TSTP Solution File: GRP170-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP170-1 : 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 : n009.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 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP170-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.04/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:26:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.46 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable
% 0.18/0.46
% 0.18/0.46 % SZS output start Proof
% 0.18/0.46 Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.18/0.46 Axiom 2 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.18/0.46 Axiom 3 (p03a_1): least_upper_bound(a, b) = b.
% 0.18/0.46 Axiom 4 (p03a_2): least_upper_bound(c, d) = d.
% 0.18/0.46 Axiom 5 (glb_absorbtion): greatest_lower_bound(X, least_upper_bound(X, Y)) = X.
% 0.18/0.46 Axiom 6 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.18/0.46 Axiom 7 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.18/0.46 Axiom 8 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.18/0.46 Axiom 9 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.18/0.46
% 0.18/0.46 Goal 1 (prove_p03a): least_upper_bound(multiply(a, c), multiply(b, d)) = multiply(b, d).
% 0.18/0.46 Proof:
% 0.18/0.46 least_upper_bound(multiply(a, c), multiply(b, d))
% 0.18/0.46 = { by axiom 2 (symmetry_of_lub) R->L }
% 0.18/0.46 least_upper_bound(multiply(b, d), multiply(a, c))
% 0.18/0.46 = { by axiom 5 (glb_absorbtion) R->L }
% 0.18/0.46 least_upper_bound(multiply(b, d), multiply(greatest_lower_bound(a, least_upper_bound(a, b)), c))
% 0.18/0.46 = { by axiom 3 (p03a_1) }
% 0.18/0.46 least_upper_bound(multiply(b, d), multiply(greatest_lower_bound(a, b), c))
% 0.18/0.46 = { by axiom 9 (monotony_glb2) }
% 0.18/0.46 least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, c)))
% 0.18/0.46 = { by axiom 5 (glb_absorbtion) R->L }
% 0.18/0.46 least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, greatest_lower_bound(c, least_upper_bound(c, d)))))
% 0.18/0.47 = { by axiom 4 (p03a_2) }
% 0.18/0.47 least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, greatest_lower_bound(c, d))))
% 0.18/0.47 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.18/0.47 least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, greatest_lower_bound(d, c))))
% 0.18/0.47 = { by axiom 8 (monotony_glb1) }
% 0.18/0.47 least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), greatest_lower_bound(multiply(b, d), multiply(b, c))))
% 0.18/0.47 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.18/0.47 least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), greatest_lower_bound(multiply(b, c), multiply(b, d))))
% 0.18/0.47 = { by axiom 6 (associativity_of_glb) }
% 0.18/0.47 least_upper_bound(multiply(b, d), greatest_lower_bound(greatest_lower_bound(multiply(a, c), multiply(b, c)), multiply(b, d)))
% 0.18/0.47 = { by axiom 1 (symmetry_of_glb) R->L }
% 0.18/0.47 least_upper_bound(multiply(b, d), greatest_lower_bound(multiply(b, d), greatest_lower_bound(multiply(a, c), multiply(b, c))))
% 0.18/0.47 = { by axiom 7 (lub_absorbtion) }
% 0.18/0.47 multiply(b, d)
% 0.18/0.47 % SZS output end Proof
% 0.18/0.47
% 0.18/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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