%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP439-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:10:28 AM UTC 2026
% Result : Unsatisfiable 6.19s 1.21s
% Output : CNFRefutation 6.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 2
% Syntax : Number of clauses : 246 ( 246 unt; 0 nHn; 3 RR)
% Number of literals : 246 ( 245 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 18 ( 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 : 1235 ( 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(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(multiply(inverse(X5),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2) = multiply(multiply(inverse(X5),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3)))))))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),X2)) = multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X5,multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))))))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),X2))) = multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X5,multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3)))))))))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),X2)))) = inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X5,multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))))))))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X5,multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))))))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),X2)))) = X,
inference(transitivity,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
inverse(multiply(X,multiply(X9,multiply(multiply(inverse(X9),multiply(multiply(inverse(X),multiply(multiply(inverse(X2),X8),inverse(multiply(X7,multiply(X6,X8))))),inverse(multiply(X6,multiply(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(inverse(X2),multiply(X5,X3)))))),multiply(multiply(inverse(X2),X8),inverse(multiply(X7,multiply(X6,X8))))))))),X6)))) = multiply(X5,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(inverse(X2),multiply(X5,X3)))))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))) = inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))))))),X)))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(multiply(X4,multiply(X3,multiply(multiply(inverse(X3),X2),inverse(multiply(X,multiply(X4,X2))))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
X = inverse(multiply(X4,multiply(X3,multiply(multiply(inverse(X3),X2),inverse(multiply(X,multiply(X4,X2))))))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X2,X) = multiply(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X5,X3))))))),X),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(multiply(X3,X2),inverse(multiply(X,multiply(X7,X2)))) = multiply(multiply(inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4))))))),X2),inverse(multiply(X,multiply(X7,X2)))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(X3,X2),inverse(multiply(X,multiply(X7,X2))))) = multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4))))))),X2),inverse(multiply(X,multiply(X7,X2))))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X7,multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(X3,X2),inverse(multiply(X,multiply(X7,X2)))))) = multiply(X7,multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4))))))),X2),inverse(multiply(X,multiply(X7,X2)))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
inverse(multiply(X7,multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(X3,X2),inverse(multiply(X,multiply(X7,X2))))))) = inverse(multiply(X7,multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4))))))),X2),inverse(multiply(X,multiply(X7,X2))))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(multiply(X7,multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4))))))),X2),inverse(multiply(X,multiply(X7,X2))))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
inverse(multiply(X7,multiply(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))),multiply(multiply(X3,X2),inverse(multiply(X,multiply(X7,X2))))))) = X,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
inverse(multiply(X,multiply(multiply(X7,multiply(X6,multiply(multiply(inverse(X6),X5),inverse(multiply(inverse(X4),multiply(X7,X5)))))),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X8,multiply(X7,multiply(multiply(inverse(X7),X6),inverse(multiply(inverse(X5),multiply(X8,X6)))))),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3)))))))) = multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),X3),inverse(multiply(X2,multiply(X,X3))))),X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))))))) = multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))))))),X) = multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))))))),X)) = multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))))))),X))) = multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))))))),X)))) = inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
X2 = inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(multiply(inverse(X5),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2) = multiply(multiply(inverse(X5),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3)))))))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2)) = multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X) = multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))))),X),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)) = multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))))),X)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))) = multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))))),X))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))) = inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))))),X)))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(X4,multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))))))),X)))) = X4,
inference(substitution,[status(thm)],[c10]) ).
cnf(c38,plain,
inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),multiply(multiply(inverse(X4),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))) = X4,
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))) = X6,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),inverse(multiply(X,multiply(multiply(X9,multiply(X8,multiply(multiply(inverse(X8),X7),inverse(multiply(inverse(X6),multiply(X9,X7)))))),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))))))),X)))) = X6,
inference(transitivity,[status(thm)],[c28,c39]) ).
cnf(c41,plain,
multiply(X4,multiply(X3,multiply(multiply(inverse(X3),X2),inverse(multiply(inverse(X),multiply(X4,X2)))))) = X,
inference(transitivity,[status(thm)],[c12,c40]) ).
cnf(c42,plain,
multiply(inverse(X2),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X)))))) = multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5))))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5))))) = multiply(inverse(X2),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X)))))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(inverse(X4),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X4),X)))))) = X3,
inference(substitution,[status(thm)],[c41]) ).
cnf(c45,plain,
X3 = multiply(inverse(X4),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X4),X)))))),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(X4,inverse(multiply(X3,X4))) = multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(X5,multiply(X4,inverse(multiply(X3,X4)))) = multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4)))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X3,X4))))) = multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4))))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X3,X4)))))) = inverse(multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4)))))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(X4),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X4),X)))))) = X3,
inference(substitution,[status(thm)],[c41]) ).
cnf(c51,plain,
X3 = multiply(inverse(X4),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X4),X)))))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(X3,X4) = multiply(X3,multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X))))))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
inverse(multiply(X3,X4)) = inverse(multiply(X3,multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4))) = multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X))))))))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4)))) = multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))))))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4))))) = multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X))))))))))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
inverse(multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4)))))) = inverse(multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))))))))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))))))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
inverse(multiply(inverse(X5),multiply(X5,multiply(multiply(inverse(X5),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(inverse(X5),X)))))),inverse(multiply(X3,X4)))))) = X3,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
inverse(multiply(inverse(X3),multiply(X3,multiply(X2,inverse(multiply(X,X2)))))) = X,
inference(transitivity,[status(thm)],[c49,c59]) ).
cnf(c61,plain,
X = inverse(multiply(inverse(X3),multiply(X3,multiply(X2,inverse(multiply(X,X2)))))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X) = multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),inverse(multiply(inverse(X4),multiply(X4,multiply(X2,inverse(multiply(X,X2))))))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)) = multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),inverse(multiply(inverse(X4),multiply(X4,multiply(X2,inverse(multiply(X,X2)))))))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))) = multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),inverse(multiply(inverse(X4),multiply(X4,multiply(X2,inverse(multiply(X,X2))))))))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),inverse(multiply(inverse(X4),multiply(X4,multiply(X2,inverse(multiply(X,X2))))))))) = X4,
inference(substitution,[status(thm)],[c41]) ).
cnf(c66,plain,
multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))) = X4,
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
X4 = multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(X4,X5) = multiply(X4,multiply(X5,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
inverse(multiply(X4,X5)) = inverse(multiply(X4,multiply(X5,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(inverse(X5),inverse(multiply(X4,X6))) = multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)))))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(X5,multiply(inverse(X5),inverse(multiply(X4,X6)))) = multiply(X5,multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,X6))))) = multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)))))))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
inverse(multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,X6)))))) = inverse(multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(inverse(X4),multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))) = inverse(X4),
inference(substitution,[status(thm)],[c66]) ).
cnf(c75,plain,
inverse(X4) = multiply(inverse(X4),multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)))))) = multiply(multiply(inverse(X5),multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)))))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(X5,multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))) = multiply(X5,multiply(multiply(inverse(X5),multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)))))))) = multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X)))))))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
inverse(multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))))) = inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
inverse(multiply(X6,multiply(X5,multiply(multiply(inverse(X5),multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c81,plain,
inverse(multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,multiply(X6,multiply(X3,multiply(multiply(inverse(X3),multiply(X2,inverse(multiply(X,X2)))),X))))))))) = X4,
inference(transitivity,[status(thm)],[c79,c80]) ).
cnf(c82,plain,
inverse(multiply(X3,multiply(X2,multiply(inverse(X2),inverse(multiply(X,X3)))))) = X,
inference(transitivity,[status(thm)],[c73,c81]) ).
cnf(c83,plain,
inverse(multiply(X3,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X),X3)))))) = inverse(X),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X)) = multiply(inverse(X3),multiply(inverse(X2),X)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X))) = inverse(multiply(inverse(X3),multiply(inverse(X2),X))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X)))) = multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X2),X)))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X))))) = multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X2),X))))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(inverse(X2),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X)))))) = multiply(inverse(X2),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X2),X)))))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5)))))),multiply(X3,X)))))) = multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5))))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c90,plain,
multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5))))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5)))))),multiply(X3,X)))))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
inverse(multiply(inverse(X3),multiply(X3,multiply(X2,inverse(multiply(inverse(X),X2)))))) = inverse(X),
inference(substitution,[status(thm)],[c60]) ).
cnf(c92,plain,
multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(inverse(X3),X4)))))),multiply(X2,X)) = multiply(inverse(X3),multiply(X2,X)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(inverse(X3),X4)))))),multiply(X2,X))) = inverse(multiply(inverse(X3),multiply(X2,X))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5)))))),multiply(X3,X)))) = multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(X3,X)))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5)))))),multiply(X3,X))))) = multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(X3,X))))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5)))))),multiply(X3,X)))))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(X3,X)))))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X4),multiply(X3,X)))))) = X4,
inference(substitution,[status(thm)],[c41]) ).
cnf(c98,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(inverse(X4),X5)))))),multiply(X3,X)))))) = X4,
inference(transitivity,[status(thm)],[c96,c97]) ).
cnf(c99,plain,
multiply(inverse(X3),multiply(X3,multiply(X2,inverse(multiply(inverse(X),X2))))) = X,
inference(transitivity,[status(thm)],[c90,c98]) ).
cnf(c100,plain,
multiply(inverse(X2),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(X3),multiply(inverse(X2),X)))))) = X3,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(inverse(X2),multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(X3),X5)))))),multiply(inverse(X2),X)))))) = X3,
inference(transitivity,[status(thm)],[c88,c100]) ).
cnf(c102,plain,
multiply(X3,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X),X3))))) = X,
inference(transitivity,[status(thm)],[c43,c101]) ).
cnf(c103,plain,
multiply(inverse(X3),multiply(X,multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(X3)))))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(inverse(X2),X2) = multiply(inverse(X3),multiply(X,multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(X3)))))),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
inverse(multiply(X,multiply(X3,multiply(inverse(X3),inverse(multiply(X2,X)))))) = X2,
inference(substitution,[status(thm)],[c82]) ).
cnf(c106,plain,
X2 = inverse(multiply(X,multiply(X3,multiply(inverse(X3),inverse(multiply(X2,X)))))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),X2) = multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),inverse(multiply(X,multiply(X4,multiply(inverse(X4),inverse(multiply(X2,X))))))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),X2)) = multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),inverse(multiply(X,multiply(X4,multiply(inverse(X4),inverse(multiply(X2,X)))))))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),X2))) = multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),inverse(multiply(X,multiply(X4,multiply(inverse(X4),inverse(multiply(X2,X))))))))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
inverse(multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),X2)))) = inverse(multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),inverse(multiply(X,multiply(X4,multiply(inverse(X4),inverse(multiply(X2,X)))))))))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
inverse(multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),inverse(multiply(X,multiply(X4,multiply(inverse(X4),inverse(multiply(X2,X)))))))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
inverse(multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(X4),inverse(multiply(X2,X)))),X2)))) = X,
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))),X4)))) = multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))) = inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))),X4)))),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5)))))),multiply(X3,X)))))) = multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5))))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c116,plain,
multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5))))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5)))))),multiply(X3,X)))))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))) = X3,
inference(substitution,[status(thm)],[c82]) ).
cnf(c118,plain,
multiply(inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))),multiply(X2,X)) = multiply(X5,multiply(X2,X)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
inverse(multiply(inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))),multiply(X2,X))) = inverse(multiply(X5,multiply(X2,X))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5)))))),multiply(X3,X)))) = multiply(multiply(inverse(X2),X),inverse(multiply(X6,multiply(X3,X)))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5)))))),multiply(X3,X))))) = multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X6,multiply(X3,X))))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5)))))),multiply(X3,X)))))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X6,multiply(X3,X)))))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))) = X3,
inference(substitution,[status(thm)],[c82]) ).
cnf(c124,plain,
X3 = inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(X3,multiply(X5,X4)) = multiply(inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))),multiply(X5,X4)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
inverse(multiply(X3,multiply(X5,X4))) = inverse(multiply(inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))),multiply(X5,X4))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))) = multiply(multiply(inverse(X5),X4),inverse(multiply(inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))),multiply(X6,X4)))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4))))) = multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))),multiply(X6,X4))))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))) = multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))),multiply(X6,X4)))))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))),multiply(X6,X4)))))) = multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2))))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c131,plain,
multiply(X6,multiply(X5,multiply(multiply(inverse(X5),X4),inverse(multiply(X3,multiply(X6,X4)))))) = multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2))))),
inference(transitivity,[status(thm)],[c129,c130]) ).
cnf(c132,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X4,multiply(X3,X)))))) = multiply(X6,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,X6))))),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X6,X5)))))),multiply(X3,X)))))) = multiply(X8,multiply(X7,multiply(inverse(X7),inverse(multiply(X6,X8))))),
inference(transitivity,[status(thm)],[c122,c132]) ).
cnf(c134,plain,
multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2))))) = multiply(X5,multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X5))))),
inference(transitivity,[status(thm)],[c116,c133]) ).
cnf(c135,plain,
multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2))))) = multiply(X2,multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2))))),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
inverse(multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))))) = inverse(multiply(X2,multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2)))))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
multiply(inverse(X),inverse(multiply(X3,multiply(X2,multiply(inverse(X2),inverse(multiply(X4,X3))))))) = multiply(inverse(X),inverse(multiply(X3,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,X3))))))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))) = multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X6,multiply(inverse(X6),inverse(multiply(X5,X4)))))))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))),X4) = multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X6,multiply(inverse(X6),inverse(multiply(X5,X4)))))))),X4),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))),X4)) = multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X6,multiply(inverse(X6),inverse(multiply(X5,X4)))))))),X4)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))),X4))) = multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X6,multiply(inverse(X6),inverse(multiply(X5,X4)))))))),X4))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))),X4)))) = inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X6,multiply(inverse(X6),inverse(multiply(X5,X4)))))))),X4)))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X3,multiply(X5,multiply(inverse(X5),inverse(multiply(X4,X3)))))))),X3)))) = multiply(X5,multiply(inverse(X5),inverse(multiply(X4,X3)))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c144,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(X5,X4)))))))),X4)))) = multiply(X6,multiply(inverse(X6),inverse(multiply(X5,X4)))),
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
multiply(X,multiply(inverse(X),inverse(multiply(X3,X2)))) = multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2)))),
inference(transitivity,[status(thm)],[c114,c144]) ).
cnf(c146,plain,
multiply(X,multiply(inverse(X),inverse(multiply(X2,inverse(X3))))) = multiply(X3,multiply(inverse(X3),inverse(multiply(X2,inverse(X3))))),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X5),multiply(X5,multiply(X3,inverse(multiply(X4,X3)))))))),inverse(X5))))) = multiply(X5,multiply(X3,inverse(multiply(X4,X3)))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c148,plain,
multiply(X5,multiply(X3,inverse(multiply(X4,X3)))) = inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X5),multiply(X5,multiply(X3,inverse(multiply(X4,X3)))))))),inverse(X5))))),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4)))))),multiply(X3,X)))))) = multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4))))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c150,plain,
multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4))))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4)))))),multiply(X3,X)))))),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
inverse(multiply(inverse(X2),multiply(X2,multiply(X,inverse(multiply(X3,X)))))) = X3,
inference(substitution,[status(thm)],[c60]) ).
cnf(c152,plain,
multiply(inverse(multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X5,X3)))))),multiply(X2,X)) = multiply(X5,multiply(X2,X)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
inverse(multiply(inverse(multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X5,X3)))))),multiply(X2,X))) = inverse(multiply(X5,multiply(X2,X))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4)))))),multiply(X3,X)))) = multiply(multiply(inverse(X2),X),inverse(multiply(X6,multiply(X3,X)))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4)))))),multiply(X3,X))))) = multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X6,multiply(X3,X))))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4)))))),multiply(X3,X)))))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X6,multiply(X3,X)))))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
X = inverse(multiply(inverse(X3),multiply(X3,multiply(X2,inverse(multiply(X,X2)))))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c158,plain,
multiply(X3,multiply(X2,X)) = multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X3,X4)))))),multiply(X2,X)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
inverse(multiply(X3,multiply(X2,X))) = inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X3,X4)))))),multiply(X2,X))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(multiply(inverse(X2),X),inverse(multiply(X4,multiply(X3,X)))) = multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))),multiply(X3,X)))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X4,multiply(X3,X))))) = multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))),multiply(X3,X))))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X4,multiply(X3,X)))))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))),multiply(X3,X)))))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))),multiply(X3,X)))))) = multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5))))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c164,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(X4,multiply(X3,X)))))) = multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5))))),
inference(transitivity,[status(thm)],[c162,c163]) ).
cnf(c165,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),X),inverse(multiply(inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X6,X4)))))),multiply(X3,X)))))) = multiply(inverse(X8),multiply(X8,multiply(X7,inverse(multiply(X6,X7))))),
inference(transitivity,[status(thm)],[c156,c164]) ).
cnf(c166,plain,
multiply(inverse(X2),multiply(X2,multiply(X,inverse(multiply(X3,X))))) = multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X3,X4))))),
inference(transitivity,[status(thm)],[c150,c165]) ).
cnf(c167,plain,
multiply(inverse(X4),multiply(X4,multiply(X,inverse(multiply(X2,X))))) = multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X2,X3))))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
inverse(multiply(inverse(X4),multiply(X4,multiply(X,inverse(multiply(X2,X)))))) = inverse(multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X2,X3)))))),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(inverse(X),inverse(multiply(inverse(X5),multiply(X5,multiply(X2,inverse(multiply(X3,X2))))))) = multiply(inverse(X),inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X3,X4))))))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X3,inverse(multiply(X4,X3)))))))) = multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X3,inverse(multiply(X4,X3)))))))),inverse(X6)) = multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))))),inverse(X6)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X3,inverse(multiply(X4,X3)))))))),inverse(X6))) = multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))))),inverse(X6))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X3,inverse(multiply(X4,X3)))))))),inverse(X6)))) = multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))))),inverse(X6)))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X3,inverse(multiply(X4,X3)))))))),inverse(X6))))) = inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5)))))))),inverse(X6))))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X5),multiply(X5,multiply(X4,inverse(multiply(X3,X4)))))))),inverse(X5))))) = multiply(X5,multiply(X4,inverse(multiply(X3,X4)))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c176,plain,
inverse(multiply(X2,multiply(X,multiply(multiply(inverse(X),multiply(inverse(X2),inverse(multiply(inverse(X6),multiply(X6,multiply(X3,inverse(multiply(X4,X3)))))))),inverse(X6))))) = multiply(X6,multiply(X5,inverse(multiply(X4,X5)))),
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
multiply(X4,multiply(X,inverse(multiply(X2,X)))) = multiply(X4,multiply(X3,inverse(multiply(X2,X3)))),
inference(transitivity,[status(thm)],[c148,c176]) ).
cnf(c178,plain,
multiply(X3,multiply(X2,inverse(multiply(X,X2)))) = multiply(X3,multiply(inverse(X3),inverse(multiply(X,inverse(X3))))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(X3,multiply(inverse(X3),inverse(multiply(X,inverse(X3))))) = multiply(X3,multiply(X2,inverse(multiply(X,X2)))),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
multiply(X,multiply(inverse(X),inverse(multiply(X2,inverse(X4))))) = multiply(X4,multiply(X3,inverse(multiply(X2,X3)))),
inference(transitivity,[status(thm)],[c146,c179]) ).
cnf(c181,plain,
multiply(X4,multiply(inverse(X4),inverse(multiply(inverse(multiply(inverse(X3),X3)),inverse(X2))))) = multiply(X2,multiply(X,inverse(multiply(inverse(multiply(inverse(X3),X3)),X)))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))) = X6,
inference(substitution,[status(thm)],[c38]) ).
cnf(c183,plain,
X6 = inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(inverse(X6),X6) = multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
inverse(multiply(inverse(X6),X6)) = inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
multiply(inverse(X7),inverse(multiply(inverse(X6),X6))) = multiply(inverse(X7),inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(X6),X6)))) = multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))))))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(X8,multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(X6),X6))))) = multiply(X8,multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))) = X6,
inference(substitution,[status(thm)],[c38]) ).
cnf(c190,plain,
X6 = inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
inverse(X6) = inverse(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))) = multiply(inverse(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))))) = inverse(multiply(inverse(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
multiply(inverse(X7),inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))) = multiply(inverse(X7),inverse(multiply(inverse(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))))))) = multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X)))))))),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
multiply(X8,multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))))) = multiply(X8,multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
multiply(X3,multiply(inverse(X3),inverse(multiply(inverse(inverse(X2)),inverse(X2))))) = multiply(X2,multiply(X,inverse(multiply(inverse(inverse(X2)),X)))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c198,plain,
multiply(X4,multiply(X3,multiply(inverse(X3),inverse(multiply(inverse(inverse(X2)),inverse(X2)))))) = multiply(X4,multiply(X2,multiply(X,inverse(multiply(inverse(inverse(X2)),X))))),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
inverse(multiply(X,multiply(X3,multiply(inverse(X3),inverse(multiply(X2,X)))))) = X2,
inference(substitution,[status(thm)],[c82]) ).
cnf(c200,plain,
X2 = inverse(multiply(X,multiply(X3,multiply(inverse(X3),inverse(multiply(X2,X)))))),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
multiply(multiply(X3,multiply(inverse(X3),inverse(multiply(X2,X)))),X2) = multiply(multiply(X3,multiply(inverse(X3),inverse(multiply(X2,X)))),inverse(multiply(X,multiply(X3,multiply(inverse(X3),inverse(multiply(X2,X))))))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
inverse(multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))),X)))) = multiply(X4,inverse(multiply(X5,X4))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c203,plain,
multiply(X4,inverse(multiply(X5,X4))) = inverse(multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))),X)))),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
multiply(X,multiply(X2,inverse(multiply(X3,X2)))) = multiply(X,multiply(X4,inverse(multiply(X3,X4)))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c205,plain,
inverse(multiply(X,multiply(X2,inverse(multiply(X3,X2))))) = inverse(multiply(X,multiply(X4,inverse(multiply(X3,X4))))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(inverse(X2),inverse(multiply(X,multiply(X3,inverse(multiply(X4,X3)))))) = multiply(inverse(X2),inverse(multiply(X,multiply(X5,inverse(multiply(X4,X5)))))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))) = multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X6,inverse(multiply(X5,X6))))))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))),X) = multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X6,inverse(multiply(X5,X6))))))),X),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))),X)) = multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X6,inverse(multiply(X5,X6))))))),X)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))),X))) = multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X6,inverse(multiply(X5,X6))))))),X))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
inverse(multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))),X)))) = inverse(multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X6,inverse(multiply(X5,X6))))))),X)))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
inverse(multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X5,inverse(multiply(X4,X5))))))),X)))) = multiply(X5,inverse(multiply(X4,X5))),
inference(substitution,[status(thm)],[c112]) ).
cnf(c213,plain,
inverse(multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X3),inverse(multiply(X,multiply(X4,inverse(multiply(X5,X4))))))),X)))) = multiply(X6,inverse(multiply(X5,X6))),
inference(transitivity,[status(thm)],[c211,c212]) ).
cnf(c214,plain,
multiply(X,inverse(multiply(X2,X))) = multiply(X3,inverse(multiply(X2,X3))),
inference(transitivity,[status(thm)],[c203,c213]) ).
cnf(c215,plain,
multiply(X,inverse(multiply(X2,X))) = multiply(multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2)))),inverse(multiply(X2,multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2))))))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2)))),inverse(multiply(X2,multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2))))))) = multiply(X,inverse(multiply(X2,X))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
multiply(multiply(X4,multiply(inverse(X4),inverse(multiply(X3,X2)))),X3) = multiply(X,inverse(multiply(X2,X))),
inference(transitivity,[status(thm)],[c201,c216]) ).
cnf(c218,plain,
multiply(multiply(inverse(X3),multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(inverse(X3)))))),X) = multiply(X2,inverse(multiply(inverse(inverse(X3)),X2))),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(X2,inverse(multiply(inverse(inverse(X3)),X2))) = multiply(multiply(inverse(X3),multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(inverse(X3)))))),X),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
multiply(X3,multiply(X2,inverse(multiply(inverse(inverse(X3)),X2)))) = multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(inverse(X3)))))),X)),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
multiply(X4,multiply(X3,multiply(X2,inverse(multiply(inverse(inverse(X3)),X2))))) = multiply(X4,multiply(X3,multiply(multiply(inverse(X3),multiply(inverse(inverse(X3)),inverse(multiply(X,inverse(inverse(X3)))))),X))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(X3,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(inverse(X2)),inverse(multiply(X,inverse(inverse(X2)))))),X))) = X3,
inference(substitution,[status(thm)],[c66]) ).
cnf(c223,plain,
multiply(X3,multiply(X2,multiply(X,inverse(multiply(inverse(inverse(X2)),X))))) = X3,
inference(transitivity,[status(thm)],[c221,c222]) ).
cnf(c224,plain,
multiply(X3,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(inverse(X)),inverse(X)))))) = X3,
inference(transitivity,[status(thm)],[c198,c223]) ).
cnf(c225,plain,
multiply(X8,multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))))) = X8,
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
multiply(X8,multiply(X7,multiply(inverse(X7),inverse(multiply(inverse(X6),inverse(multiply(X5,multiply(X4,multiply(multiply(inverse(X4),multiply(multiply(inverse(X5),multiply(multiply(inverse(X6),X3),inverse(multiply(X2,multiply(X,X3))))),X2)),X))))))))) = X8,
inference(transitivity,[status(thm)],[c196,c225]) ).
cnf(c227,plain,
multiply(X3,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X),X))))) = X3,
inference(transitivity,[status(thm)],[c188,c226]) ).
cnf(c228,plain,
multiply(multiply(X3,multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),X2)))),multiply(X,multiply(inverse(X),inverse(multiply(inverse(X4),X4))))) = multiply(X3,multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),X2)))),
inference(substitution,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(X3,multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),X2)))) = multiply(multiply(X3,multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),X2)))),multiply(X,multiply(inverse(X),inverse(multiply(inverse(X4),X4))))),
inference(symmetry,[status(thm)],[c228]) ).
cnf(c230,plain,
X = inverse(multiply(inverse(X3),multiply(X3,multiply(X2,inverse(multiply(X,X2)))))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c231,plain,
multiply(inverse(X),X2) = multiply(inverse(X),inverse(multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X2,X3))))))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(X,multiply(inverse(X),X2)) = multiply(X,multiply(inverse(X),inverse(multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X2,X3)))))))),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
multiply(multiply(X4,multiply(X3,inverse(multiply(X2,X3)))),multiply(X,multiply(inverse(X),X2))) = multiply(multiply(X4,multiply(X3,inverse(multiply(X2,X3)))),multiply(X,multiply(inverse(X),inverse(multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X2,X3))))))))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(inverse(X6),X2))))) = multiply(multiply(X6,multiply(X5,inverse(multiply(X4,X5)))),multiply(X3,multiply(inverse(X3),inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5))))))))),
inference(substitution,[status(thm)],[c134]) ).
cnf(c235,plain,
multiply(multiply(X6,multiply(X5,inverse(multiply(X4,X5)))),multiply(X3,multiply(inverse(X3),inverse(multiply(inverse(X6),multiply(X6,multiply(X5,inverse(multiply(X4,X5))))))))) = multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(inverse(X6),X2))))),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
multiply(X2,multiply(X,multiply(inverse(X),inverse(multiply(inverse(X3),X2))))) = X3,
inference(substitution,[status(thm)],[c102]) ).
cnf(c237,plain,
multiply(multiply(X4,multiply(X3,inverse(multiply(X2,X3)))),multiply(X,multiply(inverse(X),inverse(multiply(inverse(X4),multiply(X4,multiply(X3,inverse(multiply(X2,X3))))))))) = X4,
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
multiply(multiply(X4,multiply(X3,inverse(multiply(X2,X3)))),multiply(X,multiply(inverse(X),X2))) = X4,
inference(transitivity,[status(thm)],[c233,c237]) ).
cnf(c239,plain,
multiply(multiply(X3,multiply(X2,inverse(multiply(inverse(multiply(inverse(X4),X4)),X2)))),multiply(X,multiply(inverse(X),inverse(multiply(inverse(X4),X4))))) = X3,
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(X2,multiply(X,inverse(multiply(inverse(multiply(inverse(X3),X3)),X)))) = X2,
inference(transitivity,[status(thm)],[c229,c239]) ).
cnf(c241,plain,
multiply(X3,multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(X))))) = X,
inference(transitivity,[status(thm)],[c181,c240]) ).
cnf(c242,plain,
multiply(X,multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(X3))))) = X3,
inference(substitution,[status(thm)],[c241]) ).
cnf(c243,plain,
multiply(inverse(X3),multiply(X,multiply(inverse(X),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(X3)))))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c104,c243]) ).
cnf(c245,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
$false,
inference(resolution,[status(thm)],[c1,c245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP439-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:07:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.19/1.21 Command-line arguments: --flatten-regeneralise
% 6.19/1.21
% 6.19/1.21 % SZS status Unsatisfiable
% 6.19/1.21
% 6.19/1.23 % SZS output start CNFRefutation
% See solution above
% 6.99/1.36
% 6.99/1.36 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------