TSTP Solution File: GRP193-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP193-1 : 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 : n031.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 01:17:43 EDT 2023
% Result : Unsatisfiable 0.21s 0.41s
% 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
% 0.12/0.13 % Problem : GRP193-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 20:25:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.41 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.41
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.21/0.42 Axiom 2 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.21/0.42 Axiom 3 (p8_9a_4): greatest_lower_bound(a, b) = identity.
% 0.21/0.42 Axiom 4 (p8_9a_2): least_upper_bound(identity, b) = b.
% 0.21/0.42 Axiom 5 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.21/0.42 Axiom 6 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.21/0.42 Axiom 7 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.21/0.42 Axiom 8 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.42 Axiom 9 (p8_9a_5): least_upper_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c))) = multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c)).
% 0.21/0.42
% 0.21/0.42 Goal 1 (prove_p8_9a): greatest_lower_bound(a, multiply(b, c)) = greatest_lower_bound(a, c).
% 0.21/0.42 Proof:
% 0.21/0.42 greatest_lower_bound(a, multiply(b, c))
% 0.21/0.42 = { by axiom 7 (lub_absorbtion) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), c))
% 0.21/0.42 = { by axiom 6 (associativity_of_glb) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, greatest_lower_bound(multiply(b, c), c)))
% 0.21/0.42 = { by axiom 1 (left_identity) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, greatest_lower_bound(multiply(b, c), multiply(identity, c))))
% 0.21/0.42 = { by axiom 8 (monotony_glb2) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, multiply(greatest_lower_bound(b, identity), c)))
% 0.21/0.42 = { by axiom 2 (symmetry_of_glb) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, multiply(greatest_lower_bound(identity, b), c)))
% 0.21/0.42 = { by axiom 4 (p8_9a_2) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, multiply(greatest_lower_bound(identity, least_upper_bound(identity, b)), c)))
% 0.21/0.42 = { by axiom 5 (glb_absorbtion) }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, multiply(identity, c)))
% 0.21/0.42 = { by axiom 1 (left_identity) }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, c))
% 0.21/0.42 = { by axiom 1 (left_identity) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), multiply(identity, greatest_lower_bound(a, c)))
% 0.21/0.42 = { by axiom 3 (p8_9a_4) R->L }
% 0.21/0.42 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c)))
% 0.21/0.42 = { by axiom 9 (p8_9a_5) }
% 0.21/0.42 multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c))
% 0.21/0.42 = { by axiom 3 (p8_9a_4) }
% 0.21/0.42 multiply(identity, greatest_lower_bound(a, c))
% 0.21/0.42 = { by axiom 1 (left_identity) }
% 0.21/0.42 greatest_lower_bound(a, c)
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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