TSTP Solution File: GRP584-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP584-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n011.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 01:19:00 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP584-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:14:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.42 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.42 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.42 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), double_divide(identity, identity)) = Z.
% 0.19/0.42
% 0.19/0.42 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(double_divide(X, Y))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(X, Y), identity)
% 0.19/0.42 = { by axiom 3 (multiply) R->L }
% 0.19/0.42 multiply(Y, X)
% 0.19/0.42
% 0.19/0.42 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), inverse(identity)) = Z.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), inverse(identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(X, double_divide(double_divide(identity, Y), double_divide(Z, double_divide(Y, X)))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 4 (single_axiom) }
% 0.19/0.42 Z
% 0.19/0.42
% 0.19/0.42 Lemma 7: double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(Y, inverse(X)))), inverse(identity)) = Y.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(Y, inverse(X)))), inverse(identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, identity)))), inverse(identity))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 Y
% 0.19/0.42
% 0.19/0.42 Lemma 8: double_divide(double_divide(identity, multiply(X, identity)), inverse(identity)) = X.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(double_divide(identity, multiply(X, identity)), inverse(identity))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 double_divide(double_divide(identity, inverse(double_divide(identity, X))), inverse(identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(identity, double_divide(double_divide(identity, X), identity)), inverse(identity))
% 0.19/0.42 = { by axiom 2 (identity) }
% 0.19/0.42 double_divide(double_divide(identity, double_divide(double_divide(identity, X), double_divide(X, inverse(X)))), inverse(identity))
% 0.19/0.42 = { by lemma 7 }
% 0.19/0.42 X
% 0.19/0.42
% 0.19/0.42 Lemma 9: inverse(identity) = identity.
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(identity)
% 0.19/0.42 = { by lemma 8 R->L }
% 0.19/0.42 double_divide(double_divide(identity, multiply(inverse(identity), identity)), inverse(identity))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 double_divide(double_divide(identity, inverse(double_divide(identity, inverse(identity)))), inverse(identity))
% 0.19/0.42 = { by axiom 2 (identity) R->L }
% 0.19/0.42 double_divide(double_divide(identity, inverse(identity)), inverse(identity))
% 0.19/0.42 = { by axiom 2 (identity) R->L }
% 0.19/0.42 double_divide(identity, inverse(identity))
% 0.19/0.42 = { by axiom 2 (identity) R->L }
% 0.19/0.42 identity
% 0.19/0.42
% 0.19/0.42 Lemma 10: inverse(inverse(X)) = multiply(identity, X).
% 0.19/0.42 Proof:
% 0.19/0.42 inverse(inverse(X))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 inverse(double_divide(X, identity))
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.43 multiply(identity, X)
% 0.19/0.43
% 0.19/0.43 Lemma 11: double_divide(double_divide(X, double_divide(inverse(identity), double_divide(Y, double_divide(identity, X)))), inverse(identity)) = Y.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(double_divide(X, double_divide(inverse(identity), double_divide(Y, double_divide(identity, X)))), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(X, double_divide(double_divide(identity, identity), double_divide(Y, double_divide(identity, X)))), inverse(identity))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 Y
% 0.19/0.43
% 0.19/0.43 Lemma 12: double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), inverse(Y))), inverse(identity)) = Y.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), inverse(Y))), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), double_divide(Y, identity))), inverse(identity))
% 0.19/0.43 = { by axiom 2 (identity) }
% 0.19/0.43 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, inverse(X))))), inverse(identity))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 Y
% 0.19/0.43
% 0.19/0.43 Lemma 13: double_divide(multiply(inverse(X), identity), X) = identity.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(multiply(inverse(X), identity), X)
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(multiply(double_divide(X, identity), identity), X)
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(multiply(double_divide(X, inverse(identity)), identity), X)
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(multiply(double_divide(X, inverse(identity)), inverse(identity)), X)
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(multiply(double_divide(X, inverse(identity)), inverse(identity)), X), inverse(identity)))), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(multiply(double_divide(X, double_divide(identity, identity)), inverse(identity)), X), inverse(identity)))), inverse(identity))
% 0.19/0.43 = { by lemma 5 R->L }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(inverse(double_divide(inverse(identity), double_divide(X, double_divide(identity, identity)))), X), inverse(identity)))), inverse(identity))
% 0.19/0.43 = { by lemma 11 R->L }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), double_divide(double_divide(inverse(double_divide(inverse(identity), double_divide(X, double_divide(identity, identity)))), double_divide(double_divide(identity, double_divide(inverse(identity), double_divide(X, double_divide(identity, identity)))), inverse(identity))), inverse(identity)))), inverse(identity))
% 0.19/0.43 = { by lemma 12 }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(double_divide(identity, identity), identity)), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) R->L }
% 0.19/0.43 double_divide(double_divide(identity, inverse(double_divide(identity, identity))), inverse(identity))
% 0.19/0.43 = { by lemma 5 }
% 0.19/0.43 double_divide(double_divide(identity, multiply(identity, identity)), inverse(identity))
% 0.19/0.43 = { by lemma 8 }
% 0.19/0.43 identity
% 0.19/0.43
% 0.19/0.43 Lemma 14: multiply(identity, X) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(identity, X)
% 0.19/0.43 = { by lemma 10 R->L }
% 0.19/0.43 inverse(inverse(X))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(inverse(X), identity)
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(inverse(X), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(X, identity), inverse(identity))
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(double_divide(X, inverse(identity)), inverse(identity))
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(double_divide(X, inverse(inverse(identity))), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(X, double_divide(inverse(identity), identity)), inverse(identity))
% 0.19/0.43 = { by lemma 13 R->L }
% 0.19/0.43 double_divide(double_divide(X, double_divide(inverse(identity), double_divide(multiply(inverse(double_divide(identity, X)), identity), double_divide(identity, X)))), inverse(identity))
% 0.19/0.43 = { by lemma 11 }
% 0.19/0.43 multiply(inverse(double_divide(identity, X)), identity)
% 0.19/0.43 = { by lemma 5 }
% 0.19/0.43 multiply(multiply(X, identity), identity)
% 0.19/0.43 = { by lemma 5 R->L }
% 0.19/0.43 inverse(double_divide(identity, multiply(X, identity)))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(identity, multiply(X, identity)), identity)
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(double_divide(identity, multiply(X, identity)), inverse(identity))
% 0.19/0.43 = { by lemma 8 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(a, b)
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 multiply(multiply(identity, a), b)
% 0.19/0.43 = { by lemma 10 R->L }
% 0.19/0.43 multiply(inverse(inverse(a)), b)
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 multiply(double_divide(inverse(a), identity), b)
% 0.19/0.43 = { by lemma 13 R->L }
% 0.19/0.43 multiply(double_divide(inverse(a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 multiply(identity, multiply(double_divide(inverse(a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b))
% 0.19/0.43 = { by lemma 10 R->L }
% 0.19/0.43 inverse(inverse(multiply(double_divide(inverse(a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by lemma 14 R->L }
% 0.19/0.44 inverse(inverse(multiply(double_divide(multiply(identity, inverse(a)), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 inverse(inverse(multiply(double_divide(inverse(inverse(inverse(a))), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by lemma 10 }
% 0.19/0.44 inverse(inverse(multiply(double_divide(inverse(multiply(identity, a)), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by axiom 1 (inverse) }
% 0.19/0.44 inverse(inverse(multiply(double_divide(double_divide(multiply(identity, a), identity), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 inverse(inverse(multiply(double_divide(double_divide(multiply(identity, a), inverse(identity)), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 inverse(inverse(multiply(double_divide(double_divide(inverse(inverse(a)), inverse(identity)), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by axiom 1 (inverse) }
% 0.19/0.44 inverse(inverse(multiply(double_divide(double_divide(double_divide(inverse(a), identity), inverse(identity)), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by axiom 2 (identity) }
% 0.19/0.44 inverse(inverse(multiply(double_divide(double_divide(double_divide(inverse(a), double_divide(double_divide(identity, a), inverse(double_divide(identity, a)))), inverse(identity)), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by lemma 12 }
% 0.19/0.44 inverse(inverse(multiply(double_divide(double_divide(identity, a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))), b)))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 inverse(inverse(inverse(double_divide(b, double_divide(double_divide(identity, a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b)))))))
% 0.19/0.44 = { by lemma 10 }
% 0.19/0.44 inverse(multiply(identity, double_divide(b, double_divide(double_divide(identity, a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))))))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 inverse(multiply(inverse(identity), double_divide(b, double_divide(double_divide(identity, a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b))))))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 inverse(inverse(double_divide(double_divide(b, double_divide(double_divide(identity, a), double_divide(multiply(inverse(double_divide(a, b)), identity), double_divide(a, b)))), inverse(identity))))
% 0.19/0.44 = { by lemma 6 }
% 0.19/0.44 inverse(inverse(multiply(inverse(double_divide(a, b)), identity)))
% 0.19/0.44 = { by lemma 10 }
% 0.19/0.44 multiply(identity, multiply(inverse(double_divide(a, b)), identity))
% 0.19/0.44 = { by lemma 14 }
% 0.19/0.44 multiply(inverse(double_divide(a, b)), identity)
% 0.19/0.44 = { by lemma 14 R->L }
% 0.19/0.44 multiply(multiply(identity, inverse(double_divide(a, b))), identity)
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 multiply(inverse(inverse(inverse(double_divide(a, b)))), identity)
% 0.19/0.44 = { by lemma 7 R->L }
% 0.19/0.44 double_divide(double_divide(identity, double_divide(double_divide(identity, inverse(double_divide(a, b))), double_divide(multiply(inverse(inverse(inverse(double_divide(a, b)))), identity), inverse(inverse(double_divide(a, b)))))), inverse(identity))
% 0.19/0.44 = { by lemma 13 }
% 0.19/0.44 double_divide(double_divide(identity, double_divide(double_divide(identity, inverse(double_divide(a, b))), identity)), inverse(identity))
% 0.19/0.44 = { by axiom 1 (inverse) R->L }
% 0.19/0.44 double_divide(double_divide(identity, inverse(double_divide(identity, inverse(double_divide(a, b))))), inverse(identity))
% 0.19/0.44 = { by lemma 5 }
% 0.19/0.44 double_divide(double_divide(identity, multiply(inverse(double_divide(a, b)), identity)), inverse(identity))
% 0.19/0.44 = { by lemma 8 }
% 0.19/0.44 inverse(double_divide(a, b))
% 0.19/0.44 = { by lemma 5 }
% 0.19/0.44 multiply(b, a)
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44
% 0.19/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------