TSTP Solution File: GRP170-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP170-2 : 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 : n012.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 01:17:29 EDT 2023
% Result : Unsatisfiable 0.22s 0.45s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : GRP170-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n012.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 23:51:54 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.45 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.22/0.45
% 0.22/0.45 % SZS status Unsatisfiable
% 0.22/0.45
% 0.22/0.45 % SZS output start Proof
% 0.22/0.45 Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.22/0.45 Axiom 2 (p03b_1): greatest_lower_bound(a, b) = a.
% 0.22/0.45 Axiom 3 (p03b_2): greatest_lower_bound(c, d) = c.
% 0.22/0.45 Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.22/0.45 Axiom 5 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.22/0.45 Axiom 6 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.22/0.46 Axiom 7 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.22/0.46 Axiom 8 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.22/0.46 Axiom 9 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.22/0.46
% 0.22/0.46 Lemma 10: greatest_lower_bound(X, greatest_lower_bound(X, Y)) = greatest_lower_bound(X, Y).
% 0.22/0.46 Proof:
% 0.22/0.46 greatest_lower_bound(X, greatest_lower_bound(X, Y))
% 0.22/0.46 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.22/0.46 greatest_lower_bound(greatest_lower_bound(X, Y), X)
% 0.22/0.46 = { by axiom 7 (lub_absorbtion) R->L }
% 0.22/0.46 greatest_lower_bound(greatest_lower_bound(X, Y), least_upper_bound(X, greatest_lower_bound(X, Y)))
% 0.22/0.46 = { by axiom 4 (symmetry_of_lub) R->L }
% 0.22/0.46 greatest_lower_bound(greatest_lower_bound(X, Y), least_upper_bound(greatest_lower_bound(X, Y), X))
% 0.22/0.46 = { by axiom 5 (glb_absorbtion) }
% 0.22/0.46 greatest_lower_bound(X, Y)
% 0.22/0.46
% 0.22/0.46 Lemma 11: greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, d)), multiply(b, c)) = multiply(a, c).
% 0.22/0.46 Proof:
% 0.22/0.46 greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, d)), multiply(b, c))
% 0.22/0.46 = { by axiom 6 (associativity_of_glb) R->L }
% 0.22/0.46 greatest_lower_bound(multiply(a, c), greatest_lower_bound(multiply(b, d), multiply(b, c)))
% 0.22/0.46 = { by axiom 8 (monotony_glb1) R->L }
% 0.22/0.46 greatest_lower_bound(multiply(a, c), multiply(b, greatest_lower_bound(d, c)))
% 0.22/0.46 = { by axiom 1 (symmetry_of_glb) }
% 0.22/0.46 greatest_lower_bound(multiply(a, c), multiply(b, greatest_lower_bound(c, d)))
% 0.22/0.46 = { by axiom 3 (p03b_2) }
% 0.22/0.46 greatest_lower_bound(multiply(a, c), multiply(b, c))
% 0.22/0.46 = { by axiom 9 (monotony_glb2) R->L }
% 0.22/0.46 multiply(greatest_lower_bound(a, b), c)
% 0.22/0.46 = { by axiom 2 (p03b_1) }
% 0.22/0.46 multiply(a, c)
% 0.22/0.46
% 0.22/0.46 Goal 1 (prove_p03b): greatest_lower_bound(multiply(a, c), multiply(b, d)) = multiply(a, c).
% 0.22/0.46 Proof:
% 0.22/0.46 greatest_lower_bound(multiply(a, c), multiply(b, d))
% 0.22/0.46 = { by lemma 10 R->L }
% 0.22/0.46 greatest_lower_bound(multiply(a, c), greatest_lower_bound(multiply(a, c), multiply(b, d)))
% 0.22/0.46 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.22/0.46 greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, d)), multiply(a, c))
% 0.22/0.46 = { by lemma 11 R->L }
% 0.22/0.46 greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, d)), greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, d)), multiply(b, c)))
% 0.22/0.46 = { by lemma 10 }
% 0.22/0.46 greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, d)), multiply(b, c))
% 0.22/0.46 = { by lemma 11 }
% 0.22/0.46 multiply(a, c)
% 0.22/0.46 % SZS output end Proof
% 0.22/0.46
% 0.22/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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