TSTP Solution File: GRP184-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP184-2 : 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 : n019.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 01:17:38 EDT 2023
% Result : Unsatisfiable 0.20s 0.49s
% 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 : GRP184-2 : 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
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:38:43 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.49 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.49
% 0.20/0.49 % SZS status Unsatisfiable
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% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 Axiom 1 (p21_1): inverse(identity) = identity.
% 0.20/0.49 Axiom 2 (p21_2): inverse(inverse(X)) = X.
% 0.20/0.49 Axiom 3 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.49 Axiom 4 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.20/0.49 Axiom 5 (left_identity): multiply(identity, X) = X.
% 0.20/0.49 Axiom 6 (left_inverse): multiply(inverse(X), X) = identity.
% 0.20/0.49 Axiom 7 (p21_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 0.20/0.49 Axiom 8 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.49 Axiom 9 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.49 Axiom 10 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.49 Axiom 11 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.49
% 0.20/0.49 Lemma 12: multiply(X, identity) = X.
% 0.20/0.49 Proof:
% 0.20/0.49 multiply(X, identity)
% 0.20/0.49 = { by axiom 2 (p21_2) R->L }
% 0.20/0.49 inverse(inverse(multiply(X, identity)))
% 0.20/0.49 = { by axiom 7 (p21_3) }
% 0.20/0.49 inverse(multiply(inverse(identity), inverse(X)))
% 0.20/0.49 = { by axiom 1 (p21_1) }
% 0.20/0.49 inverse(multiply(identity, inverse(X)))
% 0.20/0.49 = { by axiom 5 (left_identity) }
% 0.20/0.49 inverse(inverse(X))
% 0.20/0.49 = { by axiom 2 (p21_2) }
% 0.20/0.49 X
% 0.20/0.49
% 0.20/0.49 Goal 1 (prove_p21): multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity))) = multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity)).
% 0.20/0.49 Proof:
% 0.20/0.49 multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))
% 0.20/0.49 = { by axiom 3 (symmetry_of_lub) R->L }
% 0.20/0.49 multiply(least_upper_bound(identity, a), inverse(greatest_lower_bound(a, identity)))
% 0.20/0.49 = { by axiom 9 (monotony_lub2) }
% 0.20/0.49 least_upper_bound(multiply(identity, inverse(greatest_lower_bound(a, identity))), multiply(a, inverse(greatest_lower_bound(a, identity))))
% 0.20/0.49 = { by axiom 5 (left_identity) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), multiply(a, inverse(greatest_lower_bound(a, identity))))
% 0.20/0.49 = { by axiom 2 (p21_2) R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(inverse(multiply(a, inverse(greatest_lower_bound(a, identity))))))
% 0.20/0.49 = { by axiom 7 (p21_3) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(multiply(inverse(inverse(greatest_lower_bound(a, identity))), inverse(a))))
% 0.20/0.49 = { by axiom 2 (p21_2) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(multiply(greatest_lower_bound(a, identity), inverse(a))))
% 0.20/0.49 = { by axiom 4 (symmetry_of_glb) R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(multiply(greatest_lower_bound(identity, a), inverse(a))))
% 0.20/0.49 = { by axiom 11 (monotony_glb2) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(greatest_lower_bound(multiply(identity, inverse(a)), multiply(a, inverse(a)))))
% 0.20/0.49 = { by axiom 5 (left_identity) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(greatest_lower_bound(inverse(a), multiply(a, inverse(a)))))
% 0.20/0.49 = { by axiom 2 (p21_2) R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(greatest_lower_bound(inverse(a), multiply(inverse(inverse(a)), inverse(a)))))
% 0.20/0.49 = { by axiom 6 (left_inverse) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(greatest_lower_bound(inverse(a), identity)))
% 0.20/0.49 = { by axiom 4 (symmetry_of_glb) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(greatest_lower_bound(identity, inverse(a))))
% 0.20/0.49 = { by lemma 12 R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(greatest_lower_bound(identity, multiply(inverse(a), identity))))
% 0.20/0.49 = { by axiom 6 (left_inverse) R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(greatest_lower_bound(multiply(inverse(a), a), multiply(inverse(a), identity))))
% 0.20/0.49 = { by axiom 10 (monotony_glb1) R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(multiply(inverse(a), greatest_lower_bound(a, identity))))
% 0.20/0.49 = { by axiom 2 (p21_2) R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(multiply(inverse(a), inverse(inverse(greatest_lower_bound(a, identity))))))
% 0.20/0.49 = { by axiom 7 (p21_3) R->L }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), inverse(inverse(multiply(inverse(greatest_lower_bound(a, identity)), a))))
% 0.20/0.49 = { by axiom 2 (p21_2) }
% 0.20/0.49 least_upper_bound(inverse(greatest_lower_bound(a, identity)), multiply(inverse(greatest_lower_bound(a, identity)), a))
% 0.20/0.49 = { by lemma 12 R->L }
% 0.20/0.49 least_upper_bound(multiply(inverse(greatest_lower_bound(a, identity)), identity), multiply(inverse(greatest_lower_bound(a, identity)), a))
% 0.20/0.49 = { by axiom 8 (monotony_lub1) R->L }
% 0.20/0.49 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(identity, a))
% 0.20/0.49 = { by axiom 3 (symmetry_of_lub) }
% 0.20/0.49 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49
% 0.20/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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