TSTP Solution File: GRP191-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP191-2 : 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 : n027.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 0.20s 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
% 0.00/0.13 % Problem : GRP191-2 : 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
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 00:03:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.20/0.44 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.44 Axiom 3 (p39d_1): greatest_lower_bound(a, b) = b.
% 0.20/0.44 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.20/0.44 Axiom 5 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.44 Axiom 6 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.20/0.44 Axiom 7 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.44 Axiom 8 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.44
% 0.20/0.44 Lemma 9: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.20/0.44 Proof:
% 0.20/0.44 multiply(inverse(X), multiply(X, Y))
% 0.20/0.44 = { by axiom 5 (associativity) R->L }
% 0.20/0.44 multiply(multiply(inverse(X), X), Y)
% 0.20/0.44 = { by axiom 4 (left_inverse) }
% 0.20/0.44 multiply(identity, Y)
% 0.20/0.44 = { by axiom 1 (left_identity) }
% 0.20/0.44 Y
% 0.20/0.44
% 0.20/0.44 Goal 1 (prove_p39d): least_upper_bound(inverse(a), inverse(b)) = inverse(b).
% 0.20/0.44 Proof:
% 0.20/0.44 least_upper_bound(inverse(a), inverse(b))
% 0.20/0.44 = { by lemma 9 R->L }
% 0.20/0.44 multiply(inverse(b), multiply(b, least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by lemma 9 R->L }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(least_upper_bound(inverse(a), inverse(b)), b)), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(least_upper_bound(inverse(b), inverse(a)), b)), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 8 (monotony_lub2) }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), least_upper_bound(multiply(inverse(b), b), multiply(inverse(a), b))), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 4 (left_inverse) }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), least_upper_bound(identity, multiply(inverse(a), b))), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 4 (left_inverse) R->L }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), least_upper_bound(multiply(inverse(a), a), multiply(inverse(a), b))), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 7 (monotony_lub1) R->L }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(inverse(a), least_upper_bound(a, b))), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 3 (p39d_1) R->L }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(inverse(a), least_upper_bound(a, greatest_lower_bound(a, b)))), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 6 (lub_absorbtion) }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(inverse(a), a)), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 4 (left_inverse) }
% 0.20/0.44 multiply(inverse(b), multiply(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), identity), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 5 (associativity) }
% 0.20/0.44 multiply(inverse(b), multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(identity, least_upper_bound(inverse(a), inverse(b)))))
% 0.20/0.44 = { by axiom 1 (left_identity) }
% 0.20/0.44 multiply(inverse(b), multiply(inverse(least_upper_bound(inverse(a), inverse(b))), least_upper_bound(inverse(a), inverse(b))))
% 0.20/0.44 = { by axiom 4 (left_inverse) }
% 0.20/0.44 multiply(inverse(b), identity)
% 0.20/0.44 = { by axiom 4 (left_inverse) R->L }
% 0.20/0.44 multiply(inverse(b), multiply(inverse(inverse(b)), inverse(b)))
% 0.20/0.44 = { by lemma 9 R->L }
% 0.20/0.44 multiply(inverse(b), multiply(inverse(inverse(b)), multiply(inverse(b), multiply(b, inverse(b)))))
% 0.20/0.44 = { by lemma 9 }
% 0.20/0.44 multiply(inverse(b), multiply(b, inverse(b)))
% 0.20/0.44 = { by lemma 9 }
% 0.20/0.44 inverse(b)
% 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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