TSTP Solution File: GRP752-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP752-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:19:59 EDT 2023
% Result : Unsatisfiable 1.51s 0.57s
% Output : Proof 1.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : GRP752-1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 01:57:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 1.51/0.57 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 1.51/0.57
% 1.51/0.57 % SZS status Unsatisfiable
% 1.51/0.57
% 1.51/0.58 % SZS output start Proof
% 1.51/0.58 Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
% 1.51/0.58 Axiom 2 (f01): mult(X, ld(X, Y)) = Y.
% 1.51/0.58 Axiom 3 (f06): mult(mult(X, X), mult(Y, Z)) = mult(mult(X, Y), mult(X, Z)).
% 1.51/0.58 Axiom 4 (f07): mult(mult(X, Y), mult(Z, Z)) = mult(mult(X, Z), mult(Y, Z)).
% 1.51/0.58 Axiom 5 (f05): mult(mult(X, mult(X, X)), mult(Y, Z)) = mult(mult(X, Y), mult(mult(X, X), Z)).
% 1.51/0.58
% 1.51/0.58 Lemma 6: ld(mult(X, X), mult(mult(X, Y), mult(X, Z))) = mult(Y, Z).
% 1.51/0.58 Proof:
% 1.51/0.58 ld(mult(X, X), mult(mult(X, Y), mult(X, Z)))
% 1.51/0.58 = { by axiom 3 (f06) R->L }
% 1.51/0.58 ld(mult(X, X), mult(mult(X, X), mult(Y, Z)))
% 1.51/0.58 = { by axiom 1 (f02) }
% 1.51/0.58 mult(Y, Z)
% 1.51/0.58
% 1.51/0.58 Lemma 7: ld(mult(X, X), mult(mult(X, Y), Z)) = mult(Y, ld(X, Z)).
% 1.51/0.58 Proof:
% 1.51/0.58 ld(mult(X, X), mult(mult(X, Y), Z))
% 1.51/0.58 = { by axiom 2 (f01) R->L }
% 1.51/0.58 ld(mult(X, X), mult(mult(X, Y), mult(X, ld(X, Z))))
% 1.51/0.58 = { by lemma 6 }
% 1.51/0.58 mult(Y, ld(X, Z))
% 1.51/0.58
% 1.51/0.58 Lemma 8: ld(X, mult(Y, ld(Z, mult(X, X)))) = ld(Z, mult(Y, X)).
% 1.51/0.58 Proof:
% 1.51/0.58 ld(X, mult(Y, ld(Z, mult(X, X))))
% 1.51/0.58 = { by lemma 7 R->L }
% 1.51/0.58 ld(X, ld(mult(Z, Z), mult(mult(Z, Y), mult(X, X))))
% 1.51/0.58 = { by axiom 4 (f07) }
% 1.51/0.58 ld(X, ld(mult(Z, Z), mult(mult(Z, X), mult(Y, X))))
% 1.51/0.58 = { by lemma 7 }
% 1.51/0.58 ld(X, mult(X, ld(Z, mult(Y, X))))
% 1.51/0.58 = { by axiom 1 (f02) }
% 1.51/0.58 ld(Z, mult(Y, X))
% 1.51/0.58
% 1.51/0.58 Lemma 9: ld(mult(X, Y), mult(mult(X, X), Z)) = mult(X, ld(Y, Z)).
% 1.51/0.58 Proof:
% 1.51/0.58 ld(mult(X, Y), mult(mult(X, X), Z))
% 1.51/0.58 = { by axiom 2 (f01) R->L }
% 1.51/0.58 ld(mult(X, Y), mult(mult(X, X), mult(Y, ld(Y, Z))))
% 1.51/0.58 = { by axiom 3 (f06) }
% 1.51/0.58 ld(mult(X, Y), mult(mult(X, Y), mult(X, ld(Y, Z))))
% 1.51/0.58 = { by axiom 1 (f02) }
% 1.51/0.58 mult(X, ld(Y, Z))
% 1.51/0.58
% 1.51/0.58 Goal 1 (goals): mult(mult(a, b), c) = mult(mult(a, c), mult(b, ld(c, c))).
% 1.51/0.58 Proof:
% 1.51/0.58 mult(mult(a, b), c)
% 1.51/0.58 = { by axiom 2 (f01) R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(a, c), mult(mult(a, b), c)))
% 1.51/0.58 = { by axiom 2 (f01) R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(a, c), mult(mult(a, b), mult(a, ld(a, c)))))
% 1.51/0.58 = { by axiom 3 (f06) R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(a, c), mult(mult(a, a), mult(b, ld(a, c)))))
% 1.51/0.58 = { by lemma 9 }
% 1.51/0.58 mult(mult(a, c), mult(a, ld(c, mult(b, ld(a, c)))))
% 1.51/0.58 = { by lemma 7 R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), mult(b, ld(a, c)))))
% 1.51/0.58 = { by axiom 1 (f02) R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), mult(ld(c, mult(c, b)), ld(a, c)))))
% 1.51/0.58 = { by lemma 6 R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, c), mult(mult(c, ld(c, mult(c, b))), mult(c, ld(a, c)))))))
% 1.51/0.58 = { by axiom 2 (f01) }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, c), mult(mult(c, b), mult(c, ld(a, c)))))))
% 1.51/0.58 = { by lemma 9 R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, c), mult(mult(c, b), ld(mult(c, a), mult(mult(c, c), c)))))))
% 1.51/0.58 = { by lemma 8 R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, c), mult(mult(c, b), ld(c, mult(mult(c, c), ld(mult(c, a), mult(c, c)))))))))
% 1.51/0.58 = { by lemma 7 R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, c), ld(mult(c, c), mult(mult(c, mult(c, b)), mult(mult(c, c), ld(mult(c, a), mult(c, c)))))))))
% 1.51/0.58 = { by axiom 5 (f05) R->L }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, c), ld(mult(c, c), mult(mult(c, mult(c, c)), mult(mult(c, b), ld(mult(c, a), mult(c, c)))))))))
% 1.51/0.58 = { by lemma 7 }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, c), mult(mult(c, c), ld(c, mult(mult(c, b), ld(mult(c, a), mult(c, c)))))))))
% 1.51/0.58 = { by axiom 1 (f02) }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(c, mult(mult(c, b), ld(mult(c, a), mult(c, c)))))))
% 1.51/0.58 = { by lemma 8 }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, a), ld(mult(c, a), mult(mult(c, b), c)))))
% 1.51/0.58 = { by axiom 2 (f01) }
% 1.51/0.58 mult(mult(a, c), ld(mult(c, c), mult(mult(c, b), c)))
% 1.51/0.58 = { by lemma 7 }
% 1.51/0.58 mult(mult(a, c), mult(b, ld(c, c)))
% 1.51/0.58 % SZS output end Proof
% 1.51/0.58
% 1.51/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
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