%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP406-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:09:56 AM UTC 2026
% Result : Unsatisfiable 0.62s 0.59s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 2
% Syntax : Number of clauses : 137 ( 137 unt; 0 nHn; 3 RR)
% Number of literals : 137 ( 136 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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 : 499 ( 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)),multiply(inverse(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)),multiply(inverse(X2),multiply(inverse(X2),X2)))))),multiply(inverse(X3),multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),multiply(inverse(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)),multiply(inverse(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)),multiply(inverse(X2),multiply(inverse(X2),X2)))))),multiply(inverse(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)),multiply(inverse(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)),multiply(inverse(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)),multiply(inverse(X2),multiply(inverse(X2),X2)))))),multiply(inverse(X3),multiply(inverse(X3),X3))) = multiply(inverse(X),multiply(inverse(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)),multiply(inverse(X2),multiply(inverse(X2),X2)))))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = inverse(multiply(inverse(X),multiply(inverse(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)),multiply(inverse(X2),multiply(inverse(X2),X2)))))),multiply(inverse(X3),multiply(inverse(X3),X3))))) = multiply(X4,inverse(multiply(inverse(X),multiply(inverse(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)),multiply(inverse(X2),multiply(inverse(X2),X2)))) = multiply(X4,inverse(multiply(inverse(X),multiply(inverse(X3),multiply(inverse(X3),X3))))),
inference(transitivity,[status(thm)],[c4,c9]) ).
cnf(c11,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(X4,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X4,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),multiply(inverse(X),multiply(inverse(X),X)))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3)))))) = multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),multiply(inverse(X),multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2)),multiply(inverse(X),multiply(inverse(X),X))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(X),multiply(inverse(X2),multiply(inverse(X2),X2)))))) = X,
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
multiply(inverse(multiply(X,X5)),multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X5),multiply(inverse(X5),X5)))))) = multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),multiply(inverse(X3),multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X4),multiply(inverse(X4),X4))) = multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(X),multiply(inverse(X),X)))))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4)))) = multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X),multiply(inverse(X),X))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c19,plain,
multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X),multiply(inverse(X),X))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4)))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X5,multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X),multiply(inverse(X),X)))))) = multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(inverse(multiply(X5,X4)),multiply(X5,multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X),multiply(inverse(X),X))))))) = multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4)))))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(inverse(multiply(X5,X4)),multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4)))))) = multiply(inverse(multiply(inverse(multiply(X3,X)),X4)),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c23,plain,
multiply(inverse(multiply(X5,X4)),multiply(X5,multiply(X3,inverse(multiply(inverse(X2),multiply(inverse(X),multiply(inverse(X),X))))))) = multiply(inverse(multiply(inverse(multiply(X3,X)),X4)),X2),
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
multiply(inverse(multiply(X,X3)),multiply(X,multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))))) = multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),X3)),multiply(inverse(multiply(X5,X4)),X2)) = multiply(inverse(multiply(X,X3)),multiply(X,multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))))),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),X)),multiply(inverse(X2),multiply(inverse(X2),X2))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
multiply(X,multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),multiply(inverse(X3),multiply(inverse(X3),X3)))))) = multiply(X,X2),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(inverse(multiply(X,X3)),multiply(X,multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),X2)),multiply(inverse(X4),multiply(inverse(X4),X4))))))) = multiply(inverse(multiply(X,X3)),multiply(X,X2)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,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)],[c25,c28]) ).
cnf(c30,plain,
multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3)) = multiply(inverse(multiply(X5,X4)),multiply(X5,X3)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(inverse(multiply(X5,X4)),multiply(X5,X3)) = multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))) = inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X4),multiply(inverse(X4),X4))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),multiply(inverse(X4),multiply(inverse(X4),X4))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X4),multiply(inverse(X4),X4)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),multiply(inverse(X4),multiply(inverse(X4),X4)))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),multiply(inverse(X4),multiply(inverse(X4),X4)))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X3)),multiply(inverse(X),multiply(inverse(X),X))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c36,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X3)),multiply(inverse(X),multiply(inverse(X),X))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),X4)),multiply(inverse(multiply(X2,X)),X3))),multiply(inverse(X4),multiply(inverse(X4),X4)))) = X3,
inference(transitivity,[status(thm)],[c35,c36]) ).
cnf(c38,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X,
inference(transitivity,[status(thm)],[c34,c37]) ).
cnf(c39,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(X2,multiply(inverse(X),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X)))) = inverse(multiply(X2,multiply(inverse(X),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(X),multiply(inverse(X),X))))) = multiply(X2,inverse(multiply(X3,multiply(inverse(X),multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(X),multiply(inverse(X),X)))))) = multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(X3,multiply(inverse(X),multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X4),multiply(inverse(X4),X4))) = multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(X3,multiply(inverse(X),multiply(inverse(X),X)))))),
inference(transitivity,[status(thm)],[c17,c42]) ).
cnf(c44,plain,
multiply(inverse(multiply(inverse(multiply(X,X5)),multiply(X,X4))),multiply(inverse(X5),multiply(inverse(X5),X5))) = multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(multiply(X5,multiply(inverse(X3),multiply(inverse(X3),X3)))))) = multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X5))),multiply(inverse(X),multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(X5,multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(multiply(X5,multiply(inverse(X3),multiply(inverse(X3),X3))))))) = multiply(X5,multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X5))),multiply(inverse(X),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X3))),multiply(inverse(X),multiply(inverse(X),X)))) = X3,
inference(substitution,[status(thm)],[c38]) ).
cnf(c48,plain,
X3 = inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X3))),multiply(inverse(X),multiply(inverse(X),X)))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(X3,multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X3))),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X3))),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X3))),multiply(inverse(X),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),multiply(X2,X3))) = multiply(inverse(multiply(X,X3)),multiply(X,multiply(X2,X3))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c51,plain,
multiply(inverse(multiply(X,X3)),multiply(X,multiply(X2,X3))) = multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),multiply(X2,X3))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,multiply(X2,X3)))),multiply(inverse(multiply(X,X3)),multiply(X,multiply(X2,X3)))) = multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,multiply(X2,X3)))),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),multiply(X2,X3)))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)) = multiply(inverse(multiply(X,X2)),multiply(X,X2)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c54,plain,
multiply(inverse(multiply(X,X2)),multiply(X,X2)) = multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2))) = multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X,X2)))),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2)))) = multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X,X2)))),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2))) = multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X,X2))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c58,plain,
multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X,X2))) = multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X,X2)))) = inverse(multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2)))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X,X2)))),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2)))),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)) = multiply(inverse(multiply(X,X2)),multiply(X,X2)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c62,plain,
multiply(inverse(multiply(X,X2)),multiply(X,X2)) = multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2))) = multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2)))) = inverse(multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),multiply(X,X2)))),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)))),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(inverse(multiply(X,X2)),X2)),multiply(inverse(multiply(X,X2)),X2)))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X)))))) = multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c67,plain,
multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3))) = multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X)))))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(inverse(X),multiply(inverse(X),X))))) = inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(inverse(X),multiply(inverse(X),X))))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X2)),X)),X3)),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(X4,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c71,plain,
multiply(X4,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X2)),X)),X3)),multiply(inverse(X),multiply(inverse(X),X)))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(multiply(X4,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2))))),multiply(inverse(X3),multiply(inverse(X3),X3))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X2)),X)),X3)),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(X3),multiply(inverse(X3),X3))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
inverse(multiply(multiply(X4,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2))))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X2)),X)),X3)),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X2)),X)),X3)),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = multiply(inverse(multiply(X4,X2)),inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c75,plain,
inverse(multiply(multiply(X4,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X2),X2))))),multiply(inverse(X3),multiply(inverse(X3),X3)))) = multiply(inverse(multiply(X4,X2)),inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))))),
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
inverse(multiply(multiply(X4,inverse(multiply(inverse(X),multiply(inverse(X3),multiply(inverse(X3),X3))))),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2))))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2))))) = inverse(multiply(multiply(X4,inverse(multiply(inverse(X),multiply(inverse(X3),multiply(inverse(X3),X3))))),multiply(inverse(X),multiply(inverse(X),X)))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(X4,inverse(multiply(inverse(X),multiply(inverse(X3),multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c79,plain,
multiply(multiply(X4,inverse(multiply(inverse(X),multiply(inverse(X3),multiply(inverse(X3),X3))))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(inverse(X),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
inverse(multiply(multiply(X4,inverse(multiply(inverse(X),multiply(inverse(X3),multiply(inverse(X3),X3))))),multiply(inverse(X),multiply(inverse(X),X)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(inverse(X),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X)),multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c82,plain,
inverse(multiply(multiply(X4,inverse(multiply(inverse(X),multiply(inverse(X3),multiply(inverse(X3),X3))))),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2))))),
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))))) = multiply(inverse(multiply(X4,X3)),inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2))))),
inference(transitivity,[status(thm)],[c77,c82]) ).
cnf(c84,plain,
multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4))))),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))))),multiply(inverse(X),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(inverse(X),multiply(inverse(X),X)))) = inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))))),multiply(inverse(X),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(inverse(X),multiply(inverse(X),X))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))))),multiply(inverse(X),multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(inverse(X),multiply(inverse(X),X))))) = inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c90,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))))),multiply(inverse(X),multiply(inverse(X),X))))) = inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))),
inference(transitivity,[status(thm)],[c88,c89]) ).
cnf(c91,plain,
inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X)))) = inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(transitivity,[status(thm)],[c69,c90]) ).
cnf(c92,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(inverse(X),multiply(inverse(X),X)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(X),multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X)))))) = multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(X),multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X)))))) = multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c97,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3)))),multiply(inverse(X),multiply(inverse(X),X)))))) = multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4))),
inference(transitivity,[status(thm)],[c95,c96]) ).
cnf(c98,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2))),
inference(transitivity,[status(thm)],[c67,c97]) ).
cnf(c99,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),X3)))),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),X3)))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),X3)))),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),X3)))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),multiply(X2,X3)))),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),X3)))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c65,c100]) ).
cnf(c102,plain,
multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,multiply(X2,X3)))),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),X3)))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c60,c101]) ).
cnf(c103,plain,
multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,multiply(X2,X3)))),multiply(inverse(multiply(inverse(multiply(X2,X3)),X3)),multiply(inverse(multiply(X2,X3)),multiply(X2,X3)))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c56,c102]) ).
cnf(c104,plain,
multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,multiply(X3,X4)))),multiply(inverse(multiply(X2,X4)),multiply(X2,multiply(X3,X4)))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c52,c103]) ).
cnf(c105,plain,
multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))) = multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4))) = multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))) = inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(X3,multiply(X2,X))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(X3,multiply(X2,X))))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(X3,multiply(X2,X)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(X3,multiply(X2,X)))))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(X3,multiply(X2,X)))))) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(X),multiply(inverse(X),X))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c111,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(X),multiply(inverse(X),X))))) = multiply(X3,multiply(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X)))),multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(X3,multiply(X2,X)))))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4)))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(inverse(multiply(X3,multiply(X2,X))),multiply(X3,multiply(X2,X)))))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c109,c112]) ).
cnf(c114,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(X4,multiply(X3,X2)))))) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(X4,multiply(X3,X2)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(X4,multiply(X3,X2)))))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(X5,multiply(X4,multiply(X3,X2))) = multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(X4,multiply(X3,X2))))))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(inverse(multiply(X5,multiply(X4,multiply(X3,X2)))),multiply(X5,multiply(X4,multiply(X3,X2)))) = multiply(inverse(multiply(X5,multiply(X4,multiply(X3,X2)))),multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(X4,multiply(X3,X2)))))))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(inverse(multiply(X5,multiply(X4,multiply(X3,X2)))),multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(inverse(multiply(X4,multiply(X3,X2))),multiply(X4,multiply(X3,X2)))))))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c119,plain,
multiply(inverse(multiply(X5,multiply(X4,multiply(X3,X2)))),multiply(X5,multiply(X4,multiply(X3,X2)))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X4))),multiply(inverse(X),multiply(inverse(X),X)))),multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X4))),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X4,multiply(inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X4))),multiply(inverse(X),multiply(inverse(X),X)))) = multiply(inverse(multiply(inverse(X3),multiply(inverse(X3),X3))),multiply(inverse(X3),multiply(inverse(X3),X3))),
inference(transitivity,[status(thm)],[c49,c120]) ).
cnf(c122,plain,
multiply(X4,multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2))))))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c46,c121]) ).
cnf(c123,plain,
multiply(inverse(X3),multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),multiply(inverse(X),X))))))) = multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(inverse(multiply(inverse(X4),multiply(inverse(X4),X4))),multiply(inverse(X4),multiply(inverse(X4),X4))) = multiply(inverse(X3),multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),multiply(inverse(X),X))))))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),multiply(inverse(X),X)))))) = X3,
inference(substitution,[status(thm)],[c15]) ).
cnf(c126,plain,
multiply(inverse(X3),multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),multiply(inverse(X),X))))))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(inverse(multiply(inverse(X2),multiply(inverse(X2),X2))),multiply(inverse(X2),multiply(inverse(X2),X2))) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c124,c126]) ).
cnf(c128,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(inverse(X4),multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(X4),multiply(inverse(X2),multiply(inverse(X2),X2))))))) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c131,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(X4),multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(X4),multiply(inverse(X2),multiply(inverse(X2),X2))))))),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),multiply(inverse(X),X)))))) = X3,
inference(substitution,[status(thm)],[c15]) ).
cnf(c133,plain,
multiply(inverse(X3),multiply(inverse(multiply(X2,X)),multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),multiply(inverse(X),X))))))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X))) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c131,c133]) ).
cnf(c135,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c129,c134]) ).
cnf(c136,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
$false,
inference(resolution,[status(thm)],[c1,c136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP406-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n005.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 10:03:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.59 Command-line arguments: --flatten --complete-subsets
% 0.62/0.59
% 0.62/0.59 % SZS status Unsatisfiable
% 0.62/0.59
% 0.62/0.61 % SZS output start CNFRefutation
% See solution above
% 2.06/0.78
% 2.06/0.78 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------