TSTP Solution File: GRP193-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP193-2 : 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 : 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 01:17:44 EDT 2023
% Result : Unsatisfiable 0.20s 0.43s
% 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
% 0.07/0.13 % Problem : GRP193-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.14 % 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 : n005.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 : Tue Aug 29 01:37:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.20/0.43 Axiom 2 (p8_9b_4): greatest_lower_bound(a, b) = identity.
% 0.20/0.43 Axiom 3 (p8_9b_2): greatest_lower_bound(identity, b) = identity.
% 0.20/0.43 Axiom 4 (left_identity): multiply(identity, X) = X.
% 0.20/0.43 Axiom 5 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.20/0.43 Axiom 6 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.20/0.43 Axiom 7 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.20/0.43 Axiom 8 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.20/0.43 Axiom 9 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.43 Axiom 10 (p8_9b_5): greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c))) = greatest_lower_bound(a, multiply(b, c)).
% 0.20/0.43
% 0.20/0.43 Lemma 11: greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(Y, greatest_lower_bound(X, Z)).
% 0.20/0.43 Proof:
% 0.20/0.43 greatest_lower_bound(X, greatest_lower_bound(Y, Z))
% 0.20/0.43 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.20/0.43 greatest_lower_bound(greatest_lower_bound(Y, Z), X)
% 0.20/0.43 = { by axiom 7 (associativity_of_glb) R->L }
% 0.20/0.43 greatest_lower_bound(Y, greatest_lower_bound(Z, X))
% 0.20/0.43 = { by axiom 1 (symmetry_of_glb) }
% 0.20/0.43 greatest_lower_bound(Y, greatest_lower_bound(X, Z))
% 0.20/0.43
% 0.20/0.43 Lemma 12: least_upper_bound(X, greatest_lower_bound(Y, X)) = X.
% 0.20/0.43 Proof:
% 0.20/0.43 least_upper_bound(X, greatest_lower_bound(Y, X))
% 0.20/0.43 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.20/0.43 least_upper_bound(X, greatest_lower_bound(X, Y))
% 0.20/0.43 = { by axiom 8 (lub_absorbtion) }
% 0.20/0.43 X
% 0.20/0.43
% 0.20/0.44 Goal 1 (prove_p8_9b): greatest_lower_bound(a, multiply(b, c)) = greatest_lower_bound(a, c).
% 0.20/0.44 Proof:
% 0.20/0.44 greatest_lower_bound(a, multiply(b, c))
% 0.20/0.44 = { by lemma 12 R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(c, greatest_lower_bound(a, multiply(b, c))))
% 0.20/0.44 = { by lemma 11 R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, greatest_lower_bound(c, multiply(b, c))))
% 0.20/0.44 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, greatest_lower_bound(multiply(b, c), c)))
% 0.20/0.44 = { by axiom 4 (left_identity) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, greatest_lower_bound(multiply(b, c), multiply(identity, c))))
% 0.20/0.44 = { by axiom 9 (monotony_glb2) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, multiply(greatest_lower_bound(b, identity), c)))
% 0.20/0.44 = { by axiom 1 (symmetry_of_glb) }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, multiply(greatest_lower_bound(identity, b), c)))
% 0.20/0.44 = { by axiom 3 (p8_9b_2) }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, multiply(identity, c)))
% 0.20/0.44 = { by axiom 4 (left_identity) }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, multiply(b, c)), greatest_lower_bound(a, c))
% 0.20/0.44 = { by axiom 5 (symmetry_of_lub) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(a, multiply(b, c)))
% 0.20/0.44 = { by axiom 10 (p8_9b_5) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(greatest_lower_bound(a, multiply(b, c)), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c))))
% 0.20/0.44 = { by axiom 7 (associativity_of_glb) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(a, greatest_lower_bound(multiply(b, c), multiply(greatest_lower_bound(a, b), greatest_lower_bound(a, c)))))
% 0.20/0.44 = { by axiom 2 (p8_9b_4) }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(a, greatest_lower_bound(multiply(b, c), multiply(identity, greatest_lower_bound(a, c)))))
% 0.20/0.44 = { by axiom 4 (left_identity) }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(a, greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, c))))
% 0.20/0.44 = { by lemma 11 }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, greatest_lower_bound(a, c))))
% 0.20/0.44 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(multiply(b, c), greatest_lower_bound(greatest_lower_bound(a, c), a)))
% 0.20/0.44 = { by axiom 8 (lub_absorbtion) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(multiply(b, c), greatest_lower_bound(greatest_lower_bound(a, c), least_upper_bound(a, greatest_lower_bound(a, c)))))
% 0.20/0.44 = { by axiom 5 (symmetry_of_lub) R->L }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(multiply(b, c), greatest_lower_bound(greatest_lower_bound(a, c), least_upper_bound(greatest_lower_bound(a, c), a))))
% 0.20/0.44 = { by axiom 6 (glb_absorbtion) }
% 0.20/0.44 least_upper_bound(greatest_lower_bound(a, c), greatest_lower_bound(multiply(b, c), greatest_lower_bound(a, c)))
% 0.20/0.44 = { by lemma 12 }
% 0.20/0.44 greatest_lower_bound(a, c)
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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