%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:09:37 AM UTC 2026
% Result : Unsatisfiable 3.47s 0.98s
% Output : CNFRefutation 4.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of clauses : 142 ( 142 unt; 0 nHn; 8 RR)
% Number of literals : 142 ( 141 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 193 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p21) ).
cnf(c2,hypothesis,
inverse(inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_2) ).
cnf(c3,plain,
inverse(inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)))) = multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)) = inverse(inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(multiply(X2,Y),Z) = multiply(X2,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c6,plain,
multiply(multiply(inverse(X2),X2),X3) = multiply(inverse(X2),multiply(X2,X3)),
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/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c9,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(X2),X2) = inverse(identity),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(identity),X2),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(identity),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c14,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
multiply(inverse(identity),X2) = X2,
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c12,c15]) ).
cnf(c17,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c7,c16]) ).
cnf(c18,plain,
multiply(inverse(inverse(greatest_lower_bound(X2,identity))),multiply(inverse(greatest_lower_bound(X2,identity)),inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity))))) = inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity))) = multiply(inverse(inverse(greatest_lower_bound(X2,identity))),multiply(inverse(greatest_lower_bound(X2,identity)),inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity))))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,hypothesis,
inverse(multiply(X2,Y2)) = multiply(inverse(Y2),inverse(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_3) ).
cnf(c21,plain,
inverse(multiply(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)),greatest_lower_bound(X2,identity))) = multiply(inverse(greatest_lower_bound(X2,identity)),inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)))) = inverse(multiply(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)),greatest_lower_bound(X2,identity))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c24,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(X2,identity),
inference(congruence,[status(thm)],[c9]) ).
cnf(c27,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
least_upper_bound(X2,identity) = least_upper_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X3,least_upper_bound(X2,identity)) = multiply(X3,least_upper_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c31,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = multiply(X3,least_upper_bound(X2,inverse(identity))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
least_upper_bound(inverse(identity),X2) = least_upper_bound(X2,inverse(identity)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c34,plain,
least_upper_bound(X2,inverse(identity)) = least_upper_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X3,least_upper_bound(X2,inverse(identity))) = multiply(X3,least_upper_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c37,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = least_upper_bound(multiply(X3,inverse(identity)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c39,plain,
multiply(X2,inverse(identity)) = multiply(inverse(inverse(X2)),inverse(identity)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c41,plain,
inverse(identity) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(inverse(X2),inverse(identity)) = multiply(inverse(X2),inverse(inverse(identity))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
inverse(multiply(inverse(identity),X2)) = multiply(inverse(X2),inverse(inverse(identity))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c44,plain,
multiply(inverse(X2),inverse(inverse(identity))) = inverse(multiply(inverse(identity),X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
inverse(multiply(inverse(identity),X2)) = inverse(X2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c46,plain,
multiply(inverse(X2),inverse(inverse(identity))) = inverse(X2),
inference(transitivity,[status(thm)],[c44,c45]) ).
cnf(c47,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c42,c46]) ).
cnf(c48,plain,
multiply(inverse(inverse(X2)),inverse(identity)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(inverse(inverse(X2)),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c48,c2]) ).
cnf(c50,plain,
multiply(X2,inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c39,c49]) ).
cnf(c51,plain,
least_upper_bound(multiply(X3,inverse(identity)),multiply(X3,X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c37,c51]) ).
cnf(c53,plain,
multiply(X3,least_upper_bound(X2,inverse(identity))) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c35,c52]) ).
cnf(c54,plain,
multiply(X3,least_upper_bound(inverse(identity),X2)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c32,c53]) ).
cnf(c55,plain,
multiply(X3,least_upper_bound(X2,identity)) = least_upper_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c29,c54]) ).
cnf(c56,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)) = least_upper_bound(inverse(greatest_lower_bound(X2,identity)),multiply(inverse(greatest_lower_bound(X2,identity)),X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)),greatest_lower_bound(X2,identity)) = multiply(least_upper_bound(inverse(greatest_lower_bound(X2,identity)),multiply(inverse(greatest_lower_bound(X2,identity)),X2)),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
least_upper_bound(X2,inverse(X3)) = least_upper_bound(inverse(X3),X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c59,plain,
least_upper_bound(inverse(X3),X2) = least_upper_bound(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(least_upper_bound(inverse(X3),X2),X3) = multiply(least_upper_bound(X2,inverse(X3)),X3),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
least_upper_bound(inverse(X2),X3) = least_upper_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c62,plain,
least_upper_bound(X3,inverse(X2)) = least_upper_bound(inverse(X2),X3),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(least_upper_bound(X3,inverse(X2)),X2) = multiply(least_upper_bound(inverse(X2),X3),X2),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c65,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = least_upper_bound(inverse(identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c67,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = least_upper_bound(inverse(identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
multiply(least_upper_bound(X3,inverse(X2)),X2) = least_upper_bound(inverse(identity),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c63,c67]) ).
cnf(c69,plain,
multiply(least_upper_bound(X2,inverse(X3)),X3) = least_upper_bound(inverse(identity),multiply(X2,X3)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(least_upper_bound(inverse(X3),X2),X3) = least_upper_bound(inverse(identity),multiply(X2,X3)),
inference(transitivity,[status(thm)],[c60,c69]) ).
cnf(c71,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X2,identity)),multiply(inverse(greatest_lower_bound(X2,identity)),X2)),greatest_lower_bound(X2,identity)) = least_upper_bound(inverse(identity),multiply(multiply(inverse(greatest_lower_bound(X2,identity)),X2),greatest_lower_bound(X2,identity))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(multiply(inverse(greatest_lower_bound(X2,identity)),X2),greatest_lower_bound(X2,identity)) = multiply(inverse(greatest_lower_bound(X2,identity)),multiply(X2,greatest_lower_bound(X2,identity))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c73,plain,
least_upper_bound(inverse(identity),multiply(multiply(inverse(greatest_lower_bound(X2,identity)),X2),greatest_lower_bound(X2,identity))) = least_upper_bound(inverse(identity),multiply(inverse(greatest_lower_bound(X2,identity)),multiply(X2,greatest_lower_bound(X2,identity)))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c75,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(X2,identity),
inference(congruence,[status(thm)],[c9]) ).
cnf(c78,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,identity),
inference(transitivity,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(greatest_lower_bound(X2,identity),X3) = multiply(greatest_lower_bound(inverse(identity),X2),X3),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c74]) ).
cnf(c82,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(greatest_lower_bound(inverse(identity),X2),X3) = multiply(greatest_lower_bound(X2,inverse(identity)),X3),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c85,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(greatest_lower_bound(X3,inverse(identity)),X2) = multiply(greatest_lower_bound(inverse(identity),X3),X2),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c88,plain,
multiply(greatest_lower_bound(inverse(identity),X3),X2) = greatest_lower_bound(multiply(inverse(identity),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
greatest_lower_bound(multiply(inverse(identity),X2),multiply(X3,X2)) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c90,plain,
multiply(greatest_lower_bound(inverse(identity),X3),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c88,c89]) ).
cnf(c91,plain,
multiply(greatest_lower_bound(X3,inverse(identity)),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c86,c90]) ).
cnf(c92,plain,
multiply(greatest_lower_bound(X2,inverse(identity)),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(greatest_lower_bound(inverse(identity),X2),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c83,c92]) ).
cnf(c94,plain,
multiply(greatest_lower_bound(X2,identity),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c80,c93]) ).
cnf(c95,plain,
multiply(greatest_lower_bound(X2,identity),X2) = greatest_lower_bound(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(substitution,[status(thm)],[c74]) ).
cnf(c97,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = multiply(X3,greatest_lower_bound(X2,inverse(identity))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
greatest_lower_bound(inverse(identity),X2) = greatest_lower_bound(X2,inverse(identity)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c100,plain,
greatest_lower_bound(X2,inverse(identity)) = greatest_lower_bound(inverse(identity),X2),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(X3,greatest_lower_bound(X2,inverse(identity))) = multiply(X3,greatest_lower_bound(inverse(identity),X2)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c103,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(multiply(X3,inverse(identity)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
greatest_lower_bound(multiply(X3,inverse(identity)),multiply(X3,X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c105,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
multiply(X3,greatest_lower_bound(X2,inverse(identity))) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c101,c105]) ).
cnf(c107,plain,
multiply(X3,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c98,c106]) ).
cnf(c108,plain,
multiply(X2,greatest_lower_bound(inverse(identity),X2)) = greatest_lower_bound(X2,multiply(X2,X2)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
greatest_lower_bound(X2,multiply(X2,X2)) = multiply(X2,greatest_lower_bound(inverse(identity),X2)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(X2,greatest_lower_bound(inverse(identity),X2)) = multiply(X2,greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c111,plain,
greatest_lower_bound(X2,multiply(X2,X2)) = multiply(X2,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
multiply(greatest_lower_bound(X2,identity),X2) = multiply(X2,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c95,c111]) ).
cnf(c113,plain,
multiply(X2,greatest_lower_bound(X2,identity)) = multiply(greatest_lower_bound(X2,identity),X2),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),multiply(X2,greatest_lower_bound(X2,identity))) = multiply(inverse(greatest_lower_bound(X2,identity)),multiply(greatest_lower_bound(X2,identity),X2)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
least_upper_bound(inverse(identity),multiply(inverse(greatest_lower_bound(X2,identity)),multiply(X2,greatest_lower_bound(X2,identity)))) = least_upper_bound(inverse(identity),multiply(inverse(greatest_lower_bound(X2,identity)),multiply(greatest_lower_bound(X2,identity),X2))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),multiply(greatest_lower_bound(X2,identity),X2)) = X2,
inference(substitution,[status(thm)],[c17]) ).
cnf(c117,plain,
least_upper_bound(inverse(identity),multiply(inverse(greatest_lower_bound(X2,identity)),multiply(greatest_lower_bound(X2,identity),X2))) = least_upper_bound(inverse(identity),X2),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
least_upper_bound(inverse(identity),multiply(inverse(greatest_lower_bound(X2,identity)),multiply(greatest_lower_bound(X2,identity),X2))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c117,c27]) ).
cnf(c119,plain,
least_upper_bound(inverse(identity),multiply(inverse(greatest_lower_bound(X2,identity)),multiply(X2,greatest_lower_bound(X2,identity)))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c115,c118]) ).
cnf(c120,plain,
least_upper_bound(inverse(identity),multiply(multiply(inverse(greatest_lower_bound(X2,identity)),X2),greatest_lower_bound(X2,identity))) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c73,c119]) ).
cnf(c121,plain,
multiply(least_upper_bound(inverse(greatest_lower_bound(X2,identity)),multiply(inverse(greatest_lower_bound(X2,identity)),X2)),greatest_lower_bound(X2,identity)) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c71,c120]) ).
cnf(c122,plain,
multiply(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)),greatest_lower_bound(X2,identity)) = least_upper_bound(X2,identity),
inference(transitivity,[status(thm)],[c57,c121]) ).
cnf(c123,plain,
inverse(multiply(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)),greatest_lower_bound(X2,identity))) = inverse(least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)))) = inverse(least_upper_bound(X2,identity)),
inference(transitivity,[status(thm)],[c22,c123]) ).
cnf(c125,plain,
multiply(inverse(inverse(greatest_lower_bound(X2,identity))),multiply(inverse(greatest_lower_bound(X2,identity)),inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity))))) = multiply(inverse(inverse(greatest_lower_bound(X2,identity))),inverse(least_upper_bound(X2,identity))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
inverse(inverse(greatest_lower_bound(X2,identity))) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c127,plain,
multiply(inverse(inverse(greatest_lower_bound(X2,identity))),inverse(least_upper_bound(X2,identity))) = multiply(greatest_lower_bound(X2,identity),inverse(least_upper_bound(X2,identity))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
inverse(multiply(X2,inverse(X3))) = multiply(inverse(inverse(X3)),inverse(X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c129,plain,
multiply(inverse(inverse(X3)),inverse(X2)) = multiply(X3,inverse(X2)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c130,plain,
inverse(multiply(X2,inverse(X3))) = multiply(X3,inverse(X2)),
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
inverse(multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity)))) = multiply(greatest_lower_bound(X2,identity),inverse(least_upper_bound(X2,identity))),
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
multiply(greatest_lower_bound(X2,identity),inverse(least_upper_bound(X2,identity))) = inverse(multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity)))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(inverse(inverse(greatest_lower_bound(X2,identity))),inverse(least_upper_bound(X2,identity))) = inverse(multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity)))),
inference(transitivity,[status(thm)],[c127,c132]) ).
cnf(c134,plain,
multiply(inverse(inverse(greatest_lower_bound(X2,identity))),multiply(inverse(greatest_lower_bound(X2,identity)),inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity))))) = inverse(multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity)))),
inference(transitivity,[status(thm)],[c125,c133]) ).
cnf(c135,plain,
inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity))) = inverse(multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity)))),
inference(transitivity,[status(thm)],[c19,c134]) ).
cnf(c136,plain,
inverse(inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)))) = inverse(inverse(multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity))))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
inverse(inverse(multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity))))) = multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c138,plain,
inverse(inverse(multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)))) = multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c136,c137]) ).
cnf(c139,plain,
multiply(inverse(greatest_lower_bound(X2,identity)),least_upper_bound(X2,identity)) = multiply(least_upper_bound(X2,identity),inverse(greatest_lower_bound(X2,identity))),
inference(transitivity,[status(thm)],[c4,c138]) ).
cnf(c140,plain,
multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
$false,
inference(resolution,[status(thm)],[c1,c141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP184-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:41:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.47/0.98 Command-line arguments: --flatten --complete-subsets
% 3.47/0.98
% 3.47/0.98 % SZS status Unsatisfiable
% 3.47/0.98
% 3.47/1.00 % SZS output start CNFRefutation
% See solution above
% 4.65/1.06
% 4.65/1.06 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------