%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP419-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 10:10:06 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.53s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 95
% Number of leaves : 2
% Syntax : Number of clauses : 289 ( 289 unt; 0 nHn; 3 RR)
% Number of literals : 289 ( 288 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 21 ( 4 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 : 1094 ( 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,
inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = inverse(X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(X3) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(inverse(X3),X3) = multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),X3),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
inverse(multiply(inverse(X3),X3)) = inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),X3)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X,X3))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
X3 = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X4,inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(multiply(X4,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(X5,inverse(multiply(X4,inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))))) = multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
inverse(multiply(X5,inverse(multiply(X4,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))) = inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(multiply(X5,inverse(multiply(X4,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3)) = multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
inverse(multiply(inverse(multiply(X5,inverse(multiply(X4,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))) = inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
inverse(multiply(inverse(multiply(X5,inverse(multiply(X4,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)),
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(X4)),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(X4)),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3)) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X2)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X3,X)) = X2,
inference(transitivity,[status(thm)],[c18,c19]) ).
cnf(c21,plain,
X2 = multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X2)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X3,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X),inverse(multiply(multiply(X4,X2),inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X2))))))))),X3) = multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X),inverse(multiply(multiply(X4,X2),inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X2))))))))),multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X4,X2))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X),inverse(multiply(multiply(X4,X2),inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X2))))))))),X3)) = inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X),inverse(multiply(multiply(X4,X2),inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X2))))))))),multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X4,X2)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X),inverse(multiply(multiply(X4,X2),inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X2))))))))),multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X4,X2)))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X),inverse(multiply(multiply(X4,X2),inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,X2))))))))),X3)) = X,
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X3,X2),inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X2))))))),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(X),inverse(multiply(multiply(X5,X4),inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X4))))))))),inverse(multiply(multiply(X3,X2),inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X2))))))) = X,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
X3 = inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X5,X4),inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X5,X4),inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X4))))))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),X4) = multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5)))))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),X4)) = inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),X4)),X3) = multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))))),X3),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),X4)),X3)) = inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))))),X3)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))))),X3)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X5),inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X5))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X)))))))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c33,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))))),X5)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X)))))))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c34,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))))),X5)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X5,X4),inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X5,X4),inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X4))))))) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c36,plain,
multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4)))))))) = multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X3),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))))) = inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X3)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))))),X5) = multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X3)),X5),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))))),X5)) = inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X3)),X5)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X6,X4),inverse(multiply(inverse(multiply(X6,X4)),multiply(X6,X4))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(X6,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),X3)),X5)),
inference(transitivity,[status(thm)],[c34,c39]) ).
cnf(c41,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X7,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X7,X5),inverse(multiply(inverse(multiply(X7,X5)),multiply(X7,X5))))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X2,X),inverse(multiply(inverse(multiply(X2,X)),multiply(X2,X))))))))),inverse(multiply(multiply(X7,X5),inverse(multiply(inverse(multiply(X7,X5)),multiply(X7,X5))))))))),X3)) = inverse(multiply(inverse(multiply(inverse(multiply(X7,inverse(multiply(inverse(inverse(X6)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),X4)),X6)),
inference(transitivity,[status(thm)],[c32,c40]) ).
cnf(c42,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(X)),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),X2)),X)) = inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(X4)),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),X2)),X4)),
inference(transitivity,[status(thm)],[c31,c41]) ).
cnf(c43,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),X3)) = inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X4)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),X4)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = inverse(X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),X3) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),X3)) = inverse(multiply(inverse(X3),X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),X3)) = inverse(multiply(inverse(X4),X4)),
inference(transitivity,[status(thm)],[c43,c46]) ).
cnf(c48,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(X2),X2)),
inference(transitivity,[status(thm)],[c6,c47]) ).
cnf(c49,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(inverse(multiply(X,inverse(multiply(inverse(X),X))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(X3,inverse(multiply(inverse(X2),X2))) = multiply(X3,inverse(multiply(inverse(inverse(multiply(X,inverse(multiply(inverse(X),X))))),inverse(multiply(X,inverse(multiply(inverse(X),X))))))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
inverse(multiply(X3,inverse(multiply(inverse(X2),X2)))) = inverse(multiply(X3,inverse(multiply(inverse(inverse(multiply(X,inverse(multiply(inverse(X),X))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),X2)))),multiply(X3,X)) = multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(multiply(X,inverse(multiply(inverse(X),X))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X3,X)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3)) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c56,plain,
multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X3,X2))),inverse(multiply(X,inverse(multiply(inverse(X),X))))) = multiply(X4,inverse(multiply(X,inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X3,X2))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))) = inverse(multiply(X4,inverse(multiply(X,inverse(multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X))))))) = multiply(X2,inverse(multiply(X5,inverse(multiply(X,inverse(multiply(inverse(X),X))))))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))) = inverse(multiply(X2,inverse(multiply(X5,inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)) = multiply(inverse(multiply(X2,inverse(multiply(X5,inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = inverse(multiply(inverse(multiply(X2,inverse(multiply(X5,inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X3,X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
X2 = inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X3,X))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X3,inverse(multiply(X,inverse(multiply(inverse(X),X))))) = multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X4,X2))),inverse(multiply(X,inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
inverse(multiply(X3,inverse(multiply(X,inverse(multiply(inverse(X),X)))))) = inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X4,X2))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(X2,inverse(multiply(X4,inverse(multiply(X,inverse(multiply(inverse(X),X))))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X))))))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
inverse(multiply(X2,inverse(multiply(X4,inverse(multiply(X,inverse(multiply(inverse(X),X)))))))) = inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(inverse(multiply(X2,inverse(multiply(X4,inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(X4,inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(X4,inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3)),
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X6),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(multiply(X7,inverse(multiply(inverse(X6),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X7,X5)),
inference(transitivity,[status(thm)],[c61,c71]) ).
cnf(c73,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)) = multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X5,X3)),
inference(transitivity,[status(thm)],[c54,c72]) ).
cnf(c74,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)) = multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X4,X3)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)) = multiply(X3,inverse(multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c77,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c78,plain,
multiply(X2,inverse(multiply(inverse(X2),X2))) = multiply(X2,inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(X4,inverse(multiply(inverse(X4),X4))))),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)) = multiply(X4,inverse(multiply(inverse(X3),X3))),
inference(transitivity,[status(thm)],[c76,c78]) ).
cnf(c80,plain,
multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(multiply(X2,inverse(multiply(inverse(X2),X2))))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X3,X2)) = multiply(X2,inverse(multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c75,c79]) ).
cnf(c81,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(X3),X3)))),multiply(X4,X2)) = multiply(X2,inverse(multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c52,c80]) ).
cnf(c82,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(multiply(inverse(X3),X3)))) = multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(multiply(inverse(X3),X3)))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c85,plain,
multiply(inverse(X3),X3) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(X,inverse(multiply(inverse(X),X))))) = multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c87,plain,
inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))) = inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X))))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(X,inverse(multiply(inverse(X),X))))))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))) = inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(X,inverse(multiply(inverse(X),X)))))))),multiply(X2,X))) = multiply(inverse(X4),X4),
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c85,c93]) ).
cnf(c95,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(multiply(inverse(X3),X3)))),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,inverse(multiply(inverse(X3),X3)))) = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c83,c96]) ).
cnf(c98,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X))) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(inverse(X3),X3) = multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
inverse(multiply(inverse(X3),X3)) = inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(multiply(inverse(X3),X3)),X2)) = multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X)))),multiply(inverse(multiply(inverse(X3),X3)),X2)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X),X)))),multiply(inverse(multiply(inverse(X4),X4)),X3)) = multiply(X3,inverse(multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c103,plain,
multiply(inverse(multiply(inverse(X4),X4)),multiply(inverse(multiply(inverse(X3),X3)),X2)) = multiply(X2,inverse(multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))) = multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X))),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c94]) ).
cnf(c107,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))) = multiply(inverse(X),X),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c105,c107]) ).
cnf(c109,plain,
multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X))) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(inverse(X3),X3) = multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
inverse(multiply(inverse(X3),X3)) = inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X3),X3)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c113,plain,
multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X3),X3)) = multiply(X3,inverse(multiply(inverse(X),X))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c114,plain,
multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3)))),multiply(inverse(X2),X2)) = multiply(X4,inverse(multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(X3),X3))) = multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
inverse(multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(X3),X3)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c97]) ).
cnf(c119,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))) = inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3)))),multiply(inverse(X2),X2)) = multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(multiply(inverse(X5),X5)),inverse(multiply(inverse(X),X)))))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3)))),multiply(inverse(X2),X2))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(multiply(inverse(X5),X5)),inverse(multiply(inverse(X),X)))))),multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c97]) ).
cnf(c126,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(inverse(X3),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))) = inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))) = inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X5),X5)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3)))))),multiply(inverse(X2),X2)) = multiply(inverse(multiply(inverse(multiply(inverse(X5),X5)),inverse(multiply(inverse(X4),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X5),X5)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3)))))),multiply(inverse(X2),X2))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X5),X5)),inverse(multiply(inverse(X4),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c97]) ).
cnf(c135,plain,
multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(X2),X2)) = multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(X2),X2))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c139,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))))),multiply(inverse(X2),X2))) = X3,
inference(transitivity,[status(thm)],[c137,c138]) ).
cnf(c140,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X),X))) = X3,
inference(transitivity,[status(thm)],[c133,c139]) ).
cnf(c141,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(multiply(inverse(X4),X4)),inverse(multiply(inverse(X),X)))))),multiply(inverse(X2),X2))) = multiply(inverse(X4),X4),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X))) = multiply(inverse(X4),X4),
inference(transitivity,[status(thm)],[c124,c141]) ).
cnf(c143,plain,
inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X)))) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c117,c142]) ).
cnf(c144,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c111,c143]) ).
cnf(c145,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(multiply(X4,multiply(inverse(X3),X3)),multiply(inverse(X2),X2)) = multiply(multiply(X4,multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X)))),multiply(multiply(inverse(X2),X2),multiply(X5,multiply(inverse(X4),X4)))) = multiply(multiply(X5,multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c149,plain,
multiply(multiply(X5,multiply(inverse(X4),X4)),inverse(multiply(inverse(X3),X3))) = multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X)))),multiply(multiply(inverse(X2),X2),multiply(X5,multiply(inverse(X4),X4)))),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c151,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(inverse(X3),multiply(inverse(X2),X2)) = multiply(inverse(X3),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
inverse(multiply(inverse(X3),multiply(inverse(X2),X2))) = inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(inverse(multiply(inverse(X4),multiply(inverse(X3),X3))),multiply(inverse(X2),X2)) = multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X),X)))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X3),X3)) = multiply(X4,inverse(multiply(inverse(X),X))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c156,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c157,plain,
multiply(X3,inverse(multiply(inverse(X),X))) = multiply(X3,multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X),X)))),multiply(inverse(X3),X3)) = multiply(X4,multiply(inverse(X2),X2)),
inference(transitivity,[status(thm)],[c155,c157]) ).
cnf(c159,plain,
multiply(inverse(multiply(inverse(X4),multiply(inverse(X3),X3))),multiply(inverse(X2),X2)) = multiply(X4,multiply(inverse(X),X)),
inference(transitivity,[status(thm)],[c154,c158]) ).
cnf(c160,plain,
multiply(inverse(multiply(inverse(X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)) = multiply(X4,multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(X4,multiply(inverse(X3),X3)) = multiply(inverse(multiply(inverse(X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
multiply(multiply(inverse(X5),X5),multiply(X4,multiply(inverse(X3),X3))) = multiply(multiply(inverse(X5),X5),multiply(inverse(multiply(inverse(X4),multiply(inverse(X2),X2))),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c164,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(multiply(inverse(X),X)),X2),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),X2)) = multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X),X)),X2)),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c168,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X2),X2)),X3)) = multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(X2),X2)),X3)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X3),X3)),X4)) = multiply(X4,inverse(multiply(inverse(X),X))),
inference(substitution,[status(thm)],[c103]) ).
cnf(c171,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c172,plain,
multiply(X3,inverse(multiply(inverse(X),X))) = multiply(X3,multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(multiply(inverse(X2),X2)),X4)) = multiply(X4,multiply(inverse(X3),X3)),
inference(transitivity,[status(thm)],[c170,c172]) ).
cnf(c174,plain,
multiply(multiply(inverse(X4),X4),multiply(inverse(multiply(inverse(X),X)),X3)) = multiply(X3,multiply(inverse(X2),X2)),
inference(transitivity,[status(thm)],[c169,c173]) ).
cnf(c175,plain,
multiply(multiply(inverse(X4),X4),multiply(multiply(inverse(X3),X3),X2)) = multiply(X2,multiply(inverse(X),X)),
inference(transitivity,[status(thm)],[c166,c174]) ).
cnf(c176,plain,
multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),multiply(multiply(inverse(X5),X5),X4))) = multiply(multiply(multiply(inverse(X5),X5),X4),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(multiply(multiply(inverse(X5),X5),X4),multiply(inverse(X3),X3)) = multiply(multiply(inverse(X2),X2),multiply(multiply(inverse(X),X),multiply(multiply(inverse(X5),X5),X4))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(multiply(inverse(X),X),multiply(multiply(inverse(X4),X4),X3)) = multiply(X3,multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c179,plain,
multiply(multiply(inverse(X3),X3),multiply(multiply(inverse(X),X),multiply(multiply(inverse(X5),X5),X4))) = multiply(multiply(inverse(X3),X3),multiply(X4,multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
multiply(multiply(multiply(inverse(X5),X5),X4),multiply(inverse(X3),X3)) = multiply(multiply(inverse(X2),X2),multiply(X4,multiply(inverse(X),X))),
inference(transitivity,[status(thm)],[c177,c179]) ).
cnf(c181,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(X4),multiply(inverse(X3),X3)))),multiply(inverse(X6),X6)) = multiply(multiply(inverse(X5),X5),multiply(inverse(multiply(inverse(X4),multiply(inverse(X3),X3))),multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
multiply(multiply(inverse(X6),X6),multiply(inverse(multiply(inverse(X5),multiply(inverse(X4),X4))),multiply(inverse(X3),X3))) = multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X5),multiply(inverse(X4),X4)))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c144]) ).
cnf(c184,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X4),multiply(inverse(X3),X3)))) = multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X4),multiply(inverse(X3),X3)))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X5),multiply(inverse(X4),X4)))),multiply(inverse(X2),X2)) = multiply(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X5),multiply(inverse(X4),X4)))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c144]) ).
cnf(c188,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(inverse(X3),multiply(inverse(X2),X2)) = multiply(inverse(X3),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
inverse(multiply(inverse(X3),multiply(inverse(X2),X2))) = inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X4),multiply(inverse(X3),X3)))) = multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X5),multiply(inverse(X4),X4)))),multiply(inverse(X3),X3)) = multiply(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X5),inverse(multiply(inverse(X),X))))),multiply(inverse(X3),X3)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X5),inverse(multiply(inverse(X),X)))))),multiply(inverse(X6),X6))),multiply(inverse(X4),X4)) = multiply(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X5),inverse(multiply(inverse(X),X))))),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c159]) ).
cnf(c194,plain,
multiply(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X6),inverse(multiply(inverse(X2),X2))))),multiply(inverse(X4),X4)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X6),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X),X))),multiply(inverse(X5),X5)),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X),X))) = X4,
inference(substitution,[status(thm)],[c140]) ).
cnf(c196,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X5),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X),X))),multiply(inverse(X4),X4)) = multiply(X5,multiply(inverse(X4),X4)),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
multiply(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X5),inverse(multiply(inverse(X),X))))),multiply(inverse(X3),X3)) = multiply(X5,multiply(inverse(X4),X4)),
inference(transitivity,[status(thm)],[c194,c196]) ).
cnf(c198,plain,
multiply(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X5),multiply(inverse(X3),X3)))),multiply(inverse(X2),X2)) = multiply(X5,multiply(inverse(X4),X4)),
inference(transitivity,[status(thm)],[c192,c197]) ).
cnf(c199,plain,
multiply(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X5),multiply(inverse(X3),X3)))),multiply(inverse(X),X)) = multiply(X5,multiply(inverse(X4),X4)),
inference(transitivity,[status(thm)],[c186,c198]) ).
cnf(c200,plain,
multiply(multiply(inverse(X5),X5),multiply(inverse(multiply(inverse(X4),multiply(inverse(X2),X2))),multiply(inverse(X),X))) = multiply(X4,multiply(inverse(X3),X3)),
inference(transitivity,[status(thm)],[c182,c199]) ).
cnf(c201,plain,
multiply(multiply(inverse(X4),X4),multiply(X3,multiply(inverse(X2),X2))) = multiply(X3,multiply(inverse(X),X)),
inference(transitivity,[status(thm)],[c162,c200]) ).
cnf(c202,plain,
multiply(multiply(inverse(X2),X2),multiply(X4,multiply(inverse(X3),X3))) = multiply(X4,multiply(inverse(X),X)),
inference(substitution,[status(thm)],[c201]) ).
cnf(c203,plain,
multiply(inverse(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),X2)))),multiply(multiply(inverse(X3),X3),multiply(X5,multiply(inverse(X4),X4)))) = multiply(inverse(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),X2)))),multiply(X5,multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
inverse(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),X2)))) = inverse(multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c108]) ).
cnf(c205,plain,
multiply(inverse(multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(X3),X3)))),multiply(X5,multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(X),X)),multiply(X5,multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(inverse(multiply(inverse(X2),X2)),multiply(X4,multiply(inverse(X3),X3))) = multiply(multiply(inverse(X),X),multiply(X4,multiply(inverse(X3),X3))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c207,plain,
multiply(multiply(inverse(X),X),multiply(X4,multiply(inverse(X2),X2))) = multiply(X4,multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c201]) ).
cnf(c208,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(X4,multiply(inverse(X2),X2))) = multiply(X4,multiply(inverse(X3),X3)),
inference(transitivity,[status(thm)],[c206,c207]) ).
cnf(c209,plain,
multiply(inverse(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),X2)))),multiply(X5,multiply(inverse(X),X))) = multiply(X5,multiply(inverse(X4),X4)),
inference(transitivity,[status(thm)],[c205,c208]) ).
cnf(c210,plain,
multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X),X)))),multiply(multiply(inverse(X2),X2),multiply(X5,multiply(inverse(X4),X4)))) = multiply(X5,multiply(inverse(X3),X3)),
inference(transitivity,[status(thm)],[c203,c209]) ).
cnf(c211,plain,
multiply(multiply(X4,multiply(inverse(X3),X3)),inverse(multiply(inverse(X),X))) = multiply(X4,multiply(inverse(X2),X2)),
inference(transitivity,[status(thm)],[c149,c210]) ).
cnf(c212,plain,
multiply(multiply(X4,multiply(inverse(X3),X3)),multiply(inverse(X2),X2)) = multiply(X4,multiply(inverse(X),X)),
inference(transitivity,[status(thm)],[c147,c211]) ).
cnf(c213,plain,
multiply(multiply(inverse(X4),multiply(inverse(X2),X2)),multiply(inverse(X),X)) = multiply(inverse(X4),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(inverse(X4),multiply(inverse(X3),X3)) = multiply(multiply(inverse(X4),multiply(inverse(X2),X2)),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
inverse(multiply(inverse(X4),multiply(inverse(X3),X3))) = inverse(multiply(multiply(inverse(X4),multiply(inverse(X2),X2)),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c217,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(inverse(X3),multiply(inverse(X2),X2)) = multiply(inverse(X3),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(multiply(inverse(X4),multiply(inverse(X3),X3)),multiply(inverse(X2),X2)) = multiply(multiply(inverse(X4),inverse(multiply(inverse(X),X))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
inverse(multiply(multiply(inverse(X4),multiply(inverse(X3),X3)),multiply(inverse(X2),X2))) = inverse(multiply(multiply(inverse(X4),inverse(multiply(inverse(X),X))),multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c222,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c223,plain,
multiply(X3,multiply(inverse(X2),X2)) = multiply(X3,inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
inverse(multiply(X3,multiply(inverse(X2),X2))) = inverse(multiply(X3,inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(inverse(multiply(X4,multiply(inverse(X3),X3))),multiply(inverse(X2),X2)) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X),X)))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = multiply(X4,inverse(multiply(inverse(X3),X3))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c227,plain,
multiply(X4,inverse(multiply(inverse(X3),X3))) = multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
inverse(multiply(X4,inverse(multiply(inverse(X3),X3)))) = inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(inverse(multiply(X5,inverse(multiply(inverse(X3),X3)))),multiply(inverse(X4),X4)) = multiply(inverse(multiply(inverse(multiply(inverse(X5),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X))),multiply(inverse(X4),X4)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X5),inverse(multiply(inverse(X3),X3)))),multiply(inverse(X2),X2))),multiply(inverse(X4),X4)) = multiply(multiply(inverse(X5),inverse(multiply(inverse(X3),X3))),multiply(inverse(X),X)),
inference(substitution,[status(thm)],[c159]) ).
cnf(c231,plain,
multiply(inverse(X3),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X3),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c144]) ).
cnf(c232,plain,
multiply(multiply(inverse(X4),inverse(multiply(inverse(X3),X3))),multiply(inverse(X2),X2)) = multiply(multiply(inverse(X4),multiply(inverse(X),X)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
multiply(multiply(inverse(X4),multiply(inverse(X),X)),multiply(inverse(X2),X2)) = multiply(inverse(X4),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c212]) ).
cnf(c234,plain,
multiply(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))),multiply(inverse(X),X)) = multiply(inverse(X4),multiply(inverse(X3),X3)),
inference(transitivity,[status(thm)],[c232,c233]) ).
cnf(c235,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X5),inverse(multiply(inverse(X2),X2)))),multiply(inverse(X),X))),multiply(inverse(X4),X4)) = multiply(inverse(X5),multiply(inverse(X3),X3)),
inference(transitivity,[status(thm)],[c230,c234]) ).
cnf(c236,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(X),X)))),multiply(inverse(X3),X3)) = multiply(inverse(X4),multiply(inverse(X2),X2)),
inference(transitivity,[status(thm)],[c229,c235]) ).
cnf(c237,plain,
multiply(inverse(multiply(X4,multiply(inverse(X3),X3))),multiply(inverse(X2),X2)) = multiply(inverse(X4),multiply(inverse(X),X)),
inference(transitivity,[status(thm)],[c225,c236]) ).
cnf(c238,plain,
multiply(inverse(multiply(inverse(X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)) = multiply(inverse(inverse(X4)),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
multiply(inverse(inverse(X4)),multiply(inverse(X3),X3)) = multiply(inverse(multiply(inverse(X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(inverse(multiply(inverse(X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)) = multiply(X4,multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c159]) ).
cnf(c241,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X2),X2)) = multiply(X3,multiply(inverse(X),X)),
inference(transitivity,[status(thm)],[c239,c240]) ).
cnf(c242,plain,
multiply(inverse(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))))),multiply(inverse(X),X)) = multiply(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c241]) ).
cnf(c243,plain,
multiply(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))),multiply(inverse(X3),X3)) = multiply(inverse(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
inverse(multiply(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))),multiply(inverse(X3),X3))) = inverse(multiply(inverse(inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))))),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
multiply(inverse(multiply(multiply(multiply(inverse(X5),X5),X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)) = multiply(inverse(multiply(multiply(inverse(X5),X5),X4)),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c246,plain,
multiply(inverse(multiply(multiply(inverse(X5),X5),X4)),multiply(inverse(X3),X3)) = multiply(inverse(multiply(multiply(multiply(inverse(X5),X5),X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
inverse(multiply(multiply(multiply(inverse(X5),X5),X4),multiply(inverse(X3),X3))) = inverse(multiply(multiply(inverse(X2),X2),multiply(X4,multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c248,plain,
multiply(inverse(multiply(multiply(multiply(inverse(X6),X6),X5),multiply(inverse(X4),X4))),multiply(inverse(X3),X3)) = multiply(inverse(multiply(multiply(inverse(X2),X2),multiply(X5,multiply(inverse(X),X)))),multiply(inverse(X3),X3)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
multiply(multiply(inverse(X3),X3),multiply(X4,multiply(inverse(X2),X2))) = multiply(X4,multiply(inverse(X),X)),
inference(substitution,[status(thm)],[c201]) ).
cnf(c250,plain,
inverse(multiply(multiply(inverse(X3),X3),multiply(X4,multiply(inverse(X2),X2)))) = inverse(multiply(X4,multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
multiply(inverse(multiply(multiply(inverse(X3),X3),multiply(X5,multiply(inverse(X2),X2)))),multiply(inverse(X4),X4)) = multiply(inverse(multiply(X5,multiply(inverse(X),X))),multiply(inverse(X4),X4)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
multiply(inverse(multiply(X4,multiply(inverse(X),X))),multiply(inverse(X2),X2)) = multiply(inverse(X4),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c253,plain,
multiply(inverse(multiply(multiply(inverse(X2),X2),multiply(X5,multiply(inverse(X),X)))),multiply(inverse(X3),X3)) = multiply(inverse(X5),multiply(inverse(X4),X4)),
inference(transitivity,[status(thm)],[c251,c252]) ).
cnf(c254,plain,
multiply(inverse(multiply(multiply(multiply(inverse(X5),X5),X4),multiply(inverse(X2),X2))),multiply(inverse(X),X)) = multiply(inverse(X4),multiply(inverse(X3),X3)),
inference(transitivity,[status(thm)],[c248,c253]) ).
cnf(c255,plain,
multiply(inverse(multiply(multiply(inverse(X4),X4),X3)),multiply(inverse(X2),X2)) = multiply(inverse(X3),multiply(inverse(X),X)),
inference(transitivity,[status(thm)],[c246,c254]) ).
cnf(c256,plain,
multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4)))))),multiply(inverse(X),X)) = multiply(inverse(inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4))))),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c255]) ).
cnf(c257,plain,
multiply(inverse(inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4))))),multiply(inverse(X3),X3)) = multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4)))))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4))))),multiply(inverse(X3),X3))) = inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4)))))),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c260,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3)))))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
multiply(inverse(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4)))))),multiply(inverse(X2),X2)) = multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4)))))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
inverse(multiply(inverse(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4)))))),multiply(inverse(X2),X2))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X5),inverse(multiply(inverse(X4),X4)))))),multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3)))))),multiply(inverse(X2),X2))) = X4,
inference(substitution,[status(thm)],[c140]) ).
cnf(c266,plain,
inverse(multiply(inverse(multiply(multiply(inverse(X2),X2),inverse(multiply(inverse(X4),inverse(multiply(inverse(X3),X3)))))),multiply(inverse(X),X))) = X4,
inference(transitivity,[status(thm)],[c264,c265]) ).
cnf(c267,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2))))),multiply(inverse(X),X))) = X3,
inference(transitivity,[status(thm)],[c258,c266]) ).
cnf(c268,plain,
inverse(multiply(multiply(inverse(X3),inverse(multiply(inverse(X),X))),multiply(inverse(X2),X2))) = X3,
inference(transitivity,[status(thm)],[c244,c267]) ).
cnf(c269,plain,
inverse(multiply(multiply(inverse(X3),multiply(inverse(X2),X2)),multiply(inverse(X),X))) = X3,
inference(transitivity,[status(thm)],[c220,c268]) ).
cnf(c270,plain,
inverse(multiply(inverse(X2),multiply(inverse(X),X))) = X2,
inference(transitivity,[status(thm)],[c215,c269]) ).
cnf(c271,plain,
X2 = inverse(multiply(inverse(X2),multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c274,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
multiply(multiply(inverse(X4),X4),inverse(multiply(inverse(X3),multiply(inverse(X2),X2)))) = multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c144]) ).
cnf(c277,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
multiply(inverse(X3),multiply(inverse(X2),X2)) = multiply(inverse(X3),inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
inverse(multiply(inverse(X3),multiply(inverse(X2),X2))) = inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X4),multiply(inverse(X3),X3)))) = multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X),X))) = multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))))),
inference(substitution,[status(thm)],[c270]) ).
cnf(c282,plain,
multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(multiply(inverse(X4),inverse(multiply(inverse(X2),X2)))))),multiply(inverse(X),X))) = X4,
inference(substitution,[status(thm)],[c140]) ).
cnf(c284,plain,
multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),inverse(multiply(inverse(X),X))))) = X3,
inference(transitivity,[status(thm)],[c282,c283]) ).
cnf(c285,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(X3),multiply(inverse(X2),X2)))) = X3,
inference(transitivity,[status(thm)],[c280,c284]) ).
cnf(c286,plain,
multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(X2),multiply(inverse(X),X)))) = X2,
inference(transitivity,[status(thm)],[c275,c285]) ).
cnf(c287,plain,
multiply(multiply(inverse(X2),X2),X) = X,
inference(transitivity,[status(thm)],[c272,c286]) ).
cnf(c288,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(substitution,[status(thm)],[c287]) ).
cnf(c289,plain,
$false,
inference(resolution,[status(thm)],[c1,c288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP419-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 10:09:45 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.53 Command-line arguments: --no-flatten-goal
% 0.19/0.53
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53
% 0.75/0.59 % SZS output start CNFRefutation
% See solution above
% 2.35/0.84
% 2.35/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------