TSTP Solution File: GRP493-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP493-1 : 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 : n023.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 01:18:39 EDT 2023
% Result : Unsatisfiable 0.15s 0.34s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP493-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31 % Computer : n023.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 29 02:50:55 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.34 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.15/0.34
% 0.15/0.34 % SZS status Unsatisfiable
% 0.15/0.34
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.15/0.35 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.15/0.35 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.15/0.35 Axiom 4 (single_axiom): double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), double_divide(identity, identity)), double_divide(X, Z))) = Y.
% 0.15/0.35
% 0.15/0.35 Lemma 5: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.15/0.35 Proof:
% 0.15/0.35 inverse(double_divide(X, Y))
% 0.15/0.35 = { by axiom 1 (inverse) }
% 0.15/0.35 double_divide(double_divide(X, Y), identity)
% 0.15/0.35 = { by axiom 3 (multiply) R->L }
% 0.15/0.35 multiply(Y, X)
% 0.15/0.35
% 0.15/0.35 Lemma 6: multiply(inverse(X), X) = inverse(identity).
% 0.15/0.35 Proof:
% 0.15/0.35 multiply(inverse(X), X)
% 0.15/0.35 = { by lemma 5 R->L }
% 0.15/0.35 inverse(double_divide(X, inverse(X)))
% 0.15/0.35 = { by axiom 2 (identity) R->L }
% 0.15/0.35 inverse(identity)
% 0.15/0.35
% 0.15/0.35 Lemma 7: double_divide(identity, multiply(inverse(X), X)) = identity.
% 0.15/0.35 Proof:
% 0.15/0.35 double_divide(identity, multiply(inverse(X), X))
% 0.15/0.35 = { by lemma 6 }
% 0.15/0.35 double_divide(identity, inverse(identity))
% 0.15/0.35 = { by axiom 2 (identity) R->L }
% 0.15/0.35 identity
% 0.15/0.35
% 0.15/0.35 Lemma 8: multiply(multiply(inverse(X), X), identity) = multiply(inverse(Y), Y).
% 0.15/0.35 Proof:
% 0.15/0.35 multiply(multiply(inverse(X), X), identity)
% 0.15/0.35 = { by lemma 5 R->L }
% 0.15/0.35 inverse(double_divide(identity, multiply(inverse(X), X)))
% 0.15/0.35 = { by lemma 7 }
% 0.15/0.35 inverse(identity)
% 0.15/0.35 = { by lemma 6 R->L }
% 0.15/0.35 multiply(inverse(Y), Y)
% 0.15/0.35
% 0.15/0.35 Lemma 9: double_divide(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), double_divide(Z, multiply(inverse(W), W)))) = Z.
% 0.15/0.35 Proof:
% 0.15/0.35 double_divide(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), double_divide(Z, multiply(inverse(W), W))))
% 0.15/0.35 = { by lemma 5 R->L }
% 0.15/0.35 double_divide(multiply(inverse(X), X), inverse(double_divide(double_divide(Z, multiply(inverse(W), W)), multiply(inverse(Y), Y))))
% 0.15/0.35 = { by axiom 1 (inverse) }
% 0.15/0.35 double_divide(multiply(inverse(X), X), double_divide(double_divide(double_divide(Z, multiply(inverse(W), W)), multiply(inverse(Y), Y)), identity))
% 0.15/0.35 = { by lemma 6 }
% 0.15/0.35 double_divide(inverse(identity), double_divide(double_divide(double_divide(Z, multiply(inverse(W), W)), multiply(inverse(Y), Y)), identity))
% 0.15/0.35 = { by lemma 6 }
% 0.15/0.35 double_divide(inverse(identity), double_divide(double_divide(double_divide(Z, multiply(inverse(W), W)), inverse(identity)), identity))
% 0.15/0.35 = { by axiom 1 (inverse) }
% 0.15/0.35 double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(Z, multiply(inverse(W), W)), inverse(identity)), identity))
% 0.15/0.35 = { by lemma 7 R->L }
% 0.15/0.35 double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(Z, multiply(inverse(W), W)), inverse(identity)), double_divide(identity, multiply(inverse(W), W))))
% 0.15/0.35 = { by axiom 1 (inverse) }
% 0.15/0.35 double_divide(double_divide(identity, identity), double_divide(double_divide(double_divide(Z, multiply(inverse(W), W)), double_divide(identity, identity)), double_divide(identity, multiply(inverse(W), W))))
% 0.15/0.35 = { by axiom 4 (single_axiom) }
% 0.15/0.35 Z
% 0.15/0.35
% 0.15/0.35 Lemma 10: double_divide(multiply(inverse(X), X), multiply(inverse(Y), Y)) = identity.
% 0.15/0.35 Proof:
% 0.15/0.35 double_divide(multiply(inverse(X), X), multiply(inverse(Y), Y))
% 0.15/0.35 = { by lemma 8 R->L }
% 0.15/0.35 double_divide(multiply(inverse(X), X), multiply(multiply(inverse(Z), Z), identity))
% 0.15/0.35 = { by lemma 7 R->L }
% 0.15/0.35 double_divide(multiply(inverse(X), X), multiply(multiply(inverse(Z), Z), double_divide(identity, multiply(inverse(W), W))))
% 0.15/0.35 = { by lemma 9 }
% 0.15/0.35 identity
% 0.15/0.35
% 0.15/0.35 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = identity.
% 0.15/0.35 Proof:
% 0.15/0.35 multiply(inverse(a1), a1)
% 0.15/0.35 = { by lemma 9 R->L }
% 0.15/0.35 double_divide(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), double_divide(multiply(inverse(a1), a1), multiply(inverse(Z), Z))))
% 0.15/0.35 = { by lemma 10 }
% 0.15/0.35 double_divide(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), identity))
% 0.15/0.35 = { by lemma 8 }
% 0.15/0.35 double_divide(multiply(inverse(X), X), multiply(inverse(W), W))
% 0.15/0.35 = { by lemma 10 }
% 0.15/0.35 identity
% 0.15/0.35 % SZS output end Proof
% 0.15/0.35
% 0.15/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
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