3rd planet from the Sun.)))))
Which of these evaluate to True? Provide all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,C,E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 77395871,
"true_count": 6
},
"question": "Analyze these boolean expressions:\n\nA. (not (not not (not ((The capital of Hungary is Budapest.) and ((9 + 0) < (-20 + -1) < (2 * 0 + -8 * 7)))))) or (((The Moon orbits the Earth.) or ((((6 - -12) == (20 * 10)) or (Lightning never strikes the same place twice.)) and ((3 * -5) >= (2 * -4 + -5 * -3)))) or (not ((((-3 * 12) > (-4 * 2 * 4 * -5)) or ((2 ** 1) <= (-8 * -4 - 1 * -3))) and (Water is a liquid at room temperature.))))\nB. (not (not (not (not not ((19 * -10) >= (3 ** 1)))))) or (((not (Diamond is a solid at room temperature.)) or ((not ((10 + -11) <= (-15 * 1))) or (((6 * 10) != (-9 * -4 + -7 * 4)) or ((-16 * -2) <= (-17 * 10))))) and ((((The capital of Czech Republic is Prague.) or ((-3 - 15) == (-17 - 18))) and ((960 is a Fibonacci number.) or ((9 * 5 - -6 * -2) > (-16 * 18)))) and (((11 + 7) < (12 % 5)) and ((24 % 4) > (-8 - -16))) and ((9 * 0) >= (-12 + 6))))\nC. not (((123 is an odd number.) or ((7 + 9) <= (6 - 17))) and (not (((2 ** 2) >= (11 * 9)) or (The currency of Sweden is the Krona.))) and (not not (The chemical symbol for Iron is S.)))\nD. not not (((World War I ended occurred in 1918.) or ((-1 * -17) > (-2 - 19))) and (((The currency of India is the Rupiah.) or (The chemical symbol for Mercury is H.)) and ((The capital of Thailand is Bangkok.) and ((4 - -11) < (23 % 1) < (-11 + 4)))) and (not not (((The 1932 Olympics were held in Montreal.) and (The speed of light is approximately 300,000 km/s.)) or ((The chemical symbol for Potassium is K.) and ((4 ** 3) >= (-1 * -3))))))\nE. (not (((Jupiter is the 7th planet from the Sun.) or (Mars is the 7th planet from the Sun.)) and (((13 * -18) > (3 ** 2)) and ((-5 * -7 * 3 * -8) >= (-5 * 1 * -4 * 9))) and (not (Sound travels faster in a vacuum.)))) or ((((50 % 5) != (-9 * -2 - -3 * -2)) and ((The capital of Mexico is Mexico City.) and ((-18 + -7) <= (14 * -20))) and ((not ((10 + 6) <= (12 * -5))) or (not not (A spider has 8 legs.)))) or ((The capital of Cuba is Hanoi.) and ((-19 + -4) <= (10 + 6) <= (-4 * 16))))\nF. not (not ((((The capital of Nigeria is Bangkok.) or (Nigeria is in Africa.)) and (((-19 * 0) == (19 + -5)) and (France is in South America.))) or (Vietnam is in Asia.)))\nG. not (((not not (not ((10 * -3 - -1 * -10) < (9 * -17)))) and ((((16 - 9) != (42 % 2)) or (24 is less than or equal to 8.)) or (((15 + 12) == (24 % 1)) and ((43 % 1) >= (5 % 1))))) and (not (The capital of Ukraine is Cairo.)) and (((((8 * 16) < (-4 - -3)) or ((-12 - -11) == (4 ** 1))) or ((2 - -12) < (-1 * 10 - 2 * 1) < (-16 + -5))) and ((6 * 4 + 2 * 5) != (6 * 9))))\nH. ((not not (There are 29 days in May.)) or (not (The capital of Canada is Ottawa.))) and (not (Sound travels faster in a vacuum.)) and ((((not not (Chile is in South America.)) and (((16 - 17) != (7 * -6 - 1 * -1)) or ((-1 * -17) >= (43 % 8)))) and (Russia is in South America.)) and (not not (not ((A spider has 10 legs.) or (Earth is the 3rd planet from the Sun.)))))\n\nWhich of these evaluate to True? Provide all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 5,
"language": "en",
"num_options": 8,
"seed": 77395871,
"true_count": 6
},
"seed": 77395871,
"task_id": 677395871,
"task_type": "boolean_expressions"
} |
logic-v2 | Examine these expressions:
A. not (United States is in North America.)
B. not (((1942 is a leap year.) and ((4 ** 1) <= (-13 - -19))) and (((-19 + -1) < (3 * -12)) and (Earth is the 1st planet from the Sun.)))
C. (((Brazil is in South America.) and ((-13 - -12) <= (1 ** 2))) or ((0 * 10 * -1 * 2) == (-3 * -2))) or ((-5 + -2) == (8 * -8 + 7 * -8))
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": 3,
"language": "en",
"num_options": 3,
"seed": 38786229,
"true_count": 2
},
"question": "Examine these expressions:\n\nA. not (United States is in North America.)\nB. not (((1942 is a leap year.) and ((4 ** 1) <= (-13 - -19))) and (((-19 + -1) < (3 * -12)) and (Earth is the 1st planet from the Sun.)))\nC. (((Brazil is in South America.) and ((-13 - -12) <= (1 ** 2))) or ((0 * 10 * -1 * 2) == (-3 * -2))) or ((-5 + -2) == (8 * -8 + 7 * -8))\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": 38786229,
"true_count": 2
},
"seed": 38786229,
"task_id": 638786229,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. ((((not (空气在常温下是固体。)) and ((钻石由碳元素组成。) and (204是完全平方数。))) or ((铁在常温下是固体。) or (现代奥运会首届举办发生在1897年。)) or ((((-16 * -9) == (19 - 16)) and ((10 - 3) < (9 * -10 * -2 * 5) < (-12 - 20))) or ((土耳其的首都是安卡拉。) or (61能被10整除。)))) and (((美国宣布独立发生在1776年。) and (not (人类只使用了大脑的10%。))) and (not ((苏联解体发生在1993年。) and ((-2 * 6 + 3 * -8) <= (0 + 10)))))) or (not not ((not not (((14 * -14) >= (-3 - 8)) or (银的化学符号是Pt。))) or ((not not (老虎是爬行动物。)) or (十一月有28天。))))
B. ((((8 * -3) < (20 + -10)) and ((十月有30天。) or ((-7 * 8) >= (1 * -12))) and ((((5 * 5 * 8 * -1) <= (13 - -4) <= (-8 * 9 * 8 * 10)) and (十月有31天。)) or ((金的化学符号是Pb。) and (钠的化学符号是Pt。)))) and ((((金星是距离太阳第4近的行星。) or (水星是距离太阳第1近的行星。)) or (((2 - 17) < (2 ** 1) < (12 * 5)) or ((7 + 13) < (4 - 19) < (-12 - -10)))) or ((((33 % 1) < (-3 * -5 * 2 * 6)) or ((-18 + 14) < (9 + -2))) or (((36 % 1) <= (3 * -6)) and (铜在常温下是气体。))))) or (not not (not ((not (荷兰的首都是阿姆斯特丹。)) and ((-5 - 10) >= (4 * -6 + -7 * -5)))))
C. (not (not ((not not (现代奥运会首届举办发生在1898年。)) or (not ((2 + 12) <= (12 * 7)))))) and (not (((((9 * 0 - 10 * -4) <= (15 + 3)) or (1924年奥运会在巴黎举办。)) or (((11 - -16) >= (20 * -9)) or ((9 * -10 + 10 * 10) < (9 * -20)))) and (中国长城是在一年内建成的。)))
D. (not (not ((not (146是偶数。)) and (1920年奥运会在安特卫普举办。)))) or ((((汞在常温下是液体。) or (木星是距离太阳第3近的行星。)) or ((捷克的货币是福林。) and (银的化学符号是Ag。))) or (not (not ((-4 * -8 + 6 * 6) <= (-17 + 8))))) or ((not ((铅的化学符号是K。) and ((狗有4条腿。) and (人类每只手有五个手指。)))) or ((not ((太阳绕地球运转。) or (人类每只手有五个手指。))) and ((氧气在常温下是固体。) or ((-19 + -15) < (-9 * 1 * -6 * -9))) and ((-4 - -4) != (1 % 5))))
E. (((((5 ** 3) != (22 % 6)) or (not not (九月有30天。))) or (not not (not (羊是哺乳动物。)))) or (((水蒸气在常温下是液体。) and (英国位于南美洲。)) or ((火星是距离太阳第5近的行星。) and (not not ((-3 + -10) >= (16 * 4)))))) or ((not (not not ((8 * -8 - -3 * -3) == (3 + 17)))) and ((not not ((4 * 6 * -7 * 6) > (3 + -15))) and (((-17 * -15) <= (3 ** 1)) or (鸭子是爬行动物。)))) or (((not ((591是斐波那契数。) and ((-2 * 4 * 8 * 10) == (16 - -19)))) and (2016年奥运会在伦敦举办。)) or (not not ((月球自己发光。) and ((1936年奥运会在巴塞罗那举办。) or ((7 + 18) != (16 + -10))))))
F. ((not not (not ((波兰的首都是华沙。) and ((-14 * 12) <= (-9 - -6))))) or (((-11 * 20) == (13 * 8)) or (not not (not not ((0 * 17) != (6 - 0)))))) and ((not not (((9 + 14) >= (10 + -9)) and (地球是距离太阳第3近的行星。))) and ((((14 + -1) < (-17 - -3)) or (蜘蛛是昆虫。)) and ((新西兰位于大洋洲。) and ((-11 * -13) != (19 % 5))))) and (((鸭子有2条腿。) and ((蚂蚁是昆虫。) or ((4 * 5 * 5 * -6) != (-15 - 14)))) or (not not ((((-16 + 4) >= (-2 * 6 - 9 * -4)) or ((4 * 3 * -8 * 2) >= (-6 * 8 * 5 * -9))) and (87能被7整除。))))
G. not not ((not (蛇是爬行动物。)) or (not not (乌克兰的首都是布宜诺斯艾利斯。)))
判断哪些表达式为真。在 \boxed{} 中列出所有为真的选项，用逗号分隔。 | {
"game_data": {
"answer": "A,B,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 24467633,
"true_count": 4
},
"question": "分析以下逻辑表达式：\n\nA. ((((not (空气在常温下是固体。)) and ((钻石由碳元素组成。) and (204是完全平方数。))) or ((铁在常温下是固体。) or (现代奥运会首届举办发生在1897年。)) or ((((-16 * -9) == (19 - 16)) and ((10 - 3) < (9 * -10 * -2 * 5) < (-12 - 20))) or ((土耳其的首都是安卡拉。) or (61能被10整除。)))) and (((美国宣布独立发生在1776年。) and (not (人类只使用了大脑的10%。))) and (not ((苏联解体发生在1993年。) and ((-2 * 6 + 3 * -8) <= (0 + 10)))))) or (not not ((not not (((14 * -14) >= (-3 - 8)) or (银的化学符号是Pt。))) or ((not not (老虎是爬行动物。)) or (十一月有28天。))))\nB. ((((8 * -3) < (20 + -10)) and ((十月有30天。) or ((-7 * 8) >= (1 * -12))) and ((((5 * 5 * 8 * -1) <= (13 - -4) <= (-8 * 9 * 8 * 10)) and (十月有31天。)) or ((金的化学符号是Pb。) and (钠的化学符号是Pt。)))) and ((((金星是距离太阳第4近的行星。) or (水星是距离太阳第1近的行星。)) or (((2 - 17) < (2 ** 1) < (12 * 5)) or ((7 + 13) < (4 - 19) < (-12 - -10)))) or ((((33 % 1) < (-3 * -5 * 2 * 6)) or ((-18 + 14) < (9 + -2))) or (((36 % 1) <= (3 * -6)) and (铜在常温下是气体。))))) or (not not (not ((not (荷兰的首都是阿姆斯特丹。)) and ((-5 - 10) >= (4 * -6 + -7 * -5)))))\nC. (not (not ((not not (现代奥运会首届举办发生在1898年。)) or (not ((2 + 12) <= (12 * 7)))))) and (not (((((9 * 0 - 10 * -4) <= (15 + 3)) or (1924年奥运会在巴黎举办。)) or (((11 - -16) >= (20 * -9)) or ((9 * -10 + 10 * 10) < (9 * -20)))) and (中国长城是在一年内建成的。)))\nD. (not (not ((not (146是偶数。)) and (1920年奥运会在安特卫普举办。)))) or ((((汞在常温下是液体。) or (木星是距离太阳第3近的行星。)) or ((捷克的货币是福林。) and (银的化学符号是Ag。))) or (not (not ((-4 * -8 + 6 * 6) <= (-17 + 8))))) or ((not ((铅的化学符号是K。) and ((狗有4条腿。) and (人类每只手有五个手指。)))) or ((not ((太阳绕地球运转。) or (人类每只手有五个手指。))) and ((氧气在常温下是固体。) or ((-19 + -15) < (-9 * 1 * -6 * -9))) and ((-4 - -4) != (1 % 5))))\nE. (((((5 ** 3) != (22 % 6)) or (not not (九月有30天。))) or (not not (not (羊是哺乳动物。)))) or (((水蒸气在常温下是液体。) and (英国位于南美洲。)) or ((火星是距离太阳第5近的行星。) and (not not ((-3 + -10) >= (16 * 4)))))) or ((not (not not ((8 * -8 - -3 * -3) == (3 + 17)))) and ((not not ((4 * 6 * -7 * 6) > (3 + -15))) and (((-17 * -15) <= (3 ** 1)) or (鸭子是爬行动物。)))) or (((not ((591是斐波那契数。) and ((-2 * 4 * 8 * 10) == (16 - -19)))) and (2016年奥运会在伦敦举办。)) or (not not ((月球自己发光。) and ((1936年奥运会在巴塞罗那举办。) or ((7 + 18) != (16 + -10))))))\nF. ((not not (not ((波兰的首都是华沙。) and ((-14 * 12) <= (-9 - -6))))) or (((-11 * 20) == (13 * 8)) or (not not (not not ((0 * 17) != (6 - 0)))))) and ((not not (((9 + 14) >= (10 + -9)) and (地球是距离太阳第3近的行星。))) and ((((14 + -1) < (-17 - -3)) or (蜘蛛是昆虫。)) and ((新西兰位于大洋洲。) and ((-11 * -13) != (19 % 5))))) and (((鸭子有2条腿。) and ((蚂蚁是昆虫。) or ((4 * 5 * 5 * -6) != (-15 - 14)))) or (not not ((((-16 + 4) >= (-2 * 6 - 9 * -4)) or ((4 * 3 * -8 * 2) >= (-6 * 8 * 5 * -9))) and (87能被7整除。))))\nG. not not ((not (蛇是爬行动物。)) or (not not (乌克兰的首都是布宜诺斯艾利斯。)))\n\n判断哪些表达式为真。在 \\boxed{} 中列出所有为真的选项，用逗号分隔。"
},
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 7,
"seed": 24467633,
"true_count": 4
},
"seed": 24467633,
"task_id": 624467633,
"task_type": "boolean_expressions"
} |
logic-v2 | Consider the following logical expressions:
A. not (not not (not not (Mercury is a gas at room temperature.)))
B. not (not (A snake has 0 legs.))
C. (((Mercury is the 6th planet from the Sun.) or ((The 1908 Olympics were held in London.) and (The chemical symbol for Mercury is Co.))) and ((not (A chicken has 4 legs.)) and (((3 * 5 * -1 * 0) <= (29 % 3)) and (83 is less than or equal to 23.)))) and (not ((-16 - 5) >= (-12 * -7)))
D. not not (((((-4 * -9 - -6 * -5) >= (-9 - -1)) or ((2 + -4) == (-11 + 1))) or (((-1 * 3) != (-2 - -1)) or (The currency of Poland is the Pound.))) and (((The first iPhone was released occurred in 2007.) and (927 is a Fibonacci number.)) and (The capital of Ukraine is Rabat.)))
E. (((((-2 - 3) >= (-14 + -9)) and (Uranus is the 7th planet from the Sun.)) or (not not (174 is an even number.))) and (((-5 + -13) != (14 + -11)) or (Uranus is the 7th planet from the Sun.))) and ((A iguana is a reptile.) or ((518 is a Fibonacci number.) and (The currency of United Kingdom is the Naira.)) or (not (not not ((16 * 9) <= (12 - -12)))))
F. ((((5 ** 3) < (7 - -7) < (8 + 18)) or ((6 * -6 * 6 * -7) != (-19 * 19))) or ((The 2024 Olympics were held in Stockholm.) and (The 1968 Olympics were held in Rome.))) and (((not (Egypt is in Africa.)) and (2022 is a leap year.)) and ((((-7 * 2 * 2 * 3) < (20 - 6)) or (The Moon produces its own light.)) and (The currency of Nigeria is the Dollar.)))
Determine which expressions are true. List all true option labels separated by commas in \boxed{}. | {
"game_data": {
"answer": "A,B,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 51654069,
"true_count": 3
},
"question": "Consider the following logical expressions:\n\nA. not (not not (not not (Mercury is a gas at room temperature.)))\nB. not (not (A snake has 0 legs.))\nC. (((Mercury is the 6th planet from the Sun.) or ((The 1908 Olympics were held in London.) and (The chemical symbol for Mercury is Co.))) and ((not (A chicken has 4 legs.)) and (((3 * 5 * -1 * 0) <= (29 % 3)) and (83 is less than or equal to 23.)))) and (not ((-16 - 5) >= (-12 * -7)))\nD. not not (((((-4 * -9 - -6 * -5) >= (-9 - -1)) or ((2 + -4) == (-11 + 1))) or (((-1 * 3) != (-2 - -1)) or (The currency of Poland is the Pound.))) and (((The first iPhone was released occurred in 2007.) and (927 is a Fibonacci number.)) and (The capital of Ukraine is Rabat.)))\nE. (((((-2 - 3) >= (-14 + -9)) and (Uranus is the 7th planet from the Sun.)) or (not not (174 is an even number.))) and (((-5 + -13) != (14 + -11)) or (Uranus is the 7th planet from the Sun.))) and ((A iguana is a reptile.) or ((518 is a Fibonacci number.) and (The currency of United Kingdom is the Naira.)) or (not (not not ((16 * 9) <= (12 - -12)))))\nF. ((((5 ** 3) < (7 - -7) < (8 + 18)) or ((6 * -6 * 6 * -7) != (-19 * 19))) or ((The 2024 Olympics were held in Stockholm.) and (The 1968 Olympics were held in Rome.))) and (((not (Egypt is in Africa.)) and (2022 is a leap year.)) and ((((-7 * 2 * 2 * 3) < (20 - 6)) or (The Moon produces its own light.)) and (The currency of Nigeria is the Dollar.)))\n\nDetermine which expressions are true. List all true option labels separated by commas in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 6,
"seed": 51654069,
"true_count": 3
},
"seed": 51654069,
"task_id": 651654069,
"task_type": "boolean_expressions"
} |
logic-v2 | Review these logical expressions:
A. (((The square root of 64 is 9.) or ((-1 + -13) == (7 - -1))) or (Thailand is in Oceania.)) or (not not ((The chemical symbol for Silicon is Ca.) or (There are 30 days in January.)))
B. ((The currency of Japan is the Zloty.) and (not not (Venus is the 2nd planet from the Sun.))) or ((9 * -17) > (18 % 2))
C. not not (((The capital of France is Paris.) or ((4 ** 2) >= (1 ** 1))) or (((8 % 10) <= (-6 * 4 + 0 * 10) <= (5 * 3 * 5 * 9)) or (There are 30 days in August.)))
D. not ((((-5 * 3 - -6 * -8) <= (13 - -20)) and (The chemical symbol for Magnesium is Cu.)) and ((The chemical symbol for Oxygen is O.) or ((48 % 1) == (14 - -13))))
E. (The currency of India is the Rupee.) and (not not ((-16 * -8) != (1 * -8 + -2 * 0))) and ((40 % 7) == (1 - 10))
F. (((Christopher Columbus reached America occurred in 1492.) or ((11 % 3) != (19 - -7))) or (not ((20 * 1) < (-10 * -4 + -7 * -2)))) and (Egypt is in North America.) and (((Copper is a solid at room temperature.) or (A duck has 2 legs.)) or ((Saturn is the 5th planet from the Sun.) or ((-6 + -2) < (9 * -16) < (-14 + -5))))
G. ((15 - -14) == (11 + 15)) or ((The chemical symbol for Potassium is Na.) and ((The currency of Mexico is the Peso.) or (Air is a liquid at room temperature.)))
Which expressions are true? Answer with comma-separated labels in \boxed{}. | {
"game_data": {
"answer": "C,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 3841704,
"true_count": 2
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"question": "Review these logical expressions:\n\nA. (((The square root of 64 is 9.) or ((-1 + -13) == (7 - -1))) or (Thailand is in Oceania.)) or (not not ((The chemical symbol for Silicon is Ca.) or (There are 30 days in January.)))\nB. ((The currency of Japan is the Zloty.) and (not not (Venus is the 2nd planet from the Sun.))) or ((9 * -17) > (18 % 2))\nC. not not (((The capital of France is Paris.) or ((4 ** 2) >= (1 ** 1))) or (((8 % 10) <= (-6 * 4 + 0 * 10) <= (5 * 3 * 5 * 9)) or (There are 30 days in August.)))\nD. not ((((-5 * 3 - -6 * -8) <= (13 - -20)) and (The chemical symbol for Magnesium is Cu.)) and ((The chemical symbol for Oxygen is O.) or ((48 % 1) == (14 - -13))))\nE. (The currency of India is the Rupee.) and (not not ((-16 * -8) != (1 * -8 + -2 * 0))) and ((40 % 7) == (1 - 10))\nF. (((Christopher Columbus reached America occurred in 1492.) or ((11 % 3) != (19 - -7))) or (not ((20 * 1) < (-10 * -4 + -7 * -2)))) and (Egypt is in North America.) and (((Copper is a solid at room temperature.) or (A duck has 2 legs.)) or ((Saturn is the 5th planet from the Sun.) or ((-6 + -2) < (9 * -16) < (-14 + -5))))\nG. ((15 - -14) == (11 + 15)) or ((The chemical symbol for Potassium is Na.) and ((The currency of Mexico is the Peso.) or (Air is a liquid at room temperature.)))\n\nWhich expressions are true? Answer with comma-separated labels in \\boxed{}."
},
"metadata": {
"depth": 3,
"language": "en",
"num_options": 7,
"seed": 3841704,
"true_count": 2
},
"seed": 3841704,
"task_id": 603841704,
"task_type": "boolean_expressions"
} |
logic-v2 | 下面是几个布尔表达式：
A. (((1936年奥运会在墨西哥城举办。) or ((20 + -7) > (1 * -2 + 0 * -9))) or ((芬兰的首都是赫尔辛基。) or ((2 * 5 - 2 * 7) < (19 + -9) < (-5 * -10 - 2 * -10))) or (((第一次世界大战结束发生在1923年。) and (丹麦的货币是克朗。)) or (((9 * 5 - 0 * 1) < (2 ** 3) < (-19 + -7)) and ((8 + -17) < (9 * 4 * -10 * -3) < (-10 * 0))))) and ((not not ((光速约为每秒30万公里。) or ((5 ** 2) <= (4 - 7)))) and (not not (((18 * -2) == (0 + 18)) or ((-17 * 12) < (42 % 1)))))
B. (not not ((not not (70小于等于69。)) and (((-18 * 5) != (9 + 4)) or ((-13 * 13) > (12 - -1))))) and ((钴的化学符号是Pb。) or ((5 * -11) <= (14 % 6))) and ((鬣蜥是哺乳动物。) or (not (马有4条腿。)) or (火星是距离太阳第4近的行星。))
C. (((20 * -20) >= (-18 - -1)) or ((((4 - 18) == (-12 - 19)) and ((18 + 19) < (-19 - -14))) or (not ((-20 - 4) > (6 * 11))))) and (not ((((8 - 13) >= (-9 + 8)) or ((12 + 13) >= (-17 - 11))) or (((-2 + -14) == (9 % 1)) or ((-1 * -4 * -6 * -8) >= (-10 - -13)))))
D. not ((((挪威的首都是东京。) and ((4 ** 2) != (2 ** 2))) and ((7 * -13) < (6 * 5 * 3 * 10) < (19 % 3))) or (月球绕地球运转。))
E. (((乌克兰的首都是基辅。) and (((-2 * 6 + -4 * 2) >= (-2 * 5)) and ((17 - -13) < (15 - 20) < (2 * 11)))) and ((not not ((2 ** 1) > (38 % 10))) and ((4 ** 2) > (4 * -19)))) and (((((-4 * -1) < (19 - -14) < (7 * 10 + -3 * -7)) or ((4 ** 1) <= (9 - 14))) and ((10 + -7) <= (16 * 8))) and (((铀的化学符号是Cl。) or ((1 % 6) < (16 - -3))) or (((1 * 8 + -7 * -4) > (1 % 1)) and (德国位于欧洲。))))
F. (((not (汞在常温下是液体。)) or (((7 * -3 - 10 * 5) < (0 * -1 * -6 * -7)) and (金星是距离太阳第2近的行星。))) or (((10 % 3) != (-6 * 12)) or (匈牙利的首都是布达佩斯。))) and (((11 - -6) != (5 ** 2)) and (126是奇数。)) and (not (((氮气在常温下是气体。) or ((-4 * -18) == (6 + -11))) and (((12 + -5) <= (42 % 4)) or (莱特兄弟首次飞行发生在1908年。))))
G. (not (法国位于南极洲。)) and ((-1 * -11) < (2 + -11)) and ((((3 - 19) < (-8 * 7 + 4 * -3)) and ((中国的货币是人民币。) and ((50 % 10) <= (12 + 16) <= (0 * -9 + 9 * -2)))) and (((1964年奥运会在东京举办。) and ((-8 - -17) > (-2 + -7))) or ((59是偶数。) and (伦敦大火发生在1665年。))))
H. (((not not (蜻蜓是昆虫。)) and ((现代奥运会首届举办发生在1886年。) and (鲨鱼是鱼类。))) or (not (猪是哺乳动物。)) or (老鼠是鸟类。)) and ((not (((1 - 12) > (5 * 5)) and (1928年奥运会在阿姆斯特丹举办。))) and (((熊是哺乳动物。) and (钙的化学符号是Ca。)) or (((9 - 2) < (5 ** 2)) and ((5 ** 2) != (-3 * 7)))))
找出所有为真的表达式。在 \boxed{} 中用逗号分隔列出选项标识。 | {
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"question": "下面是几个布尔表达式：\n\nA. (((1936年奥运会在墨西哥城举办。) or ((20 + -7) > (1 * -2 + 0 * -9))) or ((芬兰的首都是赫尔辛基。) or ((2 * 5 - 2 * 7) < (19 + -9) < (-5 * -10 - 2 * -10))) or (((第一次世界大战结束发生在1923年。) and (丹麦的货币是克朗。)) or (((9 * 5 - 0 * 1) < (2 ** 3) < (-19 + -7)) and ((8 + -17) < (9 * 4 * -10 * -3) < (-10 * 0))))) and ((not not ((光速约为每秒30万公里。) or ((5 ** 2) <= (4 - 7)))) and (not not (((18 * -2) == (0 + 18)) or ((-17 * 12) < (42 % 1)))))\nB. (not not ((not not (70小于等于69。)) and (((-18 * 5) != (9 + 4)) or ((-13 * 13) > (12 - -1))))) and ((钴的化学符号是Pb。) or ((5 * -11) <= (14 % 6))) and ((鬣蜥是哺乳动物。) or (not (马有4条腿。)) or (火星是距离太阳第4近的行星。))\nC. (((20 * -20) >= (-18 - -1)) or ((((4 - 18) == (-12 - 19)) and ((18 + 19) < (-19 - -14))) or (not ((-20 - 4) > (6 * 11))))) and (not ((((8 - 13) >= (-9 + 8)) or ((12 + 13) >= (-17 - 11))) or (((-2 + -14) == (9 % 1)) or ((-1 * -4 * -6 * -8) >= (-10 - -13)))))\nD. not ((((挪威的首都是东京。) and ((4 ** 2) != (2 ** 2))) and ((7 * -13) < (6 * 5 * 3 * 10) < (19 % 3))) or (月球绕地球运转。))\nE. (((乌克兰的首都是基辅。) and (((-2 * 6 + -4 * 2) >= (-2 * 5)) and ((17 - -13) < (15 - 20) < (2 * 11)))) and ((not not ((2 ** 1) > (38 % 10))) and ((4 ** 2) > (4 * -19)))) and (((((-4 * -1) < (19 - -14) < (7 * 10 + -3 * -7)) or ((4 ** 1) <= (9 - 14))) and ((10 + -7) <= (16 * 8))) and (((铀的化学符号是Cl。) or ((1 % 6) < (16 - -3))) or (((1 * 8 + -7 * -4) > (1 % 1)) and (德国位于欧洲。))))\nF. (((not (汞在常温下是液体。)) or (((7 * -3 - 10 * 5) < (0 * -1 * -6 * -7)) and (金星是距离太阳第2近的行星。))) or (((10 % 3) != (-6 * 12)) or (匈牙利的首都是布达佩斯。))) and (((11 - -6) != (5 ** 2)) and (126是奇数。)) and (not (((氮气在常温下是气体。) or ((-4 * -18) == (6 + -11))) and (((12 + -5) <= (42 % 4)) or (莱特兄弟首次飞行发生在1908年。))))\nG. (not (法国位于南极洲。)) and ((-1 * -11) < (2 + -11)) and ((((3 - 19) < (-8 * 7 + 4 * -3)) and ((中国的货币是人民币。) and ((50 % 10) <= (12 + 16) <= (0 * -9 + 9 * -2)))) and (((1964年奥运会在东京举办。) and ((-8 - -17) > (-2 + -7))) or ((59是偶数。) and (伦敦大火发生在1665年。))))\nH. (((not not (蜻蜓是昆虫。)) and ((现代奥运会首届举办发生在1886年。) and (鲨鱼是鱼类。))) or (not (猪是哺乳动物。)) or (老鼠是鸟类。)) and ((not (((1 - 12) > (5 * 5)) and (1928年奥运会在阿姆斯特丹举办。))) and (((熊是哺乳动物。) and (钙的化学符号是Ca。)) or (((9 - 2) < (5 ** 2)) and ((5 ** 2) != (-3 * 7)))))\n\n找出所有为真的表达式。在 \\boxed{} 中用逗号分隔列出选项标识。"
},
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"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. (not not (A butterfly has 6 legs.)) or ((((-17 - 14) == (-11 * 7)) and ((-4 * 6 * 10 * 10) < (-14 * -10) < (0 * 0 * 10 * 1))) or (not ((-5 * -6 + -3 * -10) == (4 ** 3))))
B. ((((9 * -13) >= (1 + 7)) or (Copper is a gas at room temperature.)) or ((-9 * 6 * -3 * -10) >= (9 * -8 - 5 * 0))) and ((((-6 * -16) >= (-4 + -13)) or (Light travels faster than sound.)) or (not not (China is in Africa.)))
C. (36 is a prime number.) and ((((-17 + 20) != (-7 * 6)) and (Oil is a liquid at room temperature.)) or (((12 * 17) >= (11 + 4)) or (The chemical symbol for Silver is Ag.)))
D. not (not not (((14 + 5) == (-6 * 17)) and ((18 - -5) <= (0 * 0 * 6 * 0) <= (2 - -1))))
E. (not not (not not (1933 is a leap year.))) and (((14 % 7) != (12 * 0)) or ((20 - -6) == (44 % 8))) and (((-9 * -8 + -9 * 6) <= (-9 + -7)) or ((The currency of Israel is the Shekel.) and ((-12 - 0) <= (-20 - 3))))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
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"question": "Here are some boolean expressions to evaluate:\n\nA. (not not (A butterfly has 6 legs.)) or ((((-17 - 14) == (-11 * 7)) and ((-4 * 6 * 10 * 10) < (-14 * -10) < (0 * 0 * 10 * 1))) or (not ((-5 * -6 + -3 * -10) == (4 ** 3))))\nB. ((((9 * -13) >= (1 + 7)) or (Copper is a gas at room temperature.)) or ((-9 * 6 * -3 * -10) >= (9 * -8 - 5 * 0))) and ((((-6 * -16) >= (-4 + -13)) or (Light travels faster than sound.)) or (not not (China is in Africa.)))\nC. (36 is a prime number.) and ((((-17 + 20) != (-7 * 6)) and (Oil is a liquid at room temperature.)) or (((12 * 17) >= (11 + 4)) or (The chemical symbol for Silver is Ag.)))\nD. not (not not (((14 + 5) == (-6 * 17)) and ((18 - -5) <= (0 * 0 * 6 * 0) <= (2 - -1))))\nE. (not not (not not (1933 is a leap year.))) and (((14 % 7) != (12 * 0)) or ((20 - -6) == (44 % 8))) and (((-9 * -8 + -9 * 6) <= (-9 + -7)) or ((The currency of Israel is the Shekel.) and ((-12 - 0) <= (-20 - 3))))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
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"language": "en",
"num_options": 5,
"seed": 14973921,
"true_count": 2
},
"seed": 14973921,
"task_id": 614973921,
"task_type": "boolean_expressions"
} |
logic-v2 | 这里有一些需要评估的布尔表达式：
A. ((((铀的化学符号是U。) and (not not ((7 * -9 - 0 * -4) < (4 ** 2)))) or (((-3 * -5 - -9 * 9) != (4 * 10 * 1 * -4)) or ((第二次世界大战结束发生在1945年。) and ((2 ** 1) != (11 * -20))))) and (鹦鹉是哺乳动物。) and ((比利时的首都是利雅得。) or (((挪威的首都是奥斯陆。) and ((19 + 13) <= (-5 + 15))) and ((5 + -16) == (2 - 0))))) or (((((-4 - -15) < (11 - 18)) or ((1984年奥运会在洛杉矶举办。) and (镁的化学符号是Mg。))) and ((not not (地球是距离太阳第3近的行星。)) and ((15 - -18) != (5 - 7)))) or (not not (((俄罗斯的货币是比索。) and (地球上一天是24小时。)) and (金星是距离太阳第6近的行星。))))
B. not ((((not not (银的化学符号是Ag。)) or (((7 * 0 * -10 * 1) > (10 + 3)) and ((-7 * -7 - 10 * 5) > (-7 - -20)))) or (not ((-4 - 10) < (8 % 10))) or ((not (1980年奥运会在蒙特利尔举办。)) or (氧的化学符号是O。))) or (not ((土耳其的货币是瑞士法郎。) and (not not (埃及位于非洲。)))))
C. ((((185是奇数。) and (not not (2024年奥运会在安特卫普举办。))) or (猪有4条腿。)) or (not (not not ((5 ** 3) >= (-3 * -8 * -1 * -2))))) and (not (not not ((((5 * -4 + -3 * 8) != (-7 + -3)) and (2077年是闰年。)) and ((南非的货币是比索。) and (11是质数。)))))
D. (((not not (金枪鱼是鱼类。)) or (not (猫有2条腿。))) and (not not ((not not (中国的首都是北京。)) and (金星是距离太阳第7近的行星。)))) and (((墨西哥位于欧洲。) and (((三月有28天。) and ((3 ** 3) < (47 % 6))) or (not not (水星是距离太阳第7近的行星。)))) or ((not ((西班牙位于欧洲。) and (肯尼亚的首都是奥斯陆。))) or ((not not (人类首次登月发生在1970年。)) and (((-1 + 7) > (1 ** 2)) and ((5 ** 3) >= (9 * -8 - 7 * 0))))))
E. ((not (not not (((9 + 11) == (3 - -6)) and (第二次世界大战结束发生在1943年。)))) or (((-10 + 14) < (-9 + 14)) or (((3 * -8 - -10 * -1) <= (12 - 20)) and ((韩国位于北美洲。) or ((-5 - 19) < (-18 - 3)))))) and ((((鳕鱼是哺乳动物。) and (not (1980年奥运会在莫斯科举办。))) and (not (not (1995年是闰年。)))) and (not ((not (第二次世界大战结束发生在1945年。)) or (286是完全平方数。))))
F. (not (not (1964年是闰年。))) or ((not ((2是质数。) or (((20 - 17) > (-16 + -9)) and (248是斐波那契数。)))) and (not (not ((俄罗斯的首都是莫斯科。) or (韩国位于亚洲。)))))
G. ((not not ((8 % 8) < (-16 + -15))) or (1958年是闰年。) or (((((9 - 8) <= (33 % 2) <= (6 % 6)) and (鲨鱼是哺乳动物。)) or ((-19 * 11) >= (19 % 1))) or ((油在常温下是固体。) or ((瑞典的货币是里亚尔。) and (1896年奥运会在墨西哥城举办。))))) or ((not not ((((10 * 11) < (7 - -17) < (-13 * 13)) and ((0 - 12) <= (3 * 3) <= (0 + -7))) or ((火星是距离太阳最近的行星。) or (菲律宾的货币是卢比。)))) and (not not ((3 % 6) >= (9 - -2))))
找出所有为 True 的表达式。在 \boxed{} 中给出答案，用逗号分隔。 | {
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"difficulty": 1,
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"question": "这里有一些需要评估的布尔表达式：\n\nA. ((((铀的化学符号是U。) and (not not ((7 * -9 - 0 * -4) < (4 ** 2)))) or (((-3 * -5 - -9 * 9) != (4 * 10 * 1 * -4)) or ((第二次世界大战结束发生在1945年。) and ((2 ** 1) != (11 * -20))))) and (鹦鹉是哺乳动物。) and ((比利时的首都是利雅得。) or (((挪威的首都是奥斯陆。) and ((19 + 13) <= (-5 + 15))) and ((5 + -16) == (2 - 0))))) or (((((-4 - -15) < (11 - 18)) or ((1984年奥运会在洛杉矶举办。) and (镁的化学符号是Mg。))) and ((not not (地球是距离太阳第3近的行星。)) and ((15 - -18) != (5 - 7)))) or (not not (((俄罗斯的货币是比索。) and (地球上一天是24小时。)) and (金星是距离太阳第6近的行星。))))\nB. not ((((not not (银的化学符号是Ag。)) or (((7 * 0 * -10 * 1) > (10 + 3)) and ((-7 * -7 - 10 * 5) > (-7 - -20)))) or (not ((-4 - 10) < (8 % 10))) or ((not (1980年奥运会在蒙特利尔举办。)) or (氧的化学符号是O。))) or (not ((土耳其的货币是瑞士法郎。) and (not not (埃及位于非洲。)))))\nC. ((((185是奇数。) and (not not (2024年奥运会在安特卫普举办。))) or (猪有4条腿。)) or (not (not not ((5 ** 3) >= (-3 * -8 * -1 * -2))))) and (not (not not ((((5 * -4 + -3 * 8) != (-7 + -3)) and (2077年是闰年。)) and ((南非的货币是比索。) and (11是质数。)))))\nD. (((not not (金枪鱼是鱼类。)) or (not (猫有2条腿。))) and (not not ((not not (中国的首都是北京。)) and (金星是距离太阳第7近的行星。)))) and (((墨西哥位于欧洲。) and (((三月有28天。) and ((3 ** 3) < (47 % 6))) or (not not (水星是距离太阳第7近的行星。)))) or ((not ((西班牙位于欧洲。) and (肯尼亚的首都是奥斯陆。))) or ((not not (人类首次登月发生在1970年。)) and (((-1 + 7) > (1 ** 2)) and ((5 ** 3) >= (9 * -8 - 7 * 0))))))\nE. ((not (not not (((9 + 11) == (3 - -6)) and (第二次世界大战结束发生在1943年。)))) or (((-10 + 14) < (-9 + 14)) or (((3 * -8 - -10 * -1) <= (12 - 20)) and ((韩国位于北美洲。) or ((-5 - 19) < (-18 - 3)))))) and ((((鳕鱼是哺乳动物。) and (not (1980年奥运会在莫斯科举办。))) and (not (not (1995年是闰年。)))) and (not ((not (第二次世界大战结束发生在1945年。)) or (286是完全平方数。))))\nF. (not (not (1964年是闰年。))) or ((not ((2是质数。) or (((20 - 17) > (-16 + -9)) and (248是斐波那契数。)))) and (not (not ((俄罗斯的首都是莫斯科。) or (韩国位于亚洲。)))))\nG. ((not not ((8 % 8) < (-16 + -15))) or (1958年是闰年。) or (((((9 - 8) <= (33 % 2) <= (6 % 6)) and (鲨鱼是哺乳动物。)) or ((-19 * 11) >= (19 % 1))) or ((油在常温下是固体。) or ((瑞典的货币是里亚尔。) and (1896年奥运会在墨西哥城举办。))))) or ((not not ((((10 * 11) < (7 - -17) < (-13 * 13)) and ((0 - 12) <= (3 * 3) <= (0 + -7))) or ((火星是距离太阳最近的行星。) or (菲律宾的货币是卢比。)))) and (not not ((3 % 6) >= (9 - -2))))\n\n找出所有为 True 的表达式。在 \\boxed{} 中给出答案，用逗号分隔。"
},
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"language": "cn",
"num_options": 7,
"seed": 97935736,
"true_count": 3
},
"seed": 97935736,
"task_id": 697935736,
"task_type": "boolean_expressions"
} |
logic-v2 | 分析以下逻辑表达式：
A. 土耳其的货币是兰特。
B. (((-11 * 5) < (4 * -18) < (26 % 4)) or (铜的化学符号是Cu。)) or ((-1 * 4 - 10 * 2) == (2 - 16))
C. (((13 % 3) == (10 * -18)) and ((-11 * -6) != (0 + 3))) or ((2004年奥运会在雅典举办。) or (铅的化学符号是Sn。))
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",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 3,
"seed": 82009199,
"true_count": 2
},
"question": "分析以下逻辑表达式：\n\nA. 土耳其的货币是兰特。\nB. (((-11 * 5) < (4 * -18) < (26 % 4)) or (铜的化学符号是Cu。)) or ((-1 * 4 - 10 * 2) == (2 - 16))\nC. (((13 % 3) == (10 * -18)) and ((-11 * -6) != (0 + 3))) or ((2004年奥运会在雅典举办。) or (铅的化学符号是Sn。))\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": 82009199,
"true_count": 2
},
"seed": 82009199,
"task_id": 682009199,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. ((((-16 - -12) <= (-10 + -5)) and (((水星是距离太阳第5近的行星。) or ((14 + 6) < (1 * 7 + -5 * 10) < (5 * -2))) and ((铅的化学符号是Al。) and ((12 - 6) <= (-5 * -15) <= (-10 * 5))))) and (((-15 + 5) > (-3 * -10 * 0 * -7)) and ((鲨鱼是哺乳动物。) and ((45能被12整除。) and ((-7 - 1) >= (-6 - -11)))))) and (not not (((((-12 - 16) == (7 * -2)) and ((38 % 4) != (13 * 19))) or ((242是完全平方数。) and (硅的化学符号是Si。))) and (144的平方根是1。)))
B. (not not ((((汞在常温下是液体。) or (1996年奥运会在罗马举办。)) or (not not (907是斐波那契数。))) or (硫的化学符号是Hg。) or (not ((2 + -1) >= (10 - -11))))) and ((not (伦敦大火发生在1668年。)) and (not not (金枪鱼是哺乳动物。)) and (((not (85是质数。)) and ((48能被3整除。) or (1960年奥运会在雅典举办。))) or (not not ((声音在真空中传播更快。) and (乌龟是爬行动物。)))))
C. (not not (not (((电流比光速更快。) and (电流比光速更快。)) or ((美国宣布独立发生在1776年。) or (第二次世界大战结束发生在1940年。))))) or ((not ((鸭子是鱼类。) or (水蒸气在常温下是液体。))) or (哥伦比亚的首都是布加勒斯特。)) or (not (((-8 * 19) <= (6 * -8 * -8 * 6)) or (南非位于亚洲。)))
D. ((not (((二氧化碳在常温下是气体。) and (四月有30天。)) or ((-19 + 20) >= (18 + -9)))) or (not not (not ((-8 - -17) >= (19 + 5))))) and (not (((九月有31天。) or (第一部iPhone发布发生在2006年。)) or ((1960年奥运会在罗马举办。) or (埃及的首都是开罗。)))) and ((not (((土星是距离太阳第6近的行星。) or ((-6 * -7 + -5 * -7) <= (-5 * 2) <= (9 - -14))) or ((2 ** 2) > (3 ** 3)))) and (((29 % 2) >= (-4 - 3)) and ((镁的化学符号是Mg。) or (1936年奥运会在首尔举办。)) and (((-18 - 11) < (2 ** 2) < (-19 - 19)) or (钠的化学符号是Na。))))
E. not not ((not not (((锡的化学符号是Sn。) or ((-2 * -10 + -2 * 10) == (3 + -15))) or ((闪电不会两次击中同一个地方。) or ((14 + 9) <= (-5 + 14))))) or ((牛是哺乳动物。) and ((-9 * 16) >= (26 % 6))))
F. not (not not (not (not not (((-12 * -1) == (-9 * 9 * 6 * 8)) and (第一次世界大战结束发生在1918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": "C,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 5,
"language": "cn",
"num_options": 6,
"seed": 22351938,
"true_count": 2
},
"question": "检验这些表达式：\n\nA. ((((-16 - -12) <= (-10 + -5)) and (((水星是距离太阳第5近的行星。) or ((14 + 6) < (1 * 7 + -5 * 10) < (5 * -2))) and ((铅的化学符号是Al。) and ((12 - 6) <= (-5 * -15) <= (-10 * 5))))) and (((-15 + 5) > (-3 * -10 * 0 * -7)) and ((鲨鱼是哺乳动物。) and ((45能被12整除。) and ((-7 - 1) >= (-6 - -11)))))) and (not not (((((-12 - 16) == (7 * -2)) and ((38 % 4) != (13 * 19))) or ((242是完全平方数。) and (硅的化学符号是Si。))) and (144的平方根是1。)))\nB. (not not ((((汞在常温下是液体。) or (1996年奥运会在罗马举办。)) or (not not (907是斐波那契数。))) or (硫的化学符号是Hg。) or (not ((2 + -1) >= (10 - -11))))) and ((not (伦敦大火发生在1668年。)) and (not not (金枪鱼是哺乳动物。)) and (((not (85是质数。)) and ((48能被3整除。) or (1960年奥运会在雅典举办。))) or (not not ((声音在真空中传播更快。) and (乌龟是爬行动物。)))))\nC. (not not (not (((电流比光速更快。) and (电流比光速更快。)) or ((美国宣布独立发生在1776年。) or (第二次世界大战结束发生在1940年。))))) or ((not ((鸭子是鱼类。) or (水蒸气在常温下是液体。))) or (哥伦比亚的首都是布加勒斯特。)) or (not (((-8 * 19) <= (6 * -8 * -8 * 6)) or (南非位于亚洲。)))\nD. ((not (((二氧化碳在常温下是气体。) and (四月有30天。)) or ((-19 + 20) >= (18 + -9)))) or (not not (not ((-8 - -17) >= (19 + 5))))) and (not (((九月有31天。) or (第一部iPhone发布发生在2006年。)) or ((1960年奥运会在罗马举办。) or (埃及的首都是开罗。)))) and ((not (((土星是距离太阳第6近的行星。) or ((-6 * -7 + -5 * -7) <= (-5 * 2) <= (9 - -14))) or ((2 ** 2) > (3 ** 3)))) and (((29 % 2) >= (-4 - 3)) and ((镁的化学符号是Mg。) or (1936年奥运会在首尔举办。)) and (((-18 - 11) < (2 ** 2) < (-19 - 19)) or (钠的化学符号是Na。))))\nE. not not ((not not (((锡的化学符号是Sn。) or ((-2 * -10 + -2 * 10) == (3 + -15))) or ((闪电不会两次击中同一个地方。) or ((14 + 9) <= (-5 + 14))))) or ((牛是哺乳动物。) and ((-9 * 16) >= (26 % 6))))\nF. not (not not (not (not not (((-12 * -1) == (-9 * 9 * 6 * 8)) and (第一次世界大战结束发生在1918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": 5,
"language": "cn",
"num_options": 6,
"seed": 22351938,
"true_count": 2
},
"seed": 22351938,
"task_id": 622351938,
"task_type": "boolean_expressions"
} |
logic-v2 | 考虑以下布尔表达式：
A. not (not not ((-3 * -3 + -1 * 4) <= (12 + -3)))
B. not not (not ((-19 * -12) < (22 % 9)))
C. not ((5 * -6 - -8 * 5) == (-3 * -4 + 3 * 4))
D. ((47 % 1) != (-8 + -20)) or ((((12 * -11) > (-12 - 18)) and (尼日利亚的首都是马德里。)) and (not (水在常温下是气体。)))
E. (not not (((12 - 1) != (7 % 10)) and (人类首次登月发生在1969年。))) and ((17 % 4) > (-3 * 7 - -1 * -8)) and (鳟鱼是鱼类。)
F. (摩洛哥位于欧洲。) or (not ((8 * -15) > (3 ** 2)))
哪些表达式的值为 True？请在 \boxed{} 中给出答案，用逗号分隔选项标识。 | {
"game_data": {
"answer": "B,C,D,E,F",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 95384052,
"true_count": 5
},
"question": "考虑以下布尔表达式：\n\nA. not (not not ((-3 * -3 + -1 * 4) <= (12 + -3)))\nB. not not (not ((-19 * -12) < (22 % 9)))\nC. not ((5 * -6 - -8 * 5) == (-3 * -4 + 3 * 4))\nD. ((47 % 1) != (-8 + -20)) or ((((12 * -11) > (-12 - 18)) and (尼日利亚的首都是马德里。)) and (not (水在常温下是气体。)))\nE. (not not (((12 - 1) != (7 % 10)) and (人类首次登月发生在1969年。))) and ((17 % 4) > (-3 * 7 - -1 * -8)) and (鳟鱼是鱼类。)\nF. (摩洛哥位于欧洲。) or (not ((8 * -15) > (3 ** 2)))\n\n哪些表达式的值为 True？请在 \\boxed{} 中给出答案，用逗号分隔选项标识。"
},
"metadata": {
"depth": 3,
"language": "cn",
"num_options": 6,
"seed": 95384052,
"true_count": 5
},
"seed": 95384052,
"task_id": 695384052,
"task_type": "boolean_expressions"
} |
logic-v2 | 检验这些表达式：
A. (16 - 7) != (2 * 0 + 5 * 10)
B. not (((45 % 5) < (10 + -19)) and (鲨鱼是哺乳动物。))
C. (((15 + 8) == (18 + -20)) and ((-18 * -7) < (2 ** 1))) and ((钻石在常温下是固体。) and ((2 * -2 * -10 * 9) <= (14 - 4) <= (10 * 9 + 8 * 1)))
D. (((8 + 15) <= (-19 + 17) <= (13 + 1)) and (2032年是闰年。)) or (not not ((-7 + 7) != (4 * -7 - 0 * -2)))
哪些是真的？在 \boxed{} 中列出所有为真选项的标识，用逗号分隔。 | {
"game_data": {
"answer": "A,B,D",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 62179633,
"true_count": 3
},
"question": "检验这些表达式：\n\nA. (16 - 7) != (2 * 0 + 5 * 10)\nB. not (((45 % 5) < (10 + -19)) and (鲨鱼是哺乳动物。))\nC. (((15 + 8) == (18 + -20)) and ((-18 * -7) < (2 ** 1))) and ((钻石在常温下是固体。) and ((2 * -2 * -10 * 9) <= (14 - 4) <= (10 * 9 + 8 * 1)))\nD. (((8 + 15) <= (-19 + 17) <= (13 + 1)) and (2032年是闰年。)) or (not not ((-7 + 7) != (4 * -7 - 0 * -2)))\n\n哪些是真的？在 \\boxed{} 中列出所有为真选项的标识，用逗号分隔。"
},
"metadata": {
"depth": 2,
"language": "cn",
"num_options": 4,
"seed": 62179633,
"true_count": 3
},
"seed": 62179633,
"task_id": 662179633,
"task_type": "boolean_expressions"
} |
logic-v2 | Here are some boolean expressions to evaluate:
A. Whales are fish.
B. ((-7 + -10) == (-6 * 1 - -2 * -5)) and ((The currency of Philippines is the Krone.) or (Saudi Arabia is in Asia.))
C. The chemical symbol for Nitrogen is O.
D. (not (The 1988 Olympics were held in Seoul.)) and (((28 % 3) == (-19 - -6)) or ((5 * 5 - -8 * -9) >= (-4 * -9 + 10 * 2)))
E. The currency of Russia is the Ruble.
F. (not (Venus is the 4th planet from the Sun.)) or (not not ((-14 + 9) > (16 - 2)))
G. not ((3 ** 2) == (20 - -12))
Find all expressions that are True. Answer in \boxed{} with labels separated by commas. | {
"game_data": {
"answer": "E,F,G",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 30715910,
"true_count": 3
},
"question": "Here are some boolean expressions to evaluate:\n\nA. Whales are fish.\nB. ((-7 + -10) == (-6 * 1 - -2 * -5)) and ((The currency of Philippines is the Krone.) or (Saudi Arabia is in Asia.))\nC. The chemical symbol for Nitrogen is O.\nD. (not (The 1988 Olympics were held in Seoul.)) and (((28 % 3) == (-19 - -6)) or ((5 * 5 - -8 * -9) >= (-4 * -9 + 10 * 2)))\nE. The currency of Russia is the Ruble.\nF. (not (Venus is the 4th planet from the Sun.)) or (not not ((-14 + 9) > (16 - 2)))\nG. not ((3 ** 2) == (20 - -12))\n\nFind all expressions that are True. Answer in \\boxed{} with labels separated by commas."
},
"metadata": {
"depth": 2,
"language": "en",
"num_options": 7,
"seed": 30715910,
"true_count": 3
},
"seed": 30715910,
"task_id": 630715910,
"task_type": "boolean_expressions"
} |
logic-v2 | Evaluate each expression below:
A. not not ((The chemical symbol for Platinum is Pt.) or ((5 + -2) <= (-10 - -7) <= (-6 * -7)))
B. not not ((The 1932 Olympics were held in Athens.) and ((not (Neptune is the 3rd planet from the Sun.)) and ((The chemical symbol for Platinum is Pt.) or ((-4 * -6 * 0 * 5) == (19 + -3)))))
C. (not ((((4 * -10 - -8 * -10) <= (12 + -6) <= (-4 * 9 - -2 * -3)) and ((19 + 15) <= (43 % 9))) and ((-13 + -7) > (2 ** 2)))) and (((((4 ** 2) > (18 - 16)) and ((-4 + -6) <= (-4 * 10 - 7 * -8))) or (((-2 * 2 * -1 * 2) >= (20 % 5)) and ((-8 * 10 + 3 * -7) >= (-6 * 9 + 9 * -10)))) and (not (not not ((0 * -5) >= (-6 + -13)))))
D. (((((-3 * 0 * -1 * -5) <= (-14 * 10)) and (There are 31 days in August.)) and (((-1 * 2 - -2 * 7) == (12 * 15)) and ((7 - -13) < (0 * 2 * -4 * -10)))) or (New Zealand is in Oceania.)) and ((not not (not not (473 is a Fibonacci number.))) or ((-17 - -6) <= (46 % 3)) or (((Earth is the 3rd planet from the Sun.) or (30 is a perfect square.)) and ((-18 * -8) < (-6 * -6) < (34 % 4))))
E. ((not (Saudi Arabia is in Antarctica.)) or (not ((-3 + -9) == (2 ** 1))) or ((-7 - -2) >= (4 ** 3))) or (not not (not (Mars is the 4th planet from the Sun.))) or ((((The capital of Sweden is Stockholm.) and ((1 - 0) != (6 - 10))) and ((5 ** 2) > (-18 * -20))) or (((17 + 7) == (3 ** 2)) and (((1 ** 2) > (1 * -2 - -7 * 2)) and ((-14 * -8) < (-17 * -14)))))
F. (not ((not ((3 * 5) <= (-1 * 19))) or (not not (2040 is a leap year.)))) and (not (not ((Mercury is a liquid at room temperature.) and (The capital of Russia is Moscow.))))
G. (not ((((11 + -4) < (-8 + 8) < (2 + -5)) or (A spider has 8 legs.)) or ((-18 * 15) <= (-2 * 10 * 6 * -8) <= (0 * 2 - 9 * 10)))) or ((not ((The capital of Sweden is Stockholm.) and (The 1960 Olympics were held in Rome.))) or ((Argentina is in Asia.) and (The first airplane flight by the Wright Brothers occurred in 1903.)))
H. ((Earth is the 3rd planet from the Sun.) or (((4 * -4 + -1 * 1) <= (7 % 3) <= (35 % 9)) or (76 is greater than 70.)) or (not not ((-10 * 10 * -1 * -6) != (-9 - 15)))) and (not ((A cow has 4 legs.) or (2068 is a leap year.))) and ((not not ((The capital of Cuba is Havana.) and (A dolphin is an insect.))) and ((((2 * 13) >= (7 * 10 + -2 * -1)) or (The 1968 Olympics were held in Mexico City.)) and ((-8 * 10 + -3 * 6) <= (-10 + -13))))
List all options that evaluate to True, separated by commas, in \boxed{}. | {
"game_data": {
"answer": "A,D,E",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 3279209,
"true_count": 3
},
"question": "Evaluate each expression below:\n\nA. not not ((The chemical symbol for Platinum is Pt.) or ((5 + -2) <= (-10 - -7) <= (-6 * -7)))\nB. not not ((The 1932 Olympics were held in Athens.) and ((not (Neptune is the 3rd planet from the Sun.)) and ((The chemical symbol for Platinum is Pt.) or ((-4 * -6 * 0 * 5) == (19 + -3)))))\nC. (not ((((4 * -10 - -8 * -10) <= (12 + -6) <= (-4 * 9 - -2 * -3)) and ((19 + 15) <= (43 % 9))) and ((-13 + -7) > (2 ** 2)))) and (((((4 ** 2) > (18 - 16)) and ((-4 + -6) <= (-4 * 10 - 7 * -8))) or (((-2 * 2 * -1 * 2) >= (20 % 5)) and ((-8 * 10 + 3 * -7) >= (-6 * 9 + 9 * -10)))) and (not (not not ((0 * -5) >= (-6 + -13)))))\nD. (((((-3 * 0 * -1 * -5) <= (-14 * 10)) and (There are 31 days in August.)) and (((-1 * 2 - -2 * 7) == (12 * 15)) and ((7 - -13) < (0 * 2 * -4 * -10)))) or (New Zealand is in Oceania.)) and ((not not (not not (473 is a Fibonacci number.))) or ((-17 - -6) <= (46 % 3)) or (((Earth is the 3rd planet from the Sun.) or (30 is a perfect square.)) and ((-18 * -8) < (-6 * -6) < (34 % 4))))\nE. ((not (Saudi Arabia is in Antarctica.)) or (not ((-3 + -9) == (2 ** 1))) or ((-7 - -2) >= (4 ** 3))) or (not not (not (Mars is the 4th planet from the Sun.))) or ((((The capital of Sweden is Stockholm.) and ((1 - 0) != (6 - 10))) and ((5 ** 2) > (-18 * -20))) or (((17 + 7) == (3 ** 2)) and (((1 ** 2) > (1 * -2 - -7 * 2)) and ((-14 * -8) < (-17 * -14)))))\nF. (not ((not ((3 * 5) <= (-1 * 19))) or (not not (2040 is a leap year.)))) and (not (not ((Mercury is a liquid at room temperature.) and (The capital of Russia is Moscow.))))\nG. (not ((((11 + -4) < (-8 + 8) < (2 + -5)) or (A spider has 8 legs.)) or ((-18 * 15) <= (-2 * 10 * 6 * -8) <= (0 * 2 - 9 * 10)))) or ((not ((The capital of Sweden is Stockholm.) and (The 1960 Olympics were held in Rome.))) or ((Argentina is in Asia.) and (The first airplane flight by the Wright Brothers occurred in 1903.)))\nH. ((Earth is the 3rd planet from the Sun.) or (((4 * -4 + -1 * 1) <= (7 % 3) <= (35 % 9)) or (76 is greater than 70.)) or (not not ((-10 * 10 * -1 * -6) != (-9 - 15)))) and (not ((A cow has 4 legs.) or (2068 is a leap year.))) and ((not not ((The capital of Cuba is Havana.) and (A dolphin is an insect.))) and ((((2 * 13) >= (7 * 10 + -2 * -1)) or (The 1968 Olympics were held in Mexico City.)) and ((-8 * 10 + -3 * 6) <= (-10 + -13))))\n\nList all options that evaluate to True, separated by commas, in \\boxed{}."
},
"metadata": {
"depth": 4,
"language": "en",
"num_options": 8,
"seed": 3279209,
"true_count": 3
},
"seed": 3279209,
"task_id": 603279209,
"task_type": "boolean_expressions"
} |
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