TSTP Solution File: GRP192-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP192-1 : 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 : n001.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 01:17:43 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% 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 : GRP192-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 01:40:21 EDT 2023
% 0.19/0.33 % CPUTime :
% 0.19/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
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% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.19/0.39 Axiom 2 (p40a_1): least_upper_bound(identity, X) = X.
% 0.19/0.39 Axiom 3 (left_identity): multiply(identity, X) = X.
% 0.19/0.39 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.19/0.39 Axiom 5 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.19/0.39 Axiom 6 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.19/0.39
% 0.19/0.39 Lemma 7: least_upper_bound(X, multiply(Y, X)) = multiply(Y, X).
% 0.19/0.39 Proof:
% 0.19/0.39 least_upper_bound(X, multiply(Y, X))
% 0.19/0.39 = { by axiom 3 (left_identity) R->L }
% 0.19/0.39 least_upper_bound(multiply(identity, X), multiply(Y, X))
% 0.19/0.39 = { by axiom 6 (monotony_lub2) R->L }
% 0.19/0.39 multiply(least_upper_bound(identity, Y), X)
% 0.19/0.39 = { by axiom 2 (p40a_1) }
% 0.19/0.39 multiply(Y, X)
% 0.19/0.39
% 0.19/0.39 Lemma 8: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(X), multiply(X, Y))
% 0.19/0.39 = { by axiom 5 (associativity) R->L }
% 0.19/0.39 multiply(multiply(inverse(X), X), Y)
% 0.19/0.39 = { by axiom 4 (left_inverse) }
% 0.19/0.39 multiply(identity, Y)
% 0.19/0.39 = { by axiom 3 (left_identity) }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Lemma 9: multiply(X, Y) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(X, Y)
% 0.19/0.39 = { by lemma 7 R->L }
% 0.19/0.39 least_upper_bound(Y, multiply(X, Y))
% 0.19/0.39 = { by axiom 1 (symmetry_of_lub) R->L }
% 0.19/0.39 least_upper_bound(multiply(X, Y), Y)
% 0.19/0.39 = { by lemma 8 R->L }
% 0.19/0.39 least_upper_bound(multiply(X, Y), multiply(inverse(X), multiply(X, Y)))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 multiply(inverse(X), multiply(X, Y))
% 0.19/0.39 = { by lemma 8 }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Goal 1 (prove_p40a): multiply(a, b) = multiply(b, a).
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(a, b)
% 0.19/0.39 = { by lemma 9 R->L }
% 0.19/0.39 multiply(inverse(multiply(a, b)), multiply(a, b))
% 0.19/0.39 = { by axiom 4 (left_inverse) }
% 0.19/0.39 identity
% 0.19/0.39 = { by axiom 4 (left_inverse) R->L }
% 0.19/0.39 multiply(inverse(a), a)
% 0.19/0.39 = { by lemma 9 }
% 0.19/0.39 a
% 0.19/0.39 = { by lemma 9 R->L }
% 0.19/0.39 multiply(b, a)
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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