TSTP Solution File: GRP166-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP166-1 : 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 : n029.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 01:17:26 EDT 2023
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP166-1 : 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 : n029.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 : Tue Aug 29 01:37:26 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.41 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.14/0.41 % SZS status Unsatisfiable
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% 0.14/0.42 % SZS output start Proof
% 0.14/0.42 Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.14/0.42 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.14/0.42 Axiom 3 (lat2a_2): least_upper_bound(b, identity) = b.
% 0.14/0.42 Axiom 4 (left_identity): multiply(identity, X) = X.
% 0.14/0.42 Axiom 5 (left_inverse): multiply(inverse(X), X) = identity.
% 0.14/0.42 Axiom 6 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.14/0.42 Axiom 7 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.14/0.42 Axiom 8 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.14/0.42 Axiom 9 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.14/0.42
% 0.14/0.42 Lemma 10: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.14/0.42 Proof:
% 0.14/0.42 multiply(inverse(X), multiply(X, Y))
% 0.14/0.42 = { by axiom 8 (associativity) R->L }
% 0.14/0.42 multiply(multiply(inverse(X), X), Y)
% 0.14/0.42 = { by axiom 5 (left_inverse) }
% 0.14/0.42 multiply(identity, Y)
% 0.14/0.42 = { by axiom 4 (left_identity) }
% 0.14/0.42 Y
% 0.14/0.42
% 0.14/0.42 Lemma 11: multiply(X, identity) = X.
% 0.14/0.42 Proof:
% 0.14/0.42 multiply(X, identity)
% 0.14/0.42 = { by lemma 10 R->L }
% 0.14/0.42 multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, identity)))
% 0.14/0.42 = { by lemma 10 }
% 0.14/0.42 multiply(inverse(inverse(X)), identity)
% 0.14/0.42 = { by axiom 5 (left_inverse) R->L }
% 0.14/0.42 multiply(inverse(inverse(X)), multiply(inverse(X), X))
% 0.14/0.42 = { by lemma 10 }
% 0.14/0.42 X
% 0.14/0.42
% 0.14/0.42 Goal 1 (prove_lat2a): least_upper_bound(a, multiply(a, b)) = multiply(a, b).
% 0.14/0.42 Proof:
% 0.14/0.42 least_upper_bound(a, multiply(a, b))
% 0.14/0.42 = { by axiom 2 (symmetry_of_lub) }
% 0.14/0.42 least_upper_bound(multiply(a, b), a)
% 0.14/0.42 = { by lemma 11 R->L }
% 0.14/0.42 least_upper_bound(multiply(a, b), multiply(a, identity))
% 0.14/0.42 = { by axiom 6 (glb_absorbtion) R->L }
% 0.14/0.42 least_upper_bound(multiply(a, b), multiply(a, greatest_lower_bound(identity, least_upper_bound(identity, b))))
% 0.14/0.42 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.14/0.42 least_upper_bound(multiply(a, b), multiply(a, greatest_lower_bound(identity, least_upper_bound(b, identity))))
% 0.14/0.42 = { by axiom 3 (lat2a_2) }
% 0.14/0.42 least_upper_bound(multiply(a, b), multiply(a, greatest_lower_bound(identity, b)))
% 0.14/0.42 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.14/0.42 least_upper_bound(multiply(a, b), multiply(a, greatest_lower_bound(b, identity)))
% 0.14/0.42 = { by axiom 9 (monotony_glb1) }
% 0.14/0.42 least_upper_bound(multiply(a, b), greatest_lower_bound(multiply(a, b), multiply(a, identity)))
% 0.14/0.42 = { by lemma 11 }
% 0.14/0.42 least_upper_bound(multiply(a, b), greatest_lower_bound(multiply(a, b), a))
% 0.14/0.42 = { by axiom 7 (lub_absorbtion) }
% 0.14/0.42 multiply(a, b)
% 0.14/0.42 % SZS output end Proof
% 0.14/0.42
% 0.14/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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