TSTP Solution File: GRP186-4 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP186-4 : 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 : n002.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 0.11s 0.40s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.15 % Problem : GRP186-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8042.1875MB
% 0.07/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Aug 28 21:14:34 EDT 2023
% 0.07/0.36 % CPUTime :
% 0.11/0.40 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.11/0.40
% 0.11/0.40 % SZS status Unsatisfiable
% 0.11/0.40
% 0.11/0.40 % SZS output start Proof
% 0.11/0.40 Axiom 1 (p23x_2): inverse(inverse(X)) = X.
% 0.11/0.40 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.11/0.40 Axiom 3 (left_inverse): multiply(inverse(X), X) = identity.
% 0.11/0.40 Axiom 4 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.11/0.40
% 0.11/0.40 Goal 1 (prove_p23x): least_upper_bound(multiply(a, b), identity) = multiply(a, least_upper_bound(inverse(a), b)).
% 0.11/0.40 Proof:
% 0.11/0.40 least_upper_bound(multiply(a, b), identity)
% 0.11/0.40 = { by axiom 2 (symmetry_of_lub) }
% 0.11/0.40 least_upper_bound(identity, multiply(a, b))
% 0.11/0.40 = { by axiom 3 (left_inverse) R->L }
% 0.11/0.40 least_upper_bound(multiply(inverse(inverse(a)), inverse(a)), multiply(a, b))
% 0.11/0.40 = { by axiom 1 (p23x_2) }
% 0.11/0.40 least_upper_bound(multiply(a, inverse(a)), multiply(a, b))
% 0.11/0.40 = { by axiom 4 (monotony_lub1) R->L }
% 0.11/0.40 multiply(a, least_upper_bound(inverse(a), b))
% 0.11/0.40 % SZS output end Proof
% 0.11/0.40
% 0.11/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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