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InternBootcamp/examples/data/Intenbootcamp_eval/korLogicPropositionalLogicFormalization.jsonl
Yongkang Chen a8249acc18
update to tech report version (#10) 
* feat(run_eval): add checkpoint resume functionality and update example documentation;
- update new bootcamp benchmark dataset

* refactor(data_pipeline): optimize data generation pipeline; add multiple preset configurations for data generation

* docs: update bootcamp list and add new scripts

- Update Fulllist_InternBootcamp.md with new bootcamps and categories
- Add new scripts to .gitignore:
  - examples/pipelines/filter_autogen_configs.py
  - examples/pipelines/quickgen_data_configs_from_eval_meta.py
- Update dependencies in setup.py:
  - Add scipy and scikit-learn

* refactor(internbootcamp): update bootcamp modules and improve error handling

- Update import statements in __init__.py files
- Add timestamp to target directory name in verl_data_preprocess.py
- Improve error handling and scoring logic in bootcamp_judger.py
- Remove unnecessary comments and update puzzle descriptions in multiple files
2025-08-28 12:39:47 +08:00

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{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is divisible by 3.\np2: 7 is considered lucky.\np3: Pi is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is odd. and 2 is divisible by 3. and p2=>p1\n(2) It is not the case that It is not the case that Pi is odd.\n(3) 7 is considered lucky. and p3=>p2 and 7 is considered lucky.\n(4) It is not the case that 7 is considered lucky. and Pi is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is divisible by 3.", "p2": "7 is considered lucky.", "p3": "Pi is odd."}, "questions": ["Pi is odd. and 2 is divisible by 3. and p2=>p1", "It is not the case that It is not the case that Pi is odd.", "7 is considered lucky. and p3=>p2 and 7 is considered lucky.", "It is not the case that 7 is considered lucky. and Pi is odd."], "answers": ["((p3&p1)&(p2=>p1))", "~~p3", "((p2&p3)=>(p2&p2))", "~(p2&p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is a prime number.\np2: 2 is a prime number.\np3: Pi is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is a prime number. or Pi is even. and Pi is even. and Pi is even.\n(2) It is not the case that Blue is a prime number. and Pi is even.\n(3) It is not the case that It is not the case that 2 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is a prime number.", "p2": "2 is a prime number.", "p3": "Pi is even."}, "questions": ["Blue is a prime number. or Pi is even. and Pi is even. and Pi is even.", "It is not the case that Blue is a prime number. and Pi is even.", "It is not the case that It is not the case that 2 is a prime number."], "answers": ["((p1||p3)&(p3&p3))", "~(p1&p3)", "~~p2"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is odd.\np2: 7 is a fruit.\np3: Blue is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is odd. or 7 is a fruit. or Pi is odd. or 7 is a fruit.\n(2) It is not the case that 7 is a fruit. or It is not the case that Blue is a fruit.\n(3) It is not the case that Pi is odd. or Blue is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is odd.", "p2": "7 is a fruit.", "p3": "Blue is a fruit."}, "questions": ["Pi is odd. or 7 is a fruit. or Pi is odd. or 7 is a fruit.", "It is not the case that 7 is a fruit. or It is not the case that Blue is a fruit.", "It is not the case that Pi is odd. or Blue is a fruit."], "answers": ["((p1||p2)||(p1||p2))", "(~p2||~p3)", "~(p1||p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is divisible by 3.\np2: 4 is a prime number.\np3: 7 is a fruit.\np4: Red is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p4=>p3 or 7 is a fruit. or 5 is divisible by 3.\n(2) p3=p2=p3 and Red is considered lucky.\n(3) It is not the case that p4=>p2=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is divisible by 3.", "p2": "4 is a prime number.", "p3": "7 is a fruit.", "p4": "Red is considered lucky."}, "questions": ["p4=>p3 or 7 is a fruit. or 5 is divisible by 3.", "p3=p2=p3 and Red is considered lucky.", "It is not the case that p4=>p2=>p3"], "answers": ["((p4=>p3)||(p3||p1))", "((p3=p2)=(p3&p4))", "(~p4=>(p2=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is divisible by 3.\np2: Red is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Red is odd. and It is not the case that 2 is divisible by 3.\n(2) 2 is divisible by 3. or 2 is divisible by 3. or It is not the case that 2 is divisible by 3.\n(3) It is not the case that 2 is divisible by 3. and 2 is divisible by 3.\n(4) It is not the case that Red is odd. or It is not the case that Red is odd.\n(5) It is not the case that Red is odd. and 2 is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is divisible by 3.", "p2": "Red is odd."}, "questions": ["It is not the case that Red is odd. and It is not the case that 2 is divisible by 3.", "2 is divisible by 3. or 2 is divisible by 3. or It is not the case that 2 is divisible by 3.", "It is not the case that 2 is divisible by 3. and 2 is divisible by 3.", "It is not the case that Red is odd. or It is not the case that Red is odd.", "It is not the case that Red is odd. and 2 is divisible by 3."], "answers": ["(~p2&~p1)", "((p1||p1)||~p1)", "~(p1&p1)", "(~p2||~p2)", "~(p2&p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is even.\np2: 5 is even.\np3: 2 is divisible by 3.\np4: 4 is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 2 is divisible by 3. or 5 is even.\n(2) 4 is considered lucky. and p2= It is not the case that 4 is considered lucky.\n(3) 4 is considered lucky. and p3=>p4=p4\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is even.", "p2": "5 is even.", "p3": "2 is divisible by 3.", "p4": "4 is considered lucky."}, "questions": ["It is not the case that 2 is divisible by 3. or 5 is even.", "4 is considered lucky. and p2= It is not the case that 4 is considered lucky.", "4 is considered lucky. and p3=>p4=p4"], "answers": ["~(p3||p2)", "((p4&p2)=~p4)", "((p4&p3)=>(p4=p4))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is considered lucky.\np2: Pi is considered lucky.\np3: Square root of 3 is a common color.\np4: 7 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 7 is divisible by 3. and Blue is considered lucky. and p4=p2\n(2) p1=p2 and p4=p3\n(3) p1=>p4= It is not the case that Square root of 3 is a common color.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is considered lucky.", "p2": "Pi is considered lucky.", "p3": "Square root of 3 is a common color.", "p4": "7 is divisible by 3."}, "questions": ["7 is divisible by 3. and Blue is considered lucky. and p4=p2", "p1=p2 and p4=p3", "p1=>p4= It is not the case that Square root of 3 is a common color."], "answers": ["((p4&p1)&(p4=p2))", "((p1=p2)&(p4=p3))", "((p1=>p4)=~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is odd.\np2: 4 is a fruit.\np3: Pi is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is a fruit. and 4 is a fruit. or 5 is odd.\n(2) It is not the case that Pi is divisible by 3. or 4 is a fruit.\n(3) 5 is odd. or 4 is a fruit. and It is not the case that 5 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is odd.", "p2": "4 is a fruit.", "p3": "Pi is divisible by 3."}, "questions": ["It is not the case that 4 is a fruit. and 4 is a fruit. or 5 is odd.", "It is not the case that Pi is divisible by 3. or 4 is a fruit.", "5 is odd. or 4 is a fruit. and It is not the case that 5 is odd."], "answers": ["(~p2&(p2||p1))", "~(p3||p2)", "((p1||p2)&~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is even.\np2: 2 is a fruit.\np3: Pi is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 4 is even. and p1=>p1 and Pi is divisible by 3.\n(2) p3=>p2=>p3=>p3\n(3) p2=>p1 and Pi is divisible by 3. and 2 is a fruit.\n(4) p3=>p2 and It is not the case that Pi is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is even.", "p2": "2 is a fruit.", "p3": "Pi is divisible by 3."}, "questions": ["4 is even. and p1=>p1 and Pi is divisible by 3.", "p3=>p2=>p3=>p3", "p2=>p1 and Pi is divisible by 3. and 2 is a fruit.", "p3=>p2 and It is not the case that Pi is divisible by 3."], "answers": ["((p1&p1)=>(p1&p3))", "((p3=>p2)=>(p3=>p3))", "((p2=>p1)&(p3&p2))", "((p3=>p2)&~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is a fruit.\np2: Blue is divisible by 3.\np3: 7 is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 7 is even. or 7 is even. and It is not the case that Red is a fruit.\n(2) Blue is divisible by 3. or Red is a fruit. and Blue is divisible by 3. and Red is a fruit.\n(3) 7 is even. and Blue is divisible by 3. or It is not the case that 7 is even.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is a fruit.", "p2": "Blue is divisible by 3.", "p3": "7 is even."}, "questions": ["7 is even. or 7 is even. and It is not the case that Red is a fruit.", "Blue is divisible by 3. or Red is a fruit. and Blue is divisible by 3. and Red is a fruit.", "7 is even. and Blue is divisible by 3. or It is not the case that 7 is even."], "answers": ["((p3||p3)&~p1)", "((p2||p1)&(p2&p1))", "((p3&p2)||~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is odd.\np2: 5 is divisible by 3.\np3: 2 is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 5 is divisible by 3. and It is not the case that Square root of 3 is odd.\n(2) 2 is considered lucky. and 5 is divisible by 3. and 2 is considered lucky. and 2 is considered lucky.\n(3) 5 is divisible by 3. and 5 is divisible by 3. and It is not the case that Square root of 3 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is odd.", "p2": "5 is divisible by 3.", "p3": "2 is considered lucky."}, "questions": ["It is not the case that 5 is divisible by 3. and It is not the case that Square root of 3 is odd.", "2 is considered lucky. and 5 is divisible by 3. and 2 is considered lucky. and 2 is considered lucky.", "5 is divisible by 3. and 5 is divisible by 3. and It is not the case that Square root of 3 is odd."], "answers": ["(~p2&~p1)", "((p3&p2)&(p3&p3))", "((p2&p2)&~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is a common color.\np2: 5 is a prime number.\np3: 4 is a common color.\np4: Red is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that p4=> It is not the case that 5 is a prime number.\n(2) p1=>p4=p1=p1\n(3) 4 is a common color. or p4=p2=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is a common color.", "p2": "5 is a prime number.", "p3": "4 is a common color.", "p4": "Red is even."}, "questions": ["It is not the case that p4=> It is not the case that 5 is a prime number.", "p1=>p4=p1=p1", "4 is a common color. or p4=p2=>p1"], "answers": ["(~p4=>~p2)", "((p1=>p4)=(p1=p1))", "((p3||p4)=(p2=>p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is a prime number.\np2: 5 is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 5 is a prime number. or 5 is a prime number. or It is not the case that 4 is a prime number.\n(2) 5 is a prime number. and 5 is a prime number. or It is not the case that 5 is a prime number.\n(3) It is not the case that 5 is a prime number. and 4 is a prime number.\n(4) It is not the case that 4 is a prime number. or It is not the case that 5 is a prime number.\n(5) 5 is a prime number. or 5 is a prime number. or It is not the case that 5 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is a prime number.", "p2": "5 is a prime number."}, "questions": ["5 is a prime number. or 5 is a prime number. or It is not the case that 4 is a prime number.", "5 is a prime number. and 5 is a prime number. or It is not the case that 5 is a prime number.", "It is not the case that 5 is a prime number. and 4 is a prime number.", "It is not the case that 4 is a prime number. or It is not the case that 5 is a prime number.", "5 is a prime number. or 5 is a prime number. or It is not the case that 5 is a prime number."], "answers": ["((p2||p2)||~p1)", "((p2&p2)||~p2)", "~(p2&p1)", "(~p1||~p2)", "((p2||p2)||~p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is considered lucky.\np2: Red is odd.\np3: 2 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that 2 is odd.\n(2) It is not the case that p2=> It is not the case that 2 is odd.\n(3) p2=>p1=>p1 and 2 is odd.\n(4) It is not the case that It is not the case that Red is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is considered lucky.", "p2": "Red is odd.", "p3": "2 is odd."}, "questions": ["It is not the case that It is not the case that 2 is odd.", "It is not the case that p2=> It is not the case that 2 is odd.", "p2=>p1=>p1 and 2 is odd.", "It is not the case that It is not the case that Red is odd."], "answers": ["~~p3", "(~p2=>~p3)", "((p2=>p1)=>(p1&p3))", "~~p2"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is divisible by 3.\np2: Blue is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 2 is divisible by 3. and Blue is a prime number.\n(2) It is not the case that 2 is divisible by 3. or Blue is a prime number.\n(3) It is not the case that It is not the case that 2 is divisible by 3.\n(4) It is not the case that 2 is divisible by 3. or It is not the case that Blue is a prime number.\n(5) 2 is divisible by 3. and Blue is a prime number. and 2 is divisible by 3. or 2 is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is divisible by 3.", "p2": "Blue is a prime number."}, "questions": ["It is not the case that 2 is divisible by 3. and Blue is a prime number.", "It is not the case that 2 is divisible by 3. or Blue is a prime number.", "It is not the case that It is not the case that 2 is divisible by 3.", "It is not the case that 2 is divisible by 3. or It is not the case that Blue is a prime number.", "2 is divisible by 3. and Blue is a prime number. and 2 is divisible by 3. or 2 is divisible by 3."], "answers": ["~(p1&p2)", "~(p1||p2)", "~~p1", "(~p1||~p2)", "((p1&p2)&(p1||p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is a fruit.\np2: Red is odd.\np3: 2 is even.\np4: 5 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that p4=p2=>p4\n(2) 5 is divisible by 3. and Pi is a fruit. or p4=p2\n(3) It is not the case that 5 is divisible by 3. or 2 is even.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is a fruit.", "p2": "Red is odd.", "p3": "2 is even.", "p4": "5 is divisible by 3."}, "questions": ["It is not the case that p4=p2=>p4", "5 is divisible by 3. and Pi is a fruit. or p4=p2", "It is not the case that 5 is divisible by 3. or 2 is even."], "answers": ["(~p4=(p2=>p4))", "((p4&p1)||(p4=p2))", "~(p4||p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is divisible by 3.\np2: Blue is a common color.\np3: 2 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p1=>p3=>p3=>p3\n(2) It is not the case that It is not the case that 2 is divisible by 3.\n(3) p2=>p3=> It is not the case that 2 is divisible by 3.\n(4) Blue is a common color. and Square root of 3 is divisible by 3. and p2=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is divisible by 3.", "p2": "Blue is a common color.", "p3": "2 is divisible by 3."}, "questions": ["p1=>p3=>p3=>p3", "It is not the case that It is not the case that 2 is divisible by 3.", "p2=>p3=> It is not the case that 2 is divisible by 3.", "Blue is a common color. and Square root of 3 is divisible by 3. and p2=>p3"], "answers": ["((p1=>p3)=>(p3=>p3))", "~~p3", "((p2=>p3)=>~p3)", "((p2&p1)&(p2=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is a fruit.\np2: Square root of 3 is odd.\np3: 7 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Square root of 3 is odd. and 7 is a common color. or 7 is a common color. and Square root of 3 is odd.\n(2) It is not the case that Square root of 3 is odd. or Square root of 3 is odd.\n(3) It is not the case that It is not the case that Square root of 3 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is a fruit.", "p2": "Square root of 3 is odd.", "p3": "7 is a common color."}, "questions": ["Square root of 3 is odd. and 7 is a common color. or 7 is a common color. and Square root of 3 is odd.", "It is not the case that Square root of 3 is odd. or Square root of 3 is odd.", "It is not the case that It is not the case that Square root of 3 is odd."], "answers": ["((p2&p3)||(p3&p2))", "~(p2||p2)", "~~p2"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is a common color.\np2: 2 is a prime number.\np3: Square root of 3 is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Square root of 3 is a prime number. and 2 is a prime number.\n(2) It is not the case that It is not the case that Square root of 3 is a prime number.\n(3) p1=>p1 and It is not the case that 4 is a common color.\n(4) p1=>p1 and It is not the case that Square root of 3 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is a common color.", "p2": "2 is a prime number.", "p3": "Square root of 3 is a prime number."}, "questions": ["It is not the case that Square root of 3 is a prime number. and 2 is a prime number.", "It is not the case that It is not the case that Square root of 3 is a prime number.", "p1=>p1 and It is not the case that 4 is a common color.", "p1=>p1 and It is not the case that Square root of 3 is a prime number."], "answers": ["~(p3&p2)", "~~p3", "((p1=>p1)&~p1)", "((p1=>p1)&~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is a fruit.\np2: 7 is even.\np3: Blue is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 7 is even. or Red is a fruit. and Red is a fruit.\n(2) Blue is a prime number. or Blue is a prime number. and 7 is even. or Blue is a prime number.\n(3) Blue is a prime number. and 7 is even. and Red is a fruit. or Red is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is a fruit.", "p2": "7 is even.", "p3": "Blue is a prime number."}, "questions": ["It is not the case that 7 is even. or Red is a fruit. and Red is a fruit.", "Blue is a prime number. or Blue is a prime number. and 7 is even. or Blue is a prime number.", "Blue is a prime number. and 7 is even. and Red is a fruit. or Red is a fruit."], "answers": ["(~p2||(p1&p1))", "((p3||p3)&(p2||p3))", "((p3&p2)&(p1||p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is even.\np2: 7 is considered lucky.\np3: Square root of 3 is even.\np4: Pi is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Red is even. or p1=>p3=>p2\n(2) It is not the case that p4=p1\n(3) Pi is divisible by 3. or Pi is divisible by 3. or p4=p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is even.", "p2": "7 is considered lucky.", "p3": "Square root of 3 is even.", "p4": "Pi is divisible by 3."}, "questions": ["Red is even. or p1=>p3=>p2", "It is not the case that p4=p1", "Pi is divisible by 3. or Pi is divisible by 3. or p4=p1"], "answers": ["((p1||p1)=>(p3=>p2))", "~(p4=p1)", "((p4||p4)||(p4=p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is considered lucky.\np2: Pi is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is odd. and Pi is odd. or Pi is odd. or Pi is odd.\n(2) Pi is odd. and Pi is odd. or It is not the case that Pi is odd.\n(3) 4 is considered lucky. and 4 is considered lucky. and Pi is odd. and 4 is considered lucky.\n(4) 4 is considered lucky. and 4 is considered lucky. or Pi is odd. and 4 is considered lucky.\n(5) It is not the case that Pi is odd. or Pi is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is considered lucky.", "p2": "Pi is odd."}, "questions": ["Pi is odd. and Pi is odd. or Pi is odd. or Pi is odd.", "Pi is odd. and Pi is odd. or It is not the case that Pi is odd.", "4 is considered lucky. and 4 is considered lucky. and Pi is odd. and 4 is considered lucky.", "4 is considered lucky. and 4 is considered lucky. or Pi is odd. and 4 is considered lucky.", "It is not the case that Pi is odd. or Pi is odd."], "answers": ["((p2&p2)||(p2||p2))", "((p2&p2)||~p2)", "((p1&p1)&(p2&p1))", "((p1&p1)||(p2&p1))", "~(p2||p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is divisible by 3.\np2: Blue is a common color.\np3: 7 is a common color.\np4: 2 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p1=>p2=> It is not the case that 2 is odd.\n(2) p2=>p4=>p4 and 7 is a common color.\n(3) p1=p1=>p1 and Blue is a common color.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is divisible by 3.", "p2": "Blue is a common color.", "p3": "7 is a common color.", "p4": "2 is odd."}, "questions": ["p1=>p2=> It is not the case that 2 is odd.", "p2=>p4=>p4 and 7 is a common color.", "p1=p1=>p1 and Blue is a common color."], "answers": ["((p1=>p2)=>~p4)", "((p2=>p4)=>(p4&p3))", "((p1=p1)=>(p1&p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is even.\np2: Square root of 3 is divisible by 3.\np3: Blue is divisible by 3.\np4: 4 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p4=p3=>p4=p4\n(2) p3=>p4=> It is not the case that Square root of 3 is divisible by 3.\n(3) Square root of 3 is divisible by 3. or p4= It is not the case that 4 is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is even.", "p2": "Square root of 3 is divisible by 3.", "p3": "Blue is divisible by 3.", "p4": "4 is divisible by 3."}, "questions": ["p4=p3=>p4=p4", "p3=>p4=> It is not the case that Square root of 3 is divisible by 3.", "Square root of 3 is divisible by 3. or p4= It is not the case that 4 is divisible by 3."], "answers": ["((p4=p3)=>(p4=p4))", "((p3=>p4)=>~p2)", "((p2||p4)=~p4)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is divisible by 3.\np2: 5 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Pi is divisible by 3. or 5 is divisible by 3. and Pi is divisible by 3.\n(2) Pi is divisible by 3. and Pi is divisible by 3. or It is not the case that Pi is divisible by 3.\n(3) It is not the case that 5 is divisible by 3. or 5 is divisible by 3.\n(4) Pi is divisible by 3. or 5 is divisible by 3. and Pi is divisible by 3. or 5 is divisible by 3.\n(5) Pi is divisible by 3. or Pi is divisible by 3. and Pi is divisible by 3. or 5 is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is divisible by 3.", "p2": "5 is divisible by 3."}, "questions": ["It is not the case that Pi is divisible by 3. or 5 is divisible by 3. and Pi is divisible by 3.", "Pi is divisible by 3. and Pi is divisible by 3. or It is not the case that Pi is divisible by 3.", "It is not the case that 5 is divisible by 3. or 5 is divisible by 3.", "Pi is divisible by 3. or 5 is divisible by 3. and Pi is divisible by 3. or 5 is divisible by 3.", "Pi is divisible by 3. or Pi is divisible by 3. and Pi is divisible by 3. or 5 is divisible by 3."], "answers": ["(~p1||(p2&p1))", "((p1&p1)||~p1)", "~(p2||p2)", "((p1||p2)&(p1||p2))", "((p1||p1)&(p1||p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is odd.\np2: Square root of 3 is odd.\np3: 2 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is odd. and 2 is a common color. and p2=>p3\n(2) Square root of 3 is odd. and p3=>p2=>p2\n(3) It is not the case that p2=>p1\n(4) 2 is a common color. and Square root of 3 is odd. and p3=>p2\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is odd.", "p2": "Square root of 3 is odd.", "p3": "2 is a common color."}, "questions": ["Pi is odd. and 2 is a common color. and p2=>p3", "Square root of 3 is odd. and p3=>p2=>p2", "It is not the case that p2=>p1", "2 is a common color. and Square root of 3 is odd. and p3=>p2"], "answers": ["((p1&p3)&(p2=>p3))", "((p2&p3)=>(p2=>p2))", "~(p2=>p1)", "((p3&p2)&(p3=>p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is considered lucky.\np2: Pi is a prime number.\np3: Red is a common color.\np4: 4 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p3=p3=>p2=>p2\n(2) It is not the case that p3=>p3=>p1\n(3) It is not the case that p2=>p2=p2\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is considered lucky.", "p2": "Pi is a prime number.", "p3": "Red is a common color.", "p4": "4 is divisible by 3."}, "questions": ["p3=p3=>p2=>p2", "It is not the case that p3=>p3=>p1", "It is not the case that p2=>p2=p2"], "answers": ["((p3=p3)=>(p2=>p2))", "(~p3=>(p3=>p1))", "(~p2=>(p2=p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is odd.\np2: 7 is considered lucky.\np3: Blue is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Blue is odd. and p2=>p2\n(2) 5 is odd. and p3=>p2=>p3\n(3) p1=>p1=>p1 and 7 is considered lucky.\n(4) 7 is considered lucky. and 5 is odd. and p2=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is odd.", "p2": "7 is considered lucky.", "p3": "Blue is odd."}, "questions": ["It is not the case that Blue is odd. and p2=>p2", "5 is odd. and p3=>p2=>p3", "p1=>p1=>p1 and 7 is considered lucky.", "7 is considered lucky. and 5 is odd. and p2=>p3"], "answers": ["(~p3&(p2=>p2))", "((p1&p3)=>(p2=>p3))", "((p1=>p1)=>(p1&p2))", "((p2&p1)&(p2=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is even.\np2: 4 is odd.\np3: 7 is odd.\np4: Pi is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p3=p3 and 4 is odd. and 4 is odd.\n(2) 7 is odd. or 7 is odd. or It is not the case that Blue is even.\n(3) p2=p3 or Pi is a prime number. or 4 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is even.", "p2": "4 is odd.", "p3": "7 is odd.", "p4": "Pi is a prime number."}, "questions": ["p3=p3 and 4 is odd. and 4 is odd.", "7 is odd. or 7 is odd. or It is not the case that Blue is even.", "p2=p3 or Pi is a prime number. or 4 is odd."], "answers": ["((p3=p3)&(p2&p2))", "((p3||p3)||~p1)", "((p2=p3)||(p4||p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is a common color.\np2: Red is a common color.\np3: Square root of 3 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p1=>p1 and It is not the case that Red is a common color.\n(2) It is not the case that It is not the case that Red is a common color.\n(3) It is not the case that p3=>p3=>p3\n(4) It is not the case that p2=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is a common color.", "p2": "Red is a common color.", "p3": "Square root of 3 is a common color."}, "questions": ["p1=>p1 and It is not the case that Red is a common color.", "It is not the case that It is not the case that Red is a common color.", "It is not the case that p3=>p3=>p3", "It is not the case that p2=>p1"], "answers": ["((p1=>p1)&~p2)", "~~p2", "(~p3=>(p3=>p3))", "~(p2=>p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is odd.\np2: Blue is divisible by 3.\np3: 5 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 5 is divisible by 3. or Blue is divisible by 3. and It is not the case that 5 is divisible by 3.\n(2) Red is odd. or Blue is divisible by 3. or Blue is divisible by 3. or 5 is divisible by 3.\n(3) 5 is divisible by 3. and 5 is divisible by 3. and It is not the case that 5 is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is odd.", "p2": "Blue is divisible by 3.", "p3": "5 is divisible by 3."}, "questions": ["5 is divisible by 3. or Blue is divisible by 3. and It is not the case that 5 is divisible by 3.", "Red is odd. or Blue is divisible by 3. or Blue is divisible by 3. or 5 is divisible by 3.", "5 is divisible by 3. and 5 is divisible by 3. and It is not the case that 5 is divisible by 3."], "answers": ["((p3||p2)&~p3)", "((p1||p2)||(p2||p3))", "((p3&p3)&~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is even.\np2: 2 is considered lucky.\np3: Pi is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that 2 is considered lucky.\n(2) 2 is considered lucky. or Red is even. or Red is even. and Red is even.\n(3) It is not the case that It is not the case that Red is even.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is even.", "p2": "2 is considered lucky.", "p3": "Pi is even."}, "questions": ["It is not the case that It is not the case that 2 is considered lucky.", "2 is considered lucky. or Red is even. or Red is even. and Red is even.", "It is not the case that It is not the case that Red is even."], "answers": ["~~p2", "((p2||p1)||(p1&p1))", "~~p1"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a common color.\np2: Blue is odd.\np3: Red is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 7 is a common color. or It is not the case that Blue is odd.\n(2) Blue is odd. and Blue is odd. and It is not the case that 7 is a common color.\n(3) Red is a fruit. and Red is a fruit. and It is not the case that Blue is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a common color.", "p2": "Blue is odd.", "p3": "Red is a fruit."}, "questions": ["It is not the case that 7 is a common color. or It is not the case that Blue is odd.", "Blue is odd. and Blue is odd. and It is not the case that 7 is a common color.", "Red is a fruit. and Red is a fruit. and It is not the case that Blue is odd."], "answers": ["(~p1||~p2)", "((p2&p2)&~p1)", "((p3&p3)&~p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is even.\np2: 7 is a common color.\np3: Blue is divisible by 3.\np4: Pi is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is divisible by 3. and p3= It is not the case that Pi is divisible by 3.\n(2) It is not the case that Red is even. and p4=p4\n(3) Pi is divisible by 3. and p3=>p4=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is even.", "p2": "7 is a common color.", "p3": "Blue is divisible by 3.", "p4": "Pi is divisible by 3."}, "questions": ["Pi is divisible by 3. and p3= It is not the case that Pi is divisible by 3.", "It is not the case that Red is even. and p4=p4", "Pi is divisible by 3. and p3=>p4=>p3"], "answers": ["((p4&p3)=~p4)", "(~p1&(p4=p4))", "((p4&p3)=>(p4=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is divisible by 3.\np2: 4 is odd.\np3: Red is a fruit.\np4: Square root of 3 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 4 is odd. or p2=p4 and Blue is divisible by 3.\n(2) It is not the case that p4=p2=>p3\n(3) p4=>p2 or Blue is divisible by 3. and Square root of 3 is a common color.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is divisible by 3.", "p2": "4 is odd.", "p3": "Red is a fruit.", "p4": "Square root of 3 is a common color."}, "questions": ["4 is odd. or p2=p4 and Blue is divisible by 3.", "It is not the case that p4=p2=>p3", "p4=>p2 or Blue is divisible by 3. and Square root of 3 is a common color."], "answers": ["((p2||p2)=(p4&p1))", "(~p4=(p2=>p3))", "((p4=>p2)||(p1&p4))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is considered lucky.\np2: 5 is odd.\np3: 7 is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 2 is considered lucky. and 7 is a prime number.\n(2) p3=>p2 and p1=>p3\n(3) It is not the case that It is not the case that 7 is a prime number.\n(4) It is not the case that 2 is considered lucky. and It is not the case that 7 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is considered lucky.", "p2": "5 is odd.", "p3": "7 is a prime number."}, "questions": ["It is not the case that 2 is considered lucky. and 7 is a prime number.", "p3=>p2 and p1=>p3", "It is not the case that It is not the case that 7 is a prime number.", "It is not the case that 2 is considered lucky. and It is not the case that 7 is a prime number."], "answers": ["~(p1&p3)", "((p3=>p2)&(p1=>p3))", "~~p3", "(~p1&~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is divisible by 3.\np2: Red is odd.\np3: Blue is odd.\np4: Square root of 3 is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Square root of 3 is considered lucky. and Red is odd.\n(2) Blue is odd. and p2=p2=>p2\n(3) p2=p2=p1=p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is divisible by 3.", "p2": "Red is odd.", "p3": "Blue is odd.", "p4": "Square root of 3 is considered lucky."}, "questions": ["It is not the case that Square root of 3 is considered lucky. and Red is odd.", "Blue is odd. and p2=p2=>p2", "p2=p2=p1=p3"], "answers": ["~(p4&p2)", "((p3&p2)=(p2=>p2))", "((p2=p2)=(p1=p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is even.\np2: Square root of 3 is a fruit.\np3: 4 is a common color.\np4: Red is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is a common color. and p2=p1\n(2) It is not the case that p2=p3 and 4 is a common color.\n(3) p2=>p1 and p3=>p4\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is even.", "p2": "Square root of 3 is a fruit.", "p3": "4 is a common color.", "p4": "Red is a common color."}, "questions": ["It is not the case that 4 is a common color. and p2=p1", "It is not the case that p2=p3 and 4 is a common color.", "p2=>p1 and p3=>p4"], "answers": ["(~p3&(p2=p1))", "(~p2=(p3&p3))", "((p2=>p1)&(p3=>p4))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is divisible by 3.\np2: 5 is divisible by 3.\np3: Blue is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is odd. and p1=>p2 and 5 is divisible by 3.\n(2) It is not the case that It is not the case that 5 is divisible by 3.\n(3) It is not the case that p2=>p1 and 4 is divisible by 3.\n(4) p3=>p2=>p3=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is divisible by 3.", "p2": "5 is divisible by 3.", "p3": "Blue is odd."}, "questions": ["Blue is odd. and p1=>p2 and 5 is divisible by 3.", "It is not the case that It is not the case that 5 is divisible by 3.", "It is not the case that p2=>p1 and 4 is divisible by 3.", "p3=>p2=>p3=>p1"], "answers": ["((p3&p1)=>(p2&p2))", "~~p2", "(~p2=>(p1&p1))", "((p3=>p2)=>(p3=>p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a prime number.\np2: 5 is a prime number.\np3: Blue is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 7 is a prime number. and p2=> It is not the case that 7 is a prime number.\n(2) It is not the case that p2=>p1 and 7 is a prime number.\n(3) It is not the case that p2=>p2\n(4) It is not the case that Blue is odd. and p3=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a prime number.", "p2": "5 is a prime number.", "p3": "Blue is odd."}, "questions": ["7 is a prime number. and p2=> It is not the case that 7 is a prime number.", "It is not the case that p2=>p1 and 7 is a prime number.", "It is not the case that p2=>p2", "It is not the case that Blue is odd. and p3=>p3"], "answers": ["((p1&p2)=>~p1)", "(~p2=>(p1&p1))", "~(p2=>p2)", "(~p3&(p3=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is a prime number.\np2: 5 is odd.\np3: Pi is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is a prime number. and Pi is a common color. and It is not the case that Pi is a common color.\n(2) It is not the case that 5 is odd. or It is not the case that Blue is a prime number.\n(3) It is not the case that It is not the case that 5 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is a prime number.", "p2": "5 is odd.", "p3": "Pi is a common color."}, "questions": ["Blue is a prime number. and Pi is a common color. and It is not the case that Pi is a common color.", "It is not the case that 5 is odd. or It is not the case that Blue is a prime number.", "It is not the case that It is not the case that 5 is odd."], "answers": ["((p1&p3)&~p3)", "(~p2||~p1)", "~~p2"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is considered lucky.\np2: 2 is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 2 is a fruit. or 2 is a fruit. and It is not the case that 4 is considered lucky.\n(2) 4 is considered lucky. and 2 is a fruit. or It is not the case that 2 is a fruit.\n(3) It is not the case that 2 is a fruit. and 2 is a fruit. and 4 is considered lucky.\n(4) 2 is a fruit. or 4 is considered lucky. or 4 is considered lucky. or 4 is considered lucky.\n(5) It is not the case that 2 is a fruit. or 2 is a fruit. and 4 is considered lucky.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is considered lucky.", "p2": "2 is a fruit."}, "questions": ["2 is a fruit. or 2 is a fruit. and It is not the case that 4 is considered lucky.", "4 is considered lucky. and 2 is a fruit. or It is not the case that 2 is a fruit.", "It is not the case that 2 is a fruit. and 2 is a fruit. and 4 is considered lucky.", "2 is a fruit. or 4 is considered lucky. or 4 is considered lucky. or 4 is considered lucky.", "It is not the case that 2 is a fruit. or 2 is a fruit. and 4 is considered lucky."], "answers": ["((p2||p2)&~p1)", "((p1&p2)||~p2)", "(~p2&(p2&p1))", "((p2||p1)||(p1||p1))", "(~p2||(p2&p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is a common color.\np2: 4 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 2 is a common color. and 2 is a common color. or 2 is a common color. or 2 is a common color.\n(2) 2 is a common color. and 4 is odd. and It is not the case that 4 is odd.\n(3) It is not the case that It is not the case that 2 is a common color.\n(4) It is not the case that 4 is odd. or 2 is a common color.\n(5) It is not the case that 2 is a common color. or 4 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is a common color.", "p2": "4 is odd."}, "questions": ["2 is a common color. and 2 is a common color. or 2 is a common color. or 2 is a common color.", "2 is a common color. and 4 is odd. and It is not the case that 4 is odd.", "It is not the case that It is not the case that 2 is a common color.", "It is not the case that 4 is odd. or 2 is a common color.", "It is not the case that 2 is a common color. or 4 is odd."], "answers": ["((p1&p1)||(p1||p1))", "((p1&p2)&~p2)", "~~p1", "~(p2||p1)", "~(p1||p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a common color.\np2: 2 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 7 is a common color. or 2 is a common color.\n(2) It is not the case that 7 is a common color. and 7 is a common color. and 7 is a common color.\n(3) 2 is a common color. and 2 is a common color. and It is not the case that 7 is a common color.\n(4) It is not the case that 7 is a common color. or 2 is a common color.\n(5) It is not the case that 7 is a common color. or It is not the case that 7 is a common color.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a common color.", "p2": "2 is a common color."}, "questions": ["It is not the case that 7 is a common color. or 2 is a common color.", "It is not the case that 7 is a common color. and 7 is a common color. and 7 is a common color.", "2 is a common color. and 2 is a common color. and It is not the case that 7 is a common color.", "It is not the case that 7 is a common color. or 2 is a common color.", "It is not the case that 7 is a common color. or It is not the case that 7 is a common color."], "answers": ["~(p1||p2)", "(~p1&(p1&p1))", "((p2&p2)&~p1)", "~(p1||p2)", "(~p1||~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is a prime number.\np2: Pi is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Pi is odd. and Square root of 3 is a prime number. and Square root of 3 is a prime number.\n(2) It is not the case that Square root of 3 is a prime number. or Square root of 3 is a prime number. or Square root of 3 is a prime number.\n(3) Pi is odd. and Square root of 3 is a prime number. and Square root of 3 is a prime number. or Square root of 3 is a prime number.\n(4) It is not the case that Pi is odd. and Square root of 3 is a prime number. or Pi is odd.\n(5) Pi is odd. or Square root of 3 is a prime number. or Pi is odd. and Pi is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is a prime number.", "p2": "Pi is odd."}, "questions": ["It is not the case that Pi is odd. and Square root of 3 is a prime number. and Square root of 3 is a prime number.", "It is not the case that Square root of 3 is a prime number. or Square root of 3 is a prime number. or Square root of 3 is a prime number.", "Pi is odd. and Square root of 3 is a prime number. and Square root of 3 is a prime number. or Square root of 3 is a prime number.", "It is not the case that Pi is odd. and Square root of 3 is a prime number. or Pi is odd.", "Pi is odd. or Square root of 3 is a prime number. or Pi is odd. and Pi is odd."], "answers": ["(~p2&(p1&p1))", "(~p1||(p1||p1))", "((p2&p1)&(p1||p1))", "(~p2&(p1||p2))", "((p2||p1)||(p2&p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is a prime number.\np2: Red is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that Pi is a prime number.\n(2) It is not the case that Red is odd. and Pi is a prime number. and Pi is a prime number.\n(3) Red is odd. and Red is odd. and Red is odd. and Pi is a prime number.\n(4) It is not the case that It is not the case that Red is odd.\n(5) It is not the case that Pi is a prime number. and Red is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is a prime number.", "p2": "Red is odd."}, "questions": ["It is not the case that It is not the case that Pi is a prime number.", "It is not the case that Red is odd. and Pi is a prime number. and Pi is a prime number.", "Red is odd. and Red is odd. and Red is odd. and Pi is a prime number.", "It is not the case that It is not the case that Red is odd.", "It is not the case that Pi is a prime number. and Red is odd."], "answers": ["~~p1", "(~p2&(p1&p1))", "((p2&p2)&(p2&p1))", "~~p2", "~(p1&p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is a fruit.\np2: Square root of 3 is a prime number.\np3: 2 is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 2 is a prime number. or 5 is a fruit. or 5 is a fruit. and 5 is a fruit.\n(2) 2 is a prime number. and 2 is a prime number. and It is not the case that Square root of 3 is a prime number.\n(3) 5 is a fruit. or 2 is a prime number. or 2 is a prime number. and 2 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is a fruit.", "p2": "Square root of 3 is a prime number.", "p3": "2 is a prime number."}, "questions": ["2 is a prime number. or 5 is a fruit. or 5 is a fruit. and 5 is a fruit.", "2 is a prime number. and 2 is a prime number. and It is not the case that Square root of 3 is a prime number.", "5 is a fruit. or 2 is a prime number. or 2 is a prime number. and 2 is a prime number."], "answers": ["((p3||p1)||(p1&p1))", "((p3&p3)&~p2)", "((p1||p3)||(p3&p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is a prime number.\np2: 5 is even.\np3: 4 is a prime number.\np4: Pi is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Red is a prime number. or 4 is a prime number. and It is not the case that Pi is divisible by 3.\n(2) 5 is even. or p2=p1=>p2\n(3) p4=p1 and It is not the case that 4 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is a prime number.", "p2": "5 is even.", "p3": "4 is a prime number.", "p4": "Pi is divisible by 3."}, "questions": ["Red is a prime number. or 4 is a prime number. and It is not the case that Pi is divisible by 3.", "5 is even. or p2=p1=>p2", "p4=p1 and It is not the case that 4 is a prime number."], "answers": ["((p1||p3)&~p4)", "((p2||p2)=(p1=>p2))", "((p4=p1)&~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is odd.\np2: 7 is divisible by 3.\np3: Red is a common color.\np4: 4 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that p2= It is not the case that Blue is odd.\n(2) 4 is odd. or 4 is odd. or It is not the case that 4 is odd.\n(3) Blue is odd. and Red is a common color. or It is not the case that 4 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is odd.", "p2": "7 is divisible by 3.", "p3": "Red is a common color.", "p4": "4 is odd."}, "questions": ["It is not the case that p2= It is not the case that Blue is odd.", "4 is odd. or 4 is odd. or It is not the case that 4 is odd.", "Blue is odd. and Red is a common color. or It is not the case that 4 is odd."], "answers": ["(~p2=~p1)", "((p4||p4)||~p4)", "((p1&p3)||~p4)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is considered lucky.\np2: Square root of 3 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 2 is considered lucky. or 2 is considered lucky. or Square root of 3 is divisible by 3. or 2 is considered lucky.\n(2) It is not the case that 2 is considered lucky. or 2 is considered lucky.\n(3) Square root of 3 is divisible by 3. or Square root of 3 is divisible by 3. and 2 is considered lucky. and Square root of 3 is divisible by 3.\n(4) It is not the case that 2 is considered lucky. and Square root of 3 is divisible by 3.\n(5) It is not the case that Square root of 3 is divisible by 3. and 2 is considered lucky.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is considered lucky.", "p2": "Square root of 3 is divisible by 3."}, "questions": ["2 is considered lucky. or 2 is considered lucky. or Square root of 3 is divisible by 3. or 2 is considered lucky.", "It is not the case that 2 is considered lucky. or 2 is considered lucky.", "Square root of 3 is divisible by 3. or Square root of 3 is divisible by 3. and 2 is considered lucky. and Square root of 3 is divisible by 3.", "It is not the case that 2 is considered lucky. and Square root of 3 is divisible by 3.", "It is not the case that Square root of 3 is divisible by 3. and 2 is considered lucky."], "answers": ["((p1||p1)||(p2||p1))", "~(p1||p1)", "((p2||p2)&(p1&p2))", "~(p1&p2)", "~(p2&p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is divisible by 3.\np2: Blue is a common color.\np3: Pi is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p2=>p3=> It is not the case that Red is divisible by 3.\n(2) It is not the case that It is not the case that Blue is a common color.\n(3) Pi is odd. and p3=>p3 and Red is divisible by 3.\n(4) Blue is a common color. and Red is divisible by 3. and p1=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is divisible by 3.", "p2": "Blue is a common color.", "p3": "Pi is odd."}, "questions": ["p2=>p3=> It is not the case that Red is divisible by 3.", "It is not the case that It is not the case that Blue is a common color.", "Pi is odd. and p3=>p3 and Red is divisible by 3.", "Blue is a common color. and Red is divisible by 3. and p1=>p3"], "answers": ["((p2=>p3)=>~p1)", "~~p2", "((p3&p3)=>(p3&p1))", "((p2&p1)&(p1=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is even.\np2: 4 is odd.\np3: 5 is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 5 is a fruit. and 5 is a fruit. and Blue is even.\n(2) It is not the case that 4 is odd. and 5 is a fruit. and 4 is odd.\n(3) It is not the case that It is not the case that 5 is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is even.", "p2": "4 is odd.", "p3": "5 is a fruit."}, "questions": ["It is not the case that 5 is a fruit. and 5 is a fruit. and Blue is even.", "It is not the case that 4 is odd. and 5 is a fruit. and 4 is odd.", "It is not the case that It is not the case that 5 is a fruit."], "answers": ["(~p3&(p3&p1))", "(~p2&(p3&p2))", "~~p3"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is divisible by 3.\np2: 7 is considered lucky.\np3: 2 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 7 is considered lucky. and 2 is odd. and 7 is considered lucky.\n(2) It is not the case that Blue is divisible by 3. and Blue is divisible by 3.\n(3) Blue is divisible by 3. and 7 is considered lucky. or 2 is odd. and 2 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is divisible by 3.", "p2": "7 is considered lucky.", "p3": "2 is odd."}, "questions": ["It is not the case that 7 is considered lucky. and 2 is odd. and 7 is considered lucky.", "It is not the case that Blue is divisible by 3. and Blue is divisible by 3.", "Blue is divisible by 3. and 7 is considered lucky. or 2 is odd. and 2 is odd."], "answers": ["(~p2&(p3&p2))", "~(p1&p1)", "((p1&p2)||(p3&p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is odd.\np2: 2 is a fruit.\np3: Blue is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p1=>p3 and It is not the case that Blue is a prime number.\n(2) p3=>p3=>p2=>p2\n(3) 2 is a fruit. and 2 is a fruit. and 2 is a fruit. and 2 is a fruit.\n(4) Blue is a prime number. and Blue is a prime number. and p1=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is odd.", "p2": "2 is a fruit.", "p3": "Blue is a prime number."}, "questions": ["p1=>p3 and It is not the case that Blue is a prime number.", "p3=>p3=>p2=>p2", "2 is a fruit. and 2 is a fruit. and 2 is a fruit. and 2 is a fruit.", "Blue is a prime number. and Blue is a prime number. and p1=>p1"], "answers": ["((p1=>p3)&~p3)", "((p3=>p3)=>(p2=>p2))", "((p2&p2)&(p2&p2))", "((p3&p3)&(p1=>p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is a common color.\np2: Pi is a prime number.\np3: Blue is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p2=>p3=>p3=>p3\n(2) p2=>p1=>p1 and Pi is a prime number.\n(3) It is not the case that It is not the case that Blue is a prime number.\n(4) It is not the case that p3=>p2\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is a common color.", "p2": "Pi is a prime number.", "p3": "Blue is a prime number."}, "questions": ["p2=>p3=>p3=>p3", "p2=>p1=>p1 and Pi is a prime number.", "It is not the case that It is not the case that Blue is a prime number.", "It is not the case that p3=>p2"], "answers": ["((p2=>p3)=>(p3=>p3))", "((p2=>p1)=>(p1&p2))", "~~p3", "~(p3=>p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is a fruit.\np2: Red is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is a fruit. and Red is a common color.\n(2) Red is a common color. and 4 is a fruit. and Red is a common color. or Red is a common color.\n(3) Red is a common color. or Red is a common color. and 4 is a fruit. or Red is a common color.\n(4) Red is a common color. and Red is a common color. or It is not the case that 4 is a fruit.\n(5) 4 is a fruit. and Red is a common color. and It is not the case that 4 is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is a fruit.", "p2": "Red is a common color."}, "questions": ["It is not the case that 4 is a fruit. and Red is a common color.", "Red is a common color. and 4 is a fruit. and Red is a common color. or Red is a common color.", "Red is a common color. or Red is a common color. and 4 is a fruit. or Red is a common color.", "Red is a common color. and Red is a common color. or It is not the case that 4 is a fruit.", "4 is a fruit. and Red is a common color. and It is not the case that 4 is a fruit."], "answers": ["~(p1&p2)", "((p2&p1)&(p2||p2))", "((p2||p2)&(p1||p2))", "((p2&p2)||~p1)", "((p1&p2)&~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a common color.\np2: 2 is even.\np3: 4 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 7 is a common color. and 4 is a common color.\n(2) It is not the case that 4 is a common color. and 2 is even.\n(3) It is not the case that 2 is even. and 2 is even. or 4 is a common color.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a common color.", "p2": "2 is even.", "p3": "4 is a common color."}, "questions": ["It is not the case that 7 is a common color. and 4 is a common color.", "It is not the case that 4 is a common color. and 2 is even.", "It is not the case that 2 is even. and 2 is even. or 4 is a common color."], "answers": ["~(p1&p3)", "~(p3&p2)", "(~p2&(p2||p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is a fruit.\np2: 7 is considered lucky.\np3: 5 is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is a fruit. or 4 is a fruit. or 7 is considered lucky.\n(2) 4 is a fruit. and 7 is considered lucky. or It is not the case that 4 is a fruit.\n(3) It is not the case that It is not the case that 4 is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is a fruit.", "p2": "7 is considered lucky.", "p3": "5 is a fruit."}, "questions": ["It is not the case that 4 is a fruit. or 4 is a fruit. or 7 is considered lucky.", "4 is a fruit. and 7 is considered lucky. or It is not the case that 4 is a fruit.", "It is not the case that It is not the case that 4 is a fruit."], "answers": ["(~p1||(p1||p2))", "((p1&p2)||~p1)", "~~p1"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is odd.\np2: 7 is even.\np3: Blue is even.\np4: 2 is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p1=p1 or Blue is even. or Blue is even.\n(2) p4=>p1=>p1 or 7 is even.\n(3) 7 is even. or 5 is odd. or It is not the case that 5 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is odd.", "p2": "7 is even.", "p3": "Blue is even.", "p4": "2 is considered lucky."}, "questions": ["p1=p1 or Blue is even. or Blue is even.", "p4=>p1=>p1 or 7 is even.", "7 is even. or 5 is odd. or It is not the case that 5 is odd."], "answers": ["((p1=p1)||(p3||p3))", "((p4=>p1)=>(p1||p2))", "((p2||p1)||~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is odd.\np2: 7 is a common color.\np3: Pi is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is odd. or 5 is odd. or It is not the case that Pi is odd.\n(2) It is not the case that It is not the case that Pi is odd.\n(3) Pi is odd. and Pi is odd. and 7 is a common color. and 5 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is odd.", "p2": "7 is a common color.", "p3": "Pi is odd."}, "questions": ["Pi is odd. or 5 is odd. or It is not the case that Pi is odd.", "It is not the case that It is not the case that Pi is odd.", "Pi is odd. and Pi is odd. and 7 is a common color. and 5 is odd."], "answers": ["((p3||p1)||~p3)", "~~p3", "((p3&p3)&(p2&p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a fruit.\np2: Blue is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that Blue is odd.\n(2) It is not the case that It is not the case that Blue is odd.\n(3) Blue is odd. and 7 is a fruit. or Blue is odd. or 7 is a fruit.\n(4) 7 is a fruit. and Blue is odd. and Blue is odd. and 7 is a fruit.\n(5) It is not the case that 7 is a fruit. and It is not the case that 7 is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a fruit.", "p2": "Blue is odd."}, "questions": ["It is not the case that It is not the case that Blue is odd.", "It is not the case that It is not the case that Blue is odd.", "Blue is odd. and 7 is a fruit. or Blue is odd. or 7 is a fruit.", "7 is a fruit. and Blue is odd. and Blue is odd. and 7 is a fruit.", "It is not the case that 7 is a fruit. and It is not the case that 7 is a fruit."], "answers": ["~~p2", "~~p2", "((p2&p1)||(p2||p1))", "((p1&p2)&(p2&p1))", "(~p1&~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is even.\np2: 5 is considered lucky.\np3: Square root of 3 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 7 is even. or 5 is considered lucky. or Square root of 3 is odd. and 5 is considered lucky.\n(2) 7 is even. or 7 is even. or It is not the case that 5 is considered lucky.\n(3) It is not the case that Square root of 3 is odd. or 5 is considered lucky. or 5 is considered lucky.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is even.", "p2": "5 is considered lucky.", "p3": "Square root of 3 is odd."}, "questions": ["7 is even. or 5 is considered lucky. or Square root of 3 is odd. and 5 is considered lucky.", "7 is even. or 7 is even. or It is not the case that 5 is considered lucky.", "It is not the case that Square root of 3 is odd. or 5 is considered lucky. or 5 is considered lucky."], "answers": ["((p1||p2)||(p3&p2))", "((p1||p1)||~p2)", "(~p3||(p2||p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is a common color.\np2: 5 is odd.\np3: Blue is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is divisible by 3. and Blue is divisible by 3. and 5 is odd. and Blue is divisible by 3.\n(2) It is not the case that p3=>p2\n(3) It is not the case that Blue is divisible by 3. and Pi is a common color.\n(4) p1=>p2 and p3=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is a common color.", "p2": "5 is odd.", "p3": "Blue is divisible by 3."}, "questions": ["Blue is divisible by 3. and Blue is divisible by 3. and 5 is odd. and Blue is divisible by 3.", "It is not the case that p3=>p2", "It is not the case that Blue is divisible by 3. and Pi is a common color.", "p1=>p2 and p3=>p1"], "answers": ["((p3&p3)&(p2&p3))", "~(p3=>p2)", "~(p3&p1)", "((p1=>p2)&(p3=>p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is divisible by 3.\np2: Pi is even.\np3: Blue is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Pi is even. and Pi is even.\n(2) It is not the case that It is not the case that Red is divisible by 3.\n(3) It is not the case that p3=>p2\n(4) p3=>p3=>p3 and Blue is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is divisible by 3.", "p2": "Pi is even.", "p3": "Blue is a prime number."}, "questions": ["It is not the case that Pi is even. and Pi is even.", "It is not the case that It is not the case that Red is divisible by 3.", "It is not the case that p3=>p2", "p3=>p3=>p3 and Blue is a prime number."], "answers": ["~(p2&p2)", "~~p1", "~(p3=>p2)", "((p3=>p3)=>(p3&p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is odd.\np2: 7 is odd.\np3: Blue is a fruit.\np4: Square root of 3 is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is a fruit. and p1=> It is not the case that 5 is odd.\n(2) It is not the case that 5 is odd. and Square root of 3 is even.\n(3) p1=>p2=p1 and 5 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is odd.", "p2": "7 is odd.", "p3": "Blue is a fruit.", "p4": "Square root of 3 is even."}, "questions": ["Blue is a fruit. and p1=> It is not the case that 5 is odd.", "It is not the case that 5 is odd. and Square root of 3 is even.", "p1=>p2=p1 and 5 is odd."], "answers": ["((p3&p1)=>~p1)", "~(p1&p4)", "((p1=>p2)=(p1&p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is divisible by 3.\np2: 4 is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that Red is divisible by 3.\n(2) Red is divisible by 3. or Red is divisible by 3. or Red is divisible by 3. or 4 is even.\n(3) 4 is even. and 4 is even. and Red is divisible by 3. or Red is divisible by 3.\n(4) 4 is even. or Red is divisible by 3. and It is not the case that 4 is even.\n(5) It is not the case that Red is divisible by 3. and It is not the case that Red is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is divisible by 3.", "p2": "4 is even."}, "questions": ["It is not the case that It is not the case that Red is divisible by 3.", "Red is divisible by 3. or Red is divisible by 3. or Red is divisible by 3. or 4 is even.", "4 is even. and 4 is even. and Red is divisible by 3. or Red is divisible by 3.", "4 is even. or Red is divisible by 3. and It is not the case that 4 is even.", "It is not the case that Red is divisible by 3. and It is not the case that Red is divisible by 3."], "answers": ["~~p1", "((p1||p1)||(p1||p2))", "((p2&p2)&(p1||p1))", "((p2||p1)&~p2)", "(~p1&~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is even.\np2: 2 is a prime number.\np3: Pi is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 2 is a prime number. and It is not the case that 2 is a prime number.\n(2) Pi is a common color. and Pi is a common color. and Square root of 3 is even. and 2 is a prime number.\n(3) Pi is a common color. or Square root of 3 is even. or 2 is a prime number. or Square root of 3 is even.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is even.", "p2": "2 is a prime number.", "p3": "Pi is a common color."}, "questions": ["It is not the case that 2 is a prime number. and It is not the case that 2 is a prime number.", "Pi is a common color. and Pi is a common color. and Square root of 3 is even. and 2 is a prime number.", "Pi is a common color. or Square root of 3 is even. or 2 is a prime number. or Square root of 3 is even."], "answers": ["(~p2&~p2)", "((p3&p3)&(p1&p2))", "((p3||p1)||(p2||p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is divisible by 3.\np2: Blue is even.\np3: Red is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 7 is divisible by 3. and Blue is even.\n(2) It is not the case that It is not the case that Blue is even.\n(3) It is not the case that Blue is even. and 7 is divisible by 3. and 7 is divisible by 3.\n(4) It is not the case that It is not the case that Blue is even.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is divisible by 3.", "p2": "Blue is even.", "p3": "Red is even."}, "questions": ["It is not the case that 7 is divisible by 3. and Blue is even.", "It is not the case that It is not the case that Blue is even.", "It is not the case that Blue is even. and 7 is divisible by 3. and 7 is divisible by 3.", "It is not the case that It is not the case that Blue is even."], "answers": ["~(p1&p2)", "~~p2", "(~p2&(p1&p1))", "~~p2"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is odd.\np2: 7 is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is odd. or 7 is a prime number.\n(2) It is not the case that 4 is odd. and 4 is odd. or 7 is a prime number.\n(3) It is not the case that It is not the case that 4 is odd.\n(4) It is not the case that It is not the case that 4 is odd.\n(5) 4 is odd. and 7 is a prime number. or 4 is odd. or 7 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is odd.", "p2": "7 is a prime number."}, "questions": ["It is not the case that 4 is odd. or 7 is a prime number.", "It is not the case that 4 is odd. and 4 is odd. or 7 is a prime number.", "It is not the case that It is not the case that 4 is odd.", "It is not the case that It is not the case that 4 is odd.", "4 is odd. and 7 is a prime number. or 4 is odd. or 7 is a prime number."], "answers": ["~(p1||p2)", "(~p1&(p1||p2))", "~~p1", "~~p1", "((p1&p2)||(p1||p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is odd.\np2: Pi is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is a prime number. and Square root of 3 is odd. or Square root of 3 is odd. and Square root of 3 is odd.\n(2) Square root of 3 is odd. and Square root of 3 is odd. and It is not the case that Square root of 3 is odd.\n(3) Pi is a prime number. and Square root of 3 is odd. or Square root of 3 is odd. or Pi is a prime number.\n(4) It is not the case that It is not the case that Square root of 3 is odd.\n(5) Pi is a prime number. or Square root of 3 is odd. and It is not the case that Pi is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is odd.", "p2": "Pi is a prime number."}, "questions": ["Pi is a prime number. and Square root of 3 is odd. or Square root of 3 is odd. and Square root of 3 is odd.", "Square root of 3 is odd. and Square root of 3 is odd. and It is not the case that Square root of 3 is odd.", "Pi is a prime number. and Square root of 3 is odd. or Square root of 3 is odd. or Pi is a prime number.", "It is not the case that It is not the case that Square root of 3 is odd.", "Pi is a prime number. or Square root of 3 is odd. and It is not the case that Pi is a prime number."], "answers": ["((p2&p1)||(p1&p1))", "((p1&p1)&~p1)", "((p2&p1)||(p1||p2))", "~~p1", "((p2||p1)&~p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is odd.\np2: 7 is even.\np3: Red is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Red is a prime number. or 7 is even.\n(2) It is not the case that Square root of 3 is odd. and Square root of 3 is odd. or Square root of 3 is odd.\n(3) It is not the case that 7 is even. or 7 is even.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is odd.", "p2": "7 is even.", "p3": "Red is a prime number."}, "questions": ["It is not the case that Red is a prime number. or 7 is even.", "It is not the case that Square root of 3 is odd. and Square root of 3 is odd. or Square root of 3 is odd.", "It is not the case that 7 is even. or 7 is even."], "answers": ["~(p3||p2)", "(~p1&(p1||p1))", "~(p2||p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is considered lucky.\np2: Square root of 3 is even.\np3: 2 is odd.\np4: 4 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is odd. and Square root of 3 is even.\n(2) p1=>p1=>p2 and 5 is considered lucky.\n(3) 2 is odd. or p2=>p4=p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is considered lucky.", "p2": "Square root of 3 is even.", "p3": "2 is odd.", "p4": "4 is odd."}, "questions": ["It is not the case that 4 is odd. and Square root of 3 is even.", "p1=>p1=>p2 and 5 is considered lucky.", "2 is odd. or p2=>p4=p3"], "answers": ["~(p4&p2)", "((p1=>p1)=>(p2&p1))", "((p3||p2)=>(p4=p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is divisible by 3.\np2: Pi is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Pi is a prime number. and It is not the case that Pi is a prime number.\n(2) Red is divisible by 3. or Red is divisible by 3. and It is not the case that Red is divisible by 3.\n(3) It is not the case that It is not the case that Pi is a prime number.\n(4) It is not the case that It is not the case that Pi is a prime number.\n(5) It is not the case that Red is divisible by 3. or Pi is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is divisible by 3.", "p2": "Pi is a prime number."}, "questions": ["It is not the case that Pi is a prime number. and It is not the case that Pi is a prime number.", "Red is divisible by 3. or Red is divisible by 3. and It is not the case that Red is divisible by 3.", "It is not the case that It is not the case that Pi is a prime number.", "It is not the case that It is not the case that Pi is a prime number.", "It is not the case that Red is divisible by 3. or Pi is a prime number."], "answers": ["(~p2&~p2)", "((p1||p1)&~p1)", "~~p2", "~~p2", "~(p1||p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is even.\np2: Blue is even.\np3: 4 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Square root of 3 is even. and p1=>p3\n(2) p1=>p2=> It is not the case that Square root of 3 is even.\n(3) p3=>p3 and 4 is a common color. and Square root of 3 is even.\n(4) It is not the case that It is not the case that Square root of 3 is even.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is even.", "p2": "Blue is even.", "p3": "4 is a common color."}, "questions": ["It is not the case that Square root of 3 is even. and p1=>p3", "p1=>p2=> It is not the case that Square root of 3 is even.", "p3=>p3 and 4 is a common color. and Square root of 3 is even.", "It is not the case that It is not the case that Square root of 3 is even."], "answers": ["(~p1&(p1=>p3))", "((p1=>p2)=>~p1)", "((p3=>p3)&(p3&p1))", "~~p1"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is odd.\np2: Blue is a fruit.\np3: 4 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is a fruit. and Blue is a fruit. or 7 is odd. and 4 is a common color.\n(2) 7 is odd. or Blue is a fruit. and 7 is odd. and Blue is a fruit.\n(3) It is not the case that 4 is a common color. or Blue is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is odd.", "p2": "Blue is a fruit.", "p3": "4 is a common color."}, "questions": ["Blue is a fruit. and Blue is a fruit. or 7 is odd. and 4 is a common color.", "7 is odd. or Blue is a fruit. and 7 is odd. and Blue is a fruit.", "It is not the case that 4 is a common color. or Blue is a fruit."], "answers": ["((p2&p2)||(p1&p3))", "((p1||p2)&(p1&p2))", "~(p3||p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is a fruit.\np2: 5 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 5 is odd. and 5 is odd.\n(2) It is not the case that 5 is odd. or 5 is odd. and 5 is odd.\n(3) It is not the case that 2 is a fruit. and 5 is odd.\n(4) 2 is a fruit. or 5 is odd. or 5 is odd. or 5 is odd.\n(5) 2 is a fruit. and 2 is a fruit. or It is not the case that 2 is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is a fruit.", "p2": "5 is odd."}, "questions": ["It is not the case that 5 is odd. and 5 is odd.", "It is not the case that 5 is odd. or 5 is odd. and 5 is odd.", "It is not the case that 2 is a fruit. and 5 is odd.", "2 is a fruit. or 5 is odd. or 5 is odd. or 5 is odd.", "2 is a fruit. and 2 is a fruit. or It is not the case that 2 is a fruit."], "answers": ["~(p2&p2)", "(~p2||(p2&p2))", "~(p1&p2)", "((p1||p2)||(p2||p2))", "((p1&p1)||~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is a prime number.\np2: Blue is a fruit.\np3: 4 is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 2 is a prime number. and 2 is a prime number. or 2 is a prime number.\n(2) It is not the case that Blue is a fruit. or 2 is a prime number. and 2 is a prime number.\n(3) 4 is considered lucky. or 4 is considered lucky. or It is not the case that 4 is considered lucky.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is a prime number.", "p2": "Blue is a fruit.", "p3": "4 is considered lucky."}, "questions": ["It is not the case that 2 is a prime number. and 2 is a prime number. or 2 is a prime number.", "It is not the case that Blue is a fruit. or 2 is a prime number. and 2 is a prime number.", "4 is considered lucky. or 4 is considered lucky. or It is not the case that 4 is considered lucky."], "answers": ["(~p1&(p1||p1))", "(~p2||(p1&p1))", "((p3||p3)||~p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is divisible by 3.\np2: Square root of 3 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Square root of 3 is divisible by 3. and Square root of 3 is divisible by 3. and Square root of 3 is divisible by 3.\n(2) It is not the case that Red is divisible by 3. and Red is divisible by 3. and Square root of 3 is divisible by 3.\n(3) It is not the case that Square root of 3 is divisible by 3. or Red is divisible by 3.\n(4) Square root of 3 is divisible by 3. or Red is divisible by 3. and It is not the case that Square root of 3 is divisible by 3.\n(5) It is not the case that Red is divisible by 3. and Square root of 3 is divisible by 3. and Red is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is divisible by 3.", "p2": "Square root of 3 is divisible by 3."}, "questions": ["It is not the case that Square root of 3 is divisible by 3. and Square root of 3 is divisible by 3. and Square root of 3 is divisible by 3.", "It is not the case that Red is divisible by 3. and Red is divisible by 3. and Square root of 3 is divisible by 3.", "It is not the case that Square root of 3 is divisible by 3. or Red is divisible by 3.", "Square root of 3 is divisible by 3. or Red is divisible by 3. and It is not the case that Square root of 3 is divisible by 3.", "It is not the case that Red is divisible by 3. and Square root of 3 is divisible by 3. and Red is divisible by 3."], "answers": ["(~p2&(p2&p2))", "(~p1&(p1&p2))", "~(p2||p1)", "((p2||p1)&~p2)", "(~p1&(p2&p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is divisible by 3.\np2: Pi is divisible by 3.\np3: 7 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that p1=>p2\n(2) p2=>p1 and Red is divisible by 3. and Red is divisible by 3.\n(3) p2=>p2=>p2 and Pi is divisible by 3.\n(4) Red is divisible by 3. and p1=>p2=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is divisible by 3.", "p2": "Pi is divisible by 3.", "p3": "7 is divisible by 3."}, "questions": ["It is not the case that p1=>p2", "p2=>p1 and Red is divisible by 3. and Red is divisible by 3.", "p2=>p2=>p2 and Pi is divisible by 3.", "Red is divisible by 3. and p1=>p2=>p3"], "answers": ["~(p1=>p2)", "((p2=>p1)&(p1&p1))", "((p2=>p2)=>(p2&p2))", "((p1&p1)=>(p2=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is a prime number.\np2: Pi is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that Pi is a fruit. or 4 is a prime number. or 4 is a prime number.\n(2) Pi is a fruit. or 4 is a prime number. and Pi is a fruit. or Pi is a fruit.\n(3) 4 is a prime number. or 4 is a prime number. and It is not the case that 4 is a prime number.\n(4) Pi is a fruit. and 4 is a prime number. or Pi is a fruit. and Pi is a fruit.\n(5) 4 is a prime number. and Pi is a fruit. or 4 is a prime number. or Pi is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is a prime number.", "p2": "Pi is a fruit."}, "questions": ["It is not the case that Pi is a fruit. or 4 is a prime number. or 4 is a prime number.", "Pi is a fruit. or 4 is a prime number. and Pi is a fruit. or Pi is a fruit.", "4 is a prime number. or 4 is a prime number. and It is not the case that 4 is a prime number.", "Pi is a fruit. and 4 is a prime number. or Pi is a fruit. and Pi is a fruit.", "4 is a prime number. and Pi is a fruit. or 4 is a prime number. or Pi is a fruit."], "answers": ["(~p2||(p1||p1))", "((p2||p1)&(p2||p2))", "((p1||p1)&~p1)", "((p2&p1)||(p2&p2))", "((p1&p2)||(p1||p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a fruit.\np2: Red is odd.\np3: Blue is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that Red is odd.\n(2) It is not the case that It is not the case that Blue is a common color.\n(3) Red is odd. and p1=>p3=>p2\n(4) It is not the case that Red is odd. and Red is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a fruit.", "p2": "Red is odd.", "p3": "Blue is a common color."}, "questions": ["It is not the case that It is not the case that Red is odd.", "It is not the case that It is not the case that Blue is a common color.", "Red is odd. and p1=>p3=>p2", "It is not the case that Red is odd. and Red is odd."], "answers": ["~~p2", "~~p3", "((p2&p1)=>(p3=>p2))", "~(p2&p2)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 4 is a fruit.\np2: 2 is even.\np3: 5 is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that 2 is even.\n(2) p3=>p3=>p2=>p3\n(3) It is not the case that 5 is a fruit. and 2 is even.\n(4) It is not the case that 2 is even. and p2=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "4 is a fruit.", "p2": "2 is even.", "p3": "5 is a fruit."}, "questions": ["It is not the case that It is not the case that 2 is even.", "p3=>p3=>p2=>p3", "It is not the case that 5 is a fruit. and 2 is even.", "It is not the case that 2 is even. and p2=>p1"], "answers": ["~~p2", "((p3=>p3)=>(p2=>p3))", "~(p3&p2)", "(~p2&(p2=>p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a prime number.\np2: 4 is a fruit.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is a fruit. or 7 is a prime number. or 4 is a fruit.\n(2) It is not the case that 7 is a prime number. and It is not the case that 7 is a prime number.\n(3) 7 is a prime number. and 4 is a fruit. and It is not the case that 7 is a prime number.\n(4) It is not the case that 4 is a fruit. and 7 is a prime number.\n(5) It is not the case that It is not the case that 4 is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a prime number.", "p2": "4 is a fruit."}, "questions": ["It is not the case that 4 is a fruit. or 7 is a prime number. or 4 is a fruit.", "It is not the case that 7 is a prime number. and It is not the case that 7 is a prime number.", "7 is a prime number. and 4 is a fruit. and It is not the case that 7 is a prime number.", "It is not the case that 4 is a fruit. and 7 is a prime number.", "It is not the case that It is not the case that 4 is a fruit."], "answers": ["(~p2||(p1||p2))", "(~p1&~p1)", "((p1&p2)&~p1)", "~(p2&p1)", "~~p2"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Blue is considered lucky.\np2: Red is a prime number.\np3: 7 is a fruit.\np4: 2 is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p1=p1 or 2 is a prime number. or 7 is a fruit.\n(2) 2 is a prime number. or 7 is a fruit. or Blue is considered lucky. and Blue is considered lucky.\n(3) It is not the case that 7 is a fruit. and Blue is considered lucky.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Blue is considered lucky.", "p2": "Red is a prime number.", "p3": "7 is a fruit.", "p4": "2 is a prime number."}, "questions": ["p1=p1 or 2 is a prime number. or 7 is a fruit.", "2 is a prime number. or 7 is a fruit. or Blue is considered lucky. and Blue is considered lucky.", "It is not the case that 7 is a fruit. and Blue is considered lucky."], "answers": ["((p1=p1)||(p4||p3))", "((p4||p3)||(p1&p1))", "~(p3&p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is odd.\np2: Square root of 3 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Square root of 3 is divisible by 3. or Pi is odd. and It is not the case that Pi is odd.\n(2) It is not the case that It is not the case that Square root of 3 is divisible by 3.\n(3) It is not the case that Square root of 3 is divisible by 3. or Pi is odd.\n(4) It is not the case that Pi is odd. and Pi is odd.\n(5) Pi is odd. or Pi is odd. or Pi is odd. and Pi is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is odd.", "p2": "Square root of 3 is divisible by 3."}, "questions": ["Square root of 3 is divisible by 3. or Pi is odd. and It is not the case that Pi is odd.", "It is not the case that It is not the case that Square root of 3 is divisible by 3.", "It is not the case that Square root of 3 is divisible by 3. or Pi is odd.", "It is not the case that Pi is odd. and Pi is odd.", "Pi is odd. or Pi is odd. or Pi is odd. and Pi is odd."], "answers": ["((p2||p1)&~p1)", "~~p2", "~(p2||p1)", "~(p1&p1)", "((p1||p1)||(p1&p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is divisible by 3.\np2: 4 is considered lucky.\np3: Blue is a common color.\np4: Pi is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is a common color. or p3=p1 or 5 is divisible by 3.\n(2) 5 is divisible by 3. and p1=>p4=>p1\n(3) p4=p4=>p1=>p4\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is divisible by 3.", "p2": "4 is considered lucky.", "p3": "Blue is a common color.", "p4": "Pi is a common color."}, "questions": ["Blue is a common color. or p3=p1 or 5 is divisible by 3.", "5 is divisible by 3. and p1=>p4=>p1", "p4=p4=>p1=>p4"], "answers": ["((p3||p3)=(p1||p1))", "((p1&p1)=>(p4=>p1))", "((p4=p4)=>(p1=>p4))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is divisible by 3.\np2: 4 is odd.\np3: 2 is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 4 is odd. and 4 is odd.\n(2) 2 is divisible by 3. or 4 is odd. and It is not the case that 4 is odd.\n(3) It is not the case that 2 is divisible by 3. and 5 is divisible by 3. and 5 is divisible by 3.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is divisible by 3.", "p2": "4 is odd.", "p3": "2 is divisible by 3."}, "questions": ["It is not the case that 4 is odd. and 4 is odd.", "2 is divisible by 3. or 4 is odd. and It is not the case that 4 is odd.", "It is not the case that 2 is divisible by 3. and 5 is divisible by 3. and 5 is divisible by 3."], "answers": ["~(p2&p2)", "((p3||p2)&~p2)", "(~p3&(p1&p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a prime number.\np2: 4 is a common color.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 4 is a common color. or 4 is a common color. and It is not the case that 4 is a common color.\n(2) It is not the case that 4 is a common color. or 4 is a common color. and 4 is a common color.\n(3) It is not the case that 4 is a common color. and 7 is a prime number.\n(4) It is not the case that 7 is a prime number. or 7 is a prime number. and 4 is a common color.\n(5) It is not the case that 4 is a common color. or It is not the case that 7 is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a prime number.", "p2": "4 is a common color."}, "questions": ["4 is a common color. or 4 is a common color. and It is not the case that 4 is a common color.", "It is not the case that 4 is a common color. or 4 is a common color. and 4 is a common color.", "It is not the case that 4 is a common color. and 7 is a prime number.", "It is not the case that 7 is a prime number. or 7 is a prime number. and 4 is a common color.", "It is not the case that 4 is a common color. or It is not the case that 7 is a prime number."], "answers": ["((p2||p2)&~p2)", "(~p2||(p2&p2))", "~(p2&p1)", "(~p1||(p1&p2))", "(~p2||~p1)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is odd.\np2: 7 is a common color.\np3: Blue is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is even. and 7 is a common color. or Blue is even. and Blue is even.\n(2) It is not the case that Blue is even. or It is not the case that 7 is a common color.\n(3) It is not the case that It is not the case that 5 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is odd.", "p2": "7 is a common color.", "p3": "Blue is even."}, "questions": ["Blue is even. and 7 is a common color. or Blue is even. and Blue is even.", "It is not the case that Blue is even. or It is not the case that 7 is a common color.", "It is not the case that It is not the case that 5 is odd."], "answers": ["((p3&p2)||(p3&p3))", "(~p3||~p2)", "~~p1"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is odd.\np2: 5 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Square root of 3 is odd. and 5 is odd. and 5 is odd. or 5 is odd.\n(2) It is not the case that Square root of 3 is odd. or Square root of 3 is odd.\n(3) Square root of 3 is odd. or Square root of 3 is odd. or Square root of 3 is odd. and Square root of 3 is odd.\n(4) It is not the case that It is not the case that 5 is odd.\n(5) It is not the case that Square root of 3 is odd. and 5 is odd. and 5 is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is odd.", "p2": "5 is odd."}, "questions": ["Square root of 3 is odd. and 5 is odd. and 5 is odd. or 5 is odd.", "It is not the case that Square root of 3 is odd. or Square root of 3 is odd.", "Square root of 3 is odd. or Square root of 3 is odd. or Square root of 3 is odd. and Square root of 3 is odd.", "It is not the case that It is not the case that 5 is odd.", "It is not the case that Square root of 3 is odd. and 5 is odd. and 5 is odd."], "answers": ["((p1&p2)&(p2||p2))", "~(p1||p1)", "((p1||p1)||(p1&p1))", "~~p2", "(~p1&(p2&p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is even.\np2: 2 is even.\np3: Blue is a prime number.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Blue is a prime number. and Blue is a prime number. and 5 is even. and 5 is even.\n(2) It is not the case that p1=>p2\n(3) It is not the case that It is not the case that 2 is even.\n(4) It is not the case that Blue is a prime number. and Blue is a prime number. and Blue is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is even.", "p2": "2 is even.", "p3": "Blue is a prime number."}, "questions": ["Blue is a prime number. and Blue is a prime number. and 5 is even. and 5 is even.", "It is not the case that p1=>p2", "It is not the case that It is not the case that 2 is even.", "It is not the case that Blue is a prime number. and Blue is a prime number. and Blue is a prime number."], "answers": ["((p3&p3)&(p1&p1))", "~(p1=>p2)", "~~p2", "(~p3&(p3&p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is odd.\np2: Red is a prime number.\np3: Blue is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is odd. and p3=> It is not the case that Pi is odd.\n(2) It is not the case that It is not the case that Blue is even.\n(3) It is not the case that Red is a prime number. and Blue is even.\n(4) p1=>p1=>p3 and Red is a prime number.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is odd.", "p2": "Red is a prime number.", "p3": "Blue is even."}, "questions": ["Pi is odd. and p3=> It is not the case that Pi is odd.", "It is not the case that It is not the case that Blue is even.", "It is not the case that Red is a prime number. and Blue is even.", "p1=>p1=>p3 and Red is a prime number."], "answers": ["((p1&p3)=>~p1)", "~~p3", "~(p2&p3)", "((p1=>p1)=>(p3&p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is a prime number.\np2: Red is even.\np3: 4 is a prime number.\np4: 5 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) 5 is odd. and p1=> It is not the case that Red is even.\n(2) It is not the case that p1=>p1\n(3) p2=>p3=>p2=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is a prime number.", "p2": "Red is even.", "p3": "4 is a prime number.", "p4": "5 is odd."}, "questions": ["5 is odd. and p1=> It is not the case that Red is even.", "It is not the case that p1=>p1", "p2=>p3=>p2=>p1"], "answers": ["((p4&p1)=>~p2)", "~(p1=>p1)", "((p2=>p3)=>(p2=>p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is a prime number.\np2: 2 is odd.\np3: Pi is even.\np4: 7 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) p3=p3 and p4=p1\n(2) p1=>p3 or It is not the case that Pi is even.\n(3) It is not the case that p2=p4\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is a prime number.", "p2": "2 is odd.", "p3": "Pi is even.", "p4": "7 is odd."}, "questions": ["p3=p3 and p4=p1", "p1=>p3 or It is not the case that Pi is even.", "It is not the case that p2=p4"], "answers": ["((p3=p3)&(p4=p1))", "((p1=>p3)||~p3)", "~(p2=p4)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 7 is divisible by 3.\np2: Blue is considered lucky.\np3: 4 is a fruit.\np4: Red is divisible by 3.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 7 is divisible by 3. and Red is divisible by 3.\n(2) 4 is a fruit. and Blue is considered lucky. or It is not the case that Red is divisible by 3.\n(3) It is not the case that 7 is divisible by 3. and 4 is a fruit.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "7 is divisible by 3.", "p2": "Blue is considered lucky.", "p3": "4 is a fruit.", "p4": "Red is divisible by 3."}, "questions": ["It is not the case that 7 is divisible by 3. and Red is divisible by 3.", "4 is a fruit. and Blue is considered lucky. or It is not the case that Red is divisible by 3.", "It is not the case that 7 is divisible by 3. and 4 is a fruit."], "answers": ["~(p1&p4)", "((p3&p2)||~p4)", "~(p1&p3)"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Red is a prime number.\np2: Pi is a common color.\np3: Square root of 3 is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that p2=>p3\n(2) It is not the case that p3=>p3 and Square root of 3 is considered lucky.\n(3) It is not the case that p2=>p2=>p2\n(4) Pi is a common color. and p3=>p2=>p3\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Red is a prime number.", "p2": "Pi is a common color.", "p3": "Square root of 3 is considered lucky."}, "questions": ["It is not the case that p2=>p3", "It is not the case that p3=>p3 and Square root of 3 is considered lucky.", "It is not the case that p2=>p2=>p2", "Pi is a common color. and p3=>p2=>p3"], "answers": ["~(p2=>p3)", "(~p3=>(p3&p3))", "(~p2=>(p2=>p2))", "((p2&p3)=>(p2=>p3))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 2 is divisible by 3.\np2: Square root of 3 is divisible by 3.\np3: 4 is a common color.\np4: Red is even.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that It is not the case that 2 is divisible by 3.\n(2) p1=p2=p2=>p4\n(3) Red is even. and 2 is divisible by 3. and p1=>p1\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "2 is divisible by 3.", "p2": "Square root of 3 is divisible by 3.", "p3": "4 is a common color.", "p4": "Red is even."}, "questions": ["It is not the case that It is not the case that 2 is divisible by 3.", "p1=p2=p2=>p4", "Red is even. and 2 is divisible by 3. and p1=>p1"], "answers": ["~~p1", "((p1=p2)=(p2=>p4))", "((p4&p1)&(p1=>p1))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: 5 is a common color.\np2: Pi is a common color.\np3: 4 is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is a common color. and Pi is a common color. and p2=>p2\n(2) p1=>p2 and p1=>p2\n(3) 5 is a common color. and p1=>p2 and Pi is a common color.\n(4) 5 is a common color. and Pi is a common color. and 4 is odd. and Pi is a common color.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "5 is a common color.", "p2": "Pi is a common color.", "p3": "4 is odd."}, "questions": ["Pi is a common color. and Pi is a common color. and p2=>p2", "p1=>p2 and p1=>p2", "5 is a common color. and p1=>p2 and Pi is a common color.", "5 is a common color. and Pi is a common color. and 4 is odd. and Pi is a common color."], "answers": ["((p2&p2)&(p2=>p2))", "((p1=>p2)&(p1=>p2))", "((p1&p1)=>(p2&p2))", "((p1&p2)&(p3&p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Pi is considered lucky.\np2: Blue is odd.\n\nSymbolize the following propositions using &, ||, ~:\n(1) Pi is considered lucky. and Blue is odd. and Blue is odd. and Blue is odd.\n(2) Blue is odd. and Pi is considered lucky. and Blue is odd. or Blue is odd.\n(3) It is not the case that Blue is odd. or Pi is considered lucky.\n(4) Blue is odd. or Blue is odd. or Blue is odd. and Blue is odd.\n(5) Pi is considered lucky. or Pi is considered lucky. or Blue is odd. and Blue is odd.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Pi is considered lucky.", "p2": "Blue is odd."}, "questions": ["Pi is considered lucky. and Blue is odd. and Blue is odd. and Blue is odd.", "Blue is odd. and Pi is considered lucky. and Blue is odd. or Blue is odd.", "It is not the case that Blue is odd. or Pi is considered lucky.", "Blue is odd. or Blue is odd. or Blue is odd. and Blue is odd.", "Pi is considered lucky. or Pi is considered lucky. or Blue is odd. and Blue is odd."], "answers": ["((p1&p2)&(p2&p2))", "((p2&p1)&(p2||p2))", "~(p2||p1)", "((p2||p2)||(p2&p2))", "((p1||p1)||(p2&p2))"]}}
{"data_source": "KorLogicPropositionalLogicFormalization", "prompt": "Given:\np1: Square root of 3 is a common color.\np2: 5 is odd.\np3: 4 is considered lucky.\n\nSymbolize the following propositions using &, ||, ~:\n(1) It is not the case that 5 is odd. or Square root of 3 is a common color.\n(2) Square root of 3 is a common color. or 5 is odd. or It is not the case that Square root of 3 is a common color.\n(3) 4 is considered lucky. and 4 is considered lucky. and 4 is considered lucky. and 4 is considered lucky.\n\nFormat your answers as [[...];[...];...]", "ground_truth": {"type": "symbolize", "propositions": {"p1": "Square root of 3 is a common color.", "p2": "5 is odd.", "p3": "4 is considered lucky."}, "questions": ["It is not the case that 5 is odd. or Square root of 3 is a common color.", "Square root of 3 is a common color. or 5 is odd. or It is not the case that Square root of 3 is a common color.", "4 is considered lucky. and 4 is considered lucky. and 4 is considered lucky. and 4 is considered lucky."], "answers": ["~(p2||p1)", "((p1||p2)||~p1)", "((p3&p3)&(p3&p3))"]}}
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