TSTP Solution File: GRP184-4 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP184-4 : 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 : n005.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 01:17:39 EDT 2023
% Result : Unsatisfiable 0.20s 0.46s
% 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
% 0.10/0.12 % Problem : GRP184-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.10/0.13 % 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 : n005.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 20:55:38 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.46 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.20/0.46 % SZS status Unsatisfiable
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% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 Axiom 1 (p21x_1): inverse(identity) = identity.
% 0.20/0.46 Axiom 2 (p21x_2): inverse(inverse(X)) = X.
% 0.20/0.46 Axiom 3 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.46 Axiom 4 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.20/0.46 Axiom 5 (left_identity): multiply(identity, X) = X.
% 0.20/0.46 Axiom 6 (left_inverse): multiply(inverse(X), X) = identity.
% 0.20/0.46 Axiom 7 (p21x_4): inverse(greatest_lower_bound(X, Y)) = least_upper_bound(inverse(X), inverse(Y)).
% 0.20/0.46 Axiom 8 (p21x_5): inverse(least_upper_bound(X, Y)) = greatest_lower_bound(inverse(X), inverse(Y)).
% 0.20/0.46 Axiom 9 (p21x_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 0.20/0.46 Axiom 10 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.20/0.46 Axiom 11 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.46 Axiom 12 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.46
% 0.20/0.46 Lemma 13: multiply(least_upper_bound(X, identity), Y) = least_upper_bound(Y, multiply(X, Y)).
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(least_upper_bound(X, identity), Y)
% 0.20/0.46 = { by axiom 3 (symmetry_of_lub) R->L }
% 0.20/0.46 multiply(least_upper_bound(identity, X), Y)
% 0.20/0.46 = { by axiom 11 (monotony_lub2) }
% 0.20/0.46 least_upper_bound(multiply(identity, Y), multiply(X, Y))
% 0.20/0.46 = { by axiom 5 (left_identity) }
% 0.20/0.46 least_upper_bound(Y, multiply(X, Y))
% 0.20/0.46
% 0.20/0.46 Lemma 14: multiply(X, inverse(greatest_lower_bound(X, identity))) = least_upper_bound(X, identity).
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(X, inverse(greatest_lower_bound(X, identity)))
% 0.20/0.46 = { by axiom 2 (p21x_2) R->L }
% 0.20/0.46 inverse(inverse(multiply(X, inverse(greatest_lower_bound(X, identity)))))
% 0.20/0.46 = { by axiom 9 (p21x_3) }
% 0.20/0.46 inverse(multiply(inverse(inverse(greatest_lower_bound(X, identity))), inverse(X)))
% 0.20/0.46 = { by axiom 2 (p21x_2) }
% 0.20/0.46 inverse(multiply(greatest_lower_bound(X, identity), inverse(X)))
% 0.20/0.46 = { by axiom 4 (symmetry_of_glb) R->L }
% 0.20/0.46 inverse(multiply(greatest_lower_bound(identity, X), inverse(X)))
% 0.20/0.46 = { by axiom 12 (monotony_glb2) }
% 0.20/0.46 inverse(greatest_lower_bound(multiply(identity, inverse(X)), multiply(X, inverse(X))))
% 0.20/0.46 = { by axiom 5 (left_identity) }
% 0.20/0.46 inverse(greatest_lower_bound(inverse(X), multiply(X, inverse(X))))
% 0.20/0.46 = { by axiom 2 (p21x_2) R->L }
% 0.20/0.46 inverse(greatest_lower_bound(inverse(X), multiply(inverse(inverse(X)), inverse(X))))
% 0.20/0.46 = { by axiom 6 (left_inverse) }
% 0.20/0.46 inverse(greatest_lower_bound(inverse(X), identity))
% 0.20/0.46 = { by axiom 4 (symmetry_of_glb) }
% 0.20/0.46 inverse(greatest_lower_bound(identity, inverse(X)))
% 0.20/0.46 = { by axiom 1 (p21x_1) R->L }
% 0.20/0.46 inverse(greatest_lower_bound(inverse(identity), inverse(X)))
% 0.20/0.46 = { by axiom 8 (p21x_5) R->L }
% 0.20/0.46 inverse(inverse(least_upper_bound(identity, X)))
% 0.20/0.46 = { by axiom 3 (symmetry_of_lub) }
% 0.20/0.46 inverse(inverse(least_upper_bound(X, identity)))
% 0.20/0.46 = { by axiom 2 (p21x_2) }
% 0.20/0.46 least_upper_bound(X, identity)
% 0.20/0.46
% 0.20/0.46 Goal 1 (prove_p21x): multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity))) = multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity)).
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))
% 0.20/0.46 = { by lemma 13 }
% 0.20/0.46 least_upper_bound(inverse(greatest_lower_bound(a, identity)), multiply(a, inverse(greatest_lower_bound(a, identity))))
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 least_upper_bound(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))
% 0.20/0.46 = { by axiom 3 (symmetry_of_lub) R->L }
% 0.20/0.46 least_upper_bound(least_upper_bound(a, identity), inverse(greatest_lower_bound(a, identity)))
% 0.20/0.46 = { by axiom 5 (left_identity) R->L }
% 0.20/0.46 least_upper_bound(least_upper_bound(a, identity), multiply(identity, inverse(greatest_lower_bound(a, identity))))
% 0.20/0.46 = { by axiom 6 (left_inverse) R->L }
% 0.20/0.46 least_upper_bound(least_upper_bound(a, identity), multiply(multiply(inverse(a), a), inverse(greatest_lower_bound(a, identity))))
% 0.20/0.46 = { by axiom 10 (associativity) }
% 0.20/0.46 least_upper_bound(least_upper_bound(a, identity), multiply(inverse(a), multiply(a, inverse(greatest_lower_bound(a, identity)))))
% 0.20/0.46 = { by lemma 14 }
% 0.20/0.46 least_upper_bound(least_upper_bound(a, identity), multiply(inverse(a), least_upper_bound(a, identity)))
% 0.20/0.46 = { by lemma 13 R->L }
% 0.20/0.46 multiply(least_upper_bound(inverse(a), identity), least_upper_bound(a, identity))
% 0.20/0.46 = { by axiom 3 (symmetry_of_lub) }
% 0.20/0.46 multiply(least_upper_bound(identity, inverse(a)), least_upper_bound(a, identity))
% 0.20/0.46 = { by axiom 1 (p21x_1) R->L }
% 0.20/0.46 multiply(least_upper_bound(inverse(identity), inverse(a)), least_upper_bound(a, identity))
% 0.20/0.46 = { by axiom 7 (p21x_4) R->L }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(identity, a)), least_upper_bound(a, identity))
% 0.20/0.46 = { by axiom 4 (symmetry_of_glb) }
% 0.20/0.46 multiply(inverse(greatest_lower_bound(a, identity)), least_upper_bound(a, identity))
% 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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