TSTP Solution File: GRP576-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP576-1 : 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 : n018.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 01:18:58 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP576-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.06/0.13 % 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 : n018.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 : Mon Aug 28 21:38:17 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.39 Command-line arguments: --flatten
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.41 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.41 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(Y, double_divide(Z, X)), double_divide(Z, identity))), double_divide(identity, identity)) = Y.
% 0.19/0.42
% 0.19/0.42 Lemma 5: double_divide(X, double_divide(X, identity)) = identity.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(X, double_divide(X, identity))
% 0.19/0.42 = { by axiom 1 (inverse) R->L }
% 0.19/0.42 double_divide(X, inverse(X))
% 0.19/0.42 = { by axiom 2 (identity) R->L }
% 0.19/0.42 identity
% 0.19/0.42
% 0.19/0.42 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), double_divide(identity, identity)) = Y.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), double_divide(Z, identity))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 4 (single_axiom) }
% 0.19/0.42 Y
% 0.19/0.42
% 0.19/0.42 Lemma 7: double_divide(double_divide(double_divide(X, identity), double_divide(inverse(Y), double_divide(X, identity))), double_divide(identity, identity)) = Y.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(double_divide(double_divide(X, identity), double_divide(inverse(Y), double_divide(X, identity))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 1 (inverse) R->L }
% 0.19/0.42 double_divide(double_divide(double_divide(X, identity), double_divide(inverse(Y), inverse(X))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(double_divide(X, identity), double_divide(double_divide(Y, identity), inverse(X))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 double_divide(double_divide(double_divide(X, identity), double_divide(double_divide(Y, double_divide(X, double_divide(X, identity))), inverse(X))), double_divide(identity, 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(inverse(inverse(inverse(X))), double_divide(identity, identity)) = X.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(inverse(inverse(inverse(X))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(inverse(inverse(X)), identity), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 2 (identity) }
% 0.19/0.42 double_divide(double_divide(inverse(inverse(X)), double_divide(inverse(X), inverse(inverse(X)))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(inverse(inverse(X)), double_divide(double_divide(X, identity), inverse(inverse(X)))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 2 (identity) }
% 0.19/0.42 double_divide(double_divide(inverse(inverse(X)), double_divide(double_divide(X, double_divide(inverse(X), inverse(inverse(X)))), inverse(inverse(X)))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 X
% 0.19/0.42
% 0.19/0.42 Lemma 9: double_divide(identity, identity) = identity.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(identity, identity)
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 double_divide(double_divide(double_divide(identity, identity), double_divide(inverse(double_divide(identity, identity)), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(identity, identity), identity), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 8 R->L }
% 0.19/0.42 double_divide(double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(identity, identity), double_divide(inverse(inverse(inverse(identity))), double_divide(identity, identity))), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 1 (inverse) }
% 0.19/0.42 double_divide(double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(identity, identity), double_divide(inverse(inverse(double_divide(identity, identity))), double_divide(identity, identity))), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 7 }
% 0.19/0.42 double_divide(double_divide(double_divide(identity, identity), inverse(double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 2 (identity) R->L }
% 0.19/0.42 double_divide(identity, double_divide(identity, identity))
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 identity
% 0.19/0.42
% 0.19/0.42 Lemma 10: 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 11: double_divide(X, double_divide(identity, identity)) = inverse(X).
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(X, double_divide(identity, identity))
% 0.19/0.42 = { by lemma 9 }
% 0.19/0.42 double_divide(X, identity)
% 0.19/0.42 = { by axiom 1 (inverse) R->L }
% 0.19/0.42 inverse(X)
% 0.19/0.42
% 0.19/0.42 Lemma 12: multiply(double_divide(identity, identity), X) = inverse(inverse(X)).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(double_divide(identity, identity), X)
% 0.19/0.42 = { by lemma 9 }
% 0.19/0.42 multiply(identity, X)
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 inverse(double_divide(X, identity))
% 0.19/0.42 = { by axiom 1 (inverse) R->L }
% 0.19/0.42 inverse(inverse(X))
% 0.19/0.42
% 0.19/0.42 Lemma 13: double_divide(double_divide(identity, identity), X) = inverse(X).
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(double_divide(identity, identity), X)
% 0.19/0.42 = { by lemma 8 R->L }
% 0.19/0.42 double_divide(inverse(inverse(inverse(double_divide(double_divide(identity, identity), X)))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 double_divide(inverse(inverse(multiply(X, double_divide(identity, identity)))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 11 }
% 0.19/0.42 inverse(inverse(inverse(multiply(X, double_divide(identity, identity)))))
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 inverse(inverse(inverse(inverse(double_divide(double_divide(identity, identity), X)))))
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 inverse(inverse(inverse(double_divide(double_divide(double_divide(identity, identity), X), double_divide(identity, identity)))))
% 0.19/0.42 = { by lemma 8 R->L }
% 0.19/0.42 inverse(inverse(inverse(double_divide(double_divide(double_divide(identity, identity), double_divide(inverse(inverse(inverse(X))), double_divide(identity, identity))), double_divide(identity, identity)))))
% 0.19/0.42 = { by lemma 7 }
% 0.19/0.42 inverse(inverse(inverse(inverse(inverse(X)))))
% 0.19/0.42 = { by lemma 12 R->L }
% 0.19/0.42 multiply(double_divide(identity, identity), inverse(inverse(inverse(X))))
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 inverse(double_divide(inverse(inverse(inverse(X))), double_divide(identity, identity)))
% 0.19/0.42 = { by lemma 8 }
% 0.19/0.42 inverse(X)
% 0.19/0.42
% 0.19/0.42 Lemma 14: multiply(double_divide(identity, identity), X) = X.
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(double_divide(identity, identity), X)
% 0.19/0.42 = { by axiom 1 (inverse) R->L }
% 0.19/0.42 multiply(inverse(identity), X)
% 0.19/0.42 = { by axiom 2 (identity) }
% 0.19/0.42 multiply(inverse(double_divide(X, inverse(X))), X)
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 multiply(double_divide(double_divide(X, inverse(X)), double_divide(identity, identity)), X)
% 0.19/0.42 = { by axiom 1 (inverse) R->L }
% 0.19/0.42 multiply(double_divide(double_divide(X, inverse(X)), inverse(identity)), X)
% 0.19/0.42 = { by lemma 9 R->L }
% 0.19/0.42 multiply(double_divide(double_divide(X, inverse(X)), inverse(double_divide(identity, identity))), X)
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 inverse(double_divide(X, double_divide(double_divide(X, inverse(X)), inverse(double_divide(identity, identity)))))
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 double_divide(double_divide(X, double_divide(double_divide(X, inverse(X)), inverse(double_divide(identity, identity)))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 13 R->L }
% 0.19/0.42 double_divide(double_divide(X, double_divide(double_divide(X, double_divide(double_divide(identity, identity), X)), inverse(double_divide(identity, identity)))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 X
% 0.19/0.42
% 0.19/0.42 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(a, b)
% 0.19/0.42 = { by lemma 14 R->L }
% 0.19/0.42 multiply(multiply(double_divide(identity, identity), a), b)
% 0.19/0.42 = { by lemma 12 }
% 0.19/0.42 multiply(inverse(inverse(a)), b)
% 0.19/0.42 = { by lemma 13 R->L }
% 0.19/0.42 multiply(double_divide(double_divide(identity, identity), inverse(a)), b)
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 inverse(double_divide(b, double_divide(double_divide(identity, identity), inverse(a))))
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 double_divide(double_divide(b, double_divide(double_divide(identity, identity), inverse(a))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 9 }
% 0.19/0.42 double_divide(double_divide(b, double_divide(identity, inverse(a))), double_divide(identity, identity))
% 0.19/0.42 = { by axiom 2 (identity) }
% 0.19/0.42 double_divide(double_divide(b, double_divide(double_divide(double_divide(double_divide(a, b), double_divide(identity, identity)), inverse(double_divide(double_divide(a, b), double_divide(identity, identity)))), inverse(a))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 10 }
% 0.19/0.42 double_divide(double_divide(b, double_divide(double_divide(double_divide(double_divide(a, b), double_divide(identity, identity)), multiply(double_divide(identity, identity), double_divide(a, b))), inverse(a))), double_divide(identity, identity))
% 0.19/0.42 = { by lemma 14 }
% 0.19/0.43 double_divide(double_divide(b, double_divide(double_divide(double_divide(double_divide(a, b), double_divide(identity, identity)), double_divide(a, b)), inverse(a))), double_divide(identity, identity))
% 0.19/0.43 = { by lemma 11 }
% 0.19/0.43 double_divide(double_divide(b, double_divide(double_divide(inverse(double_divide(a, b)), double_divide(a, b)), inverse(a))), double_divide(identity, identity))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 inverse(double_divide(a, b))
% 0.19/0.43 = { by lemma 10 }
% 0.19/0.43 multiply(b, a)
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43
% 0.19/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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