TSTP Solution File: GRP186-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP186-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n010.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 01:17:40 EDT 2023
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% 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 : GRP186-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n010.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 19:28:04 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.43 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.22/0.43 % SZS status Unsatisfiable
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% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.22/0.44 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.22/0.44 Axiom 3 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.22/0.44 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.22/0.44 Axiom 5 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.22/0.44
% 0.22/0.44 Lemma 6: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.22/0.44 Proof:
% 0.22/0.44 multiply(inverse(X), multiply(X, Y))
% 0.22/0.44 = { by axiom 3 (associativity) R->L }
% 0.22/0.44 multiply(multiply(inverse(X), X), Y)
% 0.22/0.44 = { by axiom 4 (left_inverse) }
% 0.22/0.44 multiply(identity, Y)
% 0.22/0.44 = { by axiom 1 (left_identity) }
% 0.22/0.44 Y
% 0.22/0.44
% 0.22/0.44 Lemma 7: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.22/0.44 Proof:
% 0.22/0.44 multiply(inverse(inverse(X)), Y)
% 0.22/0.44 = { by lemma 6 R->L }
% 0.22/0.44 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
% 0.22/0.44 = { by lemma 6 }
% 0.22/0.44 multiply(X, Y)
% 0.22/0.44
% 0.22/0.44 Goal 1 (prove_p23x): least_upper_bound(multiply(a, b), identity) = multiply(a, least_upper_bound(inverse(a), b)).
% 0.22/0.44 Proof:
% 0.22/0.44 least_upper_bound(multiply(a, b), identity)
% 0.22/0.44 = { by lemma 6 R->L }
% 0.22/0.44 multiply(inverse(inverse(a)), multiply(inverse(a), least_upper_bound(multiply(a, b), identity)))
% 0.22/0.44 = { by axiom 5 (monotony_lub1) }
% 0.22/0.44 multiply(inverse(inverse(a)), least_upper_bound(multiply(inverse(a), multiply(a, b)), multiply(inverse(a), identity)))
% 0.22/0.44 = { by lemma 6 }
% 0.22/0.44 multiply(inverse(inverse(a)), least_upper_bound(b, multiply(inverse(a), identity)))
% 0.22/0.44 = { by axiom 4 (left_inverse) R->L }
% 0.22/0.44 multiply(inverse(inverse(a)), least_upper_bound(b, multiply(inverse(a), multiply(inverse(inverse(a)), inverse(a)))))
% 0.22/0.44 = { by lemma 7 }
% 0.22/0.44 multiply(inverse(inverse(a)), least_upper_bound(b, multiply(inverse(a), multiply(a, inverse(a)))))
% 0.22/0.44 = { by lemma 6 }
% 0.22/0.44 multiply(inverse(inverse(a)), least_upper_bound(b, inverse(a)))
% 0.22/0.44 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.22/0.44 multiply(inverse(inverse(a)), least_upper_bound(inverse(a), b))
% 0.22/0.44 = { by lemma 7 }
% 0.22/0.44 multiply(a, least_upper_bound(inverse(a), b))
% 0.22/0.44 % SZS output end Proof
% 0.22/0.44
% 0.22/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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