%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP430-1 : 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 10:10:21 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.46s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 110
% Number of leaves : 2
% Syntax : Number of clauses : 308 ( 308 unt; 0 nHn; 3 RR)
% Number of literals : 308 ( 307 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 : 1182 ( 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(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X3,X5) = multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))),X5),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(X3,X5)) = multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))),X5)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(X3,X5))) = inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))),X5))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(X5,inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(X3,X5)))) = multiply(X5,inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))),X5)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X5,inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))),X5)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
multiply(X5,inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X))),multiply(X3,X5)))) = X2,
inference(transitivity,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
multiply(X,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X4,X3))),multiply(X2,inverse(X2)))))),multiply(X6,inverse(X6))),multiply(X3,X)))) = multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X4,X3))),multiply(X2,inverse(X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,X4))),multiply(X3,inverse(X3))) = multiply(X2,inverse(multiply(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,X4))),multiply(X3,inverse(X3)))))),multiply(X,inverse(X))),multiply(X4,X2)))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X2,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,X2))),multiply(X,inverse(X)))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X4,X3))),multiply(X2,inverse(X2)))))),multiply(X,inverse(X))) = multiply(X4,multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,X4))),multiply(X3,inverse(X3)))))),multiply(X,inverse(X))),multiply(X4,X2)) = multiply(multiply(X5,multiply(X,inverse(X))),multiply(X4,X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(multiply(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,X4))),multiply(X3,inverse(X3)))))),multiply(X,inverse(X))),multiply(X4,X2))) = inverse(multiply(multiply(X5,multiply(X,inverse(X))),multiply(X4,X2))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(X2,inverse(multiply(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,X4))),multiply(X3,inverse(X3)))))),multiply(X,inverse(X))),multiply(X4,X2)))) = multiply(X2,inverse(multiply(multiply(X5,multiply(X,inverse(X))),multiply(X4,X2)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,X4))),multiply(X3,inverse(X3))) = multiply(X2,inverse(multiply(multiply(X5,multiply(X,inverse(X))),multiply(X4,X2)))),
inference(transitivity,[status(thm)],[c12,c17]) ).
cnf(c19,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X4,X2))),multiply(X6,inverse(X6))) = multiply(X5,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(X2,X5)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X6,inverse(multiply(multiply(X5,multiply(X4,inverse(X4))),multiply(X3,X6)))) = multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X5,X3))),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(X6,inverse(multiply(multiply(X5,multiply(X4,inverse(X4))),multiply(X3,X6)))),multiply(X5,X7)) = multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X5,X3))),multiply(X,inverse(X))),multiply(X5,X7)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(multiply(multiply(X6,inverse(multiply(multiply(X5,multiply(X4,inverse(X4))),multiply(X3,X6)))),multiply(X5,X7))) = inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X5,X3))),multiply(X,inverse(X))),multiply(X5,X7))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X7,inverse(multiply(multiply(X6,inverse(multiply(multiply(X5,multiply(X4,inverse(X4))),multiply(X3,X6)))),multiply(X5,X7)))) = multiply(X7,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X5,X3))),multiply(X,inverse(X))),multiply(X5,X7)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X5,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,X3))),multiply(X,inverse(X))),multiply(X4,X5)))) = X3,
inference(substitution,[status(thm)],[c10]) ).
cnf(c25,plain,
multiply(X5,inverse(multiply(multiply(X4,inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),multiply(X,X4)))),multiply(X3,X5)))) = X,
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
multiply(X2,inverse(multiply(multiply(X,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),X)))),multiply(X4,X2)))) = multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))) = multiply(X2,inverse(multiply(multiply(X,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),X)))),multiply(X4,X2)))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(X,inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X4,multiply(X3,multiply(X2,inverse(X2)))))),X)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
multiply(multiply(X,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),X)))),multiply(X4,X2)) = multiply(X5,multiply(X4,X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(multiply(multiply(X,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),X)))),multiply(X4,X2))) = inverse(multiply(X5,multiply(X4,X2))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X2,inverse(multiply(multiply(X,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(multiply(multiply(X6,inverse(X6)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),X)))),multiply(X4,X2)))) = multiply(X2,inverse(multiply(X5,multiply(X4,X2)))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(multiply(X5,inverse(X5)),inverse(multiply(X4,multiply(X3,multiply(X2,inverse(X2)))))) = multiply(X,inverse(multiply(X4,multiply(X3,X)))),
inference(transitivity,[status(thm)],[c27,c31]) ).
cnf(c33,plain,
multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X)))))) = multiply(X5,inverse(multiply(X4,multiply(multiply(X3,inverse(X3)),X5)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(X5,inverse(multiply(X4,multiply(multiply(X3,inverse(X3)),X5)))) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X)))))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(multiply(X5,inverse(multiply(X4,multiply(multiply(X3,inverse(X3)),X5))))) = inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))))))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X5,inverse(multiply(multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),multiply(X6,inverse(X6))))),multiply(X7,inverse(X7))),multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),X5)))) = multiply(X6,inverse(X6)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c37,plain,
multiply(X7,inverse(X7)) = multiply(X6,inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X7,inverse(X7))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6)))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(multiply(X5,inverse(X5)),inverse(multiply(X4,multiply(X3,multiply(X,inverse(X)))))) = multiply(X2,inverse(multiply(X4,multiply(X3,X2)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c39,plain,
multiply(X3,inverse(multiply(X5,multiply(X4,X3)))) = multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(multiply(X4,inverse(multiply(X6,multiply(X5,X4)))),multiply(X3,inverse(X3))) = multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X6,multiply(X5,multiply(X2,inverse(X2)))))),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),multiply(X3,inverse(X3))) = multiply(X7,inverse(multiply(multiply(X5,multiply(X6,inverse(X6))),multiply(multiply(X4,multiply(X2,inverse(X2))),X7)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c42,plain,
multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X7,multiply(X6,multiply(X3,inverse(X3)))))),multiply(X5,inverse(X5))) = multiply(X2,inverse(multiply(multiply(X7,multiply(X,inverse(X))),multiply(multiply(X6,multiply(X3,inverse(X3))),X2)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c43,plain,
multiply(X2,inverse(multiply(multiply(X7,multiply(X,inverse(X))),multiply(multiply(X6,multiply(X3,inverse(X3))),X2)))) = multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X7,multiply(X6,multiply(X3,inverse(X3)))))),multiply(X5,inverse(X5))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,multiply(X3,multiply(X,inverse(X)))))) = multiply(X5,inverse(multiply(X4,multiply(X3,X5)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c45,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X5,multiply(X4,multiply(X,inverse(X)))))),multiply(X3,inverse(X3))) = multiply(multiply(X6,inverse(multiply(X5,multiply(X4,X6)))),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(X2,inverse(multiply(multiply(X6,multiply(X,inverse(X))),multiply(multiply(X5,multiply(X3,inverse(X3))),X2)))) = multiply(multiply(X7,inverse(multiply(X6,multiply(X5,X7)))),multiply(X4,inverse(X4))),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X6,multiply(X5,multiply(X2,inverse(X2)))))),multiply(X3,inverse(X3))) = multiply(multiply(X7,inverse(multiply(X6,multiply(X5,X7)))),multiply(X4,inverse(X4))),
inference(transitivity,[status(thm)],[c41,c46]) ).
cnf(c48,plain,
multiply(multiply(X2,inverse(multiply(X5,multiply(X4,X2)))),multiply(X,inverse(X))) = multiply(multiply(X6,inverse(multiply(X5,multiply(X4,X6)))),multiply(X3,inverse(X3))),
inference(transitivity,[status(thm)],[c40,c47]) ).
cnf(c49,plain,
multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),multiply(X4,inverse(X4))) = multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),multiply(X5,inverse(X5))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
inverse(multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),multiply(X4,inverse(X4)))) = inverse(multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),multiply(X5,inverse(X5)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),multiply(X5,inverse(X5))))) = multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(X3,inverse(multiply(X2,multiply(X,X3)))),multiply(X6,inverse(X6))))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X6,inverse(X6))))),multiply(X,inverse(X))) = multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X7,inverse(X7))))),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X7,inverse(X7))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6)) = multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X8,inverse(X8))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X7,inverse(X7))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6))) = inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X8,inverse(X8))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(X6,inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X7,inverse(X7))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6)))) = multiply(X6,inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X8,inverse(X8))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6)))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X6,inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X7,inverse(X7))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6)))) = multiply(X7,inverse(X7)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c57,plain,
multiply(X6,inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),multiply(X7,inverse(X7))))),multiply(X,inverse(X))),multiply(multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),X6)))) = multiply(X8,inverse(X8)),
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
multiply(X,inverse(X)) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c37,c57]) ).
cnf(c59,plain,
multiply(X2,inverse(X2)) = multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))) = multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))),multiply(X,X4)) = multiply(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),multiply(X2,inverse(X2))),multiply(X,X4)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))),multiply(X,X4))) = inverse(multiply(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),multiply(X2,inverse(X2))),multiply(X,X4))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X4,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))),multiply(X,X4)))) = multiply(X4,inverse(multiply(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),multiply(X2,inverse(X2))),multiply(X,X4)))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X3,inverse(multiply(multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),multiply(X2,inverse(X2))),multiply(X,X3)))) = inverse(X),
inference(substitution,[status(thm)],[c10]) ).
cnf(c65,plain,
multiply(X4,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))),multiply(X,X4)))) = inverse(X),
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
multiply(X,inverse(multiply(multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2))),multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X5,multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2)))))),X)))) = inverse(multiply(multiply(X3,inverse(X3)),inverse(multiply(X5,multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2))))))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
inverse(multiply(multiply(X3,inverse(X3)),inverse(multiply(X5,multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2))))))) = multiply(X,inverse(multiply(multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2))),multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X5,multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2)))))),X)))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(X,inverse(multiply(multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2))),multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X5,multiply(multiply(X4,inverse(X4)),multiply(X2,inverse(X2)))))),X)))) = X5,
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))))))) = X4,
inference(transitivity,[status(thm)],[c67,c68]) ).
cnf(c70,plain,
inverse(multiply(X3,inverse(multiply(X2,multiply(multiply(X,inverse(X)),X3))))) = X2,
inference(transitivity,[status(thm)],[c35,c69]) ).
cnf(c71,plain,
inverse(multiply(X,inverse(multiply(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3))),multiply(multiply(X2,inverse(X2)),X))))) = multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3))) = inverse(multiply(X,inverse(multiply(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3))),multiply(multiply(X2,inverse(X2)),X))))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(X,inverse(multiply(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3))),multiply(multiply(X2,inverse(X2)),X)))) = inverse(multiply(X2,inverse(X2))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c74,plain,
inverse(multiply(X,inverse(multiply(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3))),multiply(multiply(X2,inverse(X2)),X))))) = inverse(inverse(multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))) = inverse(inverse(multiply(X,inverse(X)))),
inference(transitivity,[status(thm)],[c72,c74]) ).
cnf(c76,plain,
multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))) = inverse(inverse(multiply(X3,inverse(X3)))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
inverse(inverse(multiply(X3,inverse(X3)))) = multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
inverse(inverse(inverse(multiply(X3,inverse(X3))))) = inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(X2,multiply(X,inverse(X))) = multiply(X2,multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c80,plain,
inverse(multiply(X2,multiply(X,inverse(X)))) = inverse(multiply(X2,multiply(X3,inverse(X3)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(inverse(X3),inverse(multiply(X2,multiply(X,inverse(X))))) = multiply(inverse(X3),inverse(multiply(X2,multiply(X3,inverse(X3))))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(X,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),X)))) = X5,
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
X5 = multiply(X,inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))),X)))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(X6,multiply(X5,X4)) = multiply(multiply(X,inverse(multiply(multiply(X5,multiply(X3,inverse(X3))),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X6,multiply(X5,multiply(X3,inverse(X3)))))),X)))),multiply(X5,X4)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
inverse(multiply(X6,multiply(X5,X4))) = inverse(multiply(multiply(X,inverse(multiply(multiply(X5,multiply(X3,inverse(X3))),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X6,multiply(X5,multiply(X3,inverse(X3)))))),X)))),multiply(X5,X4))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(X4,inverse(multiply(X6,multiply(X5,X4)))) = multiply(X4,inverse(multiply(multiply(X,inverse(multiply(multiply(X5,multiply(X3,inverse(X3))),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X6,multiply(X5,multiply(X3,inverse(X3)))))),X)))),multiply(X5,X4)))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(X4,inverse(multiply(multiply(X,inverse(multiply(multiply(X5,multiply(X3,inverse(X3))),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X6,multiply(X5,multiply(X3,inverse(X3)))))),X)))),multiply(X5,X4)))) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X6,multiply(X5,multiply(X3,inverse(X3)))))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c88,plain,
multiply(X6,inverse(multiply(multiply(X3,inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),X3)))),multiply(X4,X6)))) = multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c89,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))) = multiply(X6,inverse(multiply(multiply(X3,inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),X3)))),multiply(X4,X6)))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(X3,inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),X3)))) = X5,
inference(substitution,[status(thm)],[c2]) ).
cnf(c91,plain,
multiply(multiply(X3,inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),X3)))),multiply(X4,X6)) = multiply(X5,multiply(X4,X6)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
inverse(multiply(multiply(X3,inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),X3)))),multiply(X4,X6))) = inverse(multiply(X5,multiply(X4,X6))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(X6,inverse(multiply(multiply(X3,inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X2,inverse(X2)))))),X3)))),multiply(X4,X6)))) = multiply(X6,inverse(multiply(X5,multiply(X4,X6)))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X4,multiply(X3,multiply(X2,inverse(X2)))))) = multiply(X5,inverse(multiply(X4,multiply(X3,X5)))),
inference(transitivity,[status(thm)],[c89,c93]) ).
cnf(c95,plain,
multiply(X4,inverse(multiply(multiply(X,inverse(multiply(multiply(X5,multiply(X3,inverse(X3))),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X6,multiply(X5,multiply(X3,inverse(X3)))))),X)))),multiply(X5,X4)))) = multiply(X7,inverse(multiply(X6,multiply(X5,X7)))),
inference(transitivity,[status(thm)],[c87,c94]) ).
cnf(c96,plain,
multiply(X,inverse(multiply(X3,multiply(X2,X)))) = multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),
inference(transitivity,[status(thm)],[c86,c95]) ).
cnf(c97,plain,
multiply(X,inverse(multiply(X2,multiply(X3,X)))) = multiply(inverse(X3),inverse(multiply(X2,multiply(X3,inverse(X3))))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(inverse(X3),inverse(multiply(X2,multiply(X3,inverse(X3))))) = multiply(X,inverse(multiply(X2,multiply(X3,X)))),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(inverse(X4),inverse(multiply(X3,multiply(X2,inverse(X2))))) = multiply(X,inverse(multiply(X3,multiply(X4,X)))),
inference(transitivity,[status(thm)],[c81,c98]) ).
cnf(c100,plain,
multiply(inverse(X2),inverse(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))))) = multiply(X4,inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,X4)))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(X4,inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,X4)))) = multiply(inverse(X2),inverse(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))))),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))) = inverse(inverse(multiply(X2,inverse(X2)))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c103,plain,
inverse(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X)))) = inverse(inverse(inverse(multiply(X2,inverse(X2))))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(inverse(X3),inverse(multiply(multiply(X4,inverse(X4)),multiply(X,inverse(X))))) = multiply(inverse(X3),inverse(inverse(inverse(multiply(X2,inverse(X2)))))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(X4,inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,X4)))) = multiply(inverse(X2),inverse(inverse(inverse(multiply(X,inverse(X)))))),
inference(transitivity,[status(thm)],[c101,c104]) ).
cnf(c106,plain,
multiply(X2,inverse(multiply(multiply(X,inverse(X)),multiply(X4,X2)))) = multiply(inverse(X4),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(inverse(X4),inverse(inverse(inverse(multiply(X3,inverse(X3)))))) = multiply(X2,inverse(multiply(multiply(X,inverse(X)),multiply(X4,X2)))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(multiply(inverse(X5),inverse(inverse(inverse(multiply(X4,inverse(X4)))))),multiply(X3,inverse(X3))) = multiply(multiply(X2,inverse(multiply(multiply(X,inverse(X)),multiply(X5,X2)))),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X6,multiply(X4,multiply(X3,inverse(X3)))))),multiply(X2,inverse(X2))) = multiply(X7,inverse(multiply(multiply(X6,multiply(X5,inverse(X5))),multiply(multiply(X4,multiply(X3,inverse(X3))),X7)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c110,plain,
multiply(X7,inverse(multiply(multiply(X6,multiply(X5,inverse(X5))),multiply(multiply(X4,multiply(X3,inverse(X3))),X7)))) = multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X6,multiply(X4,multiply(X3,inverse(X3)))))),multiply(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X5,multiply(X4,multiply(X3,inverse(X3)))))) = multiply(X2,inverse(multiply(X5,multiply(X4,X2)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c112,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X6,multiply(X5,multiply(X4,inverse(X4)))))),multiply(X2,inverse(X2))) = multiply(multiply(X3,inverse(multiply(X6,multiply(X5,X3)))),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(X7,inverse(multiply(multiply(X6,multiply(X5,inverse(X5))),multiply(multiply(X4,multiply(X3,inverse(X3))),X7)))) = multiply(multiply(X2,inverse(multiply(X6,multiply(X4,X2)))),multiply(X,inverse(X))),
inference(transitivity,[status(thm)],[c110,c112]) ).
cnf(c114,plain,
multiply(X2,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))),multiply(multiply(X7,multiply(X5,inverse(X5))),X2)))) = multiply(multiply(X4,inverse(multiply(multiply(X3,inverse(X3)),multiply(X7,X4)))),multiply(X6,inverse(X6))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(multiply(X4,inverse(multiply(multiply(X3,inverse(X3)),multiply(X7,X4)))),multiply(X6,inverse(X6))) = multiply(X2,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))),multiply(multiply(X7,multiply(X5,inverse(X5))),X2)))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(X2,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))),multiply(multiply(X5,multiply(X4,inverse(X4))),X2)))) = inverse(multiply(X5,multiply(X4,inverse(X4)))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c117,plain,
multiply(multiply(X2,inverse(multiply(multiply(X,inverse(X)),multiply(X5,X2)))),multiply(X4,inverse(X4))) = inverse(multiply(X5,multiply(X3,inverse(X3)))),
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
multiply(multiply(inverse(X4),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),multiply(X2,inverse(X2))) = inverse(multiply(X4,multiply(X,inverse(X)))),
inference(transitivity,[status(thm)],[c108,c117]) ).
cnf(c119,plain,
multiply(multiply(inverse(multiply(X4,inverse(X4))),inverse(inverse(inverse(multiply(X2,inverse(X2)))))),multiply(X,inverse(X))) = inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))) = multiply(multiply(inverse(multiply(X4,inverse(X4))),inverse(inverse(inverse(multiply(X2,inverse(X2)))))),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X,inverse(multiply(multiply(X2,inverse(X2)),multiply(multiply(X4,inverse(X4)),X)))) = multiply(inverse(multiply(X4,inverse(X4))),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c122,plain,
multiply(inverse(multiply(X4,inverse(X4))),inverse(inverse(inverse(multiply(X3,inverse(X3)))))) = multiply(X,inverse(multiply(multiply(X2,inverse(X2)),multiply(multiply(X4,inverse(X4)),X)))),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(multiply(inverse(multiply(X4,inverse(X4))),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),multiply(X2,inverse(X2))) = multiply(multiply(X,inverse(multiply(multiply(X2,inverse(X2)),multiply(multiply(X4,inverse(X4)),X)))),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
X2 = inverse(multiply(X3,inverse(multiply(X2,multiply(multiply(X,inverse(X)),X3))))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c125,plain,
multiply(multiply(X3,inverse(multiply(X2,multiply(multiply(X,inverse(X)),X3)))),X2) = multiply(multiply(X3,inverse(multiply(X2,multiply(multiply(X,inverse(X)),X3)))),inverse(multiply(X3,inverse(multiply(X2,multiply(multiply(X,inverse(X)),X3)))))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(X,inverse(X)) = multiply(multiply(X4,inverse(multiply(X3,multiply(multiply(X2,inverse(X2)),X4)))),inverse(multiply(X4,inverse(multiply(X3,multiply(multiply(X2,inverse(X2)),X4)))))),
inference(substitution,[status(thm)],[c58]) ).
cnf(c127,plain,
multiply(multiply(X4,inverse(multiply(X3,multiply(multiply(X2,inverse(X2)),X4)))),inverse(multiply(X4,inverse(multiply(X3,multiply(multiply(X2,inverse(X2)),X4)))))) = multiply(X,inverse(X)),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(multiply(X4,inverse(multiply(X3,multiply(multiply(X2,inverse(X2)),X4)))),X3) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c125,c127]) ).
cnf(c129,plain,
multiply(multiply(X,inverse(multiply(multiply(X3,inverse(X3)),multiply(multiply(X4,inverse(X4)),X)))),multiply(X3,inverse(X3))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(multiply(inverse(multiply(X4,inverse(X4))),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),multiply(X2,inverse(X2))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c123,c129]) ).
cnf(c131,plain,
multiply(multiply(inverse(multiply(X3,inverse(X3))),inverse(inverse(inverse(multiply(X2,inverse(X2)))))),multiply(X,inverse(X))) = multiply(X4,inverse(X4)),
inference(substitution,[status(thm)],[c130]) ).
cnf(c132,plain,
inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X)))) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c120,c131]) ).
cnf(c133,plain,
inverse(inverse(inverse(multiply(X2,inverse(X2))))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c78,c132]) ).
cnf(c134,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(X2,inverse(X2)) = inverse(inverse(inverse(multiply(X,inverse(X))))),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
multiply(inverse(X3),multiply(X2,inverse(X2))) = multiply(inverse(X3),inverse(inverse(inverse(multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(X2,inverse(multiply(multiply(X,inverse(X)),multiply(X4,X2)))) = multiply(inverse(X4),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c138,plain,
multiply(inverse(X4),inverse(inverse(inverse(multiply(X3,inverse(X3)))))) = multiply(X2,inverse(multiply(multiply(X,inverse(X)),multiply(X4,X2)))),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(X,inverse(X)) = multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),
inference(substitution,[status(thm)],[c58]) ).
cnf(c140,plain,
multiply(multiply(X,inverse(X)),X3) = multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(inverse(X2),multiply(multiply(X,inverse(X)),X3)) = multiply(inverse(X2),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
inverse(multiply(inverse(X2),multiply(multiply(X,inverse(X)),X3))) = inverse(multiply(inverse(X2),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(X3,inverse(multiply(inverse(X2),multiply(multiply(X,inverse(X)),X3)))) = multiply(X3,inverse(multiply(inverse(X2),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3)))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(X2,inverse(multiply(inverse(X),multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),X2)))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c145,plain,
multiply(X3,inverse(multiply(inverse(X2),multiply(multiply(X,inverse(X)),X3)))) = X2,
inference(transitivity,[status(thm)],[c143,c144]) ).
cnf(c146,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(X4))),multiply(X3,inverse(X3)))),multiply(multiply(X2,inverse(X2)),X)))) = multiply(inverse(multiply(X4,inverse(X4))),multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(inverse(multiply(X4,inverse(X4))),multiply(X3,inverse(X3))) = multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(X4))),multiply(X3,inverse(X3)))),multiply(multiply(X2,inverse(X2)),X)))),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(multiply(inverse(inverse(multiply(X3,inverse(X3)))),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),multiply(X,inverse(X))) = inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,inverse(X2)))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c149,plain,
inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,inverse(X2)))) = multiply(multiply(inverse(inverse(multiply(X3,inverse(X3)))),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(multiply(inverse(inverse(multiply(X3,inverse(X3)))),inverse(inverse(inverse(multiply(X3,inverse(X3)))))),multiply(X,inverse(X))) = inverse(inverse(multiply(X2,inverse(X2)))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c151,plain,
inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,inverse(X2)))) = inverse(inverse(multiply(X,inverse(X)))),
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
multiply(inverse(multiply(inverse(multiply(X5,inverse(X5))),multiply(X4,inverse(X4)))),multiply(multiply(X3,inverse(X3)),X2)) = multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(multiply(X3,inverse(X3)),X2)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(X5))),multiply(X4,inverse(X4)))),multiply(multiply(X3,inverse(X3)),X2))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(multiply(X3,inverse(X3)),X2))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(X5))),multiply(X4,inverse(X4)))),multiply(multiply(X3,inverse(X3)),X2)))) = multiply(X2,inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(multiply(X3,inverse(X3)),X2)))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))) = inverse(inverse(multiply(X3,inverse(X3)))),
inference(substitution,[status(thm)],[c75]) ).
cnf(c156,plain,
inverse(inverse(multiply(X3,inverse(X3)))) = multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
multiply(inverse(inverse(multiply(X4,inverse(X4)))),multiply(X3,X5)) = multiply(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))),multiply(X3,X5)),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),multiply(X3,X5))) = inverse(multiply(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))),multiply(X3,X5))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(X5,inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),multiply(X3,X5)))) = multiply(X5,inverse(multiply(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))),multiply(X3,X5)))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(X4,inverse(multiply(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))),multiply(X3,X4)))) = inverse(X3),
inference(substitution,[status(thm)],[c65]) ).
cnf(c161,plain,
multiply(X3,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X,X3)))) = inverse(X),
inference(transitivity,[status(thm)],[c159,c160]) ).
cnf(c162,plain,
multiply(X2,inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(multiply(X3,inverse(X3)),X2)))) = inverse(multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(X4))),multiply(X3,inverse(X3)))),multiply(multiply(X2,inverse(X2)),X)))) = inverse(multiply(X2,inverse(X2))),
inference(transitivity,[status(thm)],[c154,c162]) ).
cnf(c164,plain,
multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,inverse(X2))) = inverse(multiply(X,inverse(X))),
inference(transitivity,[status(thm)],[c147,c163]) ).
cnf(c165,plain,
multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))) = inverse(multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
inverse(multiply(X3,inverse(X3))) = multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))) = inverse(multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c164]) ).
cnf(c168,plain,
inverse(multiply(X3,inverse(X3))) = multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(inverse(multiply(X4,inverse(X4))),multiply(X3,inverse(X3))) = multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c171,plain,
multiply(X2,inverse(X2)) = inverse(inverse(inverse(multiply(X,inverse(X))))),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X3))),inverse(inverse(inverse(multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
multiply(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,inverse(X2))),multiply(X4,inverse(X4))) = multiply(multiply(inverse(multiply(X3,inverse(X3))),inverse(inverse(inverse(multiply(X,inverse(X)))))),multiply(X4,inverse(X4))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
multiply(multiply(inverse(multiply(X2,inverse(X2))),inverse(inverse(inverse(multiply(X,inverse(X)))))),multiply(X3,inverse(X3))) = multiply(X4,inverse(X4)),
inference(substitution,[status(thm)],[c130]) ).
cnf(c175,plain,
multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),multiply(X3,inverse(X3))) = multiply(X4,inverse(X4)),
inference(transitivity,[status(thm)],[c173,c174]) ).
cnf(c176,plain,
multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c169,c175]) ).
cnf(c177,plain,
inverse(multiply(X2,inverse(X2))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c166,c176]) ).
cnf(c178,plain,
inverse(multiply(X,inverse(X))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(X2,inverse(X2)) = inverse(multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
multiply(multiply(X2,inverse(X2)),multiply(X4,X3)) = multiply(inverse(multiply(X,inverse(X))),multiply(X4,X3)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
inverse(multiply(multiply(X2,inverse(X2)),multiply(X4,X3))) = inverse(multiply(inverse(multiply(X,inverse(X))),multiply(X4,X3))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
multiply(X3,inverse(multiply(multiply(X2,inverse(X2)),multiply(X4,X3)))) = multiply(X3,inverse(multiply(inverse(multiply(X,inverse(X))),multiply(X4,X3)))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
inverse(multiply(X,inverse(X))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c184,plain,
multiply(X2,inverse(X2)) = inverse(multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
inverse(multiply(X2,inverse(X2))) = inverse(inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
multiply(inverse(multiply(X2,inverse(X2))),multiply(X4,X3)) = multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(X4,X3)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
inverse(multiply(inverse(multiply(X2,inverse(X2))),multiply(X4,X3))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(X4,X3))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(X3,inverse(multiply(inverse(multiply(X2,inverse(X2))),multiply(X4,X3)))) = multiply(X3,inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(X4,X3)))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(X2,inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(X3,X2)))) = inverse(X3),
inference(substitution,[status(thm)],[c161]) ).
cnf(c190,plain,
multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),multiply(X3,X2)))) = inverse(X3),
inference(transitivity,[status(thm)],[c188,c189]) ).
cnf(c191,plain,
multiply(X2,inverse(multiply(multiply(X,inverse(X)),multiply(X3,X2)))) = inverse(X3),
inference(transitivity,[status(thm)],[c182,c190]) ).
cnf(c192,plain,
multiply(inverse(X2),inverse(inverse(inverse(multiply(X,inverse(X)))))) = inverse(X2),
inference(transitivity,[status(thm)],[c138,c191]) ).
cnf(c193,plain,
multiply(inverse(X2),multiply(X,inverse(X))) = inverse(X2),
inference(transitivity,[status(thm)],[c136,c192]) ).
cnf(c194,plain,
multiply(inverse(inverse(X2)),multiply(X,inverse(X))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
inverse(inverse(X2)) = multiply(inverse(inverse(X2)),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
inverse(inverse(inverse(X2))) = inverse(multiply(inverse(inverse(X2)),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
inverse(inverse(inverse(inverse(X2)))) = inverse(inverse(multiply(inverse(inverse(X2)),multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
inverse(multiply(X,inverse(X))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c199,plain,
multiply(X2,inverse(X2)) = inverse(multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(inverse(inverse(X3)),multiply(X2,inverse(X2))) = multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
inverse(multiply(inverse(inverse(X3)),multiply(X2,inverse(X2)))) = inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
inverse(inverse(multiply(inverse(inverse(X3)),multiply(X2,inverse(X2))))) = inverse(inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
inverse(multiply(X,inverse(X))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c204,plain,
multiply(X2,inverse(X2)) = inverse(multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
inverse(multiply(X2,inverse(X2))) = inverse(inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(X2)))) = multiply(inverse(inverse(X3)),inverse(inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(X2))))) = inverse(multiply(inverse(inverse(X3)),inverse(inverse(multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
inverse(inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(X2)))))) = inverse(inverse(multiply(inverse(inverse(X3)),inverse(inverse(multiply(X,inverse(X))))))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2))))))),X)))) = inverse(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2)))))))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c210,plain,
inverse(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2)))))))) = multiply(X,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2))))))),X)))),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2))))))),X)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c212,plain,
inverse(multiply(multiply(X3,inverse(X3)),inverse(multiply(X2,inverse(inverse(multiply(X,inverse(X)))))))) = X2,
inference(transitivity,[status(thm)],[c210,c211]) ).
cnf(c213,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2)))))))) = X3,
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
X3 = inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2)))))))),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
multiply(multiply(X4,inverse(X4)),X3) = multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2))))))))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(multiply(multiply(X5,inverse(X5)),X4),multiply(X3,inverse(X3))) = multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X4,inverse(inverse(multiply(X2,inverse(X2))))))))),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
multiply(multiply(multiply(X7,inverse(X7)),inverse(multiply(multiply(X3,inverse(X3)),inverse(multiply(X6,inverse(inverse(multiply(X4,inverse(X4))))))))),multiply(X5,inverse(X5))) = multiply(X2,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))),multiply(inverse(multiply(X6,inverse(inverse(multiply(X4,inverse(X4)))))),X2)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c218,plain,
multiply(X2,inverse(multiply(multiply(multiply(X3,inverse(X3)),multiply(X,inverse(X))),multiply(inverse(multiply(X5,inverse(inverse(multiply(X4,inverse(X4)))))),X2)))) = inverse(inverse(multiply(X5,inverse(inverse(multiply(X4,inverse(X4))))))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c219,plain,
multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X4,inverse(inverse(multiply(X2,inverse(X2))))))))),multiply(X3,inverse(X3))) = inverse(inverse(multiply(X4,inverse(inverse(multiply(X2,inverse(X2))))))),
inference(transitivity,[status(thm)],[c217,c218]) ).
cnf(c220,plain,
multiply(multiply(multiply(X4,inverse(X4)),X3),multiply(X2,inverse(X2))) = inverse(inverse(multiply(X3,inverse(inverse(multiply(X,inverse(X))))))),
inference(transitivity,[status(thm)],[c216,c219]) ).
cnf(c221,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(X4))),multiply(X,inverse(X))) = inverse(inverse(multiply(inverse(inverse(X4)),inverse(inverse(multiply(X3,inverse(X3))))))),
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
inverse(inverse(multiply(inverse(inverse(X4)),inverse(inverse(multiply(X3,inverse(X3))))))) = multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(X4))),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c223,plain,
inverse(X2) = multiply(inverse(X2),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c224,plain,
inverse(inverse(X2)) = inverse(multiply(inverse(X2),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(multiply(X2,inverse(X2)),inverse(inverse(X3))) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(X3),multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
multiply(multiply(multiply(X3,inverse(X3)),inverse(inverse(X4))),multiply(X2,inverse(X2))) = multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(X4),multiply(X,inverse(X))))),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(inverse(X6),multiply(X3,inverse(X3))))),multiply(X4,inverse(X4))) = multiply(X2,inverse(multiply(multiply(inverse(X6),multiply(X,inverse(X))),multiply(multiply(X3,inverse(X3)),X2)))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c228,plain,
multiply(multiply(inverse(X4),multiply(X,inverse(X))),multiply(multiply(X3,inverse(X3)),X2)) = multiply(inverse(X4),multiply(multiply(X3,inverse(X3)),X2)),
inference(congruence,[status(thm)],[c193]) ).
cnf(c229,plain,
inverse(multiply(multiply(inverse(X4),multiply(X,inverse(X))),multiply(multiply(X3,inverse(X3)),X2))) = inverse(multiply(inverse(X4),multiply(multiply(X3,inverse(X3)),X2))),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
multiply(X2,inverse(multiply(multiply(inverse(X4),multiply(X,inverse(X))),multiply(multiply(X3,inverse(X3)),X2)))) = multiply(X2,inverse(multiply(inverse(X4),multiply(multiply(X3,inverse(X3)),X2)))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
multiply(X,inverse(multiply(inverse(X3),multiply(multiply(X2,inverse(X2)),X)))) = X3,
inference(substitution,[status(thm)],[c145]) ).
cnf(c232,plain,
multiply(X2,inverse(multiply(multiply(inverse(X4),multiply(X,inverse(X))),multiply(multiply(X3,inverse(X3)),X2)))) = X4,
inference(transitivity,[status(thm)],[c230,c231]) ).
cnf(c233,plain,
multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(X4),multiply(X,inverse(X))))),multiply(X2,inverse(X2))) = X4,
inference(transitivity,[status(thm)],[c227,c232]) ).
cnf(c234,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(X3))),multiply(X,inverse(X))) = X3,
inference(transitivity,[status(thm)],[c226,c233]) ).
cnf(c235,plain,
inverse(inverse(multiply(inverse(inverse(X2)),inverse(inverse(multiply(X,inverse(X))))))) = X2,
inference(transitivity,[status(thm)],[c222,c234]) ).
cnf(c236,plain,
inverse(inverse(multiply(inverse(inverse(X2)),inverse(multiply(X,inverse(X)))))) = X2,
inference(transitivity,[status(thm)],[c208,c235]) ).
cnf(c237,plain,
inverse(inverse(multiply(inverse(inverse(X2)),multiply(X,inverse(X))))) = X2,
inference(transitivity,[status(thm)],[c202,c236]) ).
cnf(c238,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(transitivity,[status(thm)],[c197,c237]) ).
cnf(c239,plain,
X = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(X2,inverse(inverse(X))) = multiply(inverse(inverse(inverse(inverse(X2)))),inverse(inverse(X))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
inverse(multiply(X2,inverse(multiply(X3,multiply(multiply(X,inverse(X)),X2))))) = X3,
inference(substitution,[status(thm)],[c70]) ).
cnf(c242,plain,
X3 = inverse(multiply(X2,inverse(multiply(X3,multiply(multiply(X,inverse(X)),X2))))),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
multiply(X4,multiply(X3,inverse(X3))) = multiply(inverse(multiply(X2,inverse(multiply(X4,multiply(multiply(X,inverse(X)),X2))))),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(inverse(multiply(X2,inverse(multiply(X4,multiply(multiply(X,inverse(X)),X2))))),multiply(X3,inverse(X3))) = inverse(multiply(X2,inverse(multiply(X4,multiply(multiply(X,inverse(X)),X2))))),
inference(substitution,[status(thm)],[c193]) ).
cnf(c245,plain,
inverse(multiply(X2,inverse(multiply(X3,multiply(multiply(X,inverse(X)),X2))))) = X3,
inference(substitution,[status(thm)],[c70]) ).
cnf(c246,plain,
multiply(inverse(multiply(X2,inverse(multiply(X4,multiply(multiply(X,inverse(X)),X2))))),multiply(X3,inverse(X3))) = X4,
inference(transitivity,[status(thm)],[c244,c245]) ).
cnf(c247,plain,
multiply(X2,multiply(X,inverse(X))) = X2,
inference(transitivity,[status(thm)],[c243,c246]) ).
cnf(c248,plain,
multiply(multiply(multiply(X3,inverse(X3)),X2),multiply(X,inverse(X))) = multiply(multiply(X3,inverse(X3)),X2),
inference(substitution,[status(thm)],[c247]) ).
cnf(c249,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(multiply(multiply(X3,inverse(X3)),X2),multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
inverse(inverse(multiply(X2,inverse(X2)))) = inverse(multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c251,plain,
multiply(X3,inverse(inverse(multiply(X2,inverse(X2))))) = multiply(X3,inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2)))))) = inverse(multiply(X3,inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
inverse(inverse(multiply(X3,inverse(inverse(multiply(X2,inverse(X2))))))) = inverse(inverse(multiply(X3,inverse(multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
multiply(X3,inverse(multiply(X2,inverse(X2)))) = multiply(X3,multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c255,plain,
inverse(multiply(X3,inverse(multiply(X2,inverse(X2))))) = inverse(multiply(X3,multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
inverse(inverse(multiply(X3,inverse(multiply(X2,inverse(X2)))))) = inverse(inverse(multiply(X3,multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
inverse(multiply(X2,multiply(X,inverse(X)))) = inverse(X2),
inference(congruence,[status(thm)],[c247]) ).
cnf(c258,plain,
inverse(inverse(multiply(X2,multiply(X,inverse(X))))) = inverse(inverse(X2)),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
inverse(inverse(multiply(X2,inverse(multiply(X,inverse(X)))))) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c256,c258]) ).
cnf(c260,plain,
inverse(inverse(multiply(X2,inverse(inverse(multiply(X,inverse(X))))))) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c253,c259]) ).
cnf(c261,plain,
multiply(multiply(multiply(X3,inverse(X3)),X2),multiply(X,inverse(X))) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c220,c260]) ).
cnf(c262,plain,
multiply(multiply(X2,inverse(X2)),X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c249,c261]) ).
cnf(c263,plain,
multiply(multiply(X,inverse(X)),inverse(X2)) = inverse(inverse(inverse(X2))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c264,plain,
inverse(inverse(inverse(X2))) = multiply(multiply(X,inverse(X)),inverse(X2)),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
inverse(inverse(inverse(inverse(X2)))) = inverse(multiply(multiply(X,inverse(X)),inverse(X2))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
multiply(inverse(inverse(inverse(inverse(X3)))),inverse(inverse(X2))) = multiply(inverse(multiply(multiply(X,inverse(X)),inverse(X3))),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
multiply(inverse(X2),inverse(multiply(X3,multiply(X,inverse(X))))) = multiply(X4,inverse(multiply(X3,multiply(X2,X4)))),
inference(substitution,[status(thm)],[c99]) ).
cnf(c268,plain,
multiply(X4,inverse(multiply(X3,multiply(X2,X4)))) = multiply(inverse(X2),inverse(multiply(X3,multiply(X,inverse(X))))),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
inverse(multiply(X2,multiply(X,inverse(X)))) = inverse(X2),
inference(congruence,[status(thm)],[c247]) ).
cnf(c270,plain,
multiply(inverse(X2),inverse(multiply(X3,multiply(X,inverse(X))))) = multiply(inverse(X2),inverse(X3)),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
multiply(X3,inverse(multiply(X2,multiply(X,X3)))) = multiply(inverse(X),inverse(X2)),
inference(transitivity,[status(thm)],[c268,c270]) ).
cnf(c272,plain,
multiply(X,inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(X4)),X)))) = multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(X4))),inverse(inverse(X3))),
inference(substitution,[status(thm)],[c271]) ).
cnf(c273,plain,
multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(X4))),inverse(inverse(X3))) = multiply(X,inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(X4)),X)))),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
inverse(inverse(inverse(inverse(multiply(X2,X))))) = multiply(X2,X),
inference(substitution,[status(thm)],[c238]) ).
cnf(c275,plain,
multiply(X2,X) = inverse(inverse(inverse(inverse(multiply(X2,X))))),
inference(symmetry,[status(thm)],[c274]) ).
cnf(c276,plain,
multiply(multiply(X2,X),inverse(X)) = multiply(inverse(inverse(inverse(inverse(multiply(X2,X))))),inverse(X)),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X3,X2))) = inverse(inverse(inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c278,plain,
inverse(inverse(inverse(multiply(X3,X2)))) = multiply(multiply(X,inverse(X)),inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
inverse(inverse(inverse(inverse(multiply(X3,X2))))) = inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X3,X2)))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
multiply(inverse(inverse(inverse(inverse(multiply(X3,X2))))),inverse(X2)) = multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X3,X2)))),inverse(X2)),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
multiply(X,inverse(multiply(X3,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,X3))),X)))) = multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,X3)))),inverse(X3)),
inference(substitution,[status(thm)],[c271]) ).
cnf(c282,plain,
multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,X3)))),inverse(X3)) = multiply(X,inverse(multiply(X3,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,X3))),X)))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
multiply(X,inverse(multiply(X3,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X4,X3))),X)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c284,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X3,X2)))),inverse(X2)) = X3,
inference(transitivity,[status(thm)],[c282,c283]) ).
cnf(c285,plain,
multiply(inverse(inverse(inverse(inverse(multiply(X2,X))))),inverse(X)) = X2,
inference(transitivity,[status(thm)],[c280,c284]) ).
cnf(c286,plain,
multiply(multiply(X2,X),inverse(X)) = X2,
inference(transitivity,[status(thm)],[c276,c285]) ).
cnf(c287,plain,
X2 = multiply(multiply(X2,X),inverse(X)),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
inverse(X2) = inverse(multiply(multiply(X2,X),inverse(X))),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
multiply(multiply(X,inverse(X)),inverse(X3)) = multiply(multiply(X,inverse(X)),inverse(multiply(multiply(X3,X2),inverse(X2)))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(X4)),X) = multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X4,X3),inverse(X3)))),X),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(X4)),X)) = multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X4,X3),inverse(X3)))),X)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(X4)),X))) = inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X4,X3),inverse(X3)))),X))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
multiply(X,inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(X4)),X)))) = multiply(X,inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X4,X3),inverse(X3)))),X)))),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
multiply(X,inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X4,X3),inverse(X3)))),X)))) = multiply(X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c295,plain,
multiply(X,inverse(multiply(inverse(X3),multiply(multiply(multiply(X2,inverse(X2)),inverse(X4)),X)))) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c293,c294]) ).
cnf(c296,plain,
multiply(inverse(multiply(multiply(X,inverse(X)),inverse(X3))),inverse(inverse(X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c273,c295]) ).
cnf(c297,plain,
multiply(inverse(inverse(inverse(inverse(X2)))),inverse(inverse(X))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c266,c296]) ).
cnf(c298,plain,
multiply(X2,inverse(inverse(X))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c240,c297]) ).
cnf(c299,plain,
multiply(inverse(X),inverse(inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c298]) ).
cnf(c300,plain,
multiply(inverse(X),X) = multiply(inverse(X),inverse(inverse(X))),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
multiply(X,inverse(X)) = multiply(inverse(X2),inverse(inverse(X2))),
inference(substitution,[status(thm)],[c58]) ).
cnf(c302,plain,
multiply(inverse(X2),inverse(inverse(X2))) = multiply(X,inverse(X)),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c303,plain,
multiply(inverse(X2),X2) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c300,c302]) ).
cnf(c304,plain,
multiply(inverse(a1),a1) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c303]) ).
cnf(c305,plain,
multiply(inverse(b1),b1) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c303]) ).
cnf(c306,plain,
multiply(X,inverse(X)) = multiply(inverse(b1),b1),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[c304,c306]) ).
cnf(c308,plain,
$false,
inference(resolution,[status(thm)],[c1,c307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP430-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 10:07:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.46 Command-line arguments: --no-flatten-goal
% 0.08/0.46
% 0.08/0.46 % SZS status Unsatisfiable
% 0.08/0.46
% 0.08/0.48 % SZS output start CNFRefutation
% See solution above
% 0.57/0.61
% 0.57/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------