%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP613-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 10:11:23 AM UTC 2026
% Result : Unsatisfiable 0.31s 0.62s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 3
% Syntax : Number of clauses : 146 ( 146 unt; 0 nHn; 8 RR)
% Number of literals : 146 ( 145 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 341 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c3,plain,
multiply(X,inverse(X)) = inverse(double_divide(inverse(X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(multiply(X,inverse(X)),inverse(X2)) = double_divide(inverse(double_divide(inverse(X),X)),inverse(X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
double_divide(multiply(X2,X),double_divide(inverse(X3),X3)) = double_divide(inverse(double_divide(X,X2)),double_divide(inverse(X3),X3)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X2),X) = inverse(double_divide(X,inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
multiply(X3,multiply(inverse(X2),X)) = multiply(X3,inverse(double_divide(X,inverse(X2)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
double_divide(multiply(X3,multiply(inverse(X2),X)),double_divide(X,X3)) = double_divide(multiply(X3,inverse(double_divide(X,inverse(X2)))),double_divide(X,X3)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X3,inverse(double_divide(X,inverse(X2)))) = inverse(double_divide(inverse(double_divide(X,inverse(X2))),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
double_divide(multiply(X3,inverse(double_divide(X,inverse(X2)))),double_divide(X,X3)) = double_divide(inverse(double_divide(inverse(double_divide(X,inverse(X2))),X3)),double_divide(X,X3)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
double_divide(inverse(double_divide(inverse(double_divide(A2,inverse(B2))),C)),double_divide(A2,C)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c13,plain,
double_divide(inverse(double_divide(inverse(double_divide(X,inverse(X2))),X3)),double_divide(X,X3)) = X2,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
double_divide(multiply(X3,inverse(double_divide(X,inverse(X2)))),double_divide(X,X3)) = X2,
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
double_divide(multiply(X3,multiply(inverse(X2),X)),double_divide(X,X3)) = X2,
inference(transitivity,[status(thm)],[c9,c14]) ).
cnf(c16,plain,
double_divide(multiply(X,multiply(inverse(inverse(X2)),X3)),double_divide(X3,X)) = inverse(X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
inverse(X3) = double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(inverse(X3),inverse(X4)) = multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),inverse(X4)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X4,multiply(inverse(X3),inverse(X4))) = multiply(X4,multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),inverse(X4))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
double_divide(multiply(X,multiply(inverse(X3),X2)),double_divide(X2,X)) = X3,
inference(substitution,[status(thm)],[c15]) ).
cnf(c21,plain,
X3 = double_divide(multiply(X,multiply(inverse(X3),X2)),double_divide(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X4,multiply(double_divide(X3,X2),multiply(inverse(X),multiply(X2,multiply(inverse(X4),X3))))) = multiply(double_divide(multiply(X2,multiply(inverse(X4),X3)),double_divide(X3,X2)),multiply(double_divide(X3,X2),multiply(inverse(X),multiply(X2,multiply(inverse(X4),X3))))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(double_divide(X3,X2),multiply(X2,multiply(inverse(X),X3))) = inverse(double_divide(multiply(X2,multiply(inverse(X),X3)),double_divide(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
double_divide(multiply(X2,multiply(inverse(X),X3)),double_divide(X3,X2)) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c25,plain,
inverse(double_divide(multiply(X2,multiply(inverse(X),X3)),double_divide(X3,X2))) = inverse(X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(double_divide(X3,X2),multiply(X2,multiply(inverse(X),X3))) = inverse(X),
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
multiply(double_divide(multiply(X2,multiply(inverse(X4),X3)),double_divide(X3,X2)),multiply(double_divide(X3,X2),multiply(inverse(X),multiply(X2,multiply(inverse(X4),X3))))) = inverse(X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(X4,multiply(double_divide(X3,X2),multiply(inverse(X),multiply(X2,multiply(inverse(X4),X3))))) = inverse(X),
inference(transitivity,[status(thm)],[c22,c27]) ).
cnf(c29,plain,
multiply(inverse(X3),multiply(double_divide(X,X2),multiply(inverse(X4),multiply(X2,multiply(inverse(inverse(X3)),X))))) = inverse(X4),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(X4) = multiply(inverse(X3),multiply(double_divide(X,X2),multiply(inverse(X4),multiply(X2,multiply(inverse(inverse(X3)),X))))),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),inverse(X4)) = multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),multiply(inverse(X3),multiply(double_divide(X,X2),multiply(inverse(X4),multiply(X2,multiply(inverse(inverse(X3)),X)))))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X4,multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),inverse(X4))) = multiply(X4,multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),multiply(inverse(X3),multiply(double_divide(X,X2),multiply(inverse(X4),multiply(X2,multiply(inverse(inverse(X3)),X))))))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X4,multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),multiply(inverse(X3),multiply(double_divide(X,X2),multiply(inverse(X4),multiply(X2,multiply(inverse(inverse(X3)),X))))))) = inverse(X3),
inference(substitution,[status(thm)],[c28]) ).
cnf(c34,plain,
multiply(X4,multiply(double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),inverse(X4))) = inverse(X3),
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
multiply(X2,multiply(inverse(X),inverse(X2))) = inverse(X),
inference(transitivity,[status(thm)],[c19,c34]) ).
cnf(c36,plain,
multiply(X,multiply(inverse(X2),inverse(X))) = inverse(X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(X2) = multiply(X,multiply(inverse(X2),inverse(X))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
double_divide(inverse(X2),double_divide(inverse(X),X)) = double_divide(multiply(X,multiply(inverse(X2),inverse(X))),double_divide(inverse(X),X)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
double_divide(multiply(X,multiply(inverse(X2),inverse(X))),double_divide(inverse(X),X)) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c40,plain,
double_divide(inverse(X2),double_divide(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
double_divide(inverse(double_divide(X2,X3)),double_divide(inverse(X),X)) = double_divide(X2,X3),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
double_divide(multiply(X3,X2),double_divide(inverse(X),X)) = double_divide(X2,X3),
inference(transitivity,[status(thm)],[c6,c41]) ).
cnf(c43,plain,
double_divide(multiply(inverse(X),inverse(double_divide(inverse(X2),X2))),double_divide(inverse(X2),X2)) = double_divide(inverse(double_divide(inverse(X2),X2)),inverse(X)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
double_divide(inverse(double_divide(inverse(X2),X2)),inverse(X)) = double_divide(multiply(inverse(X),inverse(double_divide(inverse(X2),X2))),double_divide(inverse(X2),X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)) = inverse(X3),
inference(substitution,[status(thm)],[c15]) ).
cnf(c46,plain,
inverse(X3) = double_divide(multiply(X2,multiply(inverse(inverse(X3)),X)),double_divide(X,X2)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(inverse(X4),inverse(X3)) = multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),inverse(X3)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
double_divide(multiply(inverse(X4),inverse(X3)),X3) = double_divide(multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),inverse(X3)),X3),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(inverse(X4),multiply(double_divide(X,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(inverse(X4)),X))))) = inverse(X3),
inference(substitution,[status(thm)],[c28]) ).
cnf(c50,plain,
inverse(X3) = multiply(inverse(X4),multiply(double_divide(X,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(inverse(X4)),X))))),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),inverse(X3)) = multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),multiply(inverse(X4),multiply(double_divide(X,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(inverse(X4)),X)))))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
double_divide(multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),inverse(X3)),X3) = double_divide(multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),multiply(inverse(X4),multiply(double_divide(X,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(inverse(X4)),X)))))),X3),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
double_divide(multiply(X2,multiply(inverse(X),X3)),double_divide(X3,X2)) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c54,plain,
X = double_divide(multiply(X2,multiply(inverse(X),X3)),double_divide(X3,X2)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
double_divide(multiply(double_divide(X4,X3),multiply(inverse(X2),multiply(X3,multiply(inverse(X),X4)))),X) = double_divide(multiply(double_divide(X4,X3),multiply(inverse(X2),multiply(X3,multiply(inverse(X),X4)))),double_divide(multiply(X3,multiply(inverse(X),X4)),double_divide(X4,X3))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
double_divide(multiply(double_divide(X4,X3),multiply(inverse(X2),multiply(X3,multiply(inverse(X),X4)))),double_divide(multiply(X3,multiply(inverse(X),X4)),double_divide(X4,X3))) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c57,plain,
double_divide(multiply(double_divide(X4,X3),multiply(inverse(X2),multiply(X3,multiply(inverse(X),X4)))),X) = X2,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
double_divide(multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),multiply(inverse(X4),multiply(double_divide(X,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(inverse(X4)),X)))))),X3) = X4,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
double_divide(multiply(double_divide(multiply(X2,multiply(inverse(inverse(X4)),X)),double_divide(X,X2)),inverse(X3)),X3) = X4,
inference(transitivity,[status(thm)],[c52,c58]) ).
cnf(c60,plain,
double_divide(multiply(inverse(X2),inverse(X)),X) = X2,
inference(transitivity,[status(thm)],[c48,c59]) ).
cnf(c61,plain,
double_divide(multiply(inverse(X),inverse(double_divide(inverse(X2),X2))),double_divide(inverse(X2),X2)) = X,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
double_divide(inverse(double_divide(inverse(X2),X2)),inverse(X)) = X,
inference(transitivity,[status(thm)],[c44,c61]) ).
cnf(c63,plain,
double_divide(multiply(X2,inverse(X2)),inverse(X)) = X,
inference(transitivity,[status(thm)],[c4,c62]) ).
cnf(c64,plain,
double_divide(multiply(X,inverse(X)),inverse(X2)) = X2,
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
X2 = double_divide(multiply(X,inverse(X)),inverse(X2)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
double_divide(inverse(X3),X2) = double_divide(inverse(X3),double_divide(multiply(X,inverse(X)),inverse(X2))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
double_divide(inverse(X3),double_divide(inverse(X3),X2)) = double_divide(inverse(X3),double_divide(inverse(X3),double_divide(multiply(X,inverse(X)),inverse(X2)))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(inverse(X2),multiply(X,inverse(X))) = inverse(double_divide(multiply(X,inverse(X)),inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
double_divide(multiply(X,inverse(X)),inverse(X2)) = X2,
inference(substitution,[status(thm)],[c63]) ).
cnf(c70,plain,
inverse(double_divide(multiply(X,inverse(X)),inverse(X2))) = inverse(X2),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(inverse(X2),multiply(X,inverse(X))) = inverse(X2),
inference(transitivity,[status(thm)],[c68,c70]) ).
cnf(c72,plain,
inverse(X2) = multiply(inverse(X2),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
double_divide(inverse(X3),double_divide(multiply(X,inverse(X)),inverse(X2))) = double_divide(multiply(inverse(X3),multiply(X,inverse(X))),double_divide(multiply(X,inverse(X)),inverse(X2))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
double_divide(inverse(X3),double_divide(inverse(X3),double_divide(multiply(X,inverse(X)),inverse(X2)))) = double_divide(inverse(X3),double_divide(multiply(inverse(X3),multiply(X,inverse(X))),double_divide(multiply(X,inverse(X)),inverse(X2)))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(double_divide(X2,inverse(X)),multiply(inverse(X),multiply(inverse(X3),X2))) = inverse(X3),
inference(substitution,[status(thm)],[c26]) ).
cnf(c76,plain,
inverse(X3) = multiply(double_divide(X2,inverse(X)),multiply(inverse(X),multiply(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
double_divide(inverse(X3),double_divide(multiply(inverse(X3),X2),double_divide(X2,inverse(X)))) = double_divide(multiply(double_divide(X2,inverse(X)),multiply(inverse(X),multiply(inverse(X3),X2))),double_divide(multiply(inverse(X3),X2),double_divide(X2,inverse(X)))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
double_divide(multiply(double_divide(X2,inverse(X)),multiply(inverse(X),multiply(inverse(X3),X2))),double_divide(multiply(inverse(X3),X2),double_divide(X2,inverse(X)))) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c79,plain,
double_divide(inverse(X3),double_divide(multiply(inverse(X3),X2),double_divide(X2,inverse(X)))) = X,
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
double_divide(inverse(X3),double_divide(multiply(inverse(X3),multiply(X,inverse(X))),double_divide(multiply(X,inverse(X)),inverse(X2)))) = X2,
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
double_divide(inverse(X3),double_divide(inverse(X3),double_divide(multiply(X,inverse(X)),inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c74,c80]) ).
cnf(c82,plain,
double_divide(inverse(X2),double_divide(inverse(X2),X)) = X,
inference(transitivity,[status(thm)],[c67,c81]) ).
cnf(c83,plain,
double_divide(inverse(inverse(X)),double_divide(inverse(inverse(X)),inverse(inverse(X)))) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
inverse(inverse(X)) = double_divide(inverse(inverse(X)),double_divide(inverse(inverse(X)),inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
double_divide(multiply(inverse(X2),inverse(inverse(X))),double_divide(inverse(inverse(X)),inverse(X))) = double_divide(inverse(inverse(X)),inverse(X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c86,plain,
double_divide(inverse(inverse(X)),inverse(X2)) = double_divide(multiply(inverse(X2),inverse(inverse(X))),double_divide(inverse(inverse(X)),inverse(X))),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
double_divide(inverse(X2),double_divide(inverse(inverse(X)),inverse(X2))) = double_divide(inverse(X2),double_divide(multiply(inverse(X2),inverse(inverse(X))),double_divide(inverse(inverse(X)),inverse(X)))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
double_divide(inverse(X2),double_divide(multiply(inverse(X2),inverse(inverse(X))),double_divide(inverse(inverse(X)),inverse(X)))) = X,
inference(substitution,[status(thm)],[c79]) ).
cnf(c89,plain,
double_divide(inverse(X2),double_divide(inverse(inverse(X)),inverse(X2))) = X,
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
double_divide(inverse(inverse(X)),double_divide(inverse(inverse(X)),inverse(inverse(X)))) = X,
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c84,c90]) ).
cnf(c92,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
double_divide(X2,X) = double_divide(inverse(inverse(X2)),X),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
double_divide(X2,double_divide(X2,X)) = double_divide(X2,double_divide(inverse(inverse(X2)),X)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c96,plain,
double_divide(X2,double_divide(inverse(inverse(X2)),X)) = double_divide(inverse(inverse(X2)),double_divide(inverse(inverse(X2)),X)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
double_divide(inverse(inverse(X2)),double_divide(inverse(inverse(X2)),X)) = X,
inference(substitution,[status(thm)],[c82]) ).
cnf(c98,plain,
double_divide(X2,double_divide(inverse(inverse(X2)),X)) = X,
inference(transitivity,[status(thm)],[c96,c97]) ).
cnf(c99,plain,
double_divide(X2,double_divide(X2,X)) = X,
inference(transitivity,[status(thm)],[c94,c98]) ).
cnf(c100,plain,
double_divide(X,double_divide(X,double_divide(X2,X))) = double_divide(X2,X),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
double_divide(X2,X) = double_divide(X,double_divide(X,double_divide(X2,X))),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c103,plain,
double_divide(X,X2) = double_divide(X,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
double_divide(X2,double_divide(X,X2)) = double_divide(X2,double_divide(X,inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c106,plain,
double_divide(X,inverse(inverse(X2))) = double_divide(inverse(inverse(X)),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
double_divide(X2,double_divide(X,inverse(inverse(X2)))) = double_divide(X2,double_divide(inverse(inverse(X)),inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c109,plain,
double_divide(X2,double_divide(inverse(inverse(X)),inverse(inverse(X2)))) = double_divide(inverse(inverse(X2)),double_divide(inverse(inverse(X)),inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
double_divide(inverse(inverse(X2)),double_divide(inverse(inverse(X)),inverse(inverse(X2)))) = X,
inference(substitution,[status(thm)],[c89]) ).
cnf(c111,plain,
double_divide(X2,double_divide(inverse(inverse(X)),inverse(inverse(X2)))) = X,
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
double_divide(X2,double_divide(X,inverse(inverse(X2)))) = X,
inference(transitivity,[status(thm)],[c107,c111]) ).
cnf(c113,plain,
double_divide(X2,double_divide(X,X2)) = X,
inference(transitivity,[status(thm)],[c104,c112]) ).
cnf(c114,plain,
double_divide(X,double_divide(X2,X)) = X2,
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
double_divide(X,double_divide(X,double_divide(X2,X))) = double_divide(X,X2),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
double_divide(X2,X) = double_divide(X,X2),
inference(transitivity,[status(thm)],[c101,c115]) ).
cnf(c117,plain,
double_divide(X,X2) = double_divide(X2,X),
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
double_divide(X2,X) = double_divide(X,X2),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
inverse(double_divide(X2,X)) = inverse(double_divide(X,X2)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c121,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
inverse(double_divide(X2,X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c119,c121]) ).
cnf(c123,plain,
inverse(double_divide(X,X2)) = multiply(X,X2),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(X,X2) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c126,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(X,X2) = multiply(X2,X),
inference(transitivity,[status(thm)],[c124,c126]) ).
cnf(c128,plain,
multiply(a1,inverse(a1)) = multiply(inverse(a1),a1),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(X,inverse(X)) = inverse(double_divide(inverse(X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c131,plain,
double_divide(inverse(X),double_divide(inverse(X),double_divide(inverse(X2),X2))) = double_divide(inverse(X2),X2),
inference(substitution,[status(thm)],[c82]) ).
cnf(c132,plain,
double_divide(inverse(X2),X2) = double_divide(inverse(X),double_divide(inverse(X),double_divide(inverse(X2),X2))),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
double_divide(inverse(X),double_divide(inverse(X2),X2)) = X,
inference(substitution,[status(thm)],[c40]) ).
cnf(c134,plain,
double_divide(inverse(X),double_divide(inverse(X),double_divide(inverse(X2),X2))) = double_divide(inverse(X),X),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
double_divide(inverse(X2),X2) = double_divide(inverse(X),X),
inference(transitivity,[status(thm)],[c132,c134]) ).
cnf(c136,plain,
double_divide(inverse(X),X) = double_divide(inverse(X2),X2),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
inverse(double_divide(inverse(X),X)) = inverse(double_divide(inverse(X2),X2)),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(X,inverse(X)) = inverse(double_divide(inverse(X),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c139,plain,
inverse(double_divide(inverse(X),X)) = multiply(X,inverse(X)),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
inverse(double_divide(inverse(X),X)) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c137,c139]) ).
cnf(c141,plain,
multiply(X,inverse(X)) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c130,c140]) ).
cnf(c142,plain,
multiply(a1,inverse(a1)) = multiply(b1,inverse(b1)),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(b1,inverse(b1)) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c127]) ).
cnf(c144,plain,
multiply(a1,inverse(a1)) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[c129,c144]) ).
cnf(c146,plain,
$false,
inference(resolution,[status(thm)],[c1,c145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP613-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n003.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sun Sep 27 10:11:25 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.62 Command-line arguments: --no-flatten-goal
% 0.31/0.62
% 0.31/0.62 % SZS status Unsatisfiable
% 0.31/0.62
% 0.31/0.64 % SZS output start CNFRefutation
% See solution above
% 0.31/0.77
% 0.31/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------