TSTP Solution File: GRP171-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP171-2 : 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 : n021.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 01:17:30 EDT 2023
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP171-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 20:31:13 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.42 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.42
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.21/0.43 Axiom 2 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.21/0.43 Axiom 3 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.21/0.43 Axiom 4 (p04c_1): least_upper_bound(identity, a) = a.
% 0.21/0.43 Axiom 5 (p04c_2): least_upper_bound(identity, b) = b.
% 0.21/0.43 Axiom 6 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.21/0.43 Axiom 7 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.21/0.43 Axiom 8 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.21/0.43 Axiom 9 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.43
% 0.21/0.43 Goal 1 (prove_p04c): greatest_lower_bound(identity, multiply(a, b)) = identity.
% 0.21/0.43 Proof:
% 0.21/0.43 greatest_lower_bound(identity, multiply(a, b))
% 0.21/0.43 = { by axiom 8 (lub_absorbtion) R->L }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(greatest_lower_bound(identity, multiply(a, b)), b))
% 0.21/0.43 = { by axiom 7 (associativity_of_glb) R->L }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, greatest_lower_bound(multiply(a, b), b)))
% 0.21/0.43 = { by axiom 2 (symmetry_of_glb) }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, greatest_lower_bound(b, multiply(a, b))))
% 0.21/0.43 = { by axiom 1 (left_identity) R->L }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, greatest_lower_bound(multiply(identity, b), multiply(a, b))))
% 0.21/0.43 = { by axiom 9 (monotony_glb2) R->L }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, a), b)))
% 0.21/0.43 = { by axiom 4 (p04c_1) R->L }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, least_upper_bound(identity, a)), b)))
% 0.21/0.43 = { by axiom 6 (glb_absorbtion) }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, multiply(identity, b)))
% 0.21/0.43 = { by axiom 1 (left_identity) }
% 0.21/0.43 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, b))
% 0.21/0.43 = { by axiom 5 (p04c_2) R->L }
% 0.21/0.44 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, least_upper_bound(identity, b)))
% 0.21/0.44 = { by axiom 6 (glb_absorbtion) }
% 0.21/0.44 least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), identity)
% 0.21/0.44 = { by axiom 3 (symmetry_of_lub) }
% 0.21/0.44 least_upper_bound(identity, greatest_lower_bound(identity, multiply(a, b)))
% 0.21/0.44 = { by axiom 8 (lub_absorbtion) }
% 0.21/0.44 identity
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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