TSTP Solution File: GRP568-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP568-1 : 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 : n022.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 01:18:56 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP568-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 23:00:54 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --no-flatten-goal
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.21/0.42 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.21/0.42 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.21/0.42 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), double_divide(identity, identity)) = Y.
% 0.21/0.42
% 0.21/0.42 Lemma 5: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), inverse(identity)) = Y.
% 0.21/0.42 Proof:
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), inverse(identity))
% 0.21/0.42 = { by axiom 1 (inverse) }
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), double_divide(identity, identity))
% 0.21/0.42 = { by axiom 4 (single_axiom) }
% 0.21/0.42 Y
% 0.21/0.42
% 0.21/0.42 Lemma 6: double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity)) = Y.
% 0.21/0.42 Proof:
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), inverse(identity))), inverse(identity))
% 0.21/0.42 = { by axiom 1 (inverse) }
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, inverse(X)), double_divide(identity, identity))), inverse(identity))
% 0.21/0.42 = { by axiom 1 (inverse) }
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, identity)), double_divide(identity, identity))), inverse(identity))
% 0.21/0.42 = { by lemma 5 }
% 0.21/0.42 Y
% 0.21/0.42
% 0.21/0.42 Lemma 7: double_divide(inverse(X), inverse(identity)) = X.
% 0.21/0.42 Proof:
% 0.21/0.42 double_divide(inverse(X), inverse(identity))
% 0.21/0.42 = { by axiom 1 (inverse) }
% 0.21/0.42 double_divide(double_divide(X, identity), inverse(identity))
% 0.21/0.42 = { by axiom 2 (identity) }
% 0.21/0.42 double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
% 0.21/0.42 = { by axiom 2 (identity) }
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(X, inverse(X)), inverse(identity))), inverse(identity))
% 0.21/0.42 = { by lemma 6 }
% 0.21/0.42 X
% 0.21/0.42
% 0.21/0.42 Lemma 8: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.21/0.42 Proof:
% 0.21/0.42 inverse(double_divide(X, Y))
% 0.21/0.42 = { by axiom 1 (inverse) }
% 0.21/0.42 double_divide(double_divide(X, Y), identity)
% 0.21/0.42 = { by axiom 3 (multiply) R->L }
% 0.21/0.42 multiply(Y, X)
% 0.21/0.42
% 0.21/0.42 Lemma 9: multiply(identity, X) = inverse(inverse(X)).
% 0.21/0.42 Proof:
% 0.21/0.42 multiply(identity, X)
% 0.21/0.42 = { by lemma 8 R->L }
% 0.21/0.42 inverse(double_divide(X, identity))
% 0.21/0.42 = { by axiom 1 (inverse) R->L }
% 0.21/0.42 inverse(inverse(X))
% 0.21/0.42
% 0.21/0.42 Lemma 10: double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), Y)), inverse(identity)) = Y.
% 0.21/0.42 Proof:
% 0.21/0.42 double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), Y)), inverse(identity))
% 0.21/0.42 = { by lemma 8 R->L }
% 0.21/0.42 double_divide(double_divide(X, inverse(double_divide(Y, double_divide(X, inverse(identity))))), inverse(identity))
% 0.21/0.42 = { by axiom 1 (inverse) }
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, inverse(identity))), identity)), inverse(identity))
% 0.21/0.42 = { by axiom 2 (identity) }
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, inverse(identity))), double_divide(identity, inverse(identity)))), inverse(identity))
% 0.21/0.42 = { by lemma 5 }
% 0.21/0.42 Y
% 0.21/0.42
% 0.21/0.42 Lemma 11: double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity)) = X.
% 0.21/0.42 Proof:
% 0.21/0.42 double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity))
% 0.21/0.42 = { by lemma 9 R->L }
% 0.21/0.42 double_divide(double_divide(identity, multiply(identity, X)), inverse(identity))
% 0.21/0.42 = { by axiom 2 (identity) }
% 0.21/0.42 double_divide(double_divide(identity, multiply(double_divide(identity, inverse(identity)), X)), inverse(identity))
% 0.21/0.42 = { by lemma 10 }
% 0.21/0.42 X
% 0.21/0.42
% 0.21/0.42 Lemma 12: double_divide(double_divide(inverse(X), X), inverse(identity)) = identity.
% 0.21/0.42 Proof:
% 0.21/0.42 double_divide(double_divide(inverse(X), X), inverse(identity))
% 0.21/0.42 = { by lemma 11 R->L }
% 0.21/0.42 double_divide(double_divide(inverse(X), double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.21/0.42 = { by lemma 6 }
% 0.21/0.42 identity
% 0.21/0.42
% 0.21/0.42 Lemma 13: inverse(identity) = identity.
% 0.21/0.42 Proof:
% 0.21/0.42 inverse(identity)
% 0.21/0.42 = { by lemma 7 R->L }
% 0.21/0.42 double_divide(inverse(inverse(identity)), inverse(identity))
% 0.21/0.42 = { by axiom 1 (inverse) }
% 0.21/0.42 double_divide(double_divide(inverse(identity), identity), inverse(identity))
% 0.21/0.42 = { by lemma 12 }
% 0.21/0.42 identity
% 0.21/0.42
% 0.21/0.42 Lemma 14: inverse(inverse(X)) = X.
% 0.21/0.42 Proof:
% 0.21/0.42 inverse(inverse(X))
% 0.21/0.42 = { by lemma 6 R->L }
% 0.21/0.42 double_divide(double_divide(X, double_divide(double_divide(inverse(inverse(X)), inverse(X)), inverse(identity))), inverse(identity))
% 0.21/0.42 = { by lemma 12 }
% 0.21/0.42 double_divide(double_divide(X, identity), inverse(identity))
% 0.21/0.42 = { by axiom 1 (inverse) R->L }
% 0.21/0.42 double_divide(inverse(X), inverse(identity))
% 0.21/0.42 = { by lemma 7 }
% 0.21/0.42 X
% 0.21/0.42
% 0.21/0.42 Lemma 15: double_divide(identity, X) = inverse(X).
% 0.21/0.42 Proof:
% 0.21/0.42 double_divide(identity, X)
% 0.21/0.42 = { by lemma 14 R->L }
% 0.21/0.42 inverse(inverse(double_divide(identity, X)))
% 0.21/0.42 = { by lemma 9 R->L }
% 0.21/0.42 multiply(identity, double_divide(identity, X))
% 0.21/0.42 = { by lemma 13 R->L }
% 0.21/0.42 multiply(inverse(identity), double_divide(identity, X))
% 0.21/0.42 = { by lemma 14 R->L }
% 0.21/0.42 multiply(inverse(identity), double_divide(identity, inverse(inverse(X))))
% 0.21/0.42 = { by lemma 8 R->L }
% 0.21/0.42 inverse(double_divide(double_divide(identity, inverse(inverse(X))), inverse(identity)))
% 0.21/0.42 = { by lemma 11 }
% 0.21/0.42 inverse(X)
% 0.21/0.42
% 0.21/0.42 Lemma 16: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.21/0.42 Proof:
% 0.21/0.42 multiply(multiply(X, Y), inverse(X))
% 0.21/0.42 = { by lemma 8 R->L }
% 0.21/0.42 multiply(inverse(double_divide(Y, X)), inverse(X))
% 0.21/0.43 = { by axiom 1 (inverse) }
% 0.21/0.43 multiply(double_divide(double_divide(Y, X), identity), inverse(X))
% 0.21/0.43 = { by lemma 8 R->L }
% 0.21/0.43 inverse(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)))
% 0.21/0.43 = { by axiom 1 (inverse) }
% 0.21/0.43 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), identity)), identity)
% 0.21/0.43 = { by lemma 13 R->L }
% 0.21/0.43 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), identity)
% 0.21/0.43 = { by lemma 13 R->L }
% 0.21/0.43 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, X), inverse(identity))), inverse(identity))
% 0.21/0.43 = { by lemma 14 R->L }
% 0.21/0.43 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.21/0.43 = { by lemma 6 }
% 0.21/0.43 Y
% 0.21/0.43
% 0.21/0.43 Lemma 17: double_divide(X, inverse(Y)) = multiply(Y, inverse(X)).
% 0.21/0.43 Proof:
% 0.21/0.43 double_divide(X, inverse(Y))
% 0.21/0.43 = { by lemma 14 R->L }
% 0.21/0.43 inverse(inverse(double_divide(X, inverse(Y))))
% 0.21/0.43 = { by lemma 9 R->L }
% 0.21/0.43 multiply(identity, double_divide(X, inverse(Y)))
% 0.21/0.43 = { by lemma 13 R->L }
% 0.21/0.43 multiply(inverse(identity), double_divide(X, inverse(Y)))
% 0.21/0.43 = { by lemma 16 R->L }
% 0.21/0.43 multiply(inverse(identity), double_divide(X, multiply(multiply(multiply(Y, double_divide(X, inverse(identity))), inverse(Y)), inverse(multiply(Y, double_divide(X, inverse(identity)))))))
% 0.21/0.43 = { by lemma 16 }
% 0.21/0.43 multiply(inverse(identity), double_divide(X, multiply(double_divide(X, inverse(identity)), inverse(multiply(Y, double_divide(X, inverse(identity)))))))
% 0.21/0.43 = { by axiom 1 (inverse) }
% 0.21/0.43 multiply(inverse(identity), double_divide(X, multiply(double_divide(X, inverse(identity)), double_divide(multiply(Y, double_divide(X, inverse(identity))), identity))))
% 0.21/0.43 = { by lemma 13 R->L }
% 0.21/0.43 multiply(inverse(identity), double_divide(X, multiply(double_divide(X, inverse(identity)), double_divide(multiply(Y, double_divide(X, inverse(identity))), inverse(identity)))))
% 0.21/0.43 = { by lemma 8 R->L }
% 0.21/0.43 multiply(inverse(identity), double_divide(X, multiply(double_divide(X, inverse(identity)), double_divide(inverse(double_divide(double_divide(X, inverse(identity)), Y)), inverse(identity)))))
% 0.21/0.43 = { by lemma 7 }
% 0.21/0.43 multiply(inverse(identity), double_divide(X, multiply(double_divide(X, inverse(identity)), double_divide(double_divide(X, inverse(identity)), Y))))
% 0.21/0.43 = { by lemma 8 R->L }
% 0.21/0.43 inverse(double_divide(double_divide(X, multiply(double_divide(X, inverse(identity)), double_divide(double_divide(X, inverse(identity)), Y))), inverse(identity)))
% 0.21/0.43 = { by lemma 10 }
% 0.21/0.43 inverse(double_divide(double_divide(X, inverse(identity)), Y))
% 0.21/0.43 = { by lemma 8 }
% 0.21/0.43 multiply(Y, double_divide(X, inverse(identity)))
% 0.21/0.43 = { by lemma 13 }
% 0.21/0.43 multiply(Y, double_divide(X, identity))
% 0.21/0.43 = { by axiom 1 (inverse) R->L }
% 0.21/0.43 multiply(Y, inverse(X))
% 0.21/0.43
% 0.21/0.43 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.21/0.43 Proof:
% 0.21/0.43 multiply(a, b)
% 0.21/0.43 = { by lemma 8 R->L }
% 0.21/0.43 inverse(double_divide(b, a))
% 0.21/0.43 = { by lemma 14 R->L }
% 0.21/0.43 inverse(inverse(inverse(double_divide(b, a))))
% 0.21/0.43 = { by lemma 9 R->L }
% 0.21/0.43 multiply(identity, inverse(double_divide(b, a)))
% 0.21/0.43 = { by lemma 17 R->L }
% 0.21/0.43 double_divide(double_divide(b, a), inverse(identity))
% 0.21/0.43 = { by lemma 5 R->L }
% 0.21/0.43 double_divide(double_divide(b, double_divide(double_divide(identity, double_divide(double_divide(a, double_divide(identity, double_divide(b, inverse(identity)))), double_divide(identity, double_divide(b, inverse(identity))))), inverse(identity))), inverse(identity))
% 0.21/0.43 = { by lemma 15 }
% 0.21/0.43 double_divide(double_divide(b, double_divide(inverse(double_divide(double_divide(a, double_divide(identity, double_divide(b, inverse(identity)))), double_divide(identity, double_divide(b, inverse(identity))))), inverse(identity))), inverse(identity))
% 0.21/0.43 = { by lemma 7 }
% 0.21/0.43 double_divide(double_divide(b, double_divide(double_divide(a, double_divide(identity, double_divide(b, inverse(identity)))), double_divide(identity, double_divide(b, inverse(identity))))), inverse(identity))
% 0.21/0.43 = { by lemma 15 }
% 0.21/0.43 double_divide(double_divide(b, double_divide(double_divide(a, double_divide(identity, double_divide(b, inverse(identity)))), inverse(double_divide(b, inverse(identity))))), inverse(identity))
% 0.21/0.43 = { by lemma 15 }
% 0.21/0.43 double_divide(double_divide(b, double_divide(double_divide(a, inverse(double_divide(b, inverse(identity)))), inverse(double_divide(b, inverse(identity))))), inverse(identity))
% 0.21/0.43 = { by lemma 17 }
% 0.21/0.43 double_divide(double_divide(b, multiply(double_divide(b, inverse(identity)), inverse(double_divide(a, inverse(double_divide(b, inverse(identity))))))), inverse(identity))
% 0.21/0.43 = { by lemma 8 }
% 0.21/0.43 double_divide(double_divide(b, multiply(double_divide(b, inverse(identity)), multiply(inverse(double_divide(b, inverse(identity))), a))), inverse(identity))
% 0.21/0.43 = { by lemma 10 }
% 0.21/0.43 multiply(inverse(double_divide(b, inverse(identity))), a)
% 0.21/0.43 = { by lemma 8 }
% 0.21/0.43 multiply(multiply(inverse(identity), b), a)
% 0.21/0.43 = { by lemma 13 }
% 0.21/0.43 multiply(multiply(identity, b), a)
% 0.21/0.43 = { by lemma 9 }
% 0.21/0.43 multiply(inverse(inverse(b)), a)
% 0.21/0.43 = { by lemma 14 }
% 0.21/0.43 multiply(b, a)
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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