TSTP Solution File: GRP491-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP491-1 : 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 01:18:38 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP491-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 22:03:35 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.40 Command-line arguments: --flatten
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.21/0.41 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.21/0.41 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.21/0.41 Axiom 4 (single_axiom): double_divide(double_divide(identity, X), double_divide(identity, double_divide(double_divide(double_divide(X, Y), identity), double_divide(Z, Y)))) = Z.
% 0.21/0.41
% 0.21/0.41 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.21/0.41 Proof:
% 0.21/0.41 inverse(double_divide(X, Y))
% 0.21/0.41 = { by axiom 1 (inverse) }
% 0.21/0.41 double_divide(double_divide(X, Y), identity)
% 0.21/0.41 = { by axiom 3 (multiply) R->L }
% 0.21/0.41 multiply(Y, X)
% 0.21/0.41
% 0.21/0.41 Lemma 6: double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(Y, X), double_divide(Z, Y)))) = Z.
% 0.21/0.41 Proof:
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(Y, X), double_divide(Z, Y))))
% 0.21/0.41 = { by lemma 5 R->L }
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, double_divide(inverse(double_divide(X, Y)), double_divide(Z, Y))))
% 0.21/0.41 = { by axiom 1 (inverse) }
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, double_divide(double_divide(double_divide(X, Y), identity), double_divide(Z, Y))))
% 0.21/0.41 = { by axiom 4 (single_axiom) }
% 0.21/0.41 Z
% 0.21/0.41
% 0.21/0.41 Lemma 7: double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(Y), X)))) = Y.
% 0.21/0.41 Proof:
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(Y), X))))
% 0.21/0.41 = { by axiom 1 (inverse) }
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(Y), X), identity)))
% 0.21/0.41 = { by axiom 2 (identity) }
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(Y), X), double_divide(Y, inverse(Y)))))
% 0.21/0.41 = { by lemma 6 }
% 0.21/0.41 Y
% 0.21/0.41
% 0.21/0.41 Lemma 8: double_divide(double_divide(identity, X), double_divide(identity, inverse(inverse(identity)))) = X.
% 0.21/0.41 Proof:
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, inverse(inverse(identity))))
% 0.21/0.41 = { by axiom 2 (identity) }
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, inverse(inverse(double_divide(X, inverse(X))))))
% 0.21/0.41 = { by lemma 5 }
% 0.21/0.41 double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(X), X))))
% 0.21/0.41 = { by lemma 7 }
% 0.21/0.41 X
% 0.21/0.41
% 0.21/0.41 Lemma 9: double_divide(identity, inverse(inverse(identity))) = identity.
% 0.21/0.41 Proof:
% 0.21/0.41 double_divide(identity, inverse(inverse(identity)))
% 0.21/0.41 = { by lemma 8 R->L }
% 0.21/0.41 double_divide(double_divide(identity, double_divide(identity, inverse(inverse(identity)))), double_divide(identity, inverse(inverse(identity))))
% 0.21/0.41 = { by axiom 2 (identity) }
% 0.21/0.41 double_divide(double_divide(double_divide(identity, inverse(identity)), double_divide(identity, inverse(inverse(identity)))), double_divide(identity, inverse(inverse(identity))))
% 0.21/0.41 = { by lemma 8 }
% 0.21/0.41 double_divide(inverse(identity), double_divide(identity, inverse(inverse(identity))))
% 0.21/0.41 = { by axiom 1 (inverse) }
% 0.21/0.41 double_divide(double_divide(identity, identity), double_divide(identity, inverse(inverse(identity))))
% 0.21/0.41 = { by lemma 8 }
% 0.21/0.41 identity
% 0.21/0.41
% 0.21/0.41 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(identity, a2)
% 0.21/0.41 = { by lemma 6 R->L }
% 0.21/0.41 double_divide(double_divide(identity, a2), double_divide(identity, double_divide(multiply(identity, a2), double_divide(multiply(identity, a2), identity))))
% 0.21/0.41 = { by axiom 1 (inverse) R->L }
% 0.21/0.41 double_divide(double_divide(identity, a2), double_divide(identity, double_divide(multiply(identity, a2), inverse(multiply(identity, a2)))))
% 0.21/0.41 = { by axiom 2 (identity) R->L }
% 0.21/0.41 double_divide(double_divide(identity, a2), double_divide(identity, identity))
% 0.21/0.41 = { by axiom 1 (inverse) R->L }
% 0.21/0.41 double_divide(double_divide(identity, a2), inverse(identity))
% 0.21/0.41 = { by lemma 7 R->L }
% 0.21/0.41 double_divide(double_divide(identity, a2), double_divide(double_divide(identity, X), double_divide(identity, inverse(multiply(inverse(inverse(identity)), X)))))
% 0.21/0.41 = { by axiom 1 (inverse) }
% 0.21/0.41 double_divide(double_divide(identity, a2), double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(inverse(identity)), X), identity))))
% 0.21/0.41 = { by lemma 9 R->L }
% 0.21/0.41 double_divide(double_divide(identity, a2), double_divide(double_divide(identity, X), double_divide(identity, double_divide(multiply(inverse(inverse(identity)), X), double_divide(identity, inverse(inverse(identity)))))))
% 0.21/0.41 = { by lemma 6 }
% 0.21/0.41 double_divide(double_divide(identity, a2), identity)
% 0.21/0.41 = { by lemma 9 R->L }
% 0.21/0.41 double_divide(double_divide(identity, a2), double_divide(identity, inverse(inverse(identity))))
% 0.21/0.41 = { by lemma 8 }
% 0.21/0.41 a2
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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