%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP178-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:34 AM UTC 2026
% Result : Unsatisfiable 15.67s 2.45s
% Output : CNFRefutation 15.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of clauses : 86 ( 86 unt; 0 nHn; 25 RR)
% Number of literals : 86 ( 85 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 131 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p09b) ).
cnf(c2,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c3,plain,
greatest_lower_bound(multiply(b,c),a) = greatest_lower_bound(a,multiply(b,c)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(b,c),a),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(multiply(X2,Y2),Z) = multiply(X2,multiply(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c6,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c11,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c9,c10]) ).
cnf(c12,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c7,c11]) ).
cnf(c13,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c16,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c20,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c12]) ).
cnf(c22,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c18,c22]) ).
cnf(c24,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
a = multiply(a,identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
greatest_lower_bound(multiply(b,c),a) = greatest_lower_bound(multiply(b,c),multiply(a,identity)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,axiom,
greatest_lower_bound(identity,c) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c28,plain,
identity = greatest_lower_bound(identity,c),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(a,identity) = multiply(a,greatest_lower_bound(identity,c)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
greatest_lower_bound(multiply(b,c),multiply(a,identity)) = greatest_lower_bound(multiply(b,c),multiply(a,greatest_lower_bound(identity,c))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
greatest_lower_bound(c,identity) = greatest_lower_bound(identity,c),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
greatest_lower_bound(identity,c) = greatest_lower_bound(c,identity),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(a,greatest_lower_bound(identity,c)) = multiply(a,greatest_lower_bound(c,identity)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
greatest_lower_bound(multiply(b,c),multiply(a,greatest_lower_bound(identity,c))) = greatest_lower_bound(multiply(b,c),multiply(a,greatest_lower_bound(c,identity))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),greatest_lower_bound(X3,multiply(X3,X2)))) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c36,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),greatest_lower_bound(X3,multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c38,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c40,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
greatest_lower_bound(identity,multiply(inverse(X3),X2)) = multiply(inverse(X3),greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
greatest_lower_bound(identity,multiply(inverse(X3),multiply(X3,X2))) = multiply(inverse(X3),greatest_lower_bound(X3,multiply(X3,X2))),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(inverse(X3),greatest_lower_bound(X3,multiply(X3,X2))) = greatest_lower_bound(identity,multiply(inverse(X3),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
greatest_lower_bound(identity,multiply(inverse(X3),multiply(X3,X2))) = greatest_lower_bound(identity,X2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c46,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
greatest_lower_bound(identity,multiply(inverse(X3),multiply(X3,X2))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
multiply(inverse(X3),greatest_lower_bound(X3,multiply(X3,X2))) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c44,c47]) ).
cnf(c49,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),greatest_lower_bound(X3,multiply(X3,X2)))) = multiply(inverse(inverse(X3)),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(inverse(X3)),greatest_lower_bound(X2,identity)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c51,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),greatest_lower_bound(X3,multiply(X3,X2)))) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c49,c50]) ).
cnf(c52,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c36,c51]) ).
cnf(c53,plain,
greatest_lower_bound(a,multiply(a,c)) = multiply(a,greatest_lower_bound(c,identity)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(a,greatest_lower_bound(c,identity)) = greatest_lower_bound(a,multiply(a,c)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
greatest_lower_bound(multiply(b,c),multiply(a,greatest_lower_bound(c,identity))) = greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,multiply(a,c))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
greatest_lower_bound(multiply(X2,X4),X3) = greatest_lower_bound(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c57,plain,
greatest_lower_bound(X2,multiply(X4,X3)) = greatest_lower_bound(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(X2,multiply(X5,X3))) = greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(multiply(X5,X3),X2)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c60,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(multiply(X5,X3),X2)) = greatest_lower_bound(greatest_lower_bound(multiply(X4,X3),multiply(X5,X3)),X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c62,plain,
multiply(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(multiply(X4,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
greatest_lower_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c65,plain,
multiply(greatest_lower_bound(X4,X2),X3) = multiply(greatest_lower_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
greatest_lower_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,X4),X3),
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X4,X3),X2),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
greatest_lower_bound(greatest_lower_bound(multiply(X4,X3),multiply(X5,X3)),X2) = greatest_lower_bound(multiply(greatest_lower_bound(X5,X4),X3),X2),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(multiply(X5,X3),X2)) = greatest_lower_bound(multiply(greatest_lower_bound(X5,X4),X3),X2),
inference(transitivity,[status(thm)],[c60,c68]) ).
cnf(c70,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(X2,multiply(X5,X3))) = greatest_lower_bound(multiply(greatest_lower_bound(X5,X4),X3),X2),
inference(transitivity,[status(thm)],[c58,c69]) ).
cnf(c71,plain,
greatest_lower_bound(multiply(b,X3),greatest_lower_bound(X2,multiply(a,X3))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),X3),X2),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c73,plain,
multiply(greatest_lower_bound(a,b),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),X3),X2) = greatest_lower_bound(multiply(identity,X3),X2),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
greatest_lower_bound(multiply(identity,X3),X2) = greatest_lower_bound(X3,X2),
inference(congruence,[status(thm)],[c10]) ).
cnf(c76,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c77,plain,
greatest_lower_bound(multiply(identity,X3),X2) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c75,c76]) ).
cnf(c78,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),X3),X2) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c74,c77]) ).
cnf(c79,plain,
greatest_lower_bound(multiply(b,X3),greatest_lower_bound(X2,multiply(a,X3))) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c71,c78]) ).
cnf(c80,plain,
greatest_lower_bound(multiply(b,c),greatest_lower_bound(a,multiply(a,c))) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
greatest_lower_bound(multiply(b,c),multiply(a,greatest_lower_bound(c,identity))) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c55,c80]) ).
cnf(c82,plain,
greatest_lower_bound(multiply(b,c),multiply(a,greatest_lower_bound(identity,c))) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c34,c81]) ).
cnf(c83,plain,
greatest_lower_bound(multiply(b,c),multiply(a,identity)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c30,c82]) ).
cnf(c84,plain,
greatest_lower_bound(multiply(b,c),a) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c26,c83]) ).
cnf(c85,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(transitivity,[status(thm)],[c4,c84]) ).
cnf(c86,plain,
$false,
inference(resolution,[status(thm)],[c1,c85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP178-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:36:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.67/2.45 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 15.67/2.45
% 15.67/2.45 % SZS status Unsatisfiable
% 15.67/2.45
% 15.67/2.45 % SZS output start CNFRefutation
% See solution above
% 15.67/2.48
% 15.67/2.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------