TSTP Solution File: GRP181-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP181-3 : 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 01:17:35 EDT 2023
% Result : Unsatisfiable 2.64s 0.68s
% Output : Proof 2.64s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP181-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.03/0.13 % 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 : Mon Aug 28 23:24:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.64/0.68 Command-line arguments: --flatten
% 2.64/0.68
% 2.64/0.68 % SZS status Unsatisfiable
% 2.64/0.68
% 2.64/0.68 % SZS output start Proof
% 2.64/0.68 Axiom 1 (left_identity): multiply(identity, X) = X.
% 2.64/0.68 Axiom 2 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 2.64/0.68 Axiom 3 (p12x_1): greatest_lower_bound(a, c) = greatest_lower_bound(b, c).
% 2.64/0.68 Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 2.64/0.68 Axiom 5 (p12x_2): least_upper_bound(a, c) = least_upper_bound(b, c).
% 2.64/0.68 Axiom 6 (left_inverse): multiply(inverse(X), X) = identity.
% 2.64/0.68 Axiom 7 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 2.64/0.68 Axiom 8 (p12x_4): inverse(least_upper_bound(X, Y)) = greatest_lower_bound(inverse(X), inverse(Y)).
% 2.64/0.68 Axiom 9 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 2.64/0.68 Axiom 10 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 2.64/0.68
% 2.64/0.68 Lemma 11: multiply(inverse(X), multiply(X, Y)) = Y.
% 2.64/0.68 Proof:
% 2.64/0.68 multiply(inverse(X), multiply(X, Y))
% 2.64/0.68 = { by axiom 7 (associativity) R->L }
% 2.64/0.68 multiply(multiply(inverse(X), X), Y)
% 2.64/0.68 = { by axiom 6 (left_inverse) }
% 2.64/0.68 multiply(identity, Y)
% 2.64/0.68 = { by axiom 1 (left_identity) }
% 2.64/0.68 Y
% 2.64/0.68
% 2.64/0.68 Lemma 12: multiply(inverse(least_upper_bound(Y, X)), Y) = multiply(inverse(X), greatest_lower_bound(Y, X)).
% 2.64/0.68 Proof:
% 2.64/0.68 multiply(inverse(least_upper_bound(Y, X)), Y)
% 2.64/0.68 = { by axiom 4 (symmetry_of_lub) R->L }
% 2.64/0.68 multiply(inverse(least_upper_bound(X, Y)), Y)
% 2.64/0.68 = { by axiom 8 (p12x_4) }
% 2.64/0.68 multiply(greatest_lower_bound(inverse(X), inverse(Y)), Y)
% 2.64/0.68 = { by axiom 2 (symmetry_of_glb) R->L }
% 2.64/0.68 multiply(greatest_lower_bound(inverse(Y), inverse(X)), Y)
% 2.64/0.68 = { by axiom 10 (monotony_glb2) }
% 2.64/0.68 greatest_lower_bound(multiply(inverse(Y), Y), multiply(inverse(X), Y))
% 2.64/0.68 = { by axiom 6 (left_inverse) }
% 2.64/0.68 greatest_lower_bound(identity, multiply(inverse(X), Y))
% 2.64/0.68 = { by axiom 6 (left_inverse) R->L }
% 2.64/0.68 greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(X), Y))
% 2.64/0.68 = { by axiom 9 (monotony_glb1) R->L }
% 2.64/0.68 multiply(inverse(X), greatest_lower_bound(X, Y))
% 2.64/0.68 = { by axiom 2 (symmetry_of_glb) }
% 2.64/0.68 multiply(inverse(X), greatest_lower_bound(Y, X))
% 2.64/0.68
% 2.64/0.68 Goal 1 (prove_p12x): a = b.
% 2.64/0.68 Proof:
% 2.64/0.68 a
% 2.64/0.68 = { by lemma 11 R->L }
% 2.64/0.68 multiply(inverse(inverse(least_upper_bound(a, c))), multiply(inverse(least_upper_bound(a, c)), a))
% 2.64/0.68 = { by lemma 12 }
% 2.64/0.68 multiply(inverse(inverse(least_upper_bound(a, c))), multiply(inverse(c), greatest_lower_bound(a, c)))
% 2.64/0.68 = { by axiom 3 (p12x_1) }
% 2.64/0.68 multiply(inverse(inverse(least_upper_bound(a, c))), multiply(inverse(c), greatest_lower_bound(b, c)))
% 2.64/0.68 = { by lemma 12 R->L }
% 2.64/0.68 multiply(inverse(inverse(least_upper_bound(a, c))), multiply(inverse(least_upper_bound(b, c)), b))
% 2.64/0.68 = { by axiom 5 (p12x_2) R->L }
% 2.64/0.68 multiply(inverse(inverse(least_upper_bound(a, c))), multiply(inverse(least_upper_bound(a, c)), b))
% 2.64/0.68 = { by lemma 11 }
% 2.64/0.68 b
% 2.64/0.68 % SZS output end Proof
% 2.64/0.68
% 2.64/0.68 RESULT: Unsatisfiable (the axioms are contradictory).
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