TSTP Solution File: GRP167-5 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP167-5 : 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 : n020.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 01:17:28 EDT 2023
% Result : Unsatisfiable 0.20s 0.44s
% 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
% 0.07/0.12 % Problem : GRP167-5 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % 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 : Tue Aug 29 02:40:58 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
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% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.20/0.45 Axiom 2 (idempotence_of_gld): greatest_lower_bound(X, X) = X.
% 0.20/0.45 Axiom 3 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.20/0.45 Axiom 4 (lat4_2): negative_part(X) = greatest_lower_bound(X, identity).
% 0.20/0.45 Axiom 5 (idempotence_of_lub): least_upper_bound(X, X) = X.
% 0.20/0.45 Axiom 6 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.45 Axiom 7 (lat4_1): positive_part(X) = least_upper_bound(X, identity).
% 0.20/0.45 Axiom 8 (left_inverse): multiply(inverse(X), X) = identity.
% 0.20/0.45 Axiom 9 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.45 Axiom 10 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.20/0.45 Axiom 11 (p10): inverse(least_upper_bound(X, Y)) = greatest_lower_bound(inverse(X), inverse(Y)).
% 0.20/0.45 Axiom 12 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.45 Axiom 13 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.45
% 0.20/0.45 Lemma 14: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(inverse(X), multiply(X, Y))
% 0.20/0.45 = { by axiom 9 (associativity) R->L }
% 0.20/0.45 multiply(multiply(inverse(X), X), Y)
% 0.20/0.45 = { by axiom 8 (left_inverse) }
% 0.20/0.45 multiply(identity, Y)
% 0.20/0.45 = { by axiom 1 (left_identity) }
% 0.20/0.45 Y
% 0.20/0.45
% 0.20/0.45 Lemma 15: multiply(inverse(identity), X) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(inverse(identity), X)
% 0.20/0.45 = { by axiom 1 (left_identity) R->L }
% 0.20/0.45 multiply(inverse(identity), multiply(identity, X))
% 0.20/0.45 = { by lemma 14 }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 16: multiply(inverse(inverse(X)), identity) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 multiply(inverse(inverse(X)), identity)
% 0.20/0.45 = { by axiom 8 (left_inverse) R->L }
% 0.20/0.45 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.20/0.45 = { by lemma 14 }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 17: greatest_lower_bound(X, multiply(Y, X)) = multiply(negative_part(Y), X).
% 0.20/0.45 Proof:
% 0.20/0.45 greatest_lower_bound(X, multiply(Y, X))
% 0.20/0.45 = { by axiom 3 (symmetry_of_glb) R->L }
% 0.20/0.45 greatest_lower_bound(multiply(Y, X), X)
% 0.20/0.45 = { by axiom 1 (left_identity) R->L }
% 0.20/0.45 greatest_lower_bound(multiply(Y, X), multiply(identity, X))
% 0.20/0.45 = { by axiom 12 (monotony_glb2) R->L }
% 0.20/0.45 multiply(greatest_lower_bound(Y, identity), X)
% 0.20/0.45 = { by axiom 4 (lat4_2) R->L }
% 0.20/0.45 multiply(negative_part(Y), X)
% 0.20/0.45
% 0.20/0.45 Goal 1 (prove_lat4): a = multiply(positive_part(a), negative_part(a)).
% 0.20/0.45 Proof:
% 0.20/0.45 a
% 0.20/0.45 = { by lemma 14 R->L }
% 0.20/0.45 multiply(inverse(negative_part(inverse(a))), multiply(negative_part(inverse(a)), a))
% 0.20/0.45 = { by lemma 17 R->L }
% 0.20/0.45 multiply(inverse(negative_part(inverse(a))), greatest_lower_bound(a, multiply(inverse(a), a)))
% 0.20/0.45 = { by axiom 8 (left_inverse) }
% 0.20/0.45 multiply(inverse(negative_part(inverse(a))), greatest_lower_bound(a, identity))
% 0.20/0.45 = { by axiom 4 (lat4_2) R->L }
% 0.20/0.45 multiply(inverse(negative_part(inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 4 (lat4_2) }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(inverse(a), identity)), negative_part(a))
% 0.20/0.45 = { by axiom 3 (symmetry_of_glb) }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(identity, inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 8 (left_inverse) R->L }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(multiply(inverse(negative_part(inverse(identity))), negative_part(inverse(identity))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 2 (idempotence_of_gld) R->L }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(multiply(inverse(negative_part(inverse(identity))), greatest_lower_bound(negative_part(inverse(identity)), negative_part(inverse(identity)))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by lemma 15 R->L }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(multiply(inverse(negative_part(inverse(identity))), greatest_lower_bound(negative_part(inverse(identity)), multiply(inverse(identity), negative_part(inverse(identity))))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by lemma 17 }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(multiply(inverse(negative_part(inverse(identity))), multiply(negative_part(inverse(identity)), negative_part(inverse(identity)))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by lemma 14 }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(negative_part(inverse(identity)), inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 4 (lat4_2) }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), identity), inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 8 (left_inverse) R->L }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), multiply(inverse(positive_part(inverse(identity))), positive_part(inverse(identity)))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 5 (idempotence_of_lub) R->L }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), multiply(inverse(positive_part(inverse(identity))), least_upper_bound(positive_part(inverse(identity)), positive_part(inverse(identity))))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by lemma 15 R->L }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), multiply(inverse(positive_part(inverse(identity))), least_upper_bound(positive_part(inverse(identity)), multiply(inverse(identity), positive_part(inverse(identity)))))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 6 (symmetry_of_lub) R->L }
% 0.20/0.45 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), multiply(inverse(positive_part(inverse(identity))), least_upper_bound(multiply(inverse(identity), positive_part(inverse(identity))), positive_part(inverse(identity))))), inverse(a))), negative_part(a))
% 0.20/0.45 = { by axiom 1 (left_identity) R->L }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), multiply(inverse(positive_part(inverse(identity))), least_upper_bound(multiply(inverse(identity), positive_part(inverse(identity))), multiply(identity, positive_part(inverse(identity)))))), inverse(a))), negative_part(a))
% 0.20/0.46 = { by axiom 13 (monotony_lub2) R->L }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), multiply(inverse(positive_part(inverse(identity))), multiply(least_upper_bound(inverse(identity), identity), positive_part(inverse(identity))))), inverse(a))), negative_part(a))
% 0.20/0.46 = { by axiom 7 (lat4_1) R->L }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), multiply(inverse(positive_part(inverse(identity))), multiply(positive_part(inverse(identity)), positive_part(inverse(identity))))), inverse(a))), negative_part(a))
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), positive_part(inverse(identity))), inverse(a))), negative_part(a))
% 0.20/0.46 = { by axiom 7 (lat4_1) }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(greatest_lower_bound(inverse(identity), least_upper_bound(inverse(identity), identity)), inverse(a))), negative_part(a))
% 0.20/0.46 = { by axiom 10 (glb_absorbtion) }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(inverse(identity), inverse(a))), negative_part(a))
% 0.20/0.46 = { by axiom 11 (p10) R->L }
% 0.20/0.46 multiply(inverse(inverse(least_upper_bound(identity, a))), negative_part(a))
% 0.20/0.46 = { by axiom 6 (symmetry_of_lub) R->L }
% 0.20/0.46 multiply(inverse(inverse(least_upper_bound(a, identity))), negative_part(a))
% 0.20/0.46 = { by axiom 7 (lat4_1) R->L }
% 0.20/0.46 multiply(inverse(inverse(positive_part(a))), negative_part(a))
% 0.20/0.46 = { by lemma 16 R->L }
% 0.20/0.46 multiply(multiply(inverse(inverse(inverse(inverse(positive_part(a))))), identity), negative_part(a))
% 0.20/0.46 = { by lemma 14 R->L }
% 0.20/0.46 multiply(multiply(inverse(inverse(inverse(inverse(positive_part(a))))), multiply(inverse(inverse(inverse(positive_part(a)))), multiply(inverse(inverse(positive_part(a))), identity))), negative_part(a))
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 multiply(multiply(inverse(inverse(positive_part(a))), identity), negative_part(a))
% 0.20/0.46 = { by lemma 16 }
% 0.20/0.46 multiply(positive_part(a), negative_part(a))
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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