Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition qcore is true if proposition x2a is true. Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition x4b is true if proposition x4a is not true. Proposition x1a is true if proposition x1b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition s0 is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x2b is true if proposition x2a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x1a is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x0a is true. Proposition x0b is true if proposition x0a is not true. Proposition x2a is true if proposition x2b is not true. Proposition t0 is true if proposition t1 is true. Proposition x5a is true if proposition x5b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition qcore is true if proposition x2a is true. Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition x4b is true if proposition x4a is not true. Proposition x1a is true if proposition x1b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition s0 is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x2b is true if proposition x2a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x1a is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x0a is true. Proposition x0b is true if proposition x0a is not true. Proposition x2a is true if proposition x2b is not true. Proposition t0 is true if proposition t1 is true. Proposition x5a is true if proposition x5b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition qcore is true if proposition x2a is true. Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition x4b is true if proposition x4a is not true. Proposition x1a is true if proposition x1b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition s0 is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x2b is true if proposition x2a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x1a is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x0a is true. Proposition x0b is true if proposition x0a is not true. Proposition x2a is true if proposition x2b is not true. Proposition t0 is true if proposition t1 is true. Proposition x5a is true if proposition x5b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition qcore is true if proposition x2a is true. Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition x4b is true if proposition x4a is not true. Proposition x1a is true if proposition x1b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition s0 is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x2b is true if proposition x2a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x1a is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x0a is true. Proposition x0b is true if proposition x0a is not true. Proposition x2a is true if proposition x2b is not true. Proposition t0 is true if proposition t1 is true. Proposition x5a is true if proposition x5b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition qcore is true if proposition x5a is true. Proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition x1a is true if proposition x1b is not true. Proposition t0 is true if proposition t1 is true. Proposition x3b is true if proposition x3a is not true. Proposition x5b is true if proposition x5a is not true. Proposition x4b is true if proposition x4a is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition x3a is true if proposition x3b is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition qcore is true if proposition x5a is true. Proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition x1a is true if proposition x1b is not true. Proposition t0 is true if proposition t1 is true. Proposition x3b is true if proposition x3a is not true. Proposition x5b is true if proposition x5a is not true. Proposition x4b is true if proposition x4a is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition x3a is true if proposition x3b is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition qcore is true if proposition x5a is true. Proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition x1a is true if proposition x1b is not true. Proposition t0 is true if proposition t1 is true. Proposition x3b is true if proposition x3a is not true. Proposition x5b is true if proposition x5a is not true. Proposition x4b is true if proposition x4a is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition x3a is true if proposition x3b is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition qcore is true if proposition x5a is true. Proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition x1a is true if proposition x1b is not true. Proposition t0 is true if proposition t1 is true. Proposition x3b is true if proposition x3a is not true. Proposition x5b is true if proposition x5a is not true. Proposition x4b is true if proposition x4a is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition x3a is true if proposition x3b is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition qcore is true if proposition x5a is true. Proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition qcore is true if proposition x3a is true. Proposition x1a is true if proposition x1b is not true. Proposition t0 is true if proposition t1 is true. Proposition x3b is true if proposition x3a is not true. Proposition x5b is true if proposition x5a is not true. Proposition x4b is true if proposition x4a is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition x3a is true if proposition x3b is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition qcore is true if proposition x3a is true. Proposition x2a is true if proposition x2b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition x5b is true if proposition x5a is not true. Proposition etrue is true. Proposition x0a is true if proposition x0b is not true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition qcore is true if proposition x3a is true. Proposition x2a is true if proposition x2b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition x5b is true if proposition x5a is not true. Proposition etrue is true. Proposition x0a is true if proposition x0b is not true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition qcore is true if proposition x3a is true. Proposition x2a is true if proposition x2b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition x5b is true if proposition x5a is not true. Proposition etrue is true. Proposition x0a is true if proposition x0b is not true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition qcore is true if proposition x3a is true. Proposition x2a is true if proposition x2b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition x5b is true if proposition x5a is not true. Proposition etrue is true. Proposition x0a is true if proposition x0b is not true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition x3a is true if proposition x3b is not true. Proposition q is true if proposition qcore is true and proposition wide is true and proposition etrue is true. Proposition s0 is true. Proposition qcore is true if proposition x3a is true. Proposition x2a is true if proposition x2b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition qcore is true if proposition x2a is true. Proposition qcore is true if proposition x4a is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x0a is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition x5b is true if proposition x5a is not true. Proposition etrue is true. Proposition x0a is true if proposition x0b is not true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition t3 is true if proposition qcore is true. Proposition x4b is true if proposition x4a is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x5b is true if proposition x5a is not true. Proposition x0a is true if proposition x0b is not true. Proposition x2a is true if proposition x2b is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x5a is true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x4a is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x0b is true if proposition x0a is not true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x0a is true. Proposition x3a is true if proposition x3b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition t3 is true if proposition qcore is true. Proposition x4b is true if proposition x4a is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x5b is true if proposition x5a is not true. Proposition x0a is true if proposition x0b is not true. Proposition x2a is true if proposition x2b is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x5a is true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x4a is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x0b is true if proposition x0a is not true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x0a is true. Proposition x3a is true if proposition x3b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition t3 is true if proposition qcore is true. Proposition x4b is true if proposition x4a is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x5b is true if proposition x5a is not true. Proposition x0a is true if proposition x0b is not true. Proposition x2a is true if proposition x2b is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x5a is true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x4a is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x0b is true if proposition x0a is not true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x0a is true. Proposition x3a is true if proposition x3b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition t3 is true if proposition qcore is true. Proposition x4b is true if proposition x4a is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x5b is true if proposition x5a is not true. Proposition x0a is true if proposition x0b is not true. Proposition x2a is true if proposition x2b is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x5a is true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x4a is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x0b is true if proposition x0a is not true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x0a is true. Proposition x3a is true if proposition x3b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition t3 is true if proposition qcore is true. Proposition x4b is true if proposition x4a is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x5b is true if proposition x5a is not true. Proposition x0a is true if proposition x0b is not true. Proposition x2a is true if proposition x2b is not true. Proposition x4a is true if proposition x4b is not true. Proposition qcore is true if proposition x1a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x1b is true if proposition x1a is not true. Proposition qcore is true if proposition x5a is true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x4a is true. Proposition s0 is true. Proposition t2 is true if proposition t3 is true. Proposition x2b is true if proposition x2a is not true. Proposition x1a is true if proposition x1b is not true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x0b is true if proposition x0a is not true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x0a is true. Proposition x3a is true if proposition x3b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition t1 is true if proposition t2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition x1a is true if proposition x1b is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x0a is true. Proposition x5b is true if proposition x5a is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t5 is true if proposition qcore is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition t2 is true if proposition t3 is true. Proposition qcore is true if proposition x4a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x3a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition t1 is true if proposition t2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition x1a is true if proposition x1b is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x0a is true. Proposition x5b is true if proposition x5a is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t5 is true if proposition qcore is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition t2 is true if proposition t3 is true. Proposition qcore is true if proposition x4a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x3a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition t1 is true if proposition t2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition x1a is true if proposition x1b is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x0a is true. Proposition x5b is true if proposition x5a is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t5 is true if proposition qcore is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition t2 is true if proposition t3 is true. Proposition qcore is true if proposition x4a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x3a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition t1 is true if proposition t2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition x1a is true if proposition x1b is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x0a is true. Proposition x5b is true if proposition x5a is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t5 is true if proposition qcore is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition t2 is true if proposition t3 is true. Proposition qcore is true if proposition x4a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x3a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition t1 is true if proposition t2 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition x1a is true if proposition x1b is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x0a is true. Proposition x5b is true if proposition x5a is not true. Proposition s0 is true. Proposition t0 is true if proposition t1 is true. Proposition s2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t5 is true if proposition qcore is true. Proposition qcore is true if proposition x5a is true. Proposition x3b is true if proposition x3a is not true. Proposition t2 is true if proposition t3 is true. Proposition qcore is true if proposition x4a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x0b is true if proposition x0a is not true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true. Proposition x4b is true if proposition x4a is not true. Proposition x5a is true if proposition x5b is not true. Proposition t4 is true if proposition t5 is true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x3a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x2b is true if proposition x2a is not true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition s0 is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x4a is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition t4 is true if proposition t5 is true. Proposition x1b is true if proposition x1a is not true. Proposition x2a is true if proposition x2b is not true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition x4a is true if proposition x4b is not true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x1a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x0a is true. Proposition qcore is true if proposition x5a is true. Proposition x3a is true if proposition x3b is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition qcore is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition x2b is true if proposition x2a is not true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition s0 is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x4a is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition t4 is true if proposition t5 is true. Proposition x1b is true if proposition x1a is not true. Proposition x2a is true if proposition x2b is not true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition x4a is true if proposition x4b is not true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x1a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x0a is true. Proposition qcore is true if proposition x5a is true. Proposition x3a is true if proposition x3b is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition qcore is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition x2b is true if proposition x2a is not true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition s0 is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x4a is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition t4 is true if proposition t5 is true. Proposition x1b is true if proposition x1a is not true. Proposition x2a is true if proposition x2b is not true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition x4a is true if proposition x4b is not true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x1a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x0a is true. Proposition qcore is true if proposition x5a is true. Proposition x3a is true if proposition x3b is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition qcore is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition x2b is true if proposition x2a is not true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition s0 is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x4a is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition t4 is true if proposition t5 is true. Proposition x1b is true if proposition x1a is not true. Proposition x2a is true if proposition x2b is not true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition x4a is true if proposition x4b is not true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x1a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x0a is true. Proposition qcore is true if proposition x5a is true. Proposition x3a is true if proposition x3b is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition qcore is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition x2b is true if proposition x2a is not true. Proposition t3 is true if proposition t4 is true. Proposition qcore is true if proposition x2a is true. Proposition x5a is true if proposition x5b is not true. Proposition s0 is true. Proposition x5b is true if proposition x5a is not true. Proposition qcore is true if proposition x4a is true. Proposition x0a is true if proposition x0b is not true. Proposition wide is true if proposition s0 is true and proposition s1 is true. Proposition x0b is true if proposition x0a is not true. Proposition t4 is true if proposition t5 is true. Proposition x1b is true if proposition x1a is not true. Proposition x2a is true if proposition x2b is not true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition x4a is true if proposition x4b is not true. Proposition t2 is true if proposition t3 is true. Proposition t1 is true if proposition t2 is true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x1a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x0a is true. Proposition qcore is true if proposition x5a is true. Proposition x3a is true if proposition x3b is not true. Proposition s1 is true. Proposition x3b is true if proposition x3a is not true. Proposition qcore is true if proposition x3a is true. Proposition t0 is true if proposition t1 is true. Proposition t5 is true if proposition qcore is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition qcore is true if proposition x0a is true. Proposition x3b is true if proposition x3a is not true. Proposition x1b is true if proposition x1a is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x3a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x4a is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition x5b is true if proposition x5a is not true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x1a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x2a is true. Proposition x4a is true if proposition x4b is not true. Proposition x0a is true if proposition x0b is not true. Proposition x0b is true if proposition x0a is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition qcore is true if proposition x0a is true. Proposition x3b is true if proposition x3a is not true. Proposition x1b is true if proposition x1a is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x3a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x4a is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition x5b is true if proposition x5a is not true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x1a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x2a is true. Proposition x4a is true if proposition x4b is not true. Proposition x0a is true if proposition x0b is not true. Proposition x0b is true if proposition x0a is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition qcore is true if proposition x0a is true. Proposition x3b is true if proposition x3a is not true. Proposition x1b is true if proposition x1a is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x3a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x4a is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition x5b is true if proposition x5a is not true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x1a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x2a is true. Proposition x4a is true if proposition x4b is not true. Proposition x0a is true if proposition x0b is not true. Proposition x0b is true if proposition x0a is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition qcore is true if proposition x0a is true. Proposition x3b is true if proposition x3a is not true. Proposition x1b is true if proposition x1a is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x3a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x4a is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition x5b is true if proposition x5a is not true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x1a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x2a is true. Proposition x4a is true if proposition x4b is not true. Proposition x0a is true if proposition x0b is not true. Proposition x0b is true if proposition x0a is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition x2a is true if proposition x2b is not true. Proposition t1 is true if proposition qcore is true. Proposition etrue is true. Proposition x4b is true if proposition x4a is not true. Proposition qcore is true if proposition x0a is true. Proposition x3b is true if proposition x3a is not true. Proposition x1b is true if proposition x1a is not true. Proposition x3a is true if proposition x3b is not true. Proposition qcore is true if proposition x3a is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x4a is true. Proposition q is true if proposition t0 is true and proposition etrue is true. Proposition x5b is true if proposition x5a is not true. Proposition x1a is true if proposition x1b is not true. Proposition qcore is true if proposition x5a is true. Proposition x5a is true if proposition x5b is not true. Proposition qcore is true if proposition x1a is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x2a is true. Proposition x4a is true if proposition x4b is not true. Proposition x0a is true if proposition x0b is not true. Proposition x0b is true if proposition x0a is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x3a is true. Proposition qcore is true if proposition x5a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0b is true if proposition x0a is not true. Proposition x0a is true if proposition x0b is not true. Proposition t1 is true if proposition t2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t2 is true if proposition t3 is true. Proposition x1a is true if proposition x1b is not true. Proposition x4b is true if proposition x4a is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x3a is true if proposition x3b is not true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x5b is true if proposition x5a is not true. Proposition t3 is true if proposition qcore is true. Proposition qcore is true if proposition x4a is true. Proposition s2 is true. Proposition qcore is true if proposition x0a is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x3a is true. Proposition qcore is true if proposition x5a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0b is true if proposition x0a is not true. Proposition x0a is true if proposition x0b is not true. Proposition t1 is true if proposition t2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t2 is true if proposition t3 is true. Proposition x1a is true if proposition x1b is not true. Proposition x4b is true if proposition x4a is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x3a is true if proposition x3b is not true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x5b is true if proposition x5a is not true. Proposition t3 is true if proposition qcore is true. Proposition qcore is true if proposition x4a is true. Proposition s2 is true. Proposition qcore is true if proposition x0a is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x3a is true. Proposition qcore is true if proposition x5a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0b is true if proposition x0a is not true. Proposition x0a is true if proposition x0b is not true. Proposition t1 is true if proposition t2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t2 is true if proposition t3 is true. Proposition x1a is true if proposition x1b is not true. Proposition x4b is true if proposition x4a is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x3a is true if proposition x3b is not true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x5b is true if proposition x5a is not true. Proposition t3 is true if proposition qcore is true. Proposition qcore is true if proposition x4a is true. Proposition s2 is true. Proposition qcore is true if proposition x0a is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x3a is true. Proposition qcore is true if proposition x5a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0b is true if proposition x0a is not true. Proposition x0a is true if proposition x0b is not true. Proposition t1 is true if proposition t2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t2 is true if proposition t3 is true. Proposition x1a is true if proposition x1b is not true. Proposition x4b is true if proposition x4a is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x3a is true if proposition x3b is not true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x5b is true if proposition x5a is not true. Proposition t3 is true if proposition qcore is true. Proposition qcore is true if proposition x4a is true. Proposition s2 is true. Proposition qcore is true if proposition x0a is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition x3b is true if proposition x3a is not true. Proposition etrue is true. Proposition x2b is true if proposition x2a is not true. Proposition qcore is true if proposition x2a is true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition qcore is true if proposition x3a is true. Proposition qcore is true if proposition x5a is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true. Proposition x0b is true if proposition x0a is not true. Proposition x0a is true if proposition x0b is not true. Proposition t1 is true if proposition t2 is true. Proposition x2a is true if proposition x2b is not true. Proposition t2 is true if proposition t3 is true. Proposition x1a is true if proposition x1b is not true. Proposition x4b is true if proposition x4a is not true. Proposition s0 is true. Proposition x5a is true if proposition x5b is not true. Proposition x3a is true if proposition x3b is not true. Proposition x4a is true if proposition x4b is not true. Proposition x1b is true if proposition x1a is not true. Proposition x5b is true if proposition x5a is not true. Proposition t3 is true if proposition qcore is true. Proposition qcore is true if proposition x4a is true. Proposition s2 is true. Proposition qcore is true if proposition x0a is true. Proposition t0 is true if proposition t1 is true. Proposition s1 is true. Proposition qcore is true if proposition x1a is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition t5 is true if proposition qcore is true. Proposition x1a is true if proposition x1b is not true. Proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x0a is true and proposition x1a is true. Proposition s0 is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use the CLOSED-WORLD ASSUMPTION with NEGATION-AS-FAILURE, interpreted operationally as in Prolog-style reasoning. A positive goal is 'true' if it can be derived by a terminating proof from the rules. A positive goal is 'false' if every attempted proof of it finitely fails. The default-negated goal not G is 'true' if the goal G finitely fails, and 'false' if G succeeds. If evaluating the goal does not terminate, gets stuck because of negation (flounders), or otherwise cannot produce a definite success or finite failure, answer 'Cannot be determined.' Answer 'Definitely yes' for true, 'Definitely no' for 'false', and 'Cannot be determined' when no definite operational result is obtained.

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition t5 is true if proposition qcore is true. Proposition x1a is true if proposition x1b is not true. Proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x0a is true and proposition x1a is true. Proposition s0 is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with CREDULOUS, also called BRAVE, reasoning. An answer set is a self-consistent set of atoms that is closed under the program rules and contains exactly the atoms justified by those rules under the assumptions made in that same set. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' if the statement holds in AT LEAST ONE answer set. Answer 'Definitely no' if the statement holds in no answer sets. If the program has no answer sets, answer 'Definitely no.'

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition t5 is true if proposition qcore is true. Proposition x1a is true if proposition x1b is not true. Proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x0a is true and proposition x1a is true. Proposition s0 is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use STABLE-MODEL, also called ANSWER-SET, semantics with SKEPTICAL, also called CAUTIOUS, reasoning. Consider all answer sets of the program. Each answer set is a self-consistent scenario that is closed under the rules and contains exactly the atoms justified by those rules under its own assumptions about default negation. Equivalently, after evaluating each default-negated condition not A relative to a candidate set, the candidate must be exactly the minimal set of atoms derivable from the remaining rules. For the queried statement: Answer 'Definitely yes' only if the statement holds in EVERY answer set. Answer 'Definitely no' if there is at least one answer set in which the statement does not hold. If the program has no answer sets, then the statement vacuously holds in every answer set; answer 'Definitely yes.'

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition t5 is true if proposition qcore is true. Proposition x1a is true if proposition x1b is not true. Proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x0a is true and proposition x1a is true. Proposition s0 is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Use WELL-FOUNDED semantics, with three truth values: 'true', 'false', and 'undefined'. A statement is 'true' if it has founded support: that is, it follows from rules whose positive conditions are 'true' and whose default-negated conditions are 'false', with the justification ultimately grounded rather than relying only on unsupported circular reasoning. A statement is 'false' if all possible rules that could derive it are defeated, inapplicable, or depend only on unfounded circular support. A statement is 'undefined' if it is neither founded true nor founded false, typically because its truth depends on an unresolved cycle through default negation or on other undefined statements. Answer 'Definitely yes' if the statement is 'true'. Answer 'Definitely no' if the statement is 'false'. Answer 'Cannot be determined' if the statement is 'undefined'. For a default-negated query not G, evaluate it using the well-founded truth value of G: not G is 'true' when G is 'false', 'false' when G is 'true', and 'undefined' when G is 'undefined'.

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition t1 is true if proposition t2 is true. Proposition s2 is true. Proposition x0a is true if proposition x0b is not true. Proposition q is true if proposition t0 is true and proposition wide is true and proposition etrue is true. Proposition t3 is true if proposition t4 is true. Proposition wide is true if proposition s0 is true and proposition s1 is true and proposition s2 is true and proposition s3 is true. Proposition t4 is true if proposition t5 is true. Proposition t5 is true if proposition qcore is true. Proposition x1a is true if proposition x1b is not true. Proposition etrue is true. Proposition x1b is true if proposition x1a is not true. Proposition s1 is true. Proposition t2 is true if proposition t3 is true. Proposition t0 is true if proposition t1 is true. Proposition qcore is true if proposition x0a is true and proposition x1a is true. Proposition s0 is true. Proposition s3 is true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.


Prompt:
Answer using ordinary commonsense reasoning about the rules below.

Rules:
Proposition x0b is true if proposition x0a is not true. Proposition x1b is true if proposition x1a is not true. Proposition x1a is true if proposition x1b is not true. Proposition q is true if proposition qcore is true and proposition etrue is true. Proposition qcore is true if proposition x0a is true and proposition x1a is true. Proposition etrue is true. Proposition x0a is true if proposition x0b is not true.

Question: Is proposition q true?

Choose exactly one:
  A. Definitely yes
  B. Definitely no
  C. Cannot be determined

Think step by step, then end with a line 'ANSWER: X' where X is A, B, or C.