%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP425-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:10:08 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 87
% Number of leaves : 2
% Syntax : Number of clauses : 252 ( 252 unt; 0 nHn; 3 RR)
% Number of literals : 252 ( 251 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 17 ( 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 : 909 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c2,axiom,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X))))),multiply(X2,inverse(inverse(X))))),inverse(multiply(inverse(inverse(X)),inverse(X)))) = inverse(multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(multiply(inverse(X3),X3)) = multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X))))),multiply(X2,inverse(inverse(X))))),inverse(multiply(inverse(inverse(X)),inverse(X)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X)))),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
X3 = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X3),X3) = multiply(inverse(X3),multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X)))),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
X3 = multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X)))),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(X3) = inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X)))),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(X4),multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),X2)))),multiply(X3,inverse(X2)))),inverse(X))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),X2)))),multiply(X3,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),X2)))),multiply(X3,inverse(X2)))),inverse(X))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
X3 = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
inverse(X3) = inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X4,inverse(X3)) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(multiply(X4,inverse(X3))) = inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
inverse(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2)))))) = inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2))),
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X4,inverse(X2))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X4,inverse(X2))) = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X),X)))),X)))),multiply(X3,inverse(X))) = X2,
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
X3 = multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
inverse(X3) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X4,inverse(X3)) = multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(multiply(X4,inverse(X3))) = inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
inverse(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X)))))) = inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X)))))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X)))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))) = multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X)))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X)))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X)))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X))),
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),multiply(X4,inverse(X2)))))),multiply(X,inverse(multiply(X4,inverse(X2)))))),inverse(multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X2))))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),X2))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),X2))) = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),multiply(X4,inverse(X2)))))),multiply(X,inverse(multiply(X4,inverse(X2)))))),inverse(multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X2))))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),multiply(X4,inverse(X2)))))),multiply(X,inverse(multiply(X4,inverse(X2)))))),inverse(multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X2))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X)))),X))) = X2,
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X)))),X))) = X2,
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
X3 = multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
inverse(X3) = inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X)))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X3,inverse(X4)) = multiply(X3,inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X))))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,inverse(X4))) = multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X)))))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c46,plain,
X3 = multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(X3) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(X,inverse(X4)) = multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X3,inverse(X2))))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
inverse(multiply(X,inverse(X4))) = inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X3,inverse(X2)))))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X3,inverse(X2)))))),multiply(X,inverse(multiply(X3,inverse(X2))))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3)))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3))) = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3)))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))) = inverse(X3),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3))))) = multiply(X,inverse(X4)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3)))))) = inverse(multiply(X,inverse(X4))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(inverse(multiply(inverse(X3),X3)))))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3)))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(inverse(multiply(inverse(X3),X3)))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),X)))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c61,plain,
X2 = multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),X)))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
inverse(X2) = inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),X)))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X,inverse(X3)) = multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(multiply(X,inverse(X3))) = inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
inverse(multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))) = inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c67,c68]) ).
cnf(c70,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),X3)))),multiply(X2,inverse(X3)))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3)))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),X3)))),multiply(X5,inverse(X3))),
inference(transitivity,[status(thm)],[c59,c69]) ).
cnf(c71,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X2)))),multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c52,c70]) ).
cnf(c72,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X3,inverse(X2)))))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X3,inverse(X2)))))),multiply(X5,inverse(multiply(X3,inverse(X2))))),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c74,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))) = inverse(X3),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X))))) = multiply(X4,inverse(X3)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))))) = inverse(multiply(X4,inverse(X3))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X))))) = multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X3,inverse(X2)))))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(multiply(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c72,c77]) ).
cnf(c79,plain,
multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(multiply(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c50,c78]) ).
cnf(c80,plain,
multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X)))))) = multiply(inverse(multiply(X6,inverse(X5))),multiply(X6,inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X)))))),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X))) = X3,
inference(substitution,[status(thm)],[c39]) ).
cnf(c82,plain,
inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X)))) = inverse(X3),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(X4,inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X))))) = multiply(X4,inverse(X3)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X)))))) = multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(X3))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X)))))) = multiply(inverse(multiply(X6,inverse(X5))),multiply(X6,inverse(X4))),
inference(transitivity,[status(thm)],[c80,c84]) ).
cnf(c86,plain,
multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(X2))) = multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c44,c85]) ).
cnf(c87,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),X3)))),multiply(X4,inverse(X3)))),inverse(multiply(inverse(X3),X3)))),multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),X3)))),multiply(X4,inverse(X3)))),inverse(X2))),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),X3)))),multiply(X4,inverse(X3)))),inverse(multiply(inverse(X3),X3)))),multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),X3)))),multiply(X4,inverse(X3)))),inverse(X2))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(inverse(X5),multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),X3)))),multiply(X4,inverse(X3)))),inverse(X2))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2))),
inference(transitivity,[status(thm)],[c11,c88]) ).
cnf(c90,plain,
multiply(inverse(X4),multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X4),X3)))),multiply(X,inverse(X3)))),inverse(multiply(inverse(X3),X3)))) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))),multiply(X2,inverse(multiply(inverse(X3),X3)))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(inverse(X4),multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),X2)))),multiply(X3,inverse(X2)))),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(multiply(inverse(X2),X2)))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c92,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X4),multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),X2)))),multiply(X3,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X)))),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
multiply(inverse(X3),multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X)))),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c92,c94]) ).
cnf(c96,plain,
multiply(inverse(X3),multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X4),X4),
inference(transitivity,[status(thm)],[c90,c95]) ).
cnf(c97,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c7,c96]) ).
cnf(c98,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))),inverse(multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(inverse(X),X) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(substitution,[status(thm)],[c97]) ).
cnf(c102,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(inverse(X2)),inverse(X2))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(X3)),inverse(X2))) = multiply(inverse(multiply(inverse(inverse(X3)),inverse(X3))),multiply(inverse(inverse(X3)),inverse(X2))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(X))) = multiply(inverse(multiply(inverse(inverse(X2)),inverse(X2))),multiply(inverse(inverse(X2)),inverse(X))),
inference(substitution,[status(thm)],[c86]) ).
cnf(c105,plain,
multiply(inverse(multiply(inverse(inverse(X2)),inverse(X2))),multiply(inverse(inverse(X2)),inverse(X))) = multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(X))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(X3)),inverse(X2))) = multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c103,c105]) ).
cnf(c107,plain,
multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2))),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
inverse(multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2)))) = inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2)))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X5),X5)),multiply(inverse(inverse(multiply(inverse(X4),X4))),inverse(X3)))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X4),X4)))),multiply(X,inverse(X3)))),inverse(multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c97]) ).
cnf(c111,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X4),X4)))),multiply(X,inverse(X3)))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X4),X4)))),multiply(X,inverse(X3)))),inverse(multiply(inverse(X3),X3))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(inverse(X2),X2) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c97]) ).
cnf(c113,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(X,inverse(multiply(inverse(X3),X3))) = multiply(X,inverse(multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
inverse(multiply(X,inverse(multiply(inverse(X3),X3)))) = inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(X2))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2)))) = inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(X2)))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c120,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X2,
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X4),X4)))),multiply(X,inverse(X3)))),inverse(multiply(inverse(X2),X2))) = X3,
inference(transitivity,[status(thm)],[c111,c120]) ).
cnf(c122,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2)))),inverse(multiply(inverse(X),X))) = X2,
inference(transitivity,[status(thm)],[c109,c121]) ).
cnf(c123,plain,
multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c100,c123]) ).
cnf(c125,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X))) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(inverse(X3),X3) = multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
inverse(multiply(inverse(X3),X3)) = inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(inverse(multiply(inverse(X4),X4)),X3) = multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X3),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
inverse(multiply(inverse(multiply(inverse(X4),X4)),X3)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X3)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(X5,inverse(multiply(inverse(multiply(inverse(X4),X4)),X3))) = multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X3))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(inverse(X2),X2) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c97]) ).
cnf(c132,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))) = inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))),X) = multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X)))),X),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))),X)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X)))),X)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))),X))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X)))),X))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X))),
inference(substitution,[status(thm)],[c97]) ).
cnf(c139,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))) = inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X)))),X),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X)))),X)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X))) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(X))),multiply(X3,inverse(X)))),inverse(multiply(inverse(X),X)))),X))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X)))),inverse(multiply(inverse(X),X)))),X))) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c146,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X))) = multiply(X3,inverse(X)),
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))),X))) = multiply(X4,inverse(X)),
inference(transitivity,[status(thm)],[c137,c146]) ).
cnf(c148,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X3))) = multiply(X4,inverse(X3)),
inference(substitution,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(X2),X2)),X))) = multiply(X3,inverse(X)),
inference(transitivity,[status(thm)],[c130,c148]) ).
cnf(c150,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2))))) = multiply(X4,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2)))),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(X4,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2)))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2))))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),X3))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c124]) ).
cnf(c153,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),X3))),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),X3)))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X3))) = multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X4),X4)))),multiply(inverse(multiply(inverse(X),X)),inverse(X3))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2))) = multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),X3)))),multiply(inverse(multiply(inverse(X),X)),inverse(X2))),
inference(substitution,[status(thm)],[c106]) ).
cnf(c157,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),X3)))),multiply(inverse(multiply(inverse(X),X)),inverse(X2))) = multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X3))) = multiply(inverse(multiply(inverse(X5),X5)),multiply(inverse(inverse(multiply(inverse(X4),X4))),inverse(X3))),
inference(transitivity,[status(thm)],[c155,c157]) ).
cnf(c159,plain,
multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X4))) = multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(inverse(multiply(inverse(X5),X5))),inverse(X4))),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(inverse(multiply(inverse(X5),X5))),inverse(X4))) = multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X4))),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(inverse(multiply(inverse(X5),X5))),inverse(X4)))) = inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X4)))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
multiply(X6,inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(inverse(multiply(inverse(X5),X5))),inverse(X4))))) = multiply(X6,inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X4))))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X3))))) = multiply(X4,inverse(multiply(inverse(multiply(inverse(X),X)),inverse(X3)))),
inference(substitution,[status(thm)],[c149]) ).
cnf(c164,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(X),X)),inverse(X2)))) = multiply(X3,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c149]) ).
cnf(c165,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X),X)),inverse(X3))))) = multiply(X4,inverse(inverse(X3))),
inference(transitivity,[status(thm)],[c163,c164]) ).
cnf(c166,plain,
multiply(X4,inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X2))))) = multiply(X4,inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c162,c165]) ).
cnf(c167,plain,
multiply(X3,inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X)))) = multiply(X3,inverse(inverse(X))),
inference(transitivity,[status(thm)],[c151,c166]) ).
cnf(c168,plain,
multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X)))) = multiply(X2,inverse(inverse(X))),
inference(substitution,[status(thm)],[c167]) ).
cnf(c169,plain,
inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X))))) = inverse(multiply(X2,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X))))),multiply(X2,inverse(inverse(X)))) = multiply(inverse(multiply(X2,inverse(inverse(X)))),multiply(X2,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X))))),multiply(X2,inverse(inverse(X))))) = inverse(multiply(inverse(multiply(X2,inverse(inverse(X)))),multiply(X2,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X))))),multiply(X2,inverse(inverse(X))))),inverse(multiply(inverse(inverse(X)),inverse(X)))) = multiply(inverse(multiply(inverse(multiply(X2,inverse(inverse(X)))),multiply(X2,inverse(inverse(X))))),inverse(multiply(inverse(inverse(X)),inverse(X)))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(inverse(X)))),multiply(X2,inverse(inverse(X))))),inverse(multiply(inverse(inverse(X)),inverse(X)))) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c124]) ).
cnf(c174,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X4),X4))),inverse(X))))),multiply(X2,inverse(inverse(X))))),inverse(multiply(inverse(inverse(X)),inverse(X)))) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c172,c173]) ).
cnf(c175,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c4,c174]) ).
cnf(c176,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(multiply(inverse(X3),X3),inverse(X2)) = multiply(inverse(multiply(inverse(X),X)),inverse(X2)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(X2))) = multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X),X)),inverse(X2))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
inverse(multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(X2)))) = inverse(multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X),X)),inverse(X2)))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(multiply(inverse(X4),X4),inverse(X3)))),multiply(inverse(X2),X2)) = multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(inverse(multiply(inverse(X),X)),inverse(X3)))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c175]) ).
cnf(c183,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
inverse(multiply(inverse(X2),X2)) = inverse(inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(X3)) = multiply(inverse(inverse(multiply(inverse(X),X))),inverse(X3)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X2),X2)),inverse(X3))) = multiply(multiply(inverse(X4),X4),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(X3))),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
inverse(multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X2),X2)),inverse(X3)))) = inverse(multiply(multiply(inverse(X4),X4),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(X3)))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(inverse(multiply(inverse(X2),X2)),inverse(X4)))),multiply(inverse(X3),X3)) = multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(X4)))),multiply(inverse(X3),X3)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c175]) ).
cnf(c190,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X4)))),multiply(inverse(X3),X3)) = multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X4)))),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c175]) ).
cnf(c193,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
multiply(multiply(inverse(X4),X4),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3))) = multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
inverse(multiply(multiply(inverse(X4),X4),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3)))) = inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3)))),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X4)))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X4)))),inverse(multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(X4)))),inverse(multiply(inverse(X2),X2))) = X4,
inference(substitution,[status(thm)],[c122]) ).
cnf(c198,plain,
multiply(inverse(multiply(multiply(inverse(X4),X4),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3)))),inverse(multiply(inverse(X),X))) = X3,
inference(transitivity,[status(thm)],[c196,c197]) ).
cnf(c199,plain,
multiply(inverse(multiply(multiply(inverse(X4),X4),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(X3)))),multiply(inverse(X2),X2)) = X3,
inference(transitivity,[status(thm)],[c191,c198]) ).
cnf(c200,plain,
multiply(inverse(multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X),X)),inverse(X3)))),multiply(inverse(X2),X2)) = X3,
inference(transitivity,[status(thm)],[c188,c199]) ).
cnf(c201,plain,
multiply(inverse(multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(X2)))),multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c181,c200]) ).
cnf(c202,plain,
multiply(inverse(multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X2),X2),inverse(multiply(multiply(inverse(X5),X5),X4))))),multiply(inverse(X),X)) = multiply(multiply(inverse(X5),X5),X4),
inference(substitution,[status(thm)],[c201]) ).
cnf(c203,plain,
multiply(multiply(inverse(X5),X5),X4) = multiply(inverse(multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X2),X2),inverse(multiply(multiply(inverse(X5),X5),X4))))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c175]) ).
cnf(c205,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(multiply(inverse(X),X)),X2),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
inverse(multiply(multiply(inverse(X3),X3),X2)) = inverse(multiply(inverse(multiply(inverse(X),X)),X2)),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
multiply(multiply(inverse(X4),X4),inverse(multiply(multiply(inverse(X3),X3),X2))) = multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(inverse(X),X)),X2))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
multiply(multiply(inverse(X5),X5),multiply(multiply(inverse(X4),X4),inverse(multiply(multiply(inverse(X3),X3),X2)))) = multiply(multiply(inverse(X5),X5),multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(inverse(X),X)),X2)))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),X3))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c124]) ).
cnf(c211,plain,
multiply(inverse(X3),X3) = multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
inverse(multiply(inverse(X3),X3)) = inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
multiply(inverse(multiply(inverse(X3),X3)),X4) = multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X4),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
inverse(multiply(inverse(multiply(inverse(X3),X3)),X4)) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X4)),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
multiply(multiply(inverse(X5),X5),inverse(multiply(inverse(multiply(inverse(X3),X3)),X4))) = multiply(multiply(inverse(X5),X5),inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X4))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X5),X5),inverse(multiply(inverse(multiply(inverse(X3),X3)),X4)))) = multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X5),X5),inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X4)))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c175]) ).
cnf(c218,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(X3,multiply(inverse(X2),X2)) = multiply(X3,inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
inverse(multiply(X3,multiply(inverse(X2),X2))) = inverse(multiply(X3,inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
multiply(inverse(multiply(X4,multiply(inverse(X3),X3))),multiply(X4,inverse(X2))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X),X)))),multiply(X4,inverse(X2))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),X2)))),multiply(X4,inverse(X3))),
inference(substitution,[status(thm)],[c106]) ).
cnf(c223,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),X2)))),multiply(X4,inverse(X3))) = multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3))),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c175]) ).
cnf(c225,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X4))) = multiply(multiply(inverse(X3),X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X4))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
inverse(inverse(multiply(inverse(X2),X2))) = inverse(multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c175]) ).
cnf(c227,plain,
multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X3)) = multiply(inverse(multiply(inverse(X),X)),inverse(X3)),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
multiply(multiply(inverse(X3),X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X4))) = multiply(multiply(inverse(X3),X3),multiply(inverse(multiply(inverse(X),X)),inverse(X4))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c175]) ).
cnf(c230,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(X3)) = multiply(multiply(inverse(X2),X2),inverse(X3)),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
multiply(multiply(inverse(X3),X3),multiply(inverse(multiply(inverse(X),X)),inverse(X4))) = multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X2),X2),inverse(X4))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(multiply(inverse(X3),X3),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(X4))) = multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X2),X2),inverse(X4))),
inference(transitivity,[status(thm)],[c228,c231]) ).
cnf(c233,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(X5))) = multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(X5))),
inference(transitivity,[status(thm)],[c225,c232]) ).
cnf(c234,plain,
multiply(inverse(multiply(X5,inverse(multiply(inverse(X),X)))),multiply(X5,inverse(X4))) = multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X2),X2),inverse(X4))),
inference(transitivity,[status(thm)],[c223,c233]) ).
cnf(c235,plain,
multiply(inverse(multiply(X5,multiply(inverse(X4),X4))),multiply(X5,inverse(X3))) = multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),inverse(X3))),
inference(transitivity,[status(thm)],[c221,c234]) ).
cnf(c236,plain,
multiply(inverse(multiply(X7,multiply(inverse(X6),X6))),multiply(X7,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X3)))) = multiply(multiply(inverse(X5),X5),multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X3)))),
inference(substitution,[status(thm)],[c235]) ).
cnf(c237,plain,
multiply(multiply(inverse(X7),X7),multiply(multiply(inverse(X6),X6),inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3)))),X5)))) = multiply(inverse(multiply(X2,multiply(inverse(X),X))),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3)))),X5)))),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))),X4))) = multiply(X,inverse(X4)),
inference(substitution,[status(thm)],[c147]) ).
cnf(c239,plain,
multiply(inverse(multiply(X2,multiply(inverse(X),X))),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3)))),X5)))) = multiply(inverse(multiply(X2,multiply(inverse(X),X))),multiply(X2,inverse(X5))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(inverse(multiply(X2,multiply(inverse(X),X))),multiply(X2,inverse(X5))) = multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(X5))),
inference(substitution,[status(thm)],[c235]) ).
cnf(c241,plain,
multiply(inverse(multiply(X2,multiply(inverse(X),X))),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3)))),X7)))) = multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X5),X5),inverse(X7))),
inference(transitivity,[status(thm)],[c239,c240]) ).
cnf(c242,plain,
multiply(multiply(inverse(X7),X7),multiply(multiply(inverse(X6),X6),inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),X5)))) = multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(X5))),
inference(transitivity,[status(thm)],[c237,c241]) ).
cnf(c243,plain,
multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X5),X5),inverse(multiply(inverse(multiply(inverse(X),X)),X4)))) = multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X2),X2),inverse(X4))),
inference(transitivity,[status(thm)],[c216,c242]) ).
cnf(c244,plain,
multiply(multiply(inverse(X6),X6),multiply(multiply(inverse(X5),X5),inverse(multiply(multiply(inverse(X4),X4),X3)))) = multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),inverse(X3))),
inference(transitivity,[status(thm)],[c209,c243]) ).
cnf(c245,plain,
multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(multiply(multiply(inverse(X6),X6),X5)))) = multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),inverse(X5))),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
inverse(multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),inverse(multiply(multiply(inverse(X6),X6),X5))))) = inverse(multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),inverse(X5)))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
multiply(inverse(multiply(multiply(inverse(X5),X5),multiply(multiply(inverse(X4),X4),inverse(multiply(multiply(inverse(X7),X7),X6))))),multiply(inverse(X3),X3)) = multiply(inverse(multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),inverse(X6)))),multiply(inverse(X3),X3)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
multiply(inverse(multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),inverse(X4)))),multiply(inverse(X3),X3)) = X4,
inference(substitution,[status(thm)],[c201]) ).
cnf(c249,plain,
multiply(inverse(multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X2),X2),inverse(multiply(multiply(inverse(X5),X5),X4))))),multiply(inverse(X),X)) = X4,
inference(transitivity,[status(thm)],[c247,c248]) ).
cnf(c250,plain,
multiply(multiply(inverse(X2),X2),X) = X,
inference(transitivity,[status(thm)],[c203,c249]) ).
cnf(c251,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(substitution,[status(thm)],[c250]) ).
cnf(c252,plain,
$false,
inference(resolution,[status(thm)],[c1,c251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP425-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 10:02:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.48 Command-line arguments: --no-flatten-goal
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable
% 0.18/0.48
% 0.18/0.52 % SZS output start CNFRefutation
% See solution above
% 1.99/0.72
% 1.99/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------