TSTP Solution File: GRP190-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP190-1 : 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 : n011.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 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP190-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13 % 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 : n011.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 21:24:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.44 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.44
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.21/0.44 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.21/0.44 Axiom 3 (p39a_1): least_upper_bound(a, b) = a.
% 0.21/0.44 Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.21/0.44 Axiom 5 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.21/0.44 Axiom 6 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.21/0.44 Axiom 7 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.44
% 0.21/0.44 Lemma 8: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(inverse(X), multiply(X, Y))
% 0.21/0.44 = { by axiom 5 (associativity) R->L }
% 0.21/0.44 multiply(multiply(inverse(X), X), Y)
% 0.21/0.44 = { by axiom 4 (left_inverse) }
% 0.21/0.44 multiply(identity, Y)
% 0.21/0.44 = { by axiom 1 (left_identity) }
% 0.21/0.44 Y
% 0.21/0.44
% 0.21/0.44 Lemma 9: multiply(inverse(inverse(X)), identity) = X.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(inverse(inverse(X)), identity)
% 0.21/0.44 = { by axiom 4 (left_inverse) R->L }
% 0.21/0.44 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 X
% 0.21/0.44
% 0.21/0.44 Lemma 10: multiply(X, identity) = X.
% 0.21/0.44 Proof:
% 0.21/0.44 multiply(X, identity)
% 0.21/0.44 = { by lemma 8 R->L }
% 0.21/0.44 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, identity)))
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 multiply(inverse(inverse(X)), identity)
% 0.21/0.44 = { by lemma 9 }
% 0.21/0.44 X
% 0.21/0.44
% 0.21/0.44 Goal 1 (prove_p39a): least_upper_bound(inverse(a), inverse(b)) = inverse(b).
% 0.21/0.44 Proof:
% 0.21/0.44 least_upper_bound(inverse(a), inverse(b))
% 0.21/0.44 = { by lemma 9 R->L }
% 0.21/0.44 multiply(inverse(inverse(least_upper_bound(inverse(a), inverse(b)))), identity)
% 0.21/0.44 = { by lemma 10 R->L }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), identity)), identity)
% 0.21/0.44 = { by axiom 4 (left_inverse) R->L }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(inverse(a), a))), identity)
% 0.21/0.44 = { by axiom 3 (p39a_1) R->L }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(inverse(a), least_upper_bound(a, b)))), identity)
% 0.21/0.44 = { by axiom 6 (monotony_lub1) }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), least_upper_bound(multiply(inverse(a), a), multiply(inverse(a), b)))), identity)
% 0.21/0.44 = { by axiom 4 (left_inverse) }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), least_upper_bound(identity, multiply(inverse(a), b)))), identity)
% 0.21/0.44 = { by axiom 4 (left_inverse) R->L }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), least_upper_bound(multiply(inverse(b), b), multiply(inverse(a), b)))), identity)
% 0.21/0.44 = { by axiom 7 (monotony_lub2) R->L }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(least_upper_bound(inverse(b), inverse(a)), b))), identity)
% 0.21/0.44 = { by axiom 2 (symmetry_of_lub) }
% 0.21/0.44 multiply(inverse(multiply(inverse(least_upper_bound(inverse(a), inverse(b))), multiply(least_upper_bound(inverse(a), inverse(b)), b))), identity)
% 0.21/0.44 = { by lemma 8 }
% 0.21/0.44 multiply(inverse(b), identity)
% 0.21/0.44 = { by lemma 10 }
% 0.21/0.44 inverse(b)
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------