%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.09s 0.45s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 2
% Syntax : Number of clauses : 219 ( 219 unt; 0 nHn; 3 RR)
% Number of literals : 219 ( 218 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 643 ( 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,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))) = multiply(X5,inverse(X5)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X5,inverse(X5)) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X)),X3),X2),multiply(X4,inverse(X4)))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X)),X3),X2),multiply(X4,inverse(X4)))),multiply(inverse(multiply(multiply(X3,X2),X)),X3)) = multiply(X,multiply(inverse(multiply(multiply(X3,X2),X)),X3)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X)),X3),X2),multiply(X4,inverse(X4)))),multiply(inverse(multiply(multiply(X3,X2),X)),X3)),X2) = multiply(multiply(X,multiply(inverse(multiply(multiply(X3,X2),X)),X3)),X2),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X))) = multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))) = inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X)),X3),X2),multiply(X4,inverse(X4)))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
X = inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X)),X3),X2),multiply(X4,inverse(X4)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X,multiply(inverse(multiply(multiply(X3,X2),X)),X3)) = multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X)),X3),X2),multiply(X4,inverse(X4)))),multiply(inverse(multiply(multiply(X3,X2),X)),X3)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(multiply(X,multiply(inverse(multiply(multiply(X3,X2),X)),X3)),X2) = multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X)),X3),X2),multiply(X4,inverse(X4)))),multiply(inverse(multiply(multiply(X3,X2),X)),X3)),X2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X))) = multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))) = multiply(X5,inverse(X5)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))) = multiply(X5,inverse(X5)),
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X2)),X4),X3),multiply(X5,inverse(X5)))),multiply(inverse(multiply(multiply(X4,X3),X2)),X4)),X3),multiply(X,inverse(X)))) = multiply(X6,inverse(X6)),
inference(transitivity,[status(thm)],[c9,c17]) ).
cnf(c19,plain,
multiply(X,inverse(X)) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c4,c18]) ).
cnf(c20,plain,
multiply(X2,inverse(X2)) = multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),X2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(multiply(multiply(X4,inverse(X4)),X3),multiply(X2,inverse(X2))) = multiply(multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
inverse(multiply(multiply(multiply(X4,inverse(X4)),X3),multiply(X2,inverse(X2)))) = inverse(multiply(multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X3,inverse(X3)) = multiply(multiply(X2,X),inverse(multiply(X2,X))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c25,plain,
inverse(multiply(X3,inverse(X3))) = inverse(multiply(multiply(X2,X),inverse(multiply(X2,X)))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(inverse(multiply(X3,inverse(X3))),X2) = multiply(inverse(multiply(multiply(X2,X),inverse(multiply(X2,X)))),X2),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(multiply(inverse(multiply(X3,inverse(X3))),X2),X) = multiply(multiply(inverse(multiply(multiply(X2,X),inverse(multiply(X2,X)))),X2),X),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(multiply(multiply(inverse(multiply(X4,inverse(X4))),X3),X2),multiply(X,inverse(X))) = multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X2)))),X3),X2),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X4,inverse(X4))),X3),X2),multiply(X,inverse(X)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X2)))),X3),X2),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X2)))),X3),X2),multiply(X,inverse(X)))) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X4,inverse(X4))),X3),X2),multiply(X,inverse(X)))) = inverse(multiply(X3,X2)),
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2)))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X3)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
inverse(multiply(multiply(multiply(X4,inverse(X4)),X3),multiply(X2,inverse(X2)))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X3)),
inference(transitivity,[status(thm)],[c23,c32]) ).
cnf(c34,plain,
inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X)))) = inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),X3)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),X3)) = inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X2,inverse(X2)) = multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c37,plain,
inverse(multiply(X2,inverse(X2))) = inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(inverse(multiply(X2,inverse(X2))),X) = multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(multiply(inverse(multiply(X2,inverse(X2))),X),inverse(X)) = multiply(multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X),inverse(X)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X),inverse(X))) = inverse(multiply(multiply(inverse(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X),inverse(X))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(inverse(multiply(multiply(X4,X3),inverse(multiply(X2,inverse(X2))))),X4)),X3),multiply(X,inverse(X)))) = inverse(multiply(multiply(inverse(multiply(multiply(X4,X3),inverse(multiply(X2,inverse(X2))))),X4),X3)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c42,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X4,X3),inverse(multiply(X2,inverse(X2))))),X4),X3)) = inverse(multiply(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(inverse(multiply(multiply(X4,X3),inverse(multiply(X2,inverse(X2))))),X4)),X3),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X4)),X3),X2),multiply(X,inverse(X)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
X4 = inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X4)),X3),X2),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X4,multiply(inverse(multiply(multiply(X3,X2),X4)),X3)) = multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X4)),X3),X2),multiply(X,inverse(X)))),multiply(inverse(multiply(multiply(X3,X2),X4)),X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(multiply(X4,multiply(inverse(multiply(multiply(X3,X2),X4)),X3)),X2) = multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,X2),X4)),X3),X2),multiply(X,inverse(X)))),multiply(inverse(multiply(multiply(X3,X2),X4)),X3)),X2),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(multiply(multiply(X5,multiply(inverse(multiply(multiply(X4,X3),X5)),X4)),X3),multiply(X2,inverse(X2))) = multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X5)),X4),X3),multiply(X,inverse(X)))),multiply(inverse(multiply(multiply(X4,X3),X5)),X4)),X3),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
inverse(multiply(multiply(multiply(X5,multiply(inverse(multiply(multiply(X4,X3),X5)),X4)),X3),multiply(X2,inverse(X2)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X5)),X4),X3),multiply(X,inverse(X)))),multiply(inverse(multiply(multiply(X4,X3),X5)),X4)),X3),multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X3),X5)),X4),X3),multiply(X,inverse(X)))),multiply(inverse(multiply(multiply(X4,X3),X5)),X4)),X3),multiply(X2,inverse(X2)))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
inverse(multiply(multiply(multiply(X5,multiply(inverse(multiply(multiply(X4,X3),X5)),X4)),X3),multiply(X2,inverse(X2)))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X3,inverse(X3))),multiply(inverse(multiply(multiply(X5,X4),inverse(multiply(X3,inverse(X3))))),X5)),X4),multiply(X,inverse(X)))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X4,X3),inverse(multiply(X2,inverse(X2))))),X4),X3)) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c42,c51]) ).
cnf(c53,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2))))),X2),inverse(X2))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
inverse(multiply(multiply(inverse(multiply(X3,inverse(X3))),X2),inverse(X2))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c40,c53]) ).
cnf(c55,plain,
inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X,inverse(X)) = inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))) = multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))),inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),X2) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))),inverse(multiply(X,inverse(X)))),X2),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X))) = multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X3),inverse(X3))),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X3),inverse(X3))),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X3),inverse(X3))),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X)))) = inverse(X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X,inverse(X)))) = inverse(X3),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),X)) = inverse(X),
inference(transitivity,[status(thm)],[c35,c62]) ).
cnf(c64,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(X2))))) = inverse(inverse(inverse(inverse(X2)))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
inverse(inverse(inverse(inverse(X2)))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(X2))))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(X3,inverse(X3)) = multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(multiply(inverse(multiply(X,inverse(X))),X2))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c67,plain,
multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3))) = multiply(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(multiply(inverse(multiply(X,inverse(X))),X2))),multiply(X3,inverse(X3))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))) = inverse(multiply(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(multiply(inverse(multiply(X,inverse(X))),X2))),multiply(X3,inverse(X3)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(multiply(inverse(multiply(X,inverse(X))),X2))),multiply(X3,inverse(X3)))) = inverse(multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),X2)))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c70,plain,
inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))) = inverse(multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),X2)))),
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X)))) = inverse(multiply(X4,inverse(multiply(inverse(multiply(X3,inverse(X3))),X4)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
inverse(multiply(X4,inverse(multiply(inverse(multiply(X3,inverse(X3))),X4)))) = inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),inverse(multiply(X,inverse(X))))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c74,plain,
multiply(X2,inverse(X2)) = inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),inverse(multiply(X,inverse(X))))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))) = multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),inverse(multiply(X,inverse(X))))),inverse(multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X))) = multiply(multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),inverse(multiply(X,inverse(X))))),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X)))) = inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),inverse(multiply(X,inverse(X))))),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X,inverse(X))),inverse(multiply(X,inverse(X))))),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X)))) = multiply(X3,inverse(X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c79,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X2,inverse(X2)))),multiply(X,inverse(X)))) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
inverse(multiply(X3,inverse(multiply(inverse(multiply(X2,inverse(X2))),X3)))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c72,c79]) ).
cnf(c81,plain,
inverse(multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),X2)))) = multiply(X3,inverse(X3)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(X3,inverse(X3)) = inverse(multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),X2)))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
inverse(multiply(X3,inverse(X3))) = inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),X2))))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
inverse(inverse(multiply(X3,inverse(X3)))) = inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),X2)))))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X)))) = inverse(multiply(X4,inverse(multiply(inverse(multiply(X3,inverse(X3))),X4)))),
inference(substitution,[status(thm)],[c70]) ).
cnf(c86,plain,
inverse(multiply(X4,inverse(multiply(inverse(multiply(X3,inverse(X3))),X4)))) = inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
inverse(inverse(multiply(X4,inverse(multiply(inverse(multiply(X3,inverse(X3))),X4))))) = inverse(inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
inverse(inverse(inverse(multiply(X4,inverse(multiply(inverse(multiply(X3,inverse(X3))),X4)))))) = inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X)))))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
inverse(multiply(inverse(inverse(multiply(X3,inverse(X3)))),inverse(inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X))))))) = inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X)))))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c90,plain,
inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))))))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
inverse(multiply(multiply(multiply(X5,inverse(X5)),inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))),multiply(X4,inverse(X4)))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))))))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c92,plain,
inverse(multiply(inverse(inverse(multiply(X3,inverse(X3)))),inverse(inverse(multiply(multiply(X5,inverse(X5)),multiply(X4,inverse(X4))))))) = inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(multiply(multiply(X5,inverse(X5)),multiply(X4,inverse(X4)))))),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))))) = inverse(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2))))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c94,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2))))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,inverse(X3)),X2)),inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2))))),multiply(X,inverse(X)))) = inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c96,plain,
inverse(multiply(inverse(inverse(multiply(X4,inverse(X4)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,inverse(X3)),X2)),inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2))))),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(X2,inverse(X2)) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c98,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(multiply(X,inverse(X)),X2),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
inverse(multiply(multiply(X3,inverse(X3)),X2)) = inverse(multiply(multiply(X,inverse(X)),X2)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
multiply(inverse(multiply(multiply(X3,inverse(X3)),X2)),X) = multiply(inverse(multiply(multiply(X,inverse(X)),X2)),X),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(multiply(inverse(multiply(multiply(X3,inverse(X3)),X2)),X),inverse(X)) = multiply(multiply(inverse(multiply(multiply(X,inverse(X)),X2)),X),inverse(X)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(multiply(multiply(inverse(multiply(multiply(X4,inverse(X4)),X3)),X2),inverse(X2)),multiply(X,inverse(X))) = multiply(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),X3)),X2),inverse(X2)),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,inverse(X4)),X3)),X2),inverse(X2)),multiply(X,inverse(X)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),X3)),X2),inverse(X2)),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),X3)),X2),inverse(X2)),multiply(X,inverse(X)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c105,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,inverse(X4)),X3)),X2),inverse(X2)),multiply(X,inverse(X)))) = X3,
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X3,inverse(X3)),X2)),inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2))))),multiply(X,inverse(X)))) = X2,
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
inverse(multiply(inverse(inverse(multiply(X3,inverse(X3)))),inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X)))))) = X,
inference(transitivity,[status(thm)],[c96,c106]) ).
cnf(c108,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))))) = X2,
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X))))) = X,
inference(transitivity,[status(thm)],[c94,c108]) ).
cnf(c110,plain,
X = inverse(inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X))))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X)))),X) = multiply(inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X)))),inverse(inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),X)))))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(X,inverse(X)) = multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))),inverse(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c113,plain,
multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))),inverse(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))))) = multiply(X,inverse(X)),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),X2)))),X2) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c111,c113]) ).
cnf(c115,plain,
multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))),multiply(X2,inverse(X2))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(X,inverse(X)) = multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))),multiply(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(multiply(X,inverse(X)),inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))) = multiply(multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))),multiply(X2,inverse(X2))),inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))))),multiply(X,inverse(X))) = multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))))),multiply(X3,inverse(X3))),inverse(inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))))),multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))))),multiply(X,inverse(X)))) = inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))))),multiply(X3,inverse(X3))),inverse(inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))))),multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(X2,inverse(X2)) = multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c121,plain,
multiply(inverse(X3),multiply(X2,inverse(X2))) = multiply(inverse(X3),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(multiply(inverse(X3),multiply(X2,inverse(X2))),X3) = multiply(multiply(inverse(X3),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X3),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(multiply(multiply(inverse(X4),multiply(X3,inverse(X3))),X4),multiply(X2,inverse(X2))) = multiply(multiply(multiply(inverse(X4),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X4),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
inverse(multiply(multiply(multiply(inverse(X4),multiply(X3,inverse(X3))),X4),multiply(X2,inverse(X2)))) = inverse(multiply(multiply(multiply(inverse(X4),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X4),multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c126,plain,
multiply(X,inverse(X)) = inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X)))) = multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))),inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(inverse(X2),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))) = multiply(inverse(X2),multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))),inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(multiply(inverse(X2),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X2) = multiply(multiply(inverse(X2),multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X2),inverse(X2))),inverse(multiply(X,inverse(X))))),X2),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(multiply(multiply(inverse(X3),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2))) = multiply(multiply(multiply(inverse(X3),multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X3),inverse(X3))),inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
inverse(multiply(multiply(multiply(inverse(X3),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2)))) = inverse(multiply(multiply(multiply(inverse(X3),multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X3),inverse(X3))),inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
inverse(multiply(multiply(multiply(inverse(X4),multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),X4),inverse(X4))),inverse(multiply(X,inverse(X))))),X4),multiply(X3,inverse(X3)))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c133,plain,
inverse(multiply(multiply(multiply(inverse(X4),multiply(multiply(X,inverse(X)),inverse(multiply(X,inverse(X))))),X4),multiply(X3,inverse(X3)))) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
inverse(multiply(multiply(multiply(inverse(X4),multiply(X3,inverse(X3))),X4),multiply(X2,inverse(X2)))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c124,c133]) ).
cnf(c135,plain,
inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))),multiply(X2,inverse(X2))),inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2)))))),multiply(X,inverse(X)))) = multiply(X4,inverse(X4)),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),inverse(inverse(multiply(multiply(X4,inverse(X4)),multiply(X3,inverse(X3)))))),multiply(X,inverse(X)))) = multiply(X5,inverse(X5)),
inference(transitivity,[status(thm)],[c119,c135]) ).
cnf(c137,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(multiply(multiply(X3,inverse(X3)),multiply(X2,inverse(X2))))))) = multiply(X4,inverse(X4)),
inference(transitivity,[status(thm)],[c92,c136]) ).
cnf(c138,plain,
inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),multiply(X,inverse(X)))))) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c90,c137]) ).
cnf(c139,plain,
inverse(inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(X,inverse(X))),X2)))))) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c88,c138]) ).
cnf(c140,plain,
inverse(inverse(multiply(X2,inverse(X2)))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c84,c139]) ).
cnf(c141,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(X2,inverse(X2)) = inverse(inverse(multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(inverse(inverse(multiply(X,inverse(X)))),X2),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
inverse(multiply(multiply(X3,inverse(X3)),X2)) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c146,plain,
inverse(multiply(multiply(X2,inverse(X2)),X)) = inverse(X),
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
inverse(multiply(multiply(X,inverse(X)),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
inverse(X2) = inverse(multiply(multiply(X,inverse(X)),X2)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
inverse(inverse(X2)) = inverse(inverse(multiply(multiply(X,inverse(X)),X2))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
inverse(inverse(inverse(X2))) = inverse(inverse(inverse(multiply(multiply(X,inverse(X)),X2)))),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(inverse(inverse(multiply(X2,inverse(X2)))),inverse(inverse(inverse(X3)))) = multiply(inverse(inverse(multiply(X2,inverse(X2)))),inverse(inverse(inverse(multiply(multiply(X,inverse(X)),X3))))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),inverse(inverse(inverse(X3))))) = inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),inverse(inverse(inverse(multiply(multiply(X,inverse(X)),X3)))))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),inverse(inverse(inverse(multiply(multiply(X,inverse(X)),X3)))))) = X3,
inference(substitution,[status(thm)],[c107]) ).
cnf(c154,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(X2))))) = X2,
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(transitivity,[status(thm)],[c65,c154]) ).
cnf(c156,plain,
inverse(inverse(inverse(inverse(multiply(inverse(X),X))))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
multiply(inverse(X),X) = inverse(inverse(inverse(inverse(multiply(inverse(X),X))))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c140]) ).
cnf(c159,plain,
multiply(X2,inverse(X2)) = inverse(inverse(multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(inverse(inverse(multiply(X,inverse(X)))),X2),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2))))) = multiply(inverse(inverse(multiply(X,inverse(X)))),X2),
inference(substitution,[status(thm)],[c155]) ).
cnf(c162,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),X2) = inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2))))),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c164,plain,
inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2))) = inverse(inverse(X2)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2)))) = inverse(inverse(inverse(X2))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2))))) = inverse(inverse(inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2))))) = X2,
inference(transitivity,[status(thm)],[c166,c155]) ).
cnf(c168,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),X2) = X2,
inference(transitivity,[status(thm)],[c162,c167]) ).
cnf(c169,plain,
multiply(multiply(X2,inverse(X2)),X) = X,
inference(transitivity,[status(thm)],[c160,c168]) ).
cnf(c170,plain,
multiply(multiply(X,inverse(X)),X2) = X2,
inference(substitution,[status(thm)],[c169]) ).
cnf(c171,plain,
X2 = multiply(multiply(X,inverse(X)),X2),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(X3,multiply(X2,inverse(X2))) = multiply(multiply(multiply(X,inverse(X)),X3),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
inverse(multiply(X3,multiply(X2,inverse(X2)))) = inverse(multiply(multiply(multiply(X,inverse(X)),X3),multiply(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
inverse(multiply(multiply(multiply(X2,inverse(X2)),X4),multiply(X3,inverse(X3)))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X4)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c175,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c176,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),X3),multiply(X2,inverse(X2)))) = inverse(X3),
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
inverse(multiply(X2,multiply(X,inverse(X)))) = inverse(X2),
inference(transitivity,[status(thm)],[c173,c176]) ).
cnf(c178,plain,
inverse(X2) = inverse(multiply(X2,multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(X2,multiply(X,inverse(X)))),X2),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(X2,multiply(X,inverse(X)))),X2)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),multiply(X,inverse(X)))) = inverse(multiply(X3,multiply(X2,inverse(X2)))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c182,plain,
inverse(multiply(X3,multiply(X2,inverse(X2)))) = inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
multiply(inverse(multiply(X3,multiply(X2,inverse(X2)))),X3) = multiply(inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),multiply(X,inverse(X)))),X3),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
inverse(multiply(inverse(multiply(X3,multiply(X2,inverse(X2)))),X3)) = inverse(multiply(inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),multiply(X,inverse(X)))),X3)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
multiply(X2,inverse(X2)) = multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c186,plain,
inverse(multiply(X2,inverse(X2))) = inverse(multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X)))))))),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),
inference(substitution,[status(thm)],[c140]) ).
cnf(c188,plain,
multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))) = inverse(inverse(multiply(X,inverse(X)))),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))))) = multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
inverse(multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X)))))))) = inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X)))))))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X)))))))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c192,plain,
inverse(multiply(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X))))),inverse(multiply(inverse(multiply(X,inverse(X))),inverse(inverse(multiply(X,inverse(X)))))))) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c190,c191]) ).
cnf(c193,plain,
inverse(multiply(X2,inverse(X2))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c186,c192]) ).
cnf(c194,plain,
inverse(multiply(X,inverse(X))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
multiply(X2,inverse(X2)) = inverse(multiply(X,inverse(X))),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(X2,inverse(X2))) = multiply(multiply(X4,multiply(X3,inverse(X3))),inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(X2,inverse(X2)))) = inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(X2,inverse(X2)))),X4) = multiply(inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),inverse(multiply(X,inverse(X))))),X4),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
inverse(multiply(inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),multiply(X2,inverse(X2)))),X4)) = inverse(multiply(inverse(multiply(multiply(X4,multiply(X3,inverse(X3))),inverse(multiply(X,inverse(X))))),X4)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2)))) = inverse(multiply(inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),inverse(multiply(X,inverse(X))))),X3)),
inference(substitution,[status(thm)],[c177]) ).
cnf(c201,plain,
inverse(multiply(inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),inverse(multiply(X,inverse(X))))),X3)) = inverse(multiply(multiply(inverse(multiply(multiply(X3,multiply(X2,inverse(X2))),inverse(multiply(X,inverse(X))))),X3),multiply(X2,inverse(X2)))),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),inverse(multiply(X,inverse(X))))),X4),multiply(X2,inverse(X2)))) = multiply(X3,inverse(X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c203,plain,
inverse(multiply(inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),inverse(multiply(X,inverse(X))))),X4)) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c201,c202]) ).
cnf(c204,plain,
inverse(multiply(inverse(multiply(multiply(X4,multiply(X2,inverse(X2))),multiply(X,inverse(X)))),X4)) = multiply(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c199,c203]) ).
cnf(c205,plain,
inverse(multiply(inverse(multiply(X3,multiply(X,inverse(X)))),X3)) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c184,c204]) ).
cnf(c206,plain,
inverse(multiply(inverse(X2),X2)) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c180,c205]) ).
cnf(c207,plain,
inverse(inverse(multiply(inverse(X2),X2))) = inverse(multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
inverse(inverse(inverse(multiply(inverse(X2),X2)))) = inverse(inverse(multiply(X,inverse(X)))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
inverse(inverse(inverse(inverse(multiply(inverse(X2),X2))))) = inverse(inverse(inverse(multiply(X,inverse(X))))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
inverse(inverse(inverse(multiply(X2,inverse(X2))))) = inverse(multiply(X,inverse(X))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c211,plain,
inverse(multiply(X,inverse(X))) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c212,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = multiply(X2,inverse(X2)),
inference(transitivity,[status(thm)],[c210,c211]) ).
cnf(c213,plain,
inverse(inverse(inverse(inverse(multiply(inverse(X2),X2))))) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c209,c212]) ).
cnf(c214,plain,
multiply(inverse(X2),X2) = multiply(X,inverse(X)),
inference(transitivity,[status(thm)],[c157,c213]) ).
cnf(c215,plain,
multiply(inverse(a1),a1) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(inverse(b1),b1) = multiply(X,inverse(X)),
inference(substitution,[status(thm)],[c214]) ).
cnf(c217,plain,
multiply(X,inverse(X)) = multiply(inverse(b1),b1),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(transitivity,[status(thm)],[c215,c217]) ).
cnf(c219,plain,
$false,
inference(resolution,[status(thm)],[c1,c218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:04:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 Command-line arguments: --no-flatten-goal
% 0.09/0.45
% 0.09/0.45 % SZS status Unsatisfiable
% 0.09/0.45
% 0.09/0.47 % SZS output start CNFRefutation
% See solution above
% 1.30/0.61
% 1.30/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------