TSTP Solution File: GRP173-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP173-1 : 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 01:17:31 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% 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 : GRP173-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.13 % 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 : n011.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:38:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --flatten
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% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.19/0.40 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.19/0.40 Axiom 3 (p05a_1): least_upper_bound(identity, a) = identity.
% 0.19/0.40 Axiom 4 (left_identity): multiply(identity, X) = X.
% 0.19/0.40 Axiom 5 (p05a_2): least_upper_bound(identity, inverse(a)) = identity.
% 0.19/0.40 Axiom 6 (left_inverse): multiply(inverse(X), X) = identity.
% 0.19/0.40 Axiom 7 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.19/0.40 Axiom 8 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.19/0.40
% 0.19/0.40 Lemma 9: least_upper_bound(identity, inverse(a)) = least_upper_bound(identity, a).
% 0.19/0.40 Proof:
% 0.19/0.40 least_upper_bound(identity, inverse(a))
% 0.19/0.40 = { by axiom 5 (p05a_2) }
% 0.19/0.40 identity
% 0.19/0.40 = { by axiom 3 (p05a_1) R->L }
% 0.19/0.40 least_upper_bound(identity, a)
% 0.19/0.40
% 0.19/0.40 Lemma 10: multiply(inverse(X), X) = least_upper_bound(identity, inverse(a)).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(inverse(X), X)
% 0.19/0.40 = { by axiom 6 (left_inverse) }
% 0.19/0.40 identity
% 0.19/0.40 = { by axiom 3 (p05a_1) R->L }
% 0.19/0.40 least_upper_bound(identity, a)
% 0.19/0.40 = { by lemma 9 R->L }
% 0.19/0.40 least_upper_bound(identity, inverse(a))
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_p05a): identity = a.
% 0.19/0.40 Proof:
% 0.19/0.40 identity
% 0.19/0.40 = { by axiom 3 (p05a_1) R->L }
% 0.19/0.40 least_upper_bound(identity, a)
% 0.19/0.40 = { by lemma 9 R->L }
% 0.19/0.40 least_upper_bound(identity, inverse(a))
% 0.19/0.40 = { by lemma 10 R->L }
% 0.19/0.40 multiply(inverse(a), a)
% 0.19/0.40 = { by axiom 7 (glb_absorbtion) R->L }
% 0.19/0.40 multiply(greatest_lower_bound(inverse(a), least_upper_bound(inverse(a), least_upper_bound(identity, a))), a)
% 0.19/0.40 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.19/0.40 multiply(greatest_lower_bound(inverse(a), least_upper_bound(least_upper_bound(identity, a), inverse(a))), a)
% 0.19/0.40 = { by axiom 3 (p05a_1) }
% 0.19/0.41 multiply(greatest_lower_bound(inverse(a), least_upper_bound(identity, inverse(a))), a)
% 0.19/0.41 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.19/0.41 multiply(greatest_lower_bound(least_upper_bound(identity, inverse(a)), inverse(a)), a)
% 0.19/0.41 = { by lemma 9 }
% 0.19/0.41 multiply(greatest_lower_bound(least_upper_bound(identity, a), inverse(a)), a)
% 0.19/0.41 = { by axiom 8 (monotony_glb2) }
% 0.19/0.41 greatest_lower_bound(multiply(least_upper_bound(identity, a), a), multiply(inverse(a), a))
% 0.19/0.41 = { by axiom 3 (p05a_1) }
% 0.19/0.41 greatest_lower_bound(multiply(identity, a), multiply(inverse(a), a))
% 0.19/0.41 = { by axiom 4 (left_identity) }
% 0.19/0.41 greatest_lower_bound(a, multiply(inverse(a), a))
% 0.19/0.41 = { by lemma 10 }
% 0.19/0.41 greatest_lower_bound(a, least_upper_bound(identity, inverse(a)))
% 0.19/0.41 = { by lemma 9 }
% 0.19/0.41 greatest_lower_bound(a, least_upper_bound(identity, a))
% 0.19/0.41 = { by axiom 2 (symmetry_of_lub) }
% 0.19/0.41 greatest_lower_bound(a, least_upper_bound(a, identity))
% 0.19/0.41 = { by axiom 7 (glb_absorbtion) }
% 0.19/0.41 a
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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