%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP403-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 10:09:55 AM UTC 2026
% Result : Unsatisfiable 1.39s 0.65s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 2
% Syntax : Number of clauses : 96 ( 96 unt; 0 nHn; 3 RR)
% Number of literals : 96 ( 95 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 423 ( 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,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B)))))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))))),inverse(multiply(X3,multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))))),inverse(multiply(X3,multiply(inverse(X3),X3)))))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2)))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
inverse(multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))))) = inverse(X),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))))),inverse(multiply(X3,multiply(inverse(X3),X3)))) = multiply(inverse(X),inverse(multiply(X3,multiply(inverse(X3),X3)))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))))),inverse(multiply(X3,multiply(inverse(X3),X3))))) = inverse(multiply(inverse(X),inverse(multiply(X3,multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))))),inverse(multiply(X3,multiply(inverse(X3),X3)))))) = multiply(X4,inverse(multiply(inverse(X),inverse(multiply(X3,multiply(inverse(X3),X3)))))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2))))) = multiply(X4,inverse(multiply(inverse(X),inverse(multiply(X3,multiply(inverse(X3),X3)))))),
inference(transitivity,[status(thm)],[c4,c9]) ).
cnf(c11,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),multiply(inverse(multiply(X4,X3)),X))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),inverse(multiply(X3,multiply(inverse(X3),X3)))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),inverse(multiply(X2,multiply(inverse(X2),X2)))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),multiply(inverse(multiply(X4,X3)),X))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X,
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,X4)),X3)),multiply(inverse(multiply(X,X4)),X2))),inverse(multiply(X3,multiply(inverse(X3),X3))))) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
X4 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X4))),inverse(multiply(X,multiply(inverse(X),X))))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X5,X4) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X5))),inverse(multiply(X,multiply(inverse(X),X))))),X4),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(inverse(multiply(X6,X5)),multiply(X6,X4)) = multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X4))) = inverse(multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X4))),inverse(multiply(X5,multiply(inverse(X5),X5)))) = multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))) = inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X4))),inverse(multiply(X,multiply(inverse(X),X))))) = X4,
inference(substitution,[status(thm)],[c13]) ).
cnf(c22,plain,
X4 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X4))),inverse(multiply(X,multiply(inverse(X),X))))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X5,X4) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X5))),inverse(multiply(X,multiply(inverse(X),X))))),X4),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
inverse(multiply(X5,X4)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X5))),inverse(multiply(X,multiply(inverse(X),X))))),X4)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5)))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5)))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))) = X4,
inference(substitution,[status(thm)],[c13]) ).
cnf(c30,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(multiply(X3,X2)),X6))),inverse(multiply(X,multiply(inverse(X),X))))),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))) = X4,
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X,
inference(transitivity,[status(thm)],[c20,c30]) ).
cnf(c32,plain,
X = inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),inverse(multiply(X2,multiply(inverse(X2),X2))))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X,inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),inverse(multiply(X2,multiply(inverse(X2),X2))))),inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X))))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
inverse(multiply(X,inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),inverse(multiply(X2,multiply(inverse(X2),X2))))),inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X)))))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(inverse(multiply(X3,X2)),inverse(multiply(X,inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X))))))) = multiply(inverse(multiply(X3,X2)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),inverse(multiply(X2,multiply(inverse(X2),X2))))),inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X))))))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(inverse(multiply(X3,X2)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),inverse(multiply(X2,multiply(inverse(X2),X2))))),inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X))))))) = inverse(multiply(X2,multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
multiply(inverse(multiply(X3,X2)),inverse(multiply(X,inverse(multiply(multiply(X3,X),multiply(inverse(multiply(X3,X)),multiply(X3,X))))))) = inverse(multiply(X2,multiply(inverse(X2),X2))),
inference(transitivity,[status(thm)],[c35,c36]) ).
cnf(c38,plain,
multiply(inverse(multiply(X3,X2)),inverse(multiply(inverse(X),inverse(multiply(multiply(X3,inverse(X)),multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))))))) = inverse(multiply(X2,multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
inverse(multiply(X2,multiply(inverse(X2),X2))) = multiply(inverse(multiply(X3,X2)),inverse(multiply(inverse(X),inverse(multiply(multiply(X3,inverse(X)),multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))))))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(X)))),inverse(multiply(X2,multiply(inverse(X2),X2)))) = multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(X)))),multiply(inverse(multiply(X3,X2)),inverse(multiply(inverse(X),inverse(multiply(multiply(X3,inverse(X)),multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X))))))))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),inverse(multiply(X,multiply(inverse(X),X))))) = multiply(X4,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X3),X3)))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c42,plain,
multiply(X4,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),inverse(multiply(X,multiply(inverse(X),X))))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X3),X3))))))) = multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),inverse(multiply(X,multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),inverse(multiply(X,multiply(inverse(X),X)))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(X),inverse(multiply(X2,multiply(inverse(X2),X2))))))) = X,
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(X)))),multiply(inverse(multiply(X3,X2)),inverse(multiply(inverse(X),inverse(multiply(multiply(X3,inverse(X)),multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X))))))))) = X,
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(X)))),inverse(multiply(X2,multiply(inverse(X2),X2)))) = X,
inference(transitivity,[status(thm)],[c40,c46]) ).
cnf(c48,plain,
multiply(inverse(multiply(inverse(multiply(X,X2)),multiply(X,inverse(X3)))),inverse(multiply(X2,multiply(inverse(X2),X2)))) = X3,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
X3 = multiply(inverse(multiply(inverse(multiply(X,X2)),multiply(X,inverse(X3)))),inverse(multiply(X2,multiply(inverse(X2),X2)))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(X3),X3) = multiply(inverse(X3),multiply(inverse(multiply(inverse(multiply(X,X2)),multiply(X,inverse(X3)))),inverse(multiply(X2,multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(inverse(multiply(X,X3)),multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2))),inverse(multiply(X3,multiply(inverse(X3),X3))))))) = multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c52,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2)) = multiply(inverse(multiply(X,X3)),multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2))),inverse(multiply(X3,multiply(inverse(X3),X3))))))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2))),inverse(multiply(X3,multiply(inverse(X3),X3)))))) = multiply(X,X2),
inference(congruence,[status(thm)],[c13]) ).
cnf(c54,plain,
multiply(inverse(multiply(X,X3)),multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2))),inverse(multiply(X3,multiply(inverse(X3),X3))))))) = multiply(inverse(multiply(X,X3)),multiply(X,X2)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2)) = multiply(inverse(multiply(X,X3)),multiply(X,X2)),
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2)) = multiply(inverse(multiply(X,X3)),multiply(X,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(multiply(X3,X5)),multiply(X3,X4)) = multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X4)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X4))) = inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X4))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(inverse(multiply(inverse(multiply(X3,X6)),multiply(X3,X4))),X5) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X6)),multiply(inverse(multiply(X2,X)),X4))),X5),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(X4,multiply(inverse(multiply(inverse(multiply(X3,X6)),multiply(X3,X4))),X5)) = multiply(X4,multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X6)),multiply(inverse(multiply(X2,X)),X4))),X5)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c62,plain,
X3 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X3,multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),X4)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X5,multiply(inverse(X5),X5))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),X4)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c65,plain,
X3 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(X3,X4) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X4))),inverse(multiply(X5,multiply(inverse(X5),X5)))))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(inverse(multiply(X3,X5)),multiply(X3,X4)) = multiply(inverse(multiply(X3,X5)),multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(inverse(multiply(X3,X5)),multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))))) = multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X4)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c69,plain,
multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))))) = multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c70,plain,
multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3)) = multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c72,plain,
multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4)))))) = multiply(X5,X3),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X4,multiply(inverse(X4),X4))))))) = multiply(inverse(multiply(X5,X4)),multiply(X5,X3)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3)) = multiply(inverse(multiply(X5,X4)),multiply(X5,X3)),
inference(transitivity,[status(thm)],[c70,c73]) ).
cnf(c75,plain,
multiply(inverse(multiply(X3,X5)),multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X4))),inverse(multiply(X5,multiply(inverse(X5),X5))))))) = multiply(inverse(multiply(X6,X5)),multiply(X6,X4)),
inference(transitivity,[status(thm)],[c68,c74]) ).
cnf(c76,plain,
multiply(inverse(multiply(X,X3)),multiply(X,X2)) = multiply(inverse(multiply(X4,X3)),multiply(X4,X2)),
inference(transitivity,[status(thm)],[c67,c75]) ).
cnf(c77,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X8,X7)),X5)),multiply(inverse(multiply(X8,X7)),X6))),inverse(multiply(X5,multiply(inverse(X5),X5))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X8,X7)),X5)),multiply(inverse(multiply(X8,X7)),X6))),X4)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X5,multiply(inverse(X5),X5))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),X4)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X7)),multiply(inverse(multiply(X2,X)),X5))),inverse(multiply(X7,multiply(inverse(X7),X7))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X7)),multiply(inverse(multiply(X2,X)),X5))),X6)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X7)),multiply(inverse(multiply(X4,X3)),X8))),inverse(multiply(X7,multiply(inverse(X7),X7))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X7)),multiply(inverse(multiply(X4,X3)),X8))),X6)),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X3)),multiply(inverse(multiply(X2,X)),X4))),inverse(multiply(X3,multiply(inverse(X3),X3))))) = X4,
inference(substitution,[status(thm)],[c13]) ).
cnf(c80,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X5))),inverse(multiply(X4,multiply(inverse(X4),X4))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X5))),X3)) = multiply(X5,multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X5))),X3)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(inverse(multiply(inverse(multiply(X2,X)),X3)),multiply(inverse(multiply(X2,X)),X5)) = multiply(inverse(multiply(X4,X3)),multiply(X4,X5)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c82,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X3)),multiply(inverse(multiply(X2,X)),X5))) = inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X5))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X6))),X3) = multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X6))),X3),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(X6,multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X6))),X3)) = multiply(X6,multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X6))),X3)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X6))),inverse(multiply(X4,multiply(inverse(X4),X4))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X6))),X3)) = multiply(X6,multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X6))),X3)),
inference(transitivity,[status(thm)],[c80,c84]) ).
cnf(c86,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),inverse(multiply(X5,multiply(inverse(X5),X5))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),X4)) = multiply(X7,multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X7))),X4)),
inference(transitivity,[status(thm)],[c78,c85]) ).
cnf(c87,plain,
multiply(X3,multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X5)),multiply(inverse(multiply(X2,X)),X3))),X4)) = multiply(X7,multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X7))),X4)),
inference(transitivity,[status(thm)],[c63,c86]) ).
cnf(c88,plain,
multiply(X2,multiply(inverse(multiply(inverse(multiply(X,X4)),multiply(X,X2))),X3)) = multiply(X6,multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X6))),X3)),
inference(transitivity,[status(thm)],[c60,c87]) ).
cnf(c89,plain,
multiply(inverse(X5),multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(X5)))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = multiply(inverse(X4),multiply(inverse(multiply(inverse(multiply(X,X2)),multiply(X,inverse(X4)))),inverse(multiply(X2,multiply(inverse(X2),X2))))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(inverse(X4),multiply(inverse(multiply(inverse(multiply(X,X2)),multiply(X,inverse(X4)))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = multiply(inverse(X5),multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(X5)))),inverse(multiply(X2,multiply(inverse(X2),X2))))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,inverse(X3)))),inverse(multiply(X,multiply(inverse(X),X)))) = X3,
inference(substitution,[status(thm)],[c47]) ).
cnf(c92,plain,
multiply(inverse(X3),multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,inverse(X3)))),inverse(multiply(X,multiply(inverse(X),X))))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(inverse(X3),multiply(inverse(multiply(inverse(multiply(X,X2)),multiply(X,inverse(X3)))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = multiply(inverse(X4),X4),
inference(transitivity,[status(thm)],[c90,c92]) ).
cnf(c94,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c50,c93]) ).
cnf(c95,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
$false,
inference(resolution,[status(thm)],[c1,c95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP403-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 10:06:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.39/0.65 Command-line arguments: --no-flatten-goal
% 1.39/0.65
% 1.39/0.65 % SZS status Unsatisfiable
% 1.39/0.65
% 1.39/0.66 % SZS output start CNFRefutation
% See solution above
% 2.14/0.71
% 2.14/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------