TSTP Solution File: GRP185-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP185-2 : 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 : n005.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 01:17:39 EDT 2023
% Result : Unsatisfiable 0.20s 0.43s
% 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
% 0.11/0.12 % Problem : GRP185-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Mon Aug 28 20:14:53 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.43 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
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% 0.20/0.43 % SZS status Unsatisfiable
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% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Axiom 1 (idempotence_of_lub): least_upper_bound(X, X) = X.
% 0.20/0.43 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.43 Axiom 3 (left_identity): multiply(identity, X) = X.
% 0.20/0.43 Axiom 4 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.20/0.43 Axiom 5 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.43 Axiom 6 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.43
% 0.20/0.43 Lemma 7: multiply(least_upper_bound(X, identity), Y) = least_upper_bound(Y, multiply(X, Y)).
% 0.20/0.43 Proof:
% 0.20/0.43 multiply(least_upper_bound(X, identity), Y)
% 0.20/0.43 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.44 multiply(least_upper_bound(identity, X), Y)
% 0.20/0.44 = { by axiom 6 (monotony_lub2) }
% 0.20/0.44 least_upper_bound(multiply(identity, Y), multiply(X, Y))
% 0.20/0.44 = { by axiom 3 (left_identity) }
% 0.20/0.44 least_upper_bound(Y, multiply(X, Y))
% 0.20/0.44
% 0.20/0.44 Lemma 8: least_upper_bound(X, least_upper_bound(X, Y)) = least_upper_bound(X, Y).
% 0.20/0.44 Proof:
% 0.20/0.44 least_upper_bound(X, least_upper_bound(X, Y))
% 0.20/0.44 = { by axiom 4 (associativity_of_lub) }
% 0.20/0.44 least_upper_bound(least_upper_bound(X, X), Y)
% 0.20/0.44 = { by axiom 1 (idempotence_of_lub) }
% 0.20/0.44 least_upper_bound(X, Y)
% 0.20/0.44
% 0.20/0.44 Goal 1 (prove_p22a): least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))) = multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)).
% 0.20/0.44 Proof:
% 0.20/0.44 least_upper_bound(least_upper_bound(multiply(a, b), identity), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))
% 0.20/0.44 = { by axiom 2 (symmetry_of_lub) }
% 0.20/0.44 least_upper_bound(least_upper_bound(identity, multiply(a, b)), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity)))
% 0.20/0.44 = { by axiom 4 (associativity_of_lub) R->L }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(multiply(a, b), multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))))
% 0.20/0.44 = { by lemma 7 }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(multiply(a, b), least_upper_bound(least_upper_bound(b, identity), multiply(a, least_upper_bound(b, identity)))))
% 0.20/0.44 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(multiply(a, b), least_upper_bound(multiply(a, least_upper_bound(b, identity)), least_upper_bound(b, identity))))
% 0.20/0.44 = { by axiom 4 (associativity_of_lub) }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(least_upper_bound(multiply(a, b), multiply(a, least_upper_bound(b, identity))), least_upper_bound(b, identity)))
% 0.20/0.44 = { by axiom 5 (monotony_lub1) R->L }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(multiply(a, least_upper_bound(b, least_upper_bound(b, identity))), least_upper_bound(b, identity)))
% 0.20/0.44 = { by axiom 2 (symmetry_of_lub) }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(least_upper_bound(b, identity), multiply(a, least_upper_bound(b, least_upper_bound(b, identity)))))
% 0.20/0.44 = { by lemma 8 }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(least_upper_bound(b, identity), multiply(a, least_upper_bound(b, identity))))
% 0.20/0.44 = { by axiom 4 (associativity_of_lub) R->L }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(b, least_upper_bound(identity, multiply(a, least_upper_bound(b, identity)))))
% 0.20/0.44 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.44 least_upper_bound(identity, least_upper_bound(least_upper_bound(identity, multiply(a, least_upper_bound(b, identity))), b))
% 0.20/0.44 = { by axiom 4 (associativity_of_lub) }
% 0.20/0.44 least_upper_bound(least_upper_bound(identity, least_upper_bound(identity, multiply(a, least_upper_bound(b, identity)))), b)
% 0.20/0.44 = { by axiom 2 (symmetry_of_lub) }
% 0.20/0.44 least_upper_bound(b, least_upper_bound(identity, least_upper_bound(identity, multiply(a, least_upper_bound(b, identity)))))
% 0.20/0.44 = { by lemma 8 }
% 0.20/0.44 least_upper_bound(b, least_upper_bound(identity, multiply(a, least_upper_bound(b, identity))))
% 0.20/0.44 = { by axiom 4 (associativity_of_lub) }
% 0.20/0.44 least_upper_bound(least_upper_bound(b, identity), multiply(a, least_upper_bound(b, identity)))
% 0.20/0.44 = { by lemma 7 R->L }
% 0.20/0.44 multiply(least_upper_bound(a, identity), least_upper_bound(b, identity))
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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