TSTP Solution File: GRP497-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP497-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n026.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 01:18:40 EDT 2023
% Result : Unsatisfiable 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP497-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n026.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 29 01:41:50 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.37 Command-line arguments: --flatten
% 0.17/0.37
% 0.17/0.37 % SZS status Unsatisfiable
% 0.17/0.37
% 0.17/0.38 % SZS output start Proof
% 0.17/0.38 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.17/0.38 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.17/0.38 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.17/0.38 Axiom 4 (single_axiom): double_divide(double_divide(identity, double_divide(X, double_divide(Y, identity))), double_divide(double_divide(Y, double_divide(Z, X)), identity)) = Z.
% 0.17/0.38
% 0.17/0.38 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.17/0.38 Proof:
% 0.17/0.38 inverse(double_divide(X, Y))
% 0.17/0.38 = { by axiom 1 (inverse) }
% 0.17/0.38 double_divide(double_divide(X, Y), identity)
% 0.17/0.38 = { by axiom 3 (multiply) R->L }
% 0.17/0.38 multiply(Y, X)
% 0.17/0.38
% 0.17/0.38 Lemma 6: double_divide(double_divide(identity, double_divide(X, inverse(Y))), multiply(double_divide(Z, X), Y)) = Z.
% 0.17/0.38 Proof:
% 0.17/0.38 double_divide(double_divide(identity, double_divide(X, inverse(Y))), multiply(double_divide(Z, X), Y))
% 0.17/0.39 = { by lemma 5 R->L }
% 0.17/0.39 double_divide(double_divide(identity, double_divide(X, inverse(Y))), inverse(double_divide(Y, double_divide(Z, X))))
% 0.17/0.39 = { by axiom 1 (inverse) }
% 0.17/0.39 double_divide(double_divide(identity, double_divide(X, inverse(Y))), double_divide(double_divide(Y, double_divide(Z, X)), identity))
% 0.17/0.39 = { by axiom 1 (inverse) }
% 0.17/0.39 double_divide(double_divide(identity, double_divide(X, double_divide(Y, identity))), double_divide(double_divide(Y, double_divide(Z, X)), identity))
% 0.17/0.39 = { by axiom 4 (single_axiom) }
% 0.17/0.39 Z
% 0.17/0.39
% 0.17/0.39 Lemma 7: inverse(identity) = identity.
% 0.17/0.39 Proof:
% 0.17/0.39 inverse(identity)
% 0.17/0.39 = { by lemma 6 R->L }
% 0.17/0.39 double_divide(double_divide(identity, double_divide(inverse(identity), inverse(identity))), multiply(double_divide(inverse(identity), inverse(identity)), identity))
% 0.17/0.39 = { by lemma 5 R->L }
% 0.17/0.39 double_divide(double_divide(identity, double_divide(inverse(identity), inverse(identity))), inverse(double_divide(identity, double_divide(inverse(identity), inverse(identity)))))
% 0.17/0.39 = { by axiom 2 (identity) R->L }
% 0.17/0.39 identity
% 0.17/0.39
% 0.17/0.39 Lemma 8: multiply(identity, X) = inverse(inverse(X)).
% 0.17/0.39 Proof:
% 0.17/0.39 multiply(identity, X)
% 0.17/0.39 = { by lemma 5 R->L }
% 0.17/0.39 inverse(double_divide(X, identity))
% 0.17/0.39 = { by axiom 1 (inverse) R->L }
% 0.17/0.39 inverse(inverse(X))
% 0.17/0.39
% 0.17/0.39 Lemma 9: double_divide(identity, multiply(double_divide(X, Y), Y)) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 double_divide(identity, multiply(double_divide(X, Y), Y))
% 0.17/0.39 = { by lemma 7 R->L }
% 0.17/0.39 double_divide(inverse(identity), multiply(double_divide(X, Y), Y))
% 0.17/0.39 = { by axiom 1 (inverse) }
% 0.17/0.39 double_divide(double_divide(identity, identity), multiply(double_divide(X, Y), Y))
% 0.17/0.39 = { by axiom 2 (identity) }
% 0.17/0.39 double_divide(double_divide(identity, double_divide(Y, inverse(Y))), multiply(double_divide(X, Y), Y))
% 0.17/0.39 = { by lemma 6 }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Lemma 10: double_divide(identity, inverse(inverse(inverse(X)))) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 double_divide(identity, inverse(inverse(inverse(X))))
% 0.17/0.39 = { by lemma 8 R->L }
% 0.17/0.39 double_divide(identity, multiply(identity, inverse(X)))
% 0.17/0.39 = { by axiom 2 (identity) }
% 0.17/0.39 double_divide(identity, multiply(double_divide(X, inverse(X)), inverse(X)))
% 0.17/0.39 = { by lemma 9 }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Lemma 11: double_divide(identity, multiply(inverse(X), identity)) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 double_divide(identity, multiply(inverse(X), identity))
% 0.17/0.39 = { by axiom 1 (inverse) }
% 0.17/0.39 double_divide(identity, multiply(double_divide(X, identity), identity))
% 0.17/0.39 = { by lemma 9 }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Lemma 12: double_divide(identity, inverse(X)) = inverse(inverse(X)).
% 0.17/0.39 Proof:
% 0.17/0.39 double_divide(identity, inverse(X))
% 0.17/0.39 = { by lemma 10 R->L }
% 0.17/0.39 double_divide(identity, inverse(double_divide(identity, inverse(inverse(inverse(X))))))
% 0.17/0.39 = { by lemma 5 }
% 0.17/0.39 double_divide(identity, multiply(inverse(inverse(inverse(X))), identity))
% 0.17/0.39 = { by lemma 11 }
% 0.17/0.39 inverse(inverse(X))
% 0.17/0.39
% 0.17/0.39 Lemma 13: inverse(inverse(inverse(inverse(X)))) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 inverse(inverse(inverse(inverse(X))))
% 0.17/0.39 = { by lemma 12 R->L }
% 0.17/0.39 double_divide(identity, inverse(inverse(inverse(X))))
% 0.17/0.39 = { by lemma 10 }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Lemma 14: double_divide(identity, inverse(multiply(identity, X))) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 double_divide(identity, inverse(multiply(identity, X)))
% 0.17/0.39 = { by lemma 8 }
% 0.17/0.39 double_divide(identity, inverse(inverse(inverse(X))))
% 0.17/0.39 = { by lemma 10 }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.17/0.39 Proof:
% 0.17/0.39 multiply(identity, a2)
% 0.17/0.39 = { by lemma 9 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(multiply(identity, a2), inverse(a2)), inverse(a2)))
% 0.17/0.39 = { by lemma 14 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(multiply(identity, a2), inverse(double_divide(identity, inverse(multiply(identity, a2))))), inverse(a2)))
% 0.17/0.39 = { by lemma 12 }
% 0.17/0.39 double_divide(identity, multiply(double_divide(multiply(identity, a2), inverse(inverse(inverse(multiply(identity, a2))))), inverse(a2)))
% 0.17/0.39 = { by lemma 8 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(multiply(identity, a2), multiply(identity, inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by lemma 7 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(multiply(identity, a2), multiply(inverse(identity), inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by axiom 1 (inverse) }
% 0.17/0.39 double_divide(identity, multiply(double_divide(multiply(identity, a2), multiply(double_divide(identity, identity), inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by lemma 11 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(double_divide(identity, multiply(inverse(multiply(identity, a2)), identity)), multiply(double_divide(identity, identity), inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by lemma 5 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(double_divide(identity, inverse(double_divide(identity, inverse(multiply(identity, a2))))), multiply(double_divide(identity, identity), inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by lemma 14 }
% 0.17/0.39 double_divide(identity, multiply(double_divide(double_divide(identity, inverse(a2)), multiply(double_divide(identity, identity), inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by lemma 10 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(double_divide(identity, double_divide(identity, inverse(inverse(inverse(inverse(a2)))))), multiply(double_divide(identity, identity), inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by lemma 8 R->L }
% 0.17/0.39 double_divide(identity, multiply(double_divide(double_divide(identity, double_divide(identity, inverse(inverse(multiply(identity, a2))))), multiply(double_divide(identity, identity), inverse(multiply(identity, a2)))), inverse(a2)))
% 0.17/0.39 = { by lemma 6 }
% 0.17/0.39 double_divide(identity, multiply(identity, inverse(a2)))
% 0.17/0.39 = { by lemma 13 R->L }
% 0.17/0.39 double_divide(identity, inverse(inverse(inverse(inverse(multiply(identity, inverse(a2)))))))
% 0.17/0.39 = { by lemma 10 }
% 0.17/0.39 inverse(multiply(identity, inverse(a2)))
% 0.17/0.39 = { by lemma 8 }
% 0.17/0.39 inverse(inverse(inverse(inverse(a2))))
% 0.17/0.39 = { by lemma 13 }
% 0.17/0.39 a2
% 0.17/0.39 % SZS output end Proof
% 0.17/0.39
% 0.17/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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