TSTP Solution File: GRP190-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP190-2 : 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 : n015.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 01:17:42 EDT 2023
% Result : Unsatisfiable 0.14s 0.42s
% Output : Proof 0.21s
% 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 : GRP190-2 : 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
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 : Mon Aug 28 22:12:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.42 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.42
% 0.14/0.42 % SZS status Unsatisfiable
% 0.14/0.42
% 0.14/0.43 % SZS output start Proof
% 0.14/0.43 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.14/0.43 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.14/0.43 Axiom 3 (p39c_1): least_upper_bound(a, b) = a.
% 0.14/0.43 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.14/0.43 Axiom 5 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.14/0.43 Axiom 6 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.14/0.43 Axiom 7 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.14/0.43 Axiom 8 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.14/0.43
% 0.14/0.43 Lemma 9: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.14/0.43 Proof:
% 0.14/0.43 multiply(inverse(X), multiply(X, Y))
% 0.14/0.43 = { by axiom 5 (associativity) R->L }
% 0.14/0.43 multiply(multiply(inverse(X), X), Y)
% 0.14/0.43 = { by axiom 4 (left_inverse) }
% 0.14/0.43 multiply(identity, Y)
% 0.14/0.43 = { by axiom 1 (left_identity) }
% 0.14/0.43 Y
% 0.14/0.43
% 0.21/0.43 Goal 1 (prove_p39c): greatest_lower_bound(inverse(a), inverse(b)) = inverse(a).
% 0.21/0.43 Proof:
% 0.21/0.43 greatest_lower_bound(inverse(a), inverse(b))
% 0.21/0.43 = { by lemma 9 R->L }
% 0.21/0.43 multiply(inverse(a), multiply(a, greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by lemma 9 R->L }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(greatest_lower_bound(inverse(a), inverse(b)), a)), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 8 (monotony_glb2) }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), greatest_lower_bound(multiply(inverse(a), a), multiply(inverse(b), a))), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 4 (left_inverse) }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), greatest_lower_bound(identity, multiply(inverse(b), a))), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 4 (left_inverse) R->L }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), greatest_lower_bound(multiply(inverse(b), b), multiply(inverse(b), a))), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 7 (monotony_glb1) R->L }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(b), greatest_lower_bound(b, a))), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 3 (p39c_1) R->L }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(b), greatest_lower_bound(b, least_upper_bound(a, b)))), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(b), greatest_lower_bound(b, least_upper_bound(b, a)))), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 6 (glb_absorbtion) }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(inverse(b), b)), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 4 (left_inverse) }
% 0.21/0.43 multiply(inverse(a), multiply(multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), identity), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 5 (associativity) }
% 0.21/0.43 multiply(inverse(a), multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), multiply(identity, greatest_lower_bound(inverse(a), inverse(b)))))
% 0.21/0.43 = { by axiom 1 (left_identity) }
% 0.21/0.43 multiply(inverse(a), multiply(inverse(greatest_lower_bound(inverse(a), inverse(b))), greatest_lower_bound(inverse(a), inverse(b))))
% 0.21/0.43 = { by axiom 4 (left_inverse) }
% 0.21/0.43 multiply(inverse(a), identity)
% 0.21/0.43 = { by axiom 4 (left_inverse) R->L }
% 0.21/0.43 multiply(inverse(a), multiply(inverse(inverse(a)), inverse(a)))
% 0.21/0.43 = { by lemma 9 R->L }
% 0.21/0.43 multiply(inverse(a), multiply(inverse(inverse(a)), multiply(inverse(a), multiply(a, inverse(a)))))
% 0.21/0.43 = { by lemma 9 }
% 0.21/0.43 multiply(inverse(a), multiply(a, inverse(a)))
% 0.21/0.43 = { by lemma 9 }
% 0.21/0.43 inverse(a)
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43
% 0.21/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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