TSTP Solution File: GRP548-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP548-1 : 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 : n014.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 01:18:52 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP548-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 01:36:30 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.39 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Axiom 1 (identity): identity = divide(X, X).
% 0.20/0.40 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.20/0.40 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.20/0.40 Axiom 4 (single_axiom): divide(divide(identity, divide(X, Y)), divide(divide(Y, Z), X)) = Z.
% 0.20/0.40
% 0.20/0.40 Lemma 5: inverse(identity) = identity.
% 0.20/0.40 Proof:
% 0.20/0.40 inverse(identity)
% 0.20/0.40 = { by axiom 2 (inverse) }
% 0.20/0.40 divide(identity, identity)
% 0.20/0.40 = { by axiom 1 (identity) R->L }
% 0.20/0.40 identity
% 0.20/0.40
% 0.20/0.40 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.20/0.40 Proof:
% 0.20/0.40 divide(X, inverse(Y))
% 0.20/0.40 = { by axiom 2 (inverse) }
% 0.20/0.40 divide(X, divide(identity, Y))
% 0.20/0.40 = { by axiom 3 (multiply) R->L }
% 0.20/0.40 multiply(X, Y)
% 0.20/0.40
% 0.20/0.40 Lemma 7: divide(inverse(divide(X, Y)), divide(divide(Y, Z), X)) = Z.
% 0.20/0.40 Proof:
% 0.20/0.40 divide(inverse(divide(X, Y)), divide(divide(Y, Z), X))
% 0.20/0.40 = { by axiom 2 (inverse) }
% 0.20/0.40 divide(divide(identity, divide(X, Y)), divide(divide(Y, Z), X))
% 0.20/0.40 = { by axiom 4 (single_axiom) }
% 0.20/0.40 Z
% 0.20/0.40
% 0.20/0.40 Lemma 8: multiply(inverse(divide(X, Y)), X) = Y.
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(inverse(divide(X, Y)), X)
% 0.20/0.40 = { by lemma 6 R->L }
% 0.20/0.40 divide(inverse(divide(X, Y)), inverse(X))
% 0.20/0.40 = { by axiom 2 (inverse) }
% 0.20/0.40 divide(inverse(divide(X, Y)), divide(identity, X))
% 0.20/0.40 = { by axiom 1 (identity) }
% 0.20/0.40 divide(inverse(divide(X, Y)), divide(divide(Y, Y), X))
% 0.20/0.40 = { by lemma 7 }
% 0.20/0.40 Y
% 0.20/0.40
% 0.20/0.40 Lemma 9: multiply(identity, X) = X.
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(identity, X)
% 0.20/0.40 = { by lemma 5 R->L }
% 0.20/0.40 multiply(inverse(identity), X)
% 0.20/0.40 = { by axiom 1 (identity) }
% 0.20/0.40 multiply(inverse(divide(X, X)), X)
% 0.20/0.40 = { by lemma 8 }
% 0.20/0.40 X
% 0.20/0.40
% 0.20/0.40 Lemma 10: inverse(inverse(X)) = multiply(identity, X).
% 0.20/0.40 Proof:
% 0.20/0.40 inverse(inverse(X))
% 0.20/0.40 = { by axiom 2 (inverse) }
% 0.20/0.40 divide(identity, inverse(X))
% 0.20/0.40 = { by lemma 6 }
% 0.20/0.40 multiply(identity, X)
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(a, b)
% 0.20/0.40 = { by lemma 9 R->L }
% 0.20/0.40 multiply(multiply(identity, a), b)
% 0.20/0.40 = { by lemma 10 R->L }
% 0.20/0.40 multiply(inverse(inverse(a)), b)
% 0.20/0.40 = { by lemma 7 R->L }
% 0.20/0.40 multiply(inverse(divide(inverse(divide(identity, b)), divide(divide(b, inverse(a)), identity))), b)
% 0.20/0.40 = { by lemma 9 R->L }
% 0.20/0.40 multiply(inverse(divide(inverse(divide(identity, b)), divide(multiply(identity, divide(b, inverse(a))), identity))), b)
% 0.20/0.40 = { by lemma 10 R->L }
% 0.20/0.40 multiply(inverse(divide(inverse(divide(identity, b)), divide(inverse(inverse(divide(b, inverse(a)))), identity))), b)
% 0.20/0.40 = { by lemma 5 R->L }
% 0.20/0.40 multiply(inverse(divide(inverse(divide(identity, b)), divide(inverse(inverse(divide(b, inverse(a)))), inverse(identity)))), b)
% 0.20/0.40 = { by lemma 6 }
% 0.20/0.40 multiply(inverse(divide(inverse(divide(identity, b)), multiply(inverse(inverse(divide(b, inverse(a)))), identity))), b)
% 0.20/0.40 = { by axiom 2 (inverse) }
% 0.20/0.40 multiply(inverse(divide(inverse(divide(identity, b)), multiply(inverse(divide(identity, divide(b, inverse(a)))), identity))), b)
% 0.20/0.40 = { by lemma 8 }
% 0.20/0.40 multiply(inverse(divide(inverse(divide(identity, b)), divide(b, inverse(a)))), b)
% 0.20/0.40 = { by axiom 2 (inverse) R->L }
% 0.20/0.40 multiply(inverse(divide(inverse(inverse(b)), divide(b, inverse(a)))), b)
% 0.20/0.40 = { by lemma 10 }
% 0.20/0.40 multiply(inverse(divide(multiply(identity, b), divide(b, inverse(a)))), b)
% 0.20/0.40 = { by lemma 9 }
% 0.20/0.40 multiply(inverse(divide(b, divide(b, inverse(a)))), b)
% 0.20/0.40 = { by lemma 8 }
% 0.20/0.40 divide(b, inverse(a))
% 0.20/0.40 = { by lemma 6 }
% 0.20/0.40 multiply(b, a)
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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