%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP602-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 10:11:21 AM UTC 2026
% Result : Unsatisfiable 1.15s 0.60s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 3
% Syntax : Number of clauses : 171 ( 171 unt; 0 nHn; 3 RR)
% Number of literals : 171 ( 170 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 534 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c2,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c3,plain,
multiply(double_divide(X2,X3),X) = inverse(double_divide(X,double_divide(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(multiply(double_divide(X2,X3),X),X2) = multiply(inverse(double_divide(X,double_divide(X2,X3))),X2),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X3,multiply(multiply(double_divide(X2,X3),X),X2)) = multiply(X3,multiply(inverse(double_divide(X,double_divide(X2,X3))),X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(inverse(double_divide(X,double_divide(X2,X3))),X2) = inverse(double_divide(X2,inverse(double_divide(X,double_divide(X2,X3))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
multiply(X3,multiply(inverse(double_divide(X,double_divide(X2,X3))),X2)) = multiply(X3,inverse(double_divide(X2,inverse(double_divide(X,double_divide(X2,X3)))))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(X3,inverse(double_divide(X2,inverse(double_divide(X,double_divide(X2,X3)))))) = inverse(double_divide(inverse(double_divide(X2,inverse(double_divide(X,double_divide(X2,X3))))),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,axiom,
inverse(double_divide(inverse(double_divide(A2,inverse(double_divide(B2,double_divide(A2,C))))),C)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c10,plain,
inverse(double_divide(inverse(double_divide(X2,inverse(double_divide(X,double_divide(X2,X3))))),X3)) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(X3,inverse(double_divide(X2,inverse(double_divide(X,double_divide(X2,X3)))))) = X,
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
multiply(X3,multiply(inverse(double_divide(X,double_divide(X2,X3))),X2)) = X,
inference(transitivity,[status(thm)],[c7,c11]) ).
cnf(c13,plain,
multiply(X3,multiply(multiply(double_divide(X2,X3),X),X2)) = X,
inference(transitivity,[status(thm)],[c5,c12]) ).
cnf(c14,plain,
multiply(inverse(X3),multiply(multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)),X)) = multiply(multiply(inverse(X3),X2),X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(inverse(X3),X2),X) = multiply(inverse(X3),multiply(multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)),X)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(double_divide(X3,multiply(X2,X)),multiply(X,X3)) = inverse(double_divide(multiply(X,X3),double_divide(X3,multiply(X2,X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
multiply(X,multiply(multiply(double_divide(X2,X),multiply(multiply(double_divide(X3,double_divide(X2,X)),X4),X3)),X2)) = multiply(multiply(double_divide(X3,double_divide(X2,X)),X4),X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c18,plain,
multiply(multiply(double_divide(X4,double_divide(X3,X2)),X),X4) = multiply(X2,multiply(multiply(double_divide(X3,X2),multiply(multiply(double_divide(X4,double_divide(X3,X2)),X),X4)),X3)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(double_divide(X3,X2),multiply(multiply(double_divide(X4,double_divide(X3,X2)),X),X4)) = X,
inference(substitution,[status(thm)],[c13]) ).
cnf(c20,plain,
multiply(multiply(double_divide(X3,X2),multiply(multiply(double_divide(X4,double_divide(X3,X2)),X),X4)),X3) = multiply(X,X3),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(X2,multiply(multiply(double_divide(X3,X2),multiply(multiply(double_divide(X4,double_divide(X3,X2)),X),X4)),X3)) = multiply(X2,multiply(X,X3)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(multiply(double_divide(X4,double_divide(X3,X2)),X),X4) = multiply(X2,multiply(X,X3)),
inference(transitivity,[status(thm)],[c18,c21]) ).
cnf(c23,plain,
multiply(multiply(double_divide(X,double_divide(X4,X3)),X2),X) = multiply(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X3,multiply(X2,X4)) = multiply(multiply(double_divide(X,double_divide(X4,X3)),X2),X),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(double_divide(X4,X3),multiply(X3,multiply(X2,X4))) = multiply(double_divide(X4,X3),multiply(multiply(double_divide(X,double_divide(X4,X3)),X2),X)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(double_divide(X4,X3),multiply(multiply(double_divide(X,double_divide(X4,X3)),X2),X)) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c27,plain,
multiply(double_divide(X3,X2),multiply(X2,multiply(X,X3))) = X,
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
multiply(double_divide(X4,X3),multiply(X3,multiply(double_divide(multiply(X4,X),double_divide(X,X2)),X4))) = double_divide(multiply(X4,X),double_divide(X,X2)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
double_divide(multiply(X4,X),double_divide(X,X2)) = multiply(double_divide(X4,X3),multiply(X3,multiply(double_divide(multiply(X4,X),double_divide(X,X2)),X4))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(double_divide(X2,X),multiply(X,multiply(X3,X2))) = X3,
inference(substitution,[status(thm)],[c27]) ).
cnf(c31,plain,
X3 = multiply(double_divide(X2,X),multiply(X,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(double_divide(multiply(X3,X2),double_divide(X2,X)),X3) = multiply(double_divide(multiply(X3,X2),double_divide(X2,X)),multiply(double_divide(X2,X),multiply(X,multiply(X3,X2)))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(double_divide(multiply(X3,X2),double_divide(X2,X)),multiply(double_divide(X2,X),multiply(X,multiply(X3,X2)))) = X,
inference(substitution,[status(thm)],[c27]) ).
cnf(c34,plain,
multiply(double_divide(multiply(X3,X2),double_divide(X2,X)),X3) = X,
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
multiply(double_divide(multiply(X3,X),double_divide(X,X2)),X3) = X2,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X3,multiply(double_divide(multiply(X4,X),double_divide(X,X2)),X4)) = multiply(X3,X2),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(double_divide(X4,X3),multiply(X3,multiply(double_divide(multiply(X4,X),double_divide(X,X2)),X4))) = multiply(double_divide(X4,X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
double_divide(multiply(X4,X),double_divide(X,X2)) = multiply(double_divide(X4,X3),multiply(X3,X2)),
inference(transitivity,[status(thm)],[c29,c37]) ).
cnf(c39,plain,
double_divide(multiply(X4,X3),double_divide(X3,multiply(X2,X4))) = multiply(double_divide(X4,X),multiply(X,multiply(X2,X4))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(double_divide(X3,X),multiply(X,multiply(X2,X3))) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c41,plain,
double_divide(multiply(X3,X2),double_divide(X2,multiply(X,X3))) = X,
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
double_divide(multiply(X,X3),double_divide(X3,multiply(X2,X))) = X2,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
inverse(double_divide(multiply(X,X3),double_divide(X3,multiply(X2,X)))) = inverse(X2),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(double_divide(X3,multiply(X2,X)),multiply(X,X3)) = inverse(X2),
inference(transitivity,[status(thm)],[c16,c43]) ).
cnf(c45,plain,
multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X)) = inverse(X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
inverse(X3) = multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
double_divide(X4,inverse(X3)) = double_divide(X4,multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(double_divide(X4,inverse(X3)),multiply(multiply(X2,X),X4)) = multiply(double_divide(X4,multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))),multiply(multiply(X2,X),X4)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(double_divide(X4,multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))),multiply(multiply(X2,X),X4)) = inverse(double_divide(X,multiply(X3,X2))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c50,plain,
multiply(multiply(X3,X2),X) = inverse(double_divide(X,multiply(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
inverse(double_divide(X,multiply(X3,X2))) = multiply(multiply(X3,X2),X),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(double_divide(X4,multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))),multiply(multiply(X2,X),X4)) = multiply(multiply(X3,X2),X),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
multiply(double_divide(X4,inverse(X3)),multiply(multiply(X2,X),X4)) = multiply(multiply(X3,X2),X),
inference(transitivity,[status(thm)],[c48,c52]) ).
cnf(c54,plain,
multiply(double_divide(X3,inverse(X2)),multiply(multiply(inverse(X2),X),X3)) = multiply(multiply(X2,inverse(X2)),X),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))) = X3,
inference(substitution,[status(thm)],[c41]) ).
cnf(c56,plain,
X3 = double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(X3,inverse(X3)) = multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),inverse(X3)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X)) = inverse(X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c59,plain,
inverse(X3) = multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),inverse(X3)) = multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
double_divide(multiply(multiply(X2,X),X4),double_divide(X4,multiply(X2,X))) = multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c62,plain,
multiply(double_divide(multiply(X3,X2),double_divide(X2,multiply(X4,X3))),multiply(double_divide(X2,multiply(X4,X3)),multiply(X3,X2))) = double_divide(multiply(multiply(X3,X2),X),double_divide(X,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
double_divide(multiply(multiply(X3,X2),X),double_divide(X,multiply(X3,X2))) = multiply(double_divide(multiply(X3,X2),double_divide(X2,multiply(X4,X3))),multiply(double_divide(X2,multiply(X4,X3)),multiply(X3,X2))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c64,plain,
multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X)) = inverse(X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c65,plain,
multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))) = multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),inverse(X3)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))) = X3,
inference(substitution,[status(thm)],[c41]) ).
cnf(c67,plain,
multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),inverse(X3)) = multiply(X3,inverse(X3)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
double_divide(multiply(multiply(X3,X2),X),double_divide(X,multiply(X3,X2))) = multiply(X4,inverse(X4)),
inference(transitivity,[status(thm)],[c63,c68]) ).
cnf(c70,plain,
multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),multiply(double_divide(X,multiply(X3,X2)),multiply(X2,X))) = multiply(X4,inverse(X4)),
inference(transitivity,[status(thm)],[c62,c69]) ).
cnf(c71,plain,
multiply(double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),inverse(X3)) = multiply(X4,inverse(X4)),
inference(transitivity,[status(thm)],[c60,c70]) ).
cnf(c72,plain,
multiply(X,inverse(X)) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c57,c71]) ).
cnf(c73,plain,
multiply(X2,inverse(X2)) = multiply(X,inverse(X)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(multiply(X,inverse(X)),X2),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(X4,inverse(X4)) = multiply(double_divide(X3,double_divide(X2,X)),inverse(double_divide(X3,double_divide(X2,X)))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c76,plain,
multiply(multiply(X4,inverse(X4)),X3) = multiply(multiply(double_divide(X3,double_divide(X2,X)),inverse(double_divide(X3,double_divide(X2,X)))),X3),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(multiply(double_divide(X3,double_divide(X2,X)),inverse(double_divide(X3,double_divide(X2,X)))),X3) = multiply(X,multiply(inverse(double_divide(X3,double_divide(X2,X))),X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c78,plain,
multiply(double_divide(X2,X),X3) = inverse(double_divide(X3,double_divide(X2,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c79,plain,
inverse(double_divide(X3,double_divide(X2,X))) = multiply(double_divide(X2,X),X3),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(inverse(double_divide(X3,double_divide(X2,X))),X2) = multiply(multiply(double_divide(X2,X),X3),X2),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(X,multiply(inverse(double_divide(X3,double_divide(X2,X))),X2)) = multiply(X,multiply(multiply(double_divide(X2,X),X3),X2)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(X,multiply(multiply(double_divide(X2,X),X3),X2)) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c83,plain,
multiply(X,multiply(inverse(double_divide(X3,double_divide(X2,X))),X2)) = X3,
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
multiply(multiply(double_divide(X3,double_divide(X2,X)),inverse(double_divide(X3,double_divide(X2,X)))),X3) = X3,
inference(transitivity,[status(thm)],[c77,c83]) ).
cnf(c85,plain,
multiply(multiply(X2,inverse(X2)),X) = X,
inference(transitivity,[status(thm)],[c76,c84]) ).
cnf(c86,plain,
multiply(multiply(X,inverse(X)),X2) = X2,
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(multiply(X2,inverse(X2)),X) = X,
inference(transitivity,[status(thm)],[c74,c86]) ).
cnf(c88,plain,
multiply(double_divide(X3,inverse(X2)),multiply(multiply(inverse(X2),X),X3)) = X,
inference(transitivity,[status(thm)],[c54,c87]) ).
cnf(c89,plain,
multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)) = X2,
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)),X) = multiply(X2,X),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(inverse(X3),multiply(multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)),X)) = multiply(inverse(X3),multiply(X2,X)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(multiply(inverse(X3),X2),X) = multiply(inverse(X3),multiply(X2,X)),
inference(transitivity,[status(thm)],[c15,c91]) ).
cnf(c93,plain,
multiply(multiply(inverse(X2),X2),X) = multiply(inverse(X2),multiply(X2,X)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)) = X2,
inference(substitution,[status(thm)],[c88]) ).
cnf(c95,plain,
X2 = multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(X,X3) = multiply(X,multiply(double_divide(X2,inverse(X4)),multiply(multiply(inverse(X4),X3),X2))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(double_divide(multiply(multiply(inverse(X4),X3),X2),X),multiply(X,X3)) = multiply(double_divide(multiply(multiply(inverse(X4),X3),X2),X),multiply(X,multiply(double_divide(X2,inverse(X4)),multiply(multiply(inverse(X4),X3),X2)))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(double_divide(multiply(multiply(inverse(X4),X3),X2),X),multiply(X,multiply(double_divide(X2,inverse(X4)),multiply(multiply(inverse(X4),X3),X2)))) = double_divide(X2,inverse(X4)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c99,plain,
multiply(double_divide(multiply(multiply(inverse(X4),X3),X2),X),multiply(X,X3)) = double_divide(X2,inverse(X4)),
inference(transitivity,[status(thm)],[c97,c98]) ).
cnf(c100,plain,
multiply(double_divide(multiply(multiply(inverse(X2),X),X3),inverse(X2)),multiply(inverse(X2),X)) = double_divide(X3,inverse(X2)),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
double_divide(X3,inverse(X2)) = multiply(double_divide(multiply(multiply(inverse(X2),X),X3),inverse(X2)),multiply(inverse(X2),X)),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(double_divide(X3,inverse(X2)),X3) = multiply(multiply(double_divide(multiply(multiply(inverse(X2),X),X3),inverse(X2)),multiply(inverse(X2),X)),X3),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(multiply(double_divide(multiply(X3,X2),X),X3),X2) = inverse(double_divide(X2,multiply(double_divide(multiply(X3,X2),X),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c104,plain,
X = double_divide(multiply(X3,X2),double_divide(X2,multiply(X,X3))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c105,plain,
double_divide(multiply(X4,multiply(X3,X2)),X) = double_divide(multiply(X4,multiply(X3,X2)),double_divide(multiply(X3,X2),double_divide(X2,multiply(X,X3)))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(double_divide(multiply(X4,multiply(X3,X2)),X),X4) = multiply(double_divide(multiply(X4,multiply(X3,X2)),double_divide(multiply(X3,X2),double_divide(X2,multiply(X,X3)))),X4),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(double_divide(multiply(X4,multiply(X3,X2)),double_divide(multiply(X3,X2),double_divide(X2,multiply(X,X3)))),X4) = double_divide(X2,multiply(X,X3)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c108,plain,
multiply(double_divide(multiply(X4,multiply(X3,X2)),X),X4) = double_divide(X2,multiply(X,X3)),
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
multiply(double_divide(multiply(X,multiply(X3,X4)),double_divide(multiply(X3,X4),X2)),X) = double_divide(X4,multiply(double_divide(multiply(X3,X4),X2),X3)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
double_divide(X4,multiply(double_divide(multiply(X3,X4),X2),X3)) = multiply(double_divide(multiply(X,multiply(X3,X4)),double_divide(multiply(X3,X4),X2)),X),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(double_divide(multiply(X,multiply(X3,X4)),double_divide(multiply(X3,X4),X2)),X) = X2,
inference(substitution,[status(thm)],[c34]) ).
cnf(c112,plain,
double_divide(X3,multiply(double_divide(multiply(X2,X3),X),X2)) = X,
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
double_divide(X2,multiply(double_divide(multiply(X3,X2),X),X3)) = X,
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
inverse(double_divide(X2,multiply(double_divide(multiply(X3,X2),X),X3))) = inverse(X),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(multiply(double_divide(multiply(X3,X2),X),X3),X2) = inverse(X),
inference(transitivity,[status(thm)],[c103,c114]) ).
cnf(c116,plain,
multiply(multiply(double_divide(multiply(multiply(inverse(X2),X),X3),inverse(X2)),multiply(inverse(X2),X)),X3) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(double_divide(X2,inverse(X)),X2) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c102,c116]) ).
cnf(c118,plain,
multiply(double_divide(multiply(inverse(X2),X),inverse(X2)),multiply(inverse(X2),X)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
inverse(inverse(X2)) = multiply(double_divide(multiply(inverse(X2),X),inverse(X2)),multiply(inverse(X2),X)),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
double_divide(multiply(multiply(X4,X3),X2),double_divide(X2,X)) = multiply(double_divide(multiply(X4,X3),double_divide(X3,X4)),multiply(double_divide(X3,X4),X)),
inference(substitution,[status(thm)],[c38]) ).
cnf(c121,plain,
multiply(multiply(X,inverse(X)),X2) = X2,
inference(substitution,[status(thm)],[c85]) ).
cnf(c122,plain,
X2 = multiply(multiply(X,inverse(X)),X2),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
double_divide(X2,X3) = double_divide(X2,multiply(multiply(X,inverse(X)),X3)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
double_divide(multiply(X3,X2),double_divide(X2,X3)) = double_divide(multiply(X3,X2),double_divide(X2,multiply(multiply(X,inverse(X)),X3))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
double_divide(multiply(X3,X2),double_divide(X2,multiply(multiply(X,inverse(X)),X3))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c41]) ).
cnf(c126,plain,
double_divide(multiply(X3,X2),double_divide(X2,X3)) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
multiply(double_divide(multiply(X4,X3),double_divide(X3,X4)),multiply(double_divide(X3,X4),X2)) = multiply(multiply(X,inverse(X)),multiply(double_divide(X3,X4),X2)),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(multiply(X,inverse(X)),multiply(double_divide(X3,X4),X2)) = multiply(double_divide(X3,X4),X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c129,plain,
multiply(double_divide(multiply(X3,X2),double_divide(X2,X3)),multiply(double_divide(X2,X3),X)) = multiply(double_divide(X2,X3),X),
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
double_divide(multiply(multiply(X4,X3),X2),double_divide(X2,X)) = multiply(double_divide(X3,X4),X),
inference(transitivity,[status(thm)],[c120,c129]) ).
cnf(c131,plain,
double_divide(multiply(multiply(inverse(X3),X4),X),double_divide(X,multiply(X2,X4))) = multiply(double_divide(X4,inverse(X3)),multiply(X2,X4)),
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
multiply(double_divide(X4,inverse(X3)),multiply(X2,X4)) = double_divide(multiply(multiply(inverse(X3),X4),X),double_divide(X,multiply(X2,X4))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
double_divide(multiply(multiply(inverse(X4),X5),X2),double_divide(X2,multiply(X3,X5))) = multiply(double_divide(multiply(inverse(X4),X5),X),multiply(X,multiply(X3,X5))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c134,plain,
double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))) = X3,
inference(substitution,[status(thm)],[c41]) ).
cnf(c135,plain,
X3 = double_divide(multiply(X2,X),double_divide(X,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
multiply(X4,X2) = multiply(double_divide(multiply(X3,X),double_divide(X,multiply(X4,X3))),X2),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(multiply(X4,X2),multiply(X3,X)) = multiply(multiply(double_divide(multiply(X3,X),double_divide(X,multiply(X4,X3))),X2),multiply(X3,X)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(multiply(double_divide(multiply(X3,X),double_divide(X,multiply(X4,X3))),X2),multiply(X3,X)) = multiply(multiply(X4,X3),multiply(X2,X)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c139,plain,
multiply(multiply(X4,X2),multiply(X3,X)) = multiply(multiply(X4,X3),multiply(X2,X)),
inference(transitivity,[status(thm)],[c137,c138]) ).
cnf(c140,plain,
multiply(multiply(X3,X2),multiply(inverse(X3),X)) = multiply(multiply(X3,inverse(X3)),multiply(X2,X)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(X2,inverse(X2)) = multiply(X,inverse(X)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c142,plain,
multiply(multiply(X4,inverse(X4)),multiply(X3,X2)) = multiply(multiply(X,inverse(X)),multiply(X3,X2)),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(multiply(X,inverse(X)),multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c144,plain,
multiply(multiply(X3,inverse(X3)),multiply(X2,X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
multiply(multiply(X3,X2),multiply(inverse(X3),X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c140,c144]) ).
cnf(c146,plain,
multiply(multiply(X2,X),multiply(inverse(X2),X3)) = multiply(X,X3),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(X,X3) = multiply(multiply(X2,X),multiply(inverse(X2),X3)),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(X,multiply(X2,X4)) = multiply(X,multiply(multiply(X3,X2),multiply(inverse(X3),X4))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(double_divide(multiply(inverse(X3),X4),X),multiply(X,multiply(X2,X4))) = multiply(double_divide(multiply(inverse(X3),X4),X),multiply(X,multiply(multiply(X3,X2),multiply(inverse(X3),X4)))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(double_divide(multiply(inverse(X3),X4),X),multiply(X,multiply(multiply(X3,X2),multiply(inverse(X3),X4)))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c151,plain,
multiply(double_divide(multiply(inverse(X3),X4),X),multiply(X,multiply(X2,X4))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
double_divide(multiply(multiply(inverse(X3),X4),X),double_divide(X,multiply(X2,X4))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c133,c151]) ).
cnf(c153,plain,
multiply(double_divide(X3,inverse(X2)),multiply(X,X3)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c132,c152]) ).
cnf(c154,plain,
multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(double_divide(X,inverse(X3)),multiply(multiply(inverse(X3),X2),X)) = X2,
inference(substitution,[status(thm)],[c88]) ).
cnf(c157,plain,
multiply(X2,multiply(inverse(X2),X)) = X,
inference(transitivity,[status(thm)],[c155,c156]) ).
cnf(c158,plain,
X = multiply(X2,multiply(inverse(X2),X)),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(inverse(X2),X) = multiply(inverse(X2),multiply(X2,multiply(inverse(X2),X))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(double_divide(multiply(inverse(X2),X),inverse(X2)),multiply(inverse(X2),X)) = multiply(double_divide(multiply(inverse(X2),X),inverse(X2)),multiply(inverse(X2),multiply(X2,multiply(inverse(X2),X)))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(double_divide(multiply(inverse(X2),X),inverse(X2)),multiply(inverse(X2),multiply(X2,multiply(inverse(X2),X)))) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c162,plain,
multiply(double_divide(multiply(inverse(X2),X),inverse(X2)),multiply(inverse(X2),X)) = X2,
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c119,c162]) ).
cnf(c164,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(X2,X) = multiply(inverse(inverse(X2)),X),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
multiply(inverse(X2),multiply(X2,X)) = multiply(inverse(X2),multiply(inverse(inverse(X2)),X)),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(inverse(X2),multiply(inverse(inverse(X2)),X)) = X,
inference(substitution,[status(thm)],[c157]) ).
cnf(c168,plain,
multiply(inverse(X2),multiply(X2,X)) = X,
inference(transitivity,[status(thm)],[c166,c167]) ).
cnf(c169,plain,
multiply(multiply(inverse(X2),X2),X) = X,
inference(transitivity,[status(thm)],[c93,c168]) ).
cnf(c170,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(substitution,[status(thm)],[c169]) ).
cnf(c171,plain,
$false,
inference(resolution,[status(thm)],[c1,c170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP602-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:10:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/0.60 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.15/0.60
% 1.15/0.60 % SZS status Unsatisfiable
% 1.15/0.60
% 1.15/0.62 % SZS output start CNFRefutation
% See solution above
% 1.98/0.71
% 1.98/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------