guide/results.txt at main · kevbuh/guide · GitHub

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---------------------------proof_engine outputs------------------------------------------
CK's EXAMPLES:
------1---------
Proof:
(((not b) and (not a)) -> (not a))
≡ (not (not b and not a) or not a)  Implication Law
≡ ((not not b or not not a) or not a) DeMorgan Law 2
≡ ((b or not not a) or not a)     Simplification Law (Double Negation)
≡ ((b or a) or not a)         Simplification Law (Double Negation)
≡ (b or (a or not a))         Associative Law OR
≡ (b or 1)              Negation Law OR
≡ (1)                 Simplification Law
------2---------
Proof:
not((a or (a and b)) -> a)
≡ (not (not (a or a and b) or a))   Implication Law
≡ (not (a or not (a or a and b)))   Commutative Law OR
≡ (not (a or not a))         Absorption Law 1
≡ (not 1)               Negation Law OR
≡ (0)                 Simplification Law
-----3----------
Proof:
(a or (a and b)) -> a
≡ (not (a or a and b) or a)      Implication Law
≡ (not a or a)            Absorption Law 1
≡ (1)                 Negation Law OR
-----4----------
expr = "(((y and x) or x) and y)" # NOT TAUTOLOGY
Proof:
(((y and x) or x) and y)
≡ (y and (x and y or x))              Commutative Law AND
≡ ((x and y or x) and y)              Commutative Law AND
≡ (x and y)                           Absorption Law 1
-----5----------
Proof:
not ((c or 1) -> (a and not ((b or (not b)) and (a and (a or b)))))
≡ (not (not (c or 1) or a and not ((b or not b) and (a and (a or b))))) Implication Law
≡ (not (a and (not (b or not b) or not (a and (a or b))) or not (c or 1))) Commutative Law OR
≡ (not (a and (not (b or not b) or not (a and (a or b))) or not 1)) Simplification Law
≡ (not (a and (not (b or not b) or not a) or not 1)) Absorption Law 2
≡ (not (a and (not (b or not b) or not a) or 0)) Simplification Law
≡ (not (a and (not 1 or not a) or 0)) Negation Law OR
≡ (not (a and (not 1 or not a)))      Simplification Law
≡ (not (a and (0 or not a)))          Simplification Law
≡ (not (not a or 0) or not a)         Commutative Law OR
≡ (not (not a) or not a)              Simplification Law
≡ (1)                                 Negation Law OR
-----6----------
Proof:
not not ((b or not b) and (a and (a or b)))
≡ (not not (1 and (a and (a or b))))  Negation Law OR
≡ (1 and (a and (a or b)))            Simplification Law (Double Negation)
≡ (a and (a or b))                    Simplification Law
≡ a                                   Absorption Law 2
-----7----------
Proof:
(c or (b or not b)) or ((not (c and (c or b)) > (c or 1)) and (a and not a))
≡ ((c or (b or not b)) or not (c and (c or b)) > (c or 1) and 0) Negation Law AND
≡ ((c or (b or not b)) or 0)          Simplification Law
≡ ((c or (b or not b)) or 0)          Simplification Law
≡ ((c or 1) or 0)                     Negation Law OR
≡ (c or 1)                            Simplification Law
≡ (1)                                 Simplification Law
-----8----------
(((d and (d and ( d or a))) or (not c or c)) > (c and not c )) > (b and not b)
≡ (((d and d or (not c or c)) > (c and not c)) > (b and not b)) Absorption Law 2
≡ (((d or (not c or c)) > (c and not c)) > (b and not b)) Idempotent Law AND
≡ ((((c or not c) or d) > (c and not c)) > (b and not b)) Commutative Law OR
≡ (((1 or d) > (c and not c)) > (b and not b)) Negation Law OR
≡ ((1 > (c and not c)) > (b and not b)) Simplification Law
≡ (not (not 1 or c and not c) or b and not b) Implication Law
≡ (not (0 or c and not c) or b and not b) Simplification Law
≡ (b and not b or not (0 or c and not c)) Commutative Law OR
≡ (b and not b or not (c and not c))  Simplification Law
≡ (0 or not 0)                        Negation Law AND
≡ (not 0)                             Simplification Law
≡ (1)                                 Simplification Law
-----9----------
Proof:
(not ((a or a) and (a or b) or (a and b) and b) or ((a or a) and (a or b) or (a and b) and b))
≡ (not ((a or a) and (a or b)) and not ((a and b) and b) or ((a or a) and (a or
    b) or (a and b) and b)) DeMorgan Law 1
≡ (not ((a or a) and (a or b)) and not ((a and b) and b) or ((a or a) and (a or
    b) or a and (b and b))) Associative Law AND
≡ (not ((a or a) and (a or b)) and not ((a and b) and b) or (a and (a or b) or
    a and (b and b))) Idempotent Law OR
≡ (not ((a or a) and (a or b)) and not (a and (b and b)) or (a and (a or b) or
    a and (b and b))) Associative Law AND
≡ (not ((a or a) and (a or b)) and not (a and (b and b)) or (a or a and (b and
    b))) Absorption Law 2
≡ (not ((a or a) and (a or b)) and not (a and (b and b)) or a) Absorption Law 1
≡ (not (a and (a or b)) and not (a and (b and b)) or a) Idempotent Law OR
≡ (not a and not (a and (b and b)) or a) Absorption Law 2
≡ (not a and (not a or not (b and b)) or a) DeMorgan Law 2
≡ ((not a) or a)                      Absorption Law 2
≡ (1)                                 Negation Law OR
≡ TAUTOLOGY
-----10----------
(P and (P > Q)) > Q
≡ (not (P and (not P or Q)) or Q)     Implication Law
≡ (not ((not P or Q) and P) or Q)     Commutative Law AND
≡ (Q or not ((not P or Q) and P))     Commutative Law OR
≡ (not ((not P or Q) and P) or Q)     Commutative Law OR
≡ (not (P and (not P or Q)) or Q)     Commutative Law AND
≡ ((not P or not (not P or Q)) or Q)  DeMorgan Law 2
≡ (not P or (not (not P or Q) or Q))  Associative Law OR
≡ (not P or (not not P and not Q or Q)) DeMorgan Law 1
≡ (not P or (P and not Q or Q))       Simplification Law (Double Negation)
≡ (not P or (not Q and P or Q))       Commutative Law AND
≡ ((not Q and P or Q) or not P)       Commutative Law OR
≡ (not Q and P or (Q or not P))       Associative Law OR
≡ (P and not Q or (Q or not P))       Commutative Law AND
≡ (not Q and P or (Q or not P))       Commutative Law AND
≡ ((Q or not P) or not Q and P)       Commutative Law OR
≡ (((Q or not P) or not Q) and ((Q or not P) or P)) Distributive Law OR
≡ ((Q or (not P or not Q)) and (Q or (not P or P))) Associative Law OR
≡ ((Q or (not P or not Q)) and (Q or 1)) Negation Law OR
≡ ((Q or (not P or not Q)) and 1)     Simplification Law
≡ (((not P or not Q) or Q) and 1)     Commutative Law OR
≡ ((not P or not Q) or Q)             Simplification Law
≡ (not P or (not Q or Q))             Associative Law OR
≡ (not P or 1)                        Negation Law OR
≡ (1)                                 Simplification Law
≡ TAUTOLOGY
-----11----------
((P > Q) and not Q) > (not P)
≡ ((not Q and P > Q) > (not P))       Commutative Law AND
≡ (not (not Q and (not P or Q)) or not P) Implication Law
≡ ((not not Q or not (not P or Q)) or not P) DeMorgan Law 2
≡ ((Q or not (not P or Q)) or not P)  Simplification Law (Double Negation)
≡ ((Q or not not P and not Q) or not P) DeMorgan Law 1
≡ ((Q or P and not Q) or not P)       Simplification Law (Double Negation)
≡ (not P or (Q or P and not Q))       Commutative Law OR
≡ (P > (Q or P and not Q))            Implication Law RHS
≡ (P > (P and not Q or Q))            Commutative Law OR
≡ (not P or (P and not Q or Q))       Implication Law
≡ (not P or (not Q and P or Q))       Commutative Law AND
≡ (not P or (P and not Q or Q))       Commutative Law AND
≡ (P > (P and not Q or Q))            Implication Law RHS
≡ (P > (Q or P and not Q))            Commutative Law OR
≡ (P > (P and not Q or Q))            Commutative Law OR
≡ (not P or (P and not Q or Q))       Implication Law
≡ ((P and not Q or Q) or not P)       Commutative Law OR
≡ (not P or (Q or P and not Q))       Commutative Law OR
≡ (not P or (Q or P) and (Q or not Q)) Distributive Law OR
≡ ((not P or (Q or P)) and (not P or (Q or not Q))) Distributive Law OR
≡ (((Q or P) or not P) and (not P or (Q or not Q))) Commutative Law OR
≡ (((Q or P) or not P) and (not P or 1)) Negation Law OR
≡ (((Q or P) or not P) and 1)         Simplification Law
≡ ((Q or P) or not P)                 Identity Law
≡ (Q or (P or not P))                 Associative Law OR
≡ (Q or 1)                            Negation Law OR
≡ (1)                                 Simplification Law
≡ TAUTOLOGY
-----12----------
((P or Q) and not P ) > Q
≡ (not ((P or Q) and not P) or Q)     Implication Law
≡ ((not (P or Q) or not not P) or Q)  DeMorgan Law 2
≡ ((not (P or Q) or P) or Q)          Simplification Law (Double Negation)
≡ ((not P and not Q or P) or Q)       DeMorgan Law 1
≡ ((not (P or Q) or P) or Q)          DeMorgan Law RHS 1
≡ ((not P and not Q or P) or Q)       DeMorgan Law 1
≡ (not P and not Q or (P or Q))       Associative Law OR
≡ (not (P or Q) or (P or Q))          DeMorgan Law RHS 1
≡ (1)                                 Negation Law OR
≡ TAUTOLOGY
-----13----------
(P > C) > (not P)
≡ (not (not P or C) or not P)         Implication Law
≡ (not P or not (not P or C))         Commutative Law OR
≡ (not (P and (not P or C)))          DeMorgan Law RHS 2
≡ (not ((not P or C) and P))          Commutative Law AND
≡ (not (P and (not P or C)))          Commutative Law AND
≡ (not (P and not P or P and C))      Distributive Law AND
≡ (not (0 or P and C))                Negation Law AND
≡ (not (P and C))                     Simplification Law
≡ NOT TAUTOLOGY
-----14----------
(P > Q) > ((P or R) > (Q or R))
≡ ((P > Q) > ((R or P) > (Q or R)))   Commutative Law OR
≡ (not (not P or Q) or (not (R or P) or (Q or R))) Implication Law
≡ (((Q or R) or not (R or P)) or not (not P or Q)) Commutative Law OR
≡ (not (not P or Q) or ((Q or R) or not (R or P))) Commutative Law OR
≡ (not (not P or Q) or (Q or (R or not (R or P)))) Associative Law OR
≡ (not not P and not Q or (Q or (R or not (R or P)))) DeMorgan Law 1
≡ (P and not Q or (Q or (R or not (R or P)))) Simplification Law (Double Negation)
≡ (P and not Q or (Q or (R or not R and not P))) DeMorgan Law 1
≡ (((R or not R and not P) or Q) or P and not Q) Commutative Law OR
≡ (P and not Q or (Q or (R or not R and not P))) Commutative Law OR
≡ (P and not Q or (Q or (R or not R) and (R or not P))) Distributive Law OR
≡ (P and not Q or (Q or (R or not R)) and (Q or (R or not P))) Distributive Law OR
≡ (P and not Q or (Q or (R or not R) and (R or not P))) Distributive Law RHS OR
≡ (P and not Q or (Q or (R or not R)) and (Q or (R or not P))) Distributive Law OR
≡ (P and not Q or (Q or 1) and (Q or (R or not P))) Negation Law OR
≡ (P and not Q or 1 and (Q or (R or not P))) Simplification Law
≡ (1 and (Q or (R or not P)) or P and not Q) Commutative Law OR
≡ ((Q or (R or not P)) or P and not Q) Simplification Law
≡ (((Q or (R or not P)) or P) and ((Q or (R or not P)) or not Q)) Distributive Law OR
≡ ((Q or ((R or not P) or P)) and ((Q or (R or not P)) or not Q)) Associative Law OR
≡ (Q or ((R or not P) or P) and not Q) Distributive Law RHS OR
≡ ((Q or ((R or not P) or P)) and (Q or not Q)) Distributive Law OR
≡ ((Q or (R or (not P or P))) and (Q or not Q)) Associative Law OR
≡ ((Q or not Q) and (Q or (R or (not P or P)))) Commutative Law AND
≡ (1 and (Q or (R or (not P or P))))  Negation Law OR
≡ (Q or (R or (not P or P)))          Simplification Law
≡ (Q or (R or 1))                     Negation Law OR
≡ (Q or 1)                            Simplification Law
≡ (1 or Q)                            Commutative Law OR
≡ (1)                                 Simplification Law
≡ TAUTOLOGY


------------------------pure llm results---------------------------------------------
Pure llm (no symbolic) results:
python3 guide/proof_engine.py --early_stop  --verbose --expr="(a or (a and b)) -> a"
Proof:
(a or (a and b)) -> a                 Absorption
≡ (a or (a and b)) -> a               Simplification
≡ a -> a                              Identity
≡ a