TSTP Solution File: GRP181-4 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP181-4 : 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 01:17:36 EDT 2023
% Result : Unsatisfiable 0.23s 0.61s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP181-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36 % Computer : n012.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Aug 28 20:25:39 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.23/0.61 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.23/0.61
% 0.23/0.61 % SZS status Unsatisfiable
% 0.23/0.61
% 0.23/0.62 % SZS output start Proof
% 0.23/0.62 Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.23/0.62 Axiom 2 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.23/0.62 Axiom 3 (p12x_4): greatest_lower_bound(a, c) = greatest_lower_bound(b, c).
% 0.23/0.62 Axiom 4 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.23/0.62 Axiom 5 (p12x_5): least_upper_bound(a, c) = least_upper_bound(b, c).
% 0.23/0.62 Axiom 6 (p12x_2): inverse(inverse(X)) = X.
% 0.23/0.62 Axiom 7 (left_inverse): multiply(inverse(X), X) = identity.
% 0.23/0.62 Axiom 8 (p12x_3): inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 0.23/0.62 Axiom 9 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.23/0.62 Axiom 10 (p12x_7): inverse(least_upper_bound(X, Y)) = greatest_lower_bound(inverse(X), inverse(Y)).
% 0.23/0.62 Axiom 11 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.23/0.62 Axiom 12 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.23/0.62
% 0.23/0.62 Lemma 13: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 0.23/0.62 Proof:
% 0.23/0.62 inverse(multiply(inverse(X), Y))
% 0.23/0.62 = { by axiom 8 (p12x_3) }
% 0.23/0.62 multiply(inverse(Y), inverse(inverse(X)))
% 0.23/0.62 = { by axiom 6 (p12x_2) }
% 0.23/0.62 multiply(inverse(Y), X)
% 0.23/0.62
% 0.23/0.62 Lemma 14: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 0.23/0.62 Proof:
% 0.23/0.62 multiply(X, inverse(multiply(Y, X)))
% 0.23/0.62 = { by axiom 6 (p12x_2) R->L }
% 0.23/0.62 multiply(inverse(inverse(X)), inverse(multiply(Y, X)))
% 0.23/0.62 = { by axiom 8 (p12x_3) }
% 0.23/0.62 multiply(inverse(inverse(X)), multiply(inverse(X), inverse(Y)))
% 0.23/0.62 = { by axiom 9 (associativity) R->L }
% 0.23/0.62 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(Y))
% 0.23/0.62 = { by axiom 7 (left_inverse) }
% 0.23/0.62 multiply(identity, inverse(Y))
% 0.23/0.62 = { by axiom 1 (left_identity) }
% 0.23/0.62 inverse(Y)
% 0.23/0.62
% 0.23/0.62 Lemma 15: multiply(inverse(greatest_lower_bound(Y, X)), Y) = multiply(inverse(X), least_upper_bound(Y, X)).
% 0.23/0.62 Proof:
% 0.23/0.62 multiply(inverse(greatest_lower_bound(Y, X)), Y)
% 0.23/0.62 = { by lemma 13 R->L }
% 0.23/0.62 inverse(multiply(inverse(Y), greatest_lower_bound(Y, X)))
% 0.23/0.62 = { by axiom 11 (monotony_glb1) }
% 0.23/0.62 inverse(greatest_lower_bound(multiply(inverse(Y), Y), multiply(inverse(Y), X)))
% 0.23/0.62 = { by axiom 7 (left_inverse) }
% 0.23/0.62 inverse(greatest_lower_bound(identity, multiply(inverse(Y), X)))
% 0.23/0.62 = { by axiom 7 (left_inverse) R->L }
% 0.23/0.62 inverse(greatest_lower_bound(multiply(inverse(X), X), multiply(inverse(Y), X)))
% 0.23/0.62 = { by axiom 12 (monotony_glb2) R->L }
% 0.23/0.62 inverse(multiply(greatest_lower_bound(inverse(X), inverse(Y)), X))
% 0.23/0.62 = { by axiom 2 (symmetry_of_glb) }
% 0.23/0.62 inverse(multiply(greatest_lower_bound(inverse(Y), inverse(X)), X))
% 0.23/0.62 = { by axiom 10 (p12x_7) R->L }
% 0.23/0.62 inverse(multiply(inverse(least_upper_bound(Y, X)), X))
% 0.23/0.62 = { by lemma 13 }
% 0.23/0.62 multiply(inverse(X), least_upper_bound(Y, X))
% 0.23/0.62
% 0.23/0.62 Goal 1 (prove_p12x): a = b.
% 0.23/0.62 Proof:
% 0.23/0.62 a
% 0.23/0.62 = { by axiom 6 (p12x_2) R->L }
% 0.23/0.62 inverse(inverse(a))
% 0.23/0.62 = { by lemma 14 R->L }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(a), least_upper_bound(c, a))))
% 0.23/0.62 = { by lemma 15 R->L }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(greatest_lower_bound(c, a)), c)))
% 0.23/0.62 = { by axiom 2 (symmetry_of_glb) R->L }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(greatest_lower_bound(a, c)), c)))
% 0.23/0.62 = { by axiom 3 (p12x_4) }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(greatest_lower_bound(b, c)), c)))
% 0.23/0.62 = { by axiom 2 (symmetry_of_glb) }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(greatest_lower_bound(c, b)), c)))
% 0.23/0.62 = { by lemma 15 }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(b), least_upper_bound(c, b))))
% 0.23/0.62 = { by axiom 4 (symmetry_of_lub) R->L }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(b), least_upper_bound(b, c))))
% 0.23/0.62 = { by axiom 5 (p12x_5) R->L }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(b), least_upper_bound(a, c))))
% 0.23/0.62 = { by axiom 4 (symmetry_of_lub) }
% 0.23/0.62 multiply(least_upper_bound(c, a), inverse(multiply(inverse(b), least_upper_bound(c, a))))
% 0.23/0.62 = { by lemma 14 }
% 0.23/0.62 inverse(inverse(b))
% 0.23/0.62 = { by axiom 6 (p12x_2) }
% 0.23/0.62 b
% 0.23/0.62 % SZS output end Proof
% 0.23/0.62
% 0.23/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------