%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO068-1 : 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 09:35:41 AM UTC 2026
% Result : Unsatisfiable 5.23s 0.90s
% Output : CNFRefutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 164
% Number of leaves : 2
% Syntax : Number of clauses : 584 ( 584 unt; 0 nHn; 3 RR)
% Number of literals : 584 ( 583 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 3126 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(b,a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_tba_axioms_2) ).
cnf(c2,axiom,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(multiply(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8)),inverse(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8))),multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7) = multiply(multiply(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8)),inverse(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8))),multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3)),inverse(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3))),multiply(X4,multiply(X3,inverse(multiply(X2,X4,X)),X),X2)) = multiply(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
multiply(multiply(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8)),inverse(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8))),multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(X7,X9,X8),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(multiply(multiply(X,X3,X4),inverse(multiply(X,X3,X4)),multiply(X,X3,X2)),inverse(multiply(multiply(X,X3,X4),inverse(multiply(X,X3,X4)),multiply(X,X3,X2))),multiply(X3,multiply(X2,inverse(multiply(X,X3,X4)),X4),X)) = multiply(X,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
multiply(X2,X4,X3) = multiply(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3)),inverse(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3))),multiply(X4,multiply(X3,inverse(multiply(X2,X4,X)),X),X2)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(multiply(X7,X9,X8),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8)),inverse(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8))),multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8)),inverse(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8))),multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
multiply(multiply(X7,X9,X8),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7),
inference(transitivity,[status(thm)],[c9,c10]) ).
cnf(c12,plain,
multiply(multiply(multiply(multiply(X8,X10,X6),inverse(multiply(X8,X10,X6)),multiply(X8,X10,X9)),inverse(multiply(multiply(X8,X10,X6),inverse(multiply(X8,X10,X6)),multiply(X8,X10,X9))),multiply(X10,multiply(X9,inverse(multiply(X8,X10,X6)),X6),X8)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X10,multiply(X9,inverse(multiply(X8,X10,X7)),X7),X8),
inference(transitivity,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
multiply(X5,multiply(X4,inverse(multiply(X3,X5,X)),X),X3) = multiply(X5,multiply(X4,inverse(multiply(X3,X5,X2)),X2),X3),
inference(transitivity,[status(thm)],[c4,c12]) ).
cnf(c14,plain,
multiply(X4,multiply(X2,inverse(multiply(X5,X4,X)),X),X5) = multiply(X4,multiply(X2,inverse(multiply(X5,X4,X3)),X3),X5),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(multiply(X7,inverse(X7),X6),inverse(multiply(multiply(X5,X4,X3),inverse(multiply(X5,X4,X3)),multiply(X5,X4,X2))),multiply(X4,multiply(X2,inverse(multiply(X5,X4,X)),X),X5)) = multiply(multiply(X7,inverse(X7),X6),inverse(multiply(multiply(X5,X4,X3),inverse(multiply(X5,X4,X3)),multiply(X5,X4,X2))),multiply(X4,multiply(X2,inverse(multiply(X5,X4,X3)),X3),X5)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(multiply(X6,inverse(X6),X5),inverse(multiply(multiply(X4,X3,X2),inverse(multiply(X4,X3,X2)),multiply(X4,X3,X))),multiply(X3,multiply(X,inverse(multiply(X4,X3,X2)),X2),X4)) = X5,
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
multiply(multiply(X7,inverse(X7),X6),inverse(multiply(multiply(X5,X4,X3),inverse(multiply(X5,X4,X3)),multiply(X5,X4,X2))),multiply(X4,multiply(X2,inverse(multiply(X5,X4,X)),X),X5)) = X6,
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5))))),multiply(inverse(X3),multiply(multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5)),inverse(multiply(X3,inverse(X3),X)),X),X3)) = X5,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
X5 = multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5))))),multiply(inverse(X3),multiply(multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5)),inverse(multiply(X3,inverse(X3),X)),X),X3)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(inverse(X6),X5,X6) = multiply(inverse(X6),multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5))))),multiply(inverse(X3),multiply(multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5)),inverse(multiply(X3,inverse(X3),X)),X),X3)),X6),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(X7,inverse(X7),X),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
X7 = multiply(multiply(X6,inverse(X6),X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X11,inverse(multiply(multiply(X10,X9,X8),X7,multiply(X10,X9,X12))),multiply(X9,multiply(X12,X7,X8),X10)) = multiply(multiply(multiply(X6,inverse(X6),X11),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),inverse(multiply(multiply(X10,X9,X8),X7,multiply(X10,X9,X12))),multiply(X9,multiply(X12,X7,X8),X10)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(multiply(X4,X3,X),inverse(multiply(X4,X3,X)),multiply(X4,X3,X2)),inverse(multiply(multiply(X4,X3,X),inverse(multiply(X4,X3,X)),multiply(X4,X3,X2))),multiply(X3,multiply(X2,inverse(multiply(X4,X3,X)),X),X4)) = multiply(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
multiply(X4,X3,X2) = multiply(multiply(multiply(X4,X3,X),inverse(multiply(X4,X3,X)),multiply(X4,X3,X2)),inverse(multiply(multiply(X4,X3,X),inverse(multiply(X4,X3,X)),multiply(X4,X3,X2))),multiply(X3,multiply(X2,inverse(multiply(X4,X3,X)),X),X4)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(multiply(X9,X8,X7),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)) = multiply(multiply(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7)),inverse(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7))),multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(multiply(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7)),inverse(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7))),multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)) = multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9),
inference(substitution,[status(thm)],[c2]) ).
cnf(c28,plain,
multiply(multiply(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7)),inverse(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7))),multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)) = multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9) = multiply(multiply(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7)),inverse(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7))),multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(multiply(X4,X3,X),inverse(multiply(X4,X3,X)),multiply(X4,X3,X2)),inverse(multiply(multiply(X4,X3,X),inverse(multiply(X4,X3,X)),multiply(X4,X3,X2))),multiply(X3,multiply(X2,inverse(multiply(X4,X3,X)),X),X4)) = multiply(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
multiply(multiply(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7)),inverse(multiply(multiply(X9,X8,X),inverse(multiply(X9,X8,X)),multiply(X9,X8,X7))),multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)) = multiply(multiply(X9,X8,X7),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X8,multiply(X7,inverse(multiply(X9,X8,X)),X),X9) = multiply(multiply(X9,X8,X7),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
multiply(multiply(multiply(multiply(X14,X13,X),inverse(multiply(X14,X13,X)),multiply(X14,X13,X12)),inverse(multiply(multiply(X14,X13,X),inverse(multiply(X14,X13,X)),multiply(X14,X13,X12))),multiply(X13,multiply(X12,inverse(multiply(X14,X13,X)),X),X14)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)) = multiply(multiply(X14,X13,X12),inverse(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7))),multiply(X10,multiply(X7,X8,X9),X11)),
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
multiply(multiply(X13,X12,X11),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(X13,X12,X11),inverse(multiply(multiply(X10,X9,X8),X7,multiply(X10,X9,X6))),multiply(X9,multiply(X6,X7,X8),X10)),
inference(transitivity,[status(thm)],[c26,c33]) ).
cnf(c35,plain,
multiply(multiply(multiply(X6,inverse(X6),X17),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),inverse(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7))),multiply(X10,multiply(X7,X8,X9),X11)) = multiply(multiply(multiply(X6,inverse(X6),X17),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),inverse(multiply(multiply(X16,X15,X14),X13,multiply(X16,X15,X12))),multiply(X15,multiply(X12,X13,X14),X16)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(multiply(X6,inverse(X6),X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = X7,
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
multiply(multiply(multiply(X6,inverse(X6),X12),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),inverse(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7))),multiply(X10,multiply(X7,X8,X9),X11)) = multiply(X12,inverse(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7))),multiply(X10,multiply(X7,X8,X9),X11)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(multiply(multiply(X6,inverse(X6),X17),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),inverse(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7))),multiply(X10,multiply(X7,X8,X9),X11)) = multiply(X17,inverse(multiply(multiply(X16,X15,X14),X13,multiply(X16,X15,X12))),multiply(X15,multiply(X12,X13,X14),X16)),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
multiply(X11,inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X11,inverse(multiply(multiply(X10,X9,X8),X7,multiply(X10,X9,X6))),multiply(X9,multiply(X6,X7,X8),X10)),
inference(transitivity,[status(thm)],[c23,c38]) ).
cnf(c40,plain,
multiply(X9,inverse(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4))),multiply(X7,multiply(X4,X5,X6),X8)) = multiply(X9,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),multiply(inverse(X3),multiply(X,inverse(multiply(X3,inverse(X3),X2)),X2),X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3)),inverse(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3))),multiply(X4,multiply(X3,inverse(multiply(X2,X4,X)),X),X2)) = multiply(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c42,plain,
multiply(X2,X4,X3) = multiply(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3)),inverse(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3))),multiply(X4,multiply(X3,inverse(multiply(X2,X4,X)),X),X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(multiply(X7,X9,X8),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8)),inverse(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8))),multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(multiply(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8)),inverse(multiply(multiply(X7,X9,X6),inverse(multiply(X7,X9,X6)),multiply(X7,X9,X8))),multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
multiply(multiply(X7,X9,X8),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X9,multiply(X8,inverse(multiply(X7,X9,X6)),X6),X7),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
multiply(multiply(X8,inverse(X8),X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(inverse(X8),multiply(X7,inverse(multiply(X8,inverse(X8),X6)),X6),X8),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(inverse(X8),multiply(X7,inverse(multiply(X8,inverse(X8),X6)),X6),X8) = multiply(multiply(X8,inverse(X8),X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(multiply(X7,inverse(X7),X6),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = X6,
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
multiply(inverse(X3),multiply(X2,inverse(multiply(X3,inverse(X3),X)),X),X3) = X2,
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
multiply(inverse(X3),multiply(X,inverse(multiply(X3,inverse(X3),X2)),X2),X3) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),multiply(inverse(X3),multiply(X,inverse(multiply(X3,inverse(X3),X2)),X2),X3)) = multiply(X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(X9,inverse(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4))),multiply(X7,multiply(X4,X5,X6),X8)) = multiply(X9,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(transitivity,[status(thm)],[c40,c51]) ).
cnf(c53,plain,
multiply(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4)),inverse(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4))),multiply(X7,multiply(X4,X5,X6),X8)) = multiply(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4)),inverse(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4))),multiply(X7,multiply(X4,X5,X6),X8)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7))),multiply(X10,multiply(X7,X8,X9),X11)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9))),multiply(X12,multiply(X9,X10,X11),X13)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9))),multiply(X12,multiply(X9,X10,X11),X13)),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6),
inference(substitution,[status(thm)],[c52]) ).
cnf(c57,plain,
multiply(multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9))),multiply(X12,multiply(X9,X10,X11),X13)),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6) = multiply(multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9))),multiply(X12,multiply(X9,X10,X11),X13)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(multiply(multiply(multiply(X10,X9,X8),X7,multiply(X10,X9,X6)),inverse(multiply(multiply(X10,X9,X8),X7,multiply(X10,X9,X6))),multiply(X9,multiply(X6,X7,X8),X10)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X9,multiply(X6,X7,X8),X10),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
multiply(multiply(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4)),inverse(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4))),multiply(X7,multiply(X4,X5,X6),X8)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X7,multiply(X4,X5,X6),X8),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
multiply(multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,multiply(X7,X8,X9),X11),
inference(transitivity,[status(thm)],[c55,c59]) ).
cnf(c61,plain,
multiply(multiply(multiply(multiply(X10,inverse(X10),X11),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X10,inverse(X10),X9)))),multiply(X10,inverse(X10),X9)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X10),multiply(X9,inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X10,inverse(X10),X9)))),X11),X10),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(inverse(X10),multiply(X9,inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X10,inverse(X10),X9)))),X11),X10) = multiply(multiply(multiply(multiply(X10,inverse(X10),X11),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X10,inverse(X10),X9)))),multiply(X10,inverse(X10),X9)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(inverse(X3),multiply(X,inverse(multiply(X3,inverse(X3),X2)),X2),X3) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c64,plain,
X = multiply(inverse(X3),multiply(X,inverse(multiply(X3,inverse(X3),X2)),X2),X3),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),multiply(inverse(X3),multiply(X,inverse(multiply(X3,inverse(X3),X2)),X2),X3)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),multiply(inverse(X3),multiply(X,inverse(multiply(X3,inverse(X3),X2)),X2),X3)) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = X4,
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),multiply(X4,inverse(X4),X3)) = X5,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(multiply(multiply(X7,inverse(X7),X8),inverse(multiply(multiply(X5,inverse(X5),X4),inverse(multiply(X5,inverse(X5),X4)),multiply(X5,inverse(X5),multiply(X7,inverse(X7),X6)))),multiply(X7,inverse(X7),X6)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X8,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(multiply(multiply(multiply(X10,inverse(X10),X11),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X10,inverse(X10),X9)))),multiply(X10,inverse(X10),X9)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X11,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(multiply(X5,inverse(X5),X),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X5,inverse(X5),X4)))),multiply(X5,inverse(X5),X4)) = X,
inference(substitution,[status(thm)],[c67]) ).
cnf(c72,plain,
X = multiply(multiply(X5,inverse(X5),X),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X5,inverse(X5),X4)))),multiply(X5,inverse(X5),X4)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X8,inverse(X8),X4),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),multiply(X8,inverse(X8),X7)))),multiply(X8,inverse(X8),X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(multiply(X11,inverse(X11),X7),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),multiply(X11,inverse(X11),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(multiply(multiply(multiply(X11,inverse(X11),X7),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),multiply(X11,inverse(X11),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X11),multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),X7),X11),
inference(substitution,[status(thm)],[c60]) ).
cnf(c76,plain,
multiply(multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X11),multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),X7),X11),
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
multiply(multiply(multiply(multiply(X10,inverse(X10),X11),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X10,inverse(X10),X9)))),multiply(X10,inverse(X10),X9)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X15),multiply(X14,inverse(multiply(multiply(X13,inverse(X13),X12),inverse(multiply(X13,inverse(X13),X12)),multiply(X13,inverse(X13),multiply(X15,inverse(X15),X14)))),X11),X15),
inference(transitivity,[status(thm)],[c70,c76]) ).
cnf(c78,plain,
multiply(inverse(X4),multiply(X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),X5),X4) = multiply(inverse(X9),multiply(X8,inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),multiply(X9,inverse(X9),X8)))),X5),X9),
inference(transitivity,[status(thm)],[c62,c77]) ).
cnf(c79,plain,
multiply(inverse(X4),multiply(X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),multiply(inverse(X7),multiply(multiply(X10,inverse(X10),multiply(X8,inverse(X8),X9)),inverse(multiply(X7,inverse(X7),X5)),X5),X7)),X4) = multiply(inverse(X10),multiply(multiply(X8,inverse(X8),X9),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),multiply(X10,inverse(X10),multiply(X8,inverse(X8),X9))))),multiply(inverse(X7),multiply(multiply(X10,inverse(X10),multiply(X8,inverse(X8),X9)),inverse(multiply(X7,inverse(X7),X5)),X5),X7)),X10),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(inverse(X10),multiply(multiply(X8,inverse(X8),X9),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),multiply(X10,inverse(X10),multiply(X8,inverse(X8),X9))))),multiply(inverse(X7),multiply(multiply(X10,inverse(X10),multiply(X8,inverse(X8),X9)),inverse(multiply(X7,inverse(X7),X5)),X5),X7)),X10) = multiply(inverse(X4),multiply(X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),multiply(inverse(X7),multiply(multiply(X10,inverse(X10),multiply(X8,inverse(X8),X9)),inverse(multiply(X7,inverse(X7),X5)),X5),X7)),X4),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
X4 = multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c82,plain,
multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4) = multiply(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(X9,inverse(multiply(X8,inverse(X8),X7)),multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4)) = multiply(X9,inverse(multiply(X8,inverse(X8),X7)),multiply(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X)) = X5,
inference(substitution,[status(thm)],[c67]) ).
cnf(c85,plain,
X5 = multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
inverse(X5) = inverse(multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(X12,inverse(X11),multiply(multiply(X11,inverse(multiply(multiply(X10,inverse(X10),X9),inverse(multiply(X10,inverse(X10),X9)),multiply(X10,inverse(X10),X8))),X8),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5)) = multiply(X12,inverse(multiply(multiply(X4,inverse(X4),X11),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X))),multiply(multiply(X11,inverse(multiply(multiply(X10,inverse(X10),X9),inverse(multiply(X10,inverse(X10),X9)),multiply(X10,inverse(X10),X8))),X8),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(multiply(X5,inverse(X5),X),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X5,inverse(X5),X4)))),multiply(X5,inverse(X5),X4)) = X,
inference(substitution,[status(thm)],[c67]) ).
cnf(c89,plain,
X = multiply(multiply(X5,inverse(X5),X),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X5,inverse(X5),X4)))),multiply(X5,inverse(X5),X4)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X8,inverse(X8),X4),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),multiply(X8,inverse(X8),X7)))),multiply(X8,inverse(X8),X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(multiply(X11,inverse(X11),X7),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),multiply(X11,inverse(X11),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(multiply(multiply(multiply(X11,inverse(X11),X7),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),multiply(X11,inverse(X11),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X11),multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),X7),X11),
inference(substitution,[status(thm)],[c60]) ).
cnf(c93,plain,
multiply(multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X11),multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),X7),X11),
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
multiply(multiply(X11,inverse(multiply(multiply(X10,inverse(X10),X9),inverse(multiply(X10,inverse(X10),X9)),multiply(X10,inverse(X10),X8))),X8),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5) = multiply(inverse(X4),multiply(X,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),X11),X4),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(X12,inverse(multiply(multiply(X4,inverse(X4),X11),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X))),multiply(multiply(X11,inverse(multiply(multiply(X10,inverse(X10),X9),inverse(multiply(X10,inverse(X10),X9)),multiply(X10,inverse(X10),X8))),X8),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5)) = multiply(X12,inverse(multiply(multiply(X4,inverse(X4),X11),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X))),multiply(inverse(X4),multiply(X,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),X11),X4)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(X8,inverse(multiply(multiply(X2,X,X11),X10,multiply(X2,X,X9))),multiply(X,multiply(X9,X10,X11),X2)) = multiply(X8,inverse(multiply(multiply(X6,inverse(X6),X7),inverse(multiply(multiply(X5,inverse(X5),X4),inverse(multiply(X5,inverse(X5),X4)),multiply(X5,inverse(X5),multiply(X6,inverse(X6),X3)))),multiply(X6,inverse(X6),X3))),multiply(inverse(X6),multiply(X3,inverse(multiply(multiply(X5,inverse(X5),X4),inverse(multiply(X5,inverse(X5),X4)),multiply(X5,inverse(X5),multiply(X6,inverse(X6),X3)))),X7),X6)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c97,plain,
multiply(X11,inverse(multiply(multiply(X9,inverse(X9),X10),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X9,inverse(X9),X6)))),multiply(X9,inverse(X9),X6))),multiply(inverse(X9),multiply(X6,inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X9,inverse(X9),X6)))),X10),X9)) = multiply(X11,inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(X9,inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X9,inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6),
inference(substitution,[status(thm)],[c52]) ).
cnf(c99,plain,
multiply(X9,inverse(multiply(multiply(X4,inverse(X4),X8),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X))),multiply(inverse(X4),multiply(X,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),X8),X4)) = multiply(X9,inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5),
inference(transitivity,[status(thm)],[c97,c98]) ).
cnf(c100,plain,
multiply(X15,inverse(multiply(multiply(X4,inverse(X4),X14),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X4,inverse(X4),X)))),multiply(X4,inverse(X4),X))),multiply(multiply(X14,inverse(multiply(multiply(X13,inverse(X13),X12),inverse(multiply(X13,inverse(X13),X12)),multiply(X13,inverse(X13),X11))),X11),inverse(multiply(multiply(X10,inverse(X10),X9),inverse(multiply(X10,inverse(X10),X9)),multiply(X10,inverse(X10),X8))),X8)) = multiply(X15,inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5),
inference(transitivity,[status(thm)],[c95,c99]) ).
cnf(c101,plain,
multiply(X11,inverse(X10),multiply(multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),X7))),X7),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4)) = multiply(X11,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(transitivity,[status(thm)],[c87,c100]) ).
cnf(c102,plain,
multiply(X12,inverse(multiply(X11,inverse(X11),X10)),multiply(multiply(multiply(X11,inverse(X11),X10),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),X7))),X7)) = multiply(X12,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(X9,inverse(multiply(X8,inverse(X8),X7)),multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4)) = multiply(X9,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(transitivity,[status(thm)],[c83,c102]) ).
cnf(c104,plain,
multiply(X10,inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X)) = multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),X7))),X7),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),X7))),X7) = multiply(X10,inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(X7,inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),multiply(multiply(X5,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X)) = multiply(X7,inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(congruence,[status(thm)],[c67]) ).
cnf(c107,plain,
multiply(X7,inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4) = multiply(X7,inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(transitivity,[status(thm)],[c105,c106]) ).
cnf(c108,plain,
multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
multiply(multiply(multiply(multiply(X14,X13,X12),X11,multiply(X14,X13,X10)),inverse(multiply(X9,inverse(X9),multiply(X8,inverse(X8),X7))),X7),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(multiply(multiply(multiply(X14,X13,X12),X11,multiply(X14,X13,X10)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6),
inference(substitution,[status(thm)],[c52]) ).
cnf(c112,plain,
multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6) = multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(multiply(multiply(multiply(X16,X15,X14),X13,multiply(X16,X15,X12)),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6),inverse(multiply(X11,inverse(X11),multiply(X10,inverse(X10),X9))),X9) = multiply(multiply(multiply(multiply(X16,X15,X14),X13,multiply(X16,X15,X12)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),inverse(multiply(X11,inverse(X11),multiply(X10,inverse(X10),X9))),X9),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)) = multiply(X8,multiply(multiply(X11,X10,X7),inverse(multiply(multiply(X11,X10,X9),X8,X)),X),multiply(X11,X10,X9)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c115,plain,
multiply(multiply(multiply(multiply(X14,X13,X12),X11,multiply(X14,X13,X10)),inverse(multiply(multiply(X6,X5,X4),X3,multiply(X6,X5,X2))),multiply(X5,multiply(X2,X3,X4),X6)),inverse(multiply(X9,inverse(X9),multiply(X8,inverse(X8),X7))),X7) = multiply(multiply(X11,multiply(multiply(X14,X13,X10),inverse(multiply(multiply(X14,X13,X12),X11,X)),X),multiply(X14,X13,X12)),inverse(multiply(X9,inverse(X9),multiply(X8,inverse(X8),X7))),X7),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(multiply(X9,X8,X7),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X9,X8,X7),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(substitution,[status(thm)],[c107]) ).
cnf(c117,plain,
multiply(multiply(X9,X8,X7),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(multiply(X9,X8,X7),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3)),inverse(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3))),multiply(X4,multiply(X3,inverse(multiply(X2,X4,X)),X),X2)) = multiply(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c119,plain,
multiply(X2,X4,X3) = multiply(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3)),inverse(multiply(multiply(X2,X4,X),inverse(multiply(X2,X4,X)),multiply(X2,X4,X3))),multiply(X4,multiply(X3,inverse(multiply(X2,X4,X)),X),X2)),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(multiply(X5,X7,X6),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(multiply(X5,X7,X4),inverse(multiply(X5,X7,X4)),multiply(X5,X7,X6)),inverse(multiply(multiply(X5,X7,X4),inverse(multiply(X5,X7,X4)),multiply(X5,X7,X6))),multiply(X7,multiply(X6,inverse(multiply(X5,X7,X4)),X4),X5)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(multiply(multiply(multiply(X5,X7,X4),inverse(multiply(X5,X7,X4)),multiply(X5,X7,X6)),inverse(multiply(multiply(X5,X7,X4),inverse(multiply(X5,X7,X4)),multiply(X5,X7,X6))),multiply(X7,multiply(X6,inverse(multiply(X5,X7,X4)),X4),X5)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X7,multiply(X6,inverse(multiply(X5,X7,X4)),X4),X5),
inference(substitution,[status(thm)],[c67]) ).
cnf(c122,plain,
multiply(multiply(X5,X7,X6),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X7,multiply(X6,inverse(multiply(X5,X7,X4)),X4),X5),
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
multiply(multiply(X7,X6,X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X6,multiply(X5,inverse(multiply(X7,X6,X4)),X4),X7),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(multiply(X7,X6,X5),inverse(multiply(X4,inverse(X4),multiply(X3,inverse(X3),X2))),X2) = multiply(X6,multiply(X5,inverse(multiply(X7,X6,X)),X),X7),
inference(transitivity,[status(thm)],[c117,c123]) ).
cnf(c125,plain,
multiply(multiply(multiply(X8,X7,X5),X9,multiply(X8,X7,X6)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X9,multiply(multiply(X8,X7,X6),inverse(multiply(multiply(X8,X7,X5),X9,X4)),X4),multiply(X8,X7,X5)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(X9,multiply(multiply(X8,X7,X6),inverse(multiply(multiply(X8,X7,X5),X9,X4)),X4),multiply(X8,X7,X5)) = multiply(multiply(multiply(X8,X7,X5),X9,multiply(X8,X7,X6)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(multiply(X12,multiply(multiply(X11,X10,X9),inverse(multiply(multiply(X11,X10,X8),X12,X7)),X7),multiply(X11,X10,X8)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(multiply(multiply(multiply(X11,X10,X8),X12,multiply(X11,X10,X9)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5)),inverse(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5))),multiply(X6,multiply(X5,X8,X4),X7)) = multiply(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c129,plain,
multiply(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5)),inverse(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5))),multiply(X6,multiply(X5,X8,X4),X7)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(multiply(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(multiply(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8)),inverse(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8))),multiply(X9,multiply(X8,X11,X7),X10)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(multiply(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8)),inverse(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8))),multiply(X9,multiply(X8,X11,X7),X10)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8)),inverse(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8))),multiply(X9,multiply(X8,X11,X7),X10)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(substitution,[status(thm)],[c107]) ).
cnf(c132,plain,
multiply(multiply(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8)),inverse(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8))),multiply(X9,multiply(X8,X11,X7),X10)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(multiply(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8)),inverse(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8))),multiply(X9,multiply(X8,X11,X7),X10)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(multiply(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10)),inverse(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10))),multiply(X11,multiply(X10,X13,X9),X12)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10)),inverse(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10))),multiply(X11,multiply(X10,X13,X9),X12)),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6),
inference(substitution,[status(thm)],[c52]) ).
cnf(c134,plain,
multiply(multiply(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10)),inverse(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10))),multiply(X11,multiply(X10,X13,X9),X12)),inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),X6))),X6) = multiply(multiply(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10)),inverse(multiply(multiply(X12,X11,X9),X13,multiply(X12,X11,X10))),multiply(X11,multiply(X10,X13,X9),X12)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(multiply(multiply(multiply(X9,X8,X6),X10,multiply(X9,X8,X7)),inverse(multiply(multiply(X9,X8,X6),X10,multiply(X9,X8,X7))),multiply(X8,multiply(X7,X10,X6),X9)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X8,multiply(X7,X10,X6),X9),
inference(substitution,[status(thm)],[c2]) ).
cnf(c136,plain,
multiply(multiply(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5)),inverse(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5))),multiply(X6,multiply(X5,X8,X4),X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X6,multiply(X5,X8,X4),X7),
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
multiply(multiply(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5)),inverse(multiply(multiply(X7,X6,X4),X8,multiply(X7,X6,X5))),multiply(X6,multiply(X5,X8,X4),X7)),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(X6,multiply(X5,X8,X4),X7),
inference(transitivity,[status(thm)],[c132,c136]) ).
cnf(c138,plain,
multiply(multiply(multiply(multiply(X10,X9,X7),X11,multiply(X10,X9,X8)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(X9,multiply(X8,X11,X7),X10),
inference(transitivity,[status(thm)],[c130,c137]) ).
cnf(c139,plain,
multiply(multiply(X9,multiply(multiply(X8,X7,X6),inverse(multiply(multiply(X8,X7,X5),X9,X4)),X4),multiply(X8,X7,X5)),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(X7,multiply(X6,X9,X5),X8),
inference(transitivity,[status(thm)],[c127,c138]) ).
cnf(c140,plain,
multiply(multiply(X6,multiply(multiply(X9,X8,X5),inverse(multiply(multiply(X9,X8,X7),X6,X)),X),multiply(X9,X8,X7)),inverse(multiply(X4,inverse(X4),multiply(X3,inverse(X3),X2))),X2) = multiply(X8,multiply(X5,X6,X7),X9),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(multiply(multiply(multiply(X13,X12,X11),X10,multiply(X13,X12,X9)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),inverse(multiply(X8,inverse(X8),multiply(X7,inverse(X7),X6))),X6) = multiply(X12,multiply(X9,X10,X11),X13),
inference(transitivity,[status(thm)],[c115,c140]) ).
cnf(c142,plain,
multiply(multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(X10,multiply(X7,X8,X9),X11),
inference(transitivity,[status(thm)],[c113,c141]) ).
cnf(c143,plain,
multiply(multiply(multiply(multiply(X11,X10,X9),X8,multiply(X11,X10,X7)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(X10,multiply(X7,X8,X9),X11),
inference(transitivity,[status(thm)],[c110,c142]) ).
cnf(c144,plain,
multiply(multiply(multiply(multiply(X11,inverse(X11),X7),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),multiply(X11,inverse(X11),X10)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(inverse(X11),multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),X7),X11),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
multiply(inverse(X11),multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),X7),X11) = multiply(multiply(multiply(multiply(X11,inverse(X11),X7),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),multiply(X11,inverse(X11),X10)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
multiply(multiply(X5,inverse(X5),X),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X5,inverse(X5),X4)))),multiply(X5,inverse(X5),X4)) = X,
inference(substitution,[status(thm)],[c67]) ).
cnf(c147,plain,
multiply(multiply(multiply(X8,inverse(X8),X4),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),multiply(X8,inverse(X8),X7)))),multiply(X8,inverse(X8),X7)),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(X4,inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(multiply(multiply(multiply(X11,inverse(X11),X7),inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),multiply(X11,inverse(X11),X10)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(multiply(X7,inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(inverse(X11),multiply(X10,inverse(multiply(multiply(X9,inverse(X9),X8),inverse(multiply(X9,inverse(X9),X8)),multiply(X9,inverse(X9),multiply(X11,inverse(X11),X10)))),X7),X11) = multiply(multiply(X7,inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(transitivity,[status(thm)],[c145,c148]) ).
cnf(c150,plain,
multiply(inverse(X10),multiply(X9,inverse(multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X8,inverse(X8),X7)),multiply(X8,inverse(X8),multiply(X10,inverse(X10),X9)))),multiply(inverse(X12),multiply(multiply(X15,inverse(X15),multiply(X13,inverse(X13),X14)),inverse(multiply(X12,inverse(X12),X11)),X11),X12)),X10) = multiply(multiply(multiply(inverse(X12),multiply(multiply(X15,inverse(X15),multiply(X13,inverse(X13),X14)),inverse(multiply(X12,inverse(X12),X11)),X11),X12),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(inverse(X2),multiply(multiply(X5,inverse(X5),multiply(X3,inverse(X3),X4)),inverse(multiply(X2,inverse(X2),X)),X),X2) = multiply(X5,inverse(X5),multiply(X3,inverse(X3),X4)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c152,plain,
multiply(multiply(inverse(X5),multiply(multiply(X8,inverse(X8),multiply(X6,inverse(X6),X7)),inverse(multiply(X5,inverse(X5),X4)),X4),X5),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(multiply(X8,inverse(X8),multiply(X6,inverse(X6),X7)),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(multiply(multiply(inverse(X8),multiply(multiply(X11,inverse(X11),multiply(X9,inverse(X9),X10)),inverse(multiply(X8,inverse(X8),X7)),X7),X8),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(multiply(multiply(X11,inverse(X11),multiply(X9,inverse(X9),X10)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(multiply(X8,inverse(X8),X7),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),
inference(substitution,[status(thm)],[c107]) ).
cnf(c155,plain,
multiply(multiply(X8,inverse(X8),X7),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4) = multiply(multiply(X8,inverse(X8),X7),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(multiply(X5,inverse(X5),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = X4,
inference(transitivity,[status(thm)],[c155,c67]) ).
cnf(c157,plain,
multiply(multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5)),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(X4,inverse(X4),X5),
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
multiply(multiply(multiply(X9,inverse(X9),multiply(X7,inverse(X7),X8)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = multiply(multiply(X7,inverse(X7),X8),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(multiply(X4,inverse(X4),X5),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = X5,
inference(substitution,[status(thm)],[c156]) ).
cnf(c160,plain,
multiply(multiply(multiply(X9,inverse(X9),multiply(X7,inverse(X7),X8)),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = X8,
inference(transitivity,[status(thm)],[c158,c159]) ).
cnf(c161,plain,
multiply(multiply(multiply(inverse(X8),multiply(multiply(X11,inverse(X11),multiply(X9,inverse(X9),X10)),inverse(multiply(X8,inverse(X8),X7)),X7),X8),inverse(multiply(X6,inverse(X6),multiply(X5,inverse(X5),X4))),X4),inverse(multiply(X3,inverse(X3),multiply(X2,inverse(X2),X))),X) = X10,
inference(transitivity,[status(thm)],[c153,c160]) ).
cnf(c162,plain,
multiply(inverse(X4),multiply(X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),multiply(inverse(X6),multiply(multiply(X9,inverse(X9),multiply(X7,inverse(X7),X8)),inverse(multiply(X6,inverse(X6),X5)),X5),X6)),X4) = X8,
inference(transitivity,[status(thm)],[c150,c161]) ).
cnf(c163,plain,
multiply(inverse(X6),multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5))))),multiply(inverse(X3),multiply(multiply(X6,inverse(X6),multiply(X4,inverse(X4),X5)),inverse(multiply(X3,inverse(X3),X)),X),X3)),X6) = X5,
inference(transitivity,[status(thm)],[c80,c162]) ).
cnf(c164,plain,
multiply(inverse(X2),X,X2) = X,
inference(transitivity,[status(thm)],[c20,c163]) ).
cnf(c165,plain,
multiply(inverse(X),multiply(X3,inverse(X2),X2),X) = multiply(X3,inverse(X2),X2),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
multiply(X3,inverse(X2),X2) = multiply(inverse(X),multiply(X3,inverse(X2),X2),X),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(inverse(X2),inverse(multiply(X2,inverse(X2),X)),X2) = inverse(multiply(X2,inverse(X2),X)),
inference(substitution,[status(thm)],[c164]) ).
cnf(c168,plain,
inverse(multiply(X2,inverse(X2),X)) = multiply(inverse(X2),inverse(multiply(X2,inverse(X2),X)),X2),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(inverse(X),inverse(multiply(X2,inverse(X2),X)),X) = inverse(multiply(X2,inverse(X2),X)),
inference(substitution,[status(thm)],[c164]) ).
cnf(c170,plain,
inverse(multiply(X2,inverse(X2),X)) = multiply(inverse(X),inverse(multiply(X2,inverse(X2),X)),X),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(inverse(X2),inverse(multiply(X2,inverse(X2),X)),X2) = multiply(inverse(X2),multiply(inverse(X),inverse(multiply(X2,inverse(X2),X)),X),X2),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
multiply(inverse(X2),multiply(inverse(X),inverse(multiply(X2,inverse(X2),X)),X),X2) = inverse(X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c173,plain,
multiply(inverse(X2),inverse(multiply(X2,inverse(X2),X)),X2) = inverse(X),
inference(transitivity,[status(thm)],[c171,c172]) ).
cnf(c174,plain,
inverse(multiply(X2,inverse(X2),X)) = inverse(X),
inference(transitivity,[status(thm)],[c168,c173]) ).
cnf(c175,plain,
inverse(multiply(X,inverse(X),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
inverse(X2) = inverse(multiply(X,inverse(X),X2)),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(X3,inverse(X2),X2) = multiply(X3,inverse(multiply(X,inverse(X),X2)),X2),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(inverse(X),multiply(X3,inverse(X2),X2),X) = multiply(inverse(X),multiply(X3,inverse(multiply(X,inverse(X),X2)),X2),X),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(multiply(X6,inverse(X6),X8),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(inverse(X6),multiply(X8,inverse(multiply(X6,inverse(X6),X7)),X7),X6),
inference(substitution,[status(thm)],[c45]) ).
cnf(c180,plain,
multiply(inverse(X6),multiply(X8,inverse(multiply(X6,inverse(X6),X7)),X7),X6) = multiply(multiply(X6,inverse(X6),X8),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
multiply(multiply(X9,inverse(X9),X10),inverse(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4))),multiply(X7,multiply(X4,X5,X6),X8)) = multiply(multiply(X9,inverse(X9),X10),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c182,plain,
multiply(multiply(X4,inverse(X4),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = X5,
inference(substitution,[status(thm)],[c67]) ).
cnf(c183,plain,
multiply(multiply(X6,inverse(X6),X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = X7,
inference(transitivity,[status(thm)],[c181,c182]) ).
cnf(c184,plain,
multiply(inverse(X),multiply(X3,inverse(multiply(X,inverse(X),X2)),X2),X) = X3,
inference(transitivity,[status(thm)],[c180,c183]) ).
cnf(c185,plain,
multiply(inverse(X),multiply(X3,inverse(X2),X2),X) = X3,
inference(transitivity,[status(thm)],[c178,c184]) ).
cnf(c186,plain,
multiply(X2,inverse(X),X) = X2,
inference(transitivity,[status(thm)],[c166,c185]) ).
cnf(c187,plain,
multiply(multiply(X2,X3,X4),inverse(X),X) = multiply(X2,X3,X4),
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(X2,X3,X4) = multiply(multiply(X2,X3,X4),inverse(X),X),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(multiply(multiply(X3,X4,X5),inverse(X2),X2),inverse(X),X) = multiply(multiply(X3,X4,X5),inverse(X2),X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c190,plain,
multiply(multiply(X3,X4,X5),inverse(X2),X2) = multiply(multiply(multiply(X3,X4,X5),inverse(X2),X2),inverse(X),X),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
inverse(X) = inverse(multiply(X2,inverse(X2),X)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c192,plain,
multiply(multiply(multiply(X4,X5,X6),inverse(X3),X3),inverse(X),X) = multiply(multiply(multiply(X4,X5,X6),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
inverse(X) = inverse(multiply(X2,inverse(X2),X)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c194,plain,
multiply(multiply(X3,X4,X5),inverse(X),X) = multiply(multiply(X3,X4,X5),inverse(multiply(X2,inverse(X2),X)),X),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
multiply(multiply(multiply(X5,X6,X7),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(multiply(multiply(X5,X6,X7),inverse(multiply(X4,inverse(X4),X3)),X3),inverse(multiply(X2,inverse(X2),X)),X),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(X),X) = multiply(X3,inverse(X3),X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c197,plain,
multiply(X3,inverse(X3),X2) = multiply(multiply(X3,inverse(X3),X2),inverse(X),X),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c174]) ).
cnf(c199,plain,
inverse(X2) = inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),X2)),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(multiply(X4,inverse(X4),X3),inverse(X2),X2) = multiply(multiply(X4,inverse(X4),X3),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),X2)),X2),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
multiply(X,inverse(X),X) = X,
inference(substitution,[status(thm)],[c186]) ).
cnf(c202,plain,
X = multiply(X,inverse(X),X),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),X2) = multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X2)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),X2)) = inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X2))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(multiply(X4,inverse(X4),X3),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),X2)),X2) = multiply(multiply(X4,inverse(X4),X3),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X2))),X2),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(multiply(X4,inverse(X4),X3),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X2))),X2) = X3,
inference(substitution,[status(thm)],[c67]) ).
cnf(c207,plain,
multiply(multiply(X4,inverse(X4),X3),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),X2)),X2) = X3,
inference(transitivity,[status(thm)],[c205,c206]) ).
cnf(c208,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(X),X) = X2,
inference(transitivity,[status(thm)],[c200,c207]) ).
cnf(c209,plain,
multiply(X2,inverse(X2),X) = X,
inference(transitivity,[status(thm)],[c197,c208]) ).
cnf(c210,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)) = multiply(X3,inverse(X3),X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(X3,inverse(X3),X) = multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
inverse(multiply(X3,inverse(X3),X)) = inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
multiply(multiply(multiply(X6,X7,X8),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(X3,inverse(X3),X)),X) = multiply(multiply(multiply(X6,X7,X8),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)) = multiply(X3,inverse(X3),X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c215,plain,
multiply(X3,inverse(X3),X) = multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
inverse(multiply(X3,inverse(X3),X)) = inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
multiply(multiply(X4,X5,X6),inverse(multiply(X3,inverse(X3),X)),X) = multiply(multiply(X4,X5,X6),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(multiply(multiply(X7,X8,X9),inverse(multiply(X6,inverse(X6),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X7,X8,X9),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(X,inverse(X),X2) = X2,
inference(substitution,[status(thm)],[c209]) ).
cnf(c220,plain,
X2 = multiply(X,inverse(X),X2),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
multiply(X2,X3,X4) = multiply(X2,X3,multiply(X,inverse(X),X4)),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(multiply(X5,X6,X7),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X5,X6,multiply(X4,inverse(X4),X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
multiply(multiply(multiply(X8,X9,X10),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X8,X9,multiply(X7,inverse(X7),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
multiply(X,inverse(X),X2) = X2,
inference(substitution,[status(thm)],[c209]) ).
cnf(c225,plain,
X2 = multiply(X,inverse(X),X2),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
multiply(X2,X3,multiply(X,inverse(X),X4)) = multiply(multiply(X,inverse(X),X2),X3,multiply(X,inverse(X),X4)),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
multiply(multiply(X5,X6,multiply(X4,inverse(X4),X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X4,inverse(X4),X5),X6,multiply(X4,inverse(X4),X7)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
multiply(multiply(multiply(X8,X9,multiply(X7,inverse(X7),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(multiply(X7,inverse(X7),X8),X9,multiply(X7,inverse(X7),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(multiply(multiply(multiply(X7,inverse(X7),X8),X9,multiply(X7,inverse(X7),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X7),multiply(X10,X9,X8),X7),
inference(substitution,[status(thm)],[c60]) ).
cnf(c230,plain,
multiply(inverse(X),multiply(X4,X3,X2),X) = multiply(X4,X3,X2),
inference(substitution,[status(thm)],[c164]) ).
cnf(c231,plain,
multiply(multiply(multiply(multiply(X7,inverse(X7),X8),X9,multiply(X7,inverse(X7),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,X9,X8),
inference(transitivity,[status(thm)],[c229,c230]) ).
cnf(c232,plain,
multiply(multiply(multiply(X8,X9,multiply(X7,inverse(X7),X10)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,X9,X8),
inference(transitivity,[status(thm)],[c228,c231]) ).
cnf(c233,plain,
multiply(multiply(multiply(X7,X8,X9),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X9,X8,X7),
inference(transitivity,[status(thm)],[c223,c232]) ).
cnf(c234,plain,
multiply(multiply(multiply(X6,X7,X8),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X8,X7,X6),
inference(transitivity,[status(thm)],[c218,c233]) ).
cnf(c235,plain,
multiply(multiply(multiply(X5,X6,X7),inverse(multiply(X4,inverse(X4),X3)),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(X7,X6,X5),
inference(transitivity,[status(thm)],[c213,c234]) ).
cnf(c236,plain,
multiply(multiply(multiply(X4,X5,X6),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(X6,X5,X4),
inference(transitivity,[status(thm)],[c195,c235]) ).
cnf(c237,plain,
multiply(multiply(multiply(X3,X4,X5),inverse(X2),X2),inverse(X),X) = multiply(X5,X4,X3),
inference(transitivity,[status(thm)],[c192,c236]) ).
cnf(c238,plain,
multiply(multiply(X2,X3,X4),inverse(X),X) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c190,c237]) ).
cnf(c239,plain,
multiply(X,X2,X3) = multiply(X3,X2,X),
inference(transitivity,[status(thm)],[c188,c238]) ).
cnf(c240,plain,
multiply(X3,X2,X) = multiply(X,X2,X3),
inference(substitution,[status(thm)],[c239]) ).
cnf(c241,plain,
multiply(multiply(X2,X4,X3),inverse(X),X) = multiply(X2,X4,X3),
inference(substitution,[status(thm)],[c186]) ).
cnf(c242,plain,
multiply(X2,X4,X3) = multiply(multiply(X2,X4,X3),inverse(X),X),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
multiply(multiply(multiply(X3,X5,X4),inverse(X2),X2),inverse(X),X) = multiply(multiply(X3,X5,X4),inverse(X2),X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c244,plain,
multiply(multiply(X3,X5,X4),inverse(X2),X2) = multiply(multiply(multiply(X3,X5,X4),inverse(X2),X2),inverse(X),X),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
inverse(X) = inverse(multiply(X2,inverse(X2),X)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c246,plain,
multiply(multiply(multiply(X4,X6,X5),inverse(X3),X3),inverse(X),X) = multiply(multiply(multiply(X4,X6,X5),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
inverse(X) = inverse(multiply(X2,inverse(X2),X)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c248,plain,
multiply(multiply(X3,X5,X4),inverse(X),X) = multiply(multiply(X3,X5,X4),inverse(multiply(X2,inverse(X2),X)),X),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
multiply(multiply(multiply(X5,X7,X6),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(multiply(multiply(X5,X7,X6),inverse(multiply(X4,inverse(X4),X3)),X3),inverse(multiply(X2,inverse(X2),X)),X),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)) = multiply(X3,inverse(X3),X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c251,plain,
multiply(X3,inverse(X3),X) = multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
inverse(multiply(X3,inverse(X3),X)) = inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
multiply(multiply(multiply(X6,X8,X7),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(X3,inverse(X3),X)),X) = multiply(multiply(multiply(X6,X8,X7),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)) = multiply(X3,inverse(X3),X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c255,plain,
multiply(X3,inverse(X3),X) = multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
inverse(multiply(X3,inverse(X3),X)) = inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
multiply(multiply(X4,X6,X5),inverse(multiply(X3,inverse(X3),X)),X) = multiply(multiply(X4,X6,X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
multiply(multiply(multiply(X7,X9,X8),inverse(multiply(X6,inverse(X6),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X7,X9,X8),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
multiply(X,inverse(X),X2) = X2,
inference(substitution,[status(thm)],[c209]) ).
cnf(c260,plain,
X2 = multiply(X,inverse(X),X2),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
multiply(X2,inverse(X),X2) = multiply(X2,inverse(X),multiply(X,inverse(X),X2)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
multiply(X3,X2,multiply(X,X2,X3)) = multiply(X3,X2,multiply(X3,X2,X)),
inference(congruence,[status(thm)],[c239]) ).
cnf(c263,plain,
multiply(multiply(X4,X3,multiply(X4,X3,X2)),inverse(X),X) = multiply(X4,X3,multiply(X4,X3,X2)),
inference(substitution,[status(thm)],[c186]) ).
cnf(c264,plain,
multiply(X4,X3,multiply(X4,X3,X2)) = multiply(multiply(X4,X3,multiply(X4,X3,X2)),inverse(X),X),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
inverse(multiply(X,inverse(X),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c174]) ).
cnf(c266,plain,
inverse(X2) = inverse(multiply(X,inverse(X),X2)),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
multiply(multiply(X5,X4,multiply(X5,X4,X3)),inverse(X2),X2) = multiply(multiply(X5,X4,multiply(X5,X4,X3)),inverse(multiply(X,inverse(X),X2)),X2),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3)) = multiply(X2,inverse(X2),X3),
inference(substitution,[status(thm)],[c209]) ).
cnf(c269,plain,
multiply(X2,inverse(X2),X3) = multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3)),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
inverse(multiply(X2,inverse(X2),X3)) = inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
multiply(multiply(X6,X5,multiply(X6,X5,X4)),inverse(multiply(X2,inverse(X2),X3)),X3) = multiply(multiply(X6,X5,multiply(X6,X5,X4)),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3))),X3),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
multiply(multiply(X11,X10,multiply(X11,X10,X9)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(X11,X10,multiply(X11,X10,X9)),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X8))),X8),
inference(substitution,[status(thm)],[c52]) ).
cnf(c273,plain,
multiply(multiply(X11,X10,multiply(X11,X10,X9)),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X8))),X8) = multiply(multiply(X11,X10,multiply(X11,X10,X9)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
multiply(multiply(X8,X7,multiply(X8,X7,X6)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X7,multiply(multiply(X8,X7,X6),inverse(multiply(X8,X7,X6)),X6),X8),
inference(substitution,[status(thm)],[c45]) ).
cnf(c275,plain,
multiply(multiply(X3,X2,X),inverse(multiply(X3,X2,X)),X) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c276,plain,
multiply(X2,multiply(multiply(X3,X2,X),inverse(multiply(X3,X2,X)),X),X3) = multiply(X2,X,X3),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
multiply(X3,X,X2) = multiply(X2,X,X3),
inference(substitution,[status(thm)],[c239]) ).
cnf(c278,plain,
multiply(X2,X,X3) = multiply(X3,X,X2),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
multiply(X2,multiply(multiply(X3,X2,X),inverse(multiply(X3,X2,X)),X),X3) = multiply(X3,X,X2),
inference(transitivity,[status(thm)],[c276,c278]) ).
cnf(c280,plain,
multiply(multiply(X8,X7,multiply(X8,X7,X6)),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X8,X6,X7),
inference(transitivity,[status(thm)],[c274,c279]) ).
cnf(c281,plain,
multiply(multiply(X6,X5,multiply(X6,X5,X4)),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3))),X3) = multiply(X6,X4,X5),
inference(transitivity,[status(thm)],[c273,c280]) ).
cnf(c282,plain,
multiply(multiply(X5,X4,multiply(X5,X4,X3)),inverse(multiply(X,inverse(X),X2)),X2) = multiply(X5,X3,X4),
inference(transitivity,[status(thm)],[c271,c281]) ).
cnf(c283,plain,
multiply(multiply(X4,X3,multiply(X4,X3,X2)),inverse(X),X) = multiply(X4,X2,X3),
inference(transitivity,[status(thm)],[c267,c282]) ).
cnf(c284,plain,
multiply(X3,X2,multiply(X3,X2,X)) = multiply(X3,X,X2),
inference(transitivity,[status(thm)],[c264,c283]) ).
cnf(c285,plain,
multiply(X3,X2,multiply(X,X2,X3)) = multiply(X3,X,X2),
inference(transitivity,[status(thm)],[c262,c284]) ).
cnf(c286,plain,
multiply(X2,inverse(X),multiply(X,inverse(X),X2)) = multiply(X2,X,inverse(X)),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
multiply(X2,X,inverse(X)) = multiply(inverse(X),X,X2),
inference(substitution,[status(thm)],[c239]) ).
cnf(c288,plain,
multiply(multiply(inverse(X2),X2,X3),inverse(X),X) = multiply(inverse(X2),X2,X3),
inference(substitution,[status(thm)],[c186]) ).
cnf(c289,plain,
multiply(inverse(X2),X2,X3) = multiply(multiply(inverse(X2),X2,X3),inverse(X),X),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
inverse(multiply(X,inverse(X),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c174]) ).
cnf(c291,plain,
inverse(X2) = inverse(multiply(X,inverse(X),X2)),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
multiply(multiply(inverse(X3),X3,X4),inverse(X2),X2) = multiply(multiply(inverse(X3),X3,X4),inverse(multiply(X,inverse(X),X2)),X2),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3)) = multiply(X2,inverse(X2),X3),
inference(substitution,[status(thm)],[c209]) ).
cnf(c294,plain,
multiply(X2,inverse(X2),X3) = multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3)),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
inverse(multiply(X2,inverse(X2),X3)) = inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
multiply(multiply(inverse(X4),X4,X5),inverse(multiply(X2,inverse(X2),X3)),X3) = multiply(multiply(inverse(X4),X4,X5),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3))),X3),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
multiply(multiply(inverse(X9),X9,X10),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(inverse(X9),X9,X10),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X8))),X8),
inference(substitution,[status(thm)],[c52]) ).
cnf(c298,plain,
multiply(multiply(inverse(X9),X9,X10),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X8))),X8) = multiply(multiply(inverse(X9),X9,X10),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c297]) ).
cnf(c299,plain,
multiply(inverse(X),inverse(inverse(X)),X) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c164]) ).
cnf(c300,plain,
inverse(inverse(X)) = multiply(inverse(X),inverse(inverse(X)),X),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
multiply(inverse(X),inverse(inverse(X)),X) = X,
inference(substitution,[status(thm)],[c209]) ).
cnf(c302,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c300,c301]) ).
cnf(c303,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
multiply(inverse(X),X,X2) = multiply(inverse(X),inverse(inverse(X)),X2),
inference(congruence,[status(thm)],[c303]) ).
cnf(c305,plain,
multiply(multiply(inverse(X6),X6,X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(multiply(inverse(X6),inverse(inverse(X6)),X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
multiply(multiply(inverse(X6),inverse(inverse(X6)),X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = X7,
inference(substitution,[status(thm)],[c2]) ).
cnf(c307,plain,
multiply(multiply(inverse(X6),X6,X7),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = X7,
inference(transitivity,[status(thm)],[c305,c306]) ).
cnf(c308,plain,
multiply(multiply(inverse(X4),X4,X5),inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),X3))),X3) = X5,
inference(transitivity,[status(thm)],[c298,c307]) ).
cnf(c309,plain,
multiply(multiply(inverse(X3),X3,X4),inverse(multiply(X,inverse(X),X2)),X2) = X4,
inference(transitivity,[status(thm)],[c296,c308]) ).
cnf(c310,plain,
multiply(multiply(inverse(X2),X2,X3),inverse(X),X) = X3,
inference(transitivity,[status(thm)],[c292,c309]) ).
cnf(c311,plain,
multiply(inverse(X),X,X2) = X2,
inference(transitivity,[status(thm)],[c289,c310]) ).
cnf(c312,plain,
multiply(X2,X,inverse(X)) = X2,
inference(transitivity,[status(thm)],[c287,c311]) ).
cnf(c313,plain,
multiply(X2,inverse(X),multiply(X,inverse(X),X2)) = X2,
inference(transitivity,[status(thm)],[c286,c312]) ).
cnf(c314,plain,
multiply(X2,inverse(X),X2) = X2,
inference(transitivity,[status(thm)],[c261,c313]) ).
cnf(c315,plain,
multiply(multiply(X2,X4,X3),inverse(X),multiply(X2,X4,X3)) = multiply(X2,X4,X3),
inference(substitution,[status(thm)],[c314]) ).
cnf(c316,plain,
multiply(X2,X4,X3) = multiply(multiply(X2,X4,X3),inverse(X),multiply(X2,X4,X3)),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
multiply(multiply(X5,X7,X6),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X5,X7,X6),inverse(X4),multiply(X5,X7,X6)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
multiply(multiply(multiply(X8,X10,X9),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(multiply(X8,X10,X9),inverse(X7),multiply(X8,X10,X9)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
multiply(multiply(multiply(multiply(X8,X10,X9),inverse(X7),multiply(X8,X10,X9)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,multiply(X9,inverse(X7),X9),X8),
inference(substitution,[status(thm)],[c60]) ).
cnf(c320,plain,
multiply(X4,multiply(X3,inverse(X),X3),X2) = multiply(X4,X3,X2),
inference(congruence,[status(thm)],[c314]) ).
cnf(c321,plain,
multiply(multiply(multiply(multiply(X8,X10,X9),inverse(X7),multiply(X8,X10,X9)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,X9,X8),
inference(transitivity,[status(thm)],[c319,c320]) ).
cnf(c322,plain,
multiply(multiply(multiply(X7,X9,X8),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X9,X8,X7),
inference(transitivity,[status(thm)],[c318,c321]) ).
cnf(c323,plain,
multiply(multiply(multiply(X6,X8,X7),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X8,X7,X6),
inference(transitivity,[status(thm)],[c258,c322]) ).
cnf(c324,plain,
multiply(multiply(multiply(X5,X7,X6),inverse(multiply(X4,inverse(X4),X3)),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(X7,X6,X5),
inference(transitivity,[status(thm)],[c253,c323]) ).
cnf(c325,plain,
multiply(multiply(multiply(X4,X6,X5),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(X6,X5,X4),
inference(transitivity,[status(thm)],[c249,c324]) ).
cnf(c326,plain,
multiply(multiply(multiply(X3,X5,X4),inverse(X2),X2),inverse(X),X) = multiply(X5,X4,X3),
inference(transitivity,[status(thm)],[c246,c325]) ).
cnf(c327,plain,
multiply(multiply(X2,X4,X3),inverse(X),X) = multiply(X4,X3,X2),
inference(transitivity,[status(thm)],[c244,c326]) ).
cnf(c328,plain,
multiply(X,X3,X2) = multiply(X3,X2,X),
inference(transitivity,[status(thm)],[c242,c327]) ).
cnf(c329,plain,
multiply(X3,X,X2) = multiply(X,X2,X3),
inference(substitution,[status(thm)],[c328]) ).
cnf(c330,plain,
multiply(X,X2,X3) = multiply(X3,X,X2),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
multiply(X3,X2,X) = multiply(X3,X,X2),
inference(transitivity,[status(thm)],[c240,c330]) ).
cnf(c332,plain,
multiply(X2,X,X2) = multiply(X2,X2,X),
inference(substitution,[status(thm)],[c331]) ).
cnf(c333,plain,
multiply(X2,X2,X) = multiply(X2,X,X2),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
multiply(X3,inverse(X2),multiply(X2,X2,X)) = multiply(X3,inverse(X2),multiply(X2,X,X2)),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c336,plain,
multiply(X2,X,X2) = multiply(X2,X,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
multiply(X3,inverse(X2),multiply(X2,X,X2)) = multiply(X3,inverse(X2),multiply(X2,X,inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
multiply(X,inverse(X),inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c209]) ).
cnf(c339,plain,
inverse(X2) = multiply(X,inverse(X),inverse(X2)),
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
inverse(inverse(X2)) = inverse(multiply(X,inverse(X),inverse(X2))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
multiply(X3,X2,inverse(inverse(X3))) = multiply(X3,X2,inverse(multiply(X,inverse(X),inverse(X3)))),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
multiply(X4,inverse(X3),multiply(X3,X2,inverse(inverse(X3)))) = multiply(X4,inverse(X3),multiply(X3,X2,inverse(multiply(X,inverse(X),inverse(X3))))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),inverse(X3))) = multiply(X2,inverse(X2),inverse(X3)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c344,plain,
multiply(X2,inverse(X2),inverse(X3)) = multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),inverse(X3))),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
inverse(multiply(X2,inverse(X2),inverse(X3))) = inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),inverse(X3)))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
multiply(X4,X3,inverse(multiply(X2,inverse(X2),inverse(X4)))) = multiply(X4,X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),inverse(X4))))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
multiply(X5,inverse(X4),multiply(X4,X3,inverse(multiply(X2,inverse(X2),inverse(X4))))) = multiply(X5,inverse(X4),multiply(X4,X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),inverse(X4)))))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
multiply(X,inverse(X),X2) = X2,
inference(substitution,[status(thm)],[c209]) ).
cnf(c349,plain,
X2 = multiply(X,inverse(X),X2),
inference(symmetry,[status(thm)],[c348]) ).
cnf(c350,plain,
multiply(X6,inverse(X5),multiply(X5,X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X5)))))) = multiply(multiply(X,inverse(X),X6),inverse(X5),multiply(X5,X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X5)))))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
multiply(X3,X,X2) = multiply(X3,X2,X),
inference(substitution,[status(thm)],[c331]) ).
cnf(c352,plain,
multiply(X3,X2,X) = multiply(X3,X,X2),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
multiply(X4,inverse(X3),multiply(X3,X2,X)) = multiply(X4,inverse(X3),multiply(X3,X,X2)),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
multiply(X3,X2,X) = multiply(X,X2,X3),
inference(substitution,[status(thm)],[c239]) ).
cnf(c355,plain,
multiply(X,X2,X3) = multiply(X2,X3,X),
inference(substitution,[status(thm)],[c328]) ).
cnf(c356,plain,
multiply(X3,X2,X) = multiply(X2,X3,X),
inference(transitivity,[status(thm)],[c354,c355]) ).
cnf(c357,plain,
multiply(inverse(X3),X4,multiply(X3,X,X2)) = multiply(X4,inverse(X3),multiply(X3,X,X2)),
inference(substitution,[status(thm)],[c356]) ).
cnf(c358,plain,
multiply(X4,inverse(X3),multiply(X3,X,X2)) = multiply(inverse(X3),X4,multiply(X3,X,X2)),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
multiply(inverse(X3),multiply(X3,X,X2),X4) = multiply(inverse(X3),X4,multiply(X3,X,X2)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c360,plain,
multiply(inverse(X3),X4,multiply(X3,X,X2)) = multiply(inverse(X3),multiply(X3,X,X2),X4),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
multiply(X,X3,X2) = multiply(X3,X,X2),
inference(substitution,[status(thm)],[c356]) ).
cnf(c362,plain,
multiply(X3,X,X2) = multiply(X,X3,X2),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
multiply(inverse(X3),multiply(X3,X,X2),X4) = multiply(inverse(X3),multiply(X,X3,X2),X4),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
multiply(X,X2,X3) = multiply(X,X3,X2),
inference(substitution,[status(thm)],[c331]) ).
cnf(c365,plain,
multiply(X,X3,X2) = multiply(X,X2,X3),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
multiply(inverse(X3),multiply(X,X3,X2),X4) = multiply(inverse(X3),multiply(X,X2,X3),X4),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
multiply(multiply(multiply(multiply(X10,inverse(X9),X9),X8,multiply(X10,inverse(X9),X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(inverse(X9),multiply(X7,X8,X9),X10),
inference(substitution,[status(thm)],[c60]) ).
cnf(c368,plain,
multiply(inverse(X9),multiply(X7,X8,X9),X10) = multiply(multiply(multiply(multiply(X10,inverse(X9),X9),X8,multiply(X10,inverse(X9),X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c367]) ).
cnf(c369,plain,
multiply(multiply(X4,inverse(X3),X3),X2,multiply(X4,inverse(X3),X)) = multiply(X4,X2,multiply(X4,inverse(X3),X)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c370,plain,
multiply(multiply(multiply(X7,inverse(X6),X6),X5,multiply(X7,inverse(X6),X4)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X7,X5,multiply(X7,inverse(X6),X4)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
multiply(multiply(multiply(multiply(X10,inverse(X9),X9),X8,multiply(X10,inverse(X9),X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X10,X8,multiply(X10,inverse(X9),X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)) = multiply(X3,inverse(X3),X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c373,plain,
inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))) = inverse(multiply(X3,inverse(X3),X)),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
multiply(multiply(X7,X5,multiply(X7,inverse(X6),X4)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X7,X5,multiply(X7,inverse(X6),X4)),inverse(multiply(X3,inverse(X3),X)),X),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
multiply(multiply(multiply(X10,X8,multiply(X10,inverse(X9),X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X10,X8,multiply(X10,inverse(X9),X7)),inverse(multiply(X6,inverse(X6),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X)) = multiply(X3,inverse(X3),X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c377,plain,
inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))) = inverse(multiply(X3,inverse(X3),X)),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
multiply(multiply(multiply(X9,X7,multiply(X9,inverse(X8),X6)),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X9,X7,multiply(X9,inverse(X8),X6)),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(X3,inverse(X3),X)),X),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
multiply(multiply(X6,X4,multiply(X6,inverse(X5),X3)),inverse(multiply(X2,inverse(X2),X)),X) = multiply(multiply(X6,X4,multiply(X6,inverse(X5),X3)),inverse(X),X),
inference(congruence,[status(thm)],[c174]) ).
cnf(c380,plain,
multiply(multiply(multiply(X8,X6,multiply(X8,inverse(X7),X5)),inverse(multiply(X4,inverse(X4),X3)),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(multiply(multiply(X8,X6,multiply(X8,inverse(X7),X5)),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
multiply(multiply(multiply(X7,X5,multiply(X7,inverse(X6),X4)),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(multiply(multiply(X7,X5,multiply(X7,inverse(X6),X4)),inverse(X3),X3),inverse(X),X),
inference(congruence,[status(thm)],[c174]) ).
cnf(c382,plain,
multiply(multiply(multiply(X6,X4,multiply(X6,inverse(X5),X3)),inverse(X2),X2),inverse(X),X) = multiply(multiply(X6,X4,multiply(X6,inverse(X5),X3)),inverse(X2),X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c383,plain,
multiply(multiply(X5,X3,multiply(X5,inverse(X4),X2)),inverse(X),X) = multiply(X5,X3,multiply(X5,inverse(X4),X2)),
inference(substitution,[status(thm)],[c186]) ).
cnf(c384,plain,
multiply(X3,inverse(X2),X) = multiply(X3,X,inverse(X2)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c385,plain,
multiply(X4,X2,multiply(X4,inverse(X3),X)) = multiply(X4,X2,multiply(X4,X,inverse(X3))),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
multiply(multiply(X5,X3,multiply(X5,inverse(X4),X2)),inverse(X),X) = multiply(X5,X3,multiply(X5,X2,inverse(X4))),
inference(transitivity,[status(thm)],[c383,c385]) ).
cnf(c387,plain,
multiply(multiply(multiply(X6,X4,multiply(X6,inverse(X5),X3)),inverse(X2),X2),inverse(X),X) = multiply(X6,X4,multiply(X6,X3,inverse(X5))),
inference(transitivity,[status(thm)],[c382,c386]) ).
cnf(c388,plain,
multiply(multiply(multiply(X7,X5,multiply(X7,inverse(X6),X4)),inverse(X3),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(X7,X5,multiply(X7,X4,inverse(X6))),
inference(transitivity,[status(thm)],[c381,c387]) ).
cnf(c389,plain,
multiply(multiply(multiply(X8,X6,multiply(X8,inverse(X7),X5)),inverse(multiply(X4,inverse(X4),X3)),X3),inverse(multiply(X2,inverse(X2),X)),X) = multiply(X8,X6,multiply(X8,X5,inverse(X7))),
inference(transitivity,[status(thm)],[c380,c388]) ).
cnf(c390,plain,
multiply(multiply(multiply(X9,X7,multiply(X9,inverse(X8),X6)),inverse(multiply(X5,inverse(X5),X4)),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X9,X7,multiply(X9,X6,inverse(X8))),
inference(transitivity,[status(thm)],[c378,c389]) ).
cnf(c391,plain,
multiply(multiply(multiply(X10,X8,multiply(X10,inverse(X9),X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,X8,multiply(X10,X7,inverse(X9))),
inference(transitivity,[status(thm)],[c375,c390]) ).
cnf(c392,plain,
multiply(multiply(multiply(multiply(X10,inverse(X9),X9),X8,multiply(X10,inverse(X9),X7)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,X8,multiply(X10,X7,inverse(X9))),
inference(transitivity,[status(thm)],[c371,c391]) ).
cnf(c393,plain,
multiply(inverse(X3),multiply(X,X2,X3),X4) = multiply(X4,X2,multiply(X4,X,inverse(X3))),
inference(transitivity,[status(thm)],[c368,c392]) ).
cnf(c394,plain,
multiply(inverse(X3),multiply(X,X3,X2),X4) = multiply(X4,X2,multiply(X4,X,inverse(X3))),
inference(transitivity,[status(thm)],[c366,c393]) ).
cnf(c395,plain,
multiply(inverse(X3),multiply(X3,X,X2),X4) = multiply(X4,X2,multiply(X4,X,inverse(X3))),
inference(transitivity,[status(thm)],[c363,c394]) ).
cnf(c396,plain,
multiply(inverse(X3),X4,multiply(X3,X,X2)) = multiply(X4,X2,multiply(X4,X,inverse(X3))),
inference(transitivity,[status(thm)],[c360,c395]) ).
cnf(c397,plain,
multiply(X4,inverse(X3),multiply(X3,X,X2)) = multiply(X4,X2,multiply(X4,X,inverse(X3))),
inference(transitivity,[status(thm)],[c358,c396]) ).
cnf(c398,plain,
multiply(X4,inverse(X3),multiply(X3,X2,X)) = multiply(X4,X2,multiply(X4,X,inverse(X3))),
inference(transitivity,[status(thm)],[c353,c397]) ).
cnf(c399,plain,
multiply(multiply(X,inverse(X),X6),inverse(X5),multiply(X5,X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X5)))))) = multiply(multiply(X,inverse(X),X6),X4,multiply(multiply(X,inverse(X),X6),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X5)))),inverse(X5))),
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
multiply(multiply(X,inverse(X),X5),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X4)))),inverse(X4)) = X5,
inference(substitution,[status(thm)],[c67]) ).
cnf(c401,plain,
multiply(multiply(X,inverse(X),X6),X4,multiply(multiply(X,inverse(X),X6),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X5)))),inverse(X5))) = multiply(multiply(X,inverse(X),X6),X4,X6),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
multiply(X,inverse(X),X2) = X2,
inference(substitution,[status(thm)],[c209]) ).
cnf(c403,plain,
multiply(multiply(X,inverse(X),X3),X2,X3) = multiply(X3,X2,X3),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
multiply(X2,X,X2) = multiply(X2,X2,X),
inference(substitution,[status(thm)],[c331]) ).
cnf(c405,plain,
multiply(multiply(X,inverse(X),X3),X2,X3) = multiply(X3,X3,X2),
inference(transitivity,[status(thm)],[c403,c404]) ).
cnf(c406,plain,
multiply(multiply(X,inverse(X),X6),X4,multiply(multiply(X,inverse(X),X6),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X5)))),inverse(X5))) = multiply(X6,X6,X4),
inference(transitivity,[status(thm)],[c401,c405]) ).
cnf(c407,plain,
multiply(multiply(X,inverse(X),X6),inverse(X5),multiply(X5,X4,inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),inverse(X5)))))) = multiply(X6,X6,X4),
inference(transitivity,[status(thm)],[c399,c406]) ).
cnf(c408,plain,
multiply(X5,inverse(X4),multiply(X4,X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),inverse(X4)))))) = multiply(X5,X5,X3),
inference(transitivity,[status(thm)],[c350,c407]) ).
cnf(c409,plain,
multiply(X4,inverse(X3),multiply(X3,X2,inverse(multiply(X,inverse(X),inverse(X3))))) = multiply(X4,X4,X2),
inference(transitivity,[status(thm)],[c347,c408]) ).
cnf(c410,plain,
multiply(X3,inverse(X2),multiply(X2,X,inverse(inverse(X2)))) = multiply(X3,X3,X),
inference(transitivity,[status(thm)],[c342,c409]) ).
cnf(c411,plain,
multiply(X3,inverse(X2),multiply(X2,X,X2)) = multiply(X3,X3,X),
inference(transitivity,[status(thm)],[c337,c410]) ).
cnf(c412,plain,
multiply(X3,inverse(X2),multiply(X2,X2,X)) = multiply(X3,X3,X),
inference(transitivity,[status(thm)],[c334,c411]) ).
cnf(c413,plain,
multiply(X2,inverse(X),multiply(X,X,X3)) = multiply(X2,X2,X3),
inference(substitution,[status(thm)],[c412]) ).
cnf(c414,plain,
multiply(X2,X,X) = multiply(X,X,X2),
inference(substitution,[status(thm)],[c239]) ).
cnf(c415,plain,
multiply(X,X,X2) = multiply(X2,X,X),
inference(symmetry,[status(thm)],[c414]) ).
cnf(c416,plain,
multiply(X2,inverse(X),multiply(X,X,X3)) = multiply(X3,X2,X2),
inference(transitivity,[status(thm)],[c413,c415]) ).
cnf(c417,plain,
multiply(X3,X2,X2) = multiply(X2,inverse(X),multiply(X,X,X3)),
inference(symmetry,[status(thm)],[c416]) ).
cnf(c418,plain,
multiply(multiply(X3,X3,X2),inverse(X),X) = multiply(X3,X3,X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c419,plain,
multiply(X3,X3,X2) = multiply(multiply(X3,X3,X2),inverse(X),X),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(X2),X2),inverse(X),X) = multiply(multiply(X4,X4,X3),inverse(X2),X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c421,plain,
multiply(multiply(X4,X4,X3),inverse(X2),X2) = multiply(multiply(multiply(X4,X4,X3),inverse(X2),X2),inverse(X),X),
inference(symmetry,[status(thm)],[c420]) ).
cnf(c422,plain,
multiply(X,X,inverse(X)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c423,plain,
X = multiply(X,X,inverse(X)),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c424,plain,
inverse(X) = inverse(multiply(X,X,inverse(X))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
multiply(multiply(X3,X3,X2),inverse(X),X) = multiply(multiply(X3,X3,X2),inverse(multiply(X,X,inverse(X))),X),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(X2),X2),inverse(X),X) = multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(X),X),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
multiply(X,X,inverse(X)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c428,plain,
X = multiply(X,X,inverse(X)),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
inverse(X) = inverse(multiply(X,X,inverse(X))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(X),X) = multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,X,inverse(X))),X),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
multiply(X3,inverse(X2),multiply(X2,X,X3)) = multiply(X3,X,multiply(X3,X3,inverse(X2))),
inference(substitution,[status(thm)],[c398]) ).
cnf(c432,plain,
multiply(X2,inverse(X),multiply(X,X,inverse(X))) = multiply(X2,X2,inverse(X)),
inference(substitution,[status(thm)],[c412]) ).
cnf(c433,plain,
multiply(X2,X2,inverse(X)) = multiply(X2,inverse(X),multiply(X,X,inverse(X))),
inference(symmetry,[status(thm)],[c432]) ).
cnf(c434,plain,
multiply(X3,X,multiply(X3,X3,inverse(X2))) = multiply(X3,X,multiply(X3,inverse(X2),multiply(X2,X2,inverse(X2)))),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
multiply(X,X,inverse(X)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c436,plain,
multiply(X2,inverse(X),multiply(X,X,inverse(X))) = multiply(X2,inverse(X),X),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
multiply(X3,X,multiply(X3,inverse(X2),multiply(X2,X2,inverse(X2)))) = multiply(X3,X,multiply(X3,inverse(X2),X2)),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
multiply(X3,X,multiply(X3,inverse(X2),X2)) = multiply(X3,X,X3),
inference(congruence,[status(thm)],[c186]) ).
cnf(c439,plain,
multiply(X2,X,X2) = multiply(X2,X2,X),
inference(substitution,[status(thm)],[c331]) ).
cnf(c440,plain,
multiply(X3,X,multiply(X3,inverse(X2),X2)) = multiply(X3,X3,X),
inference(transitivity,[status(thm)],[c438,c439]) ).
cnf(c441,plain,
multiply(X3,X,multiply(X3,inverse(X2),multiply(X2,X2,inverse(X2)))) = multiply(X3,X3,X),
inference(transitivity,[status(thm)],[c437,c440]) ).
cnf(c442,plain,
multiply(X3,X,multiply(X3,X3,inverse(X2))) = multiply(X3,X3,X),
inference(transitivity,[status(thm)],[c434,c441]) ).
cnf(c443,plain,
multiply(X3,inverse(X2),multiply(X2,X,X3)) = multiply(X3,X3,X),
inference(transitivity,[status(thm)],[c431,c442]) ).
cnf(c444,plain,
multiply(X,inverse(X),multiply(X,inverse(X),X)) = multiply(X,X,inverse(X)),
inference(substitution,[status(thm)],[c443]) ).
cnf(c445,plain,
multiply(X,X,inverse(X)) = multiply(X,inverse(X),multiply(X,inverse(X),X)),
inference(symmetry,[status(thm)],[c444]) ).
cnf(c446,plain,
inverse(multiply(X,X,inverse(X))) = inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
multiply(multiply(X3,X3,X2),inverse(multiply(X,X,inverse(X))),X) = multiply(multiply(X3,X3,X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,X,inverse(X))),X),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
multiply(X,inverse(X),multiply(X,inverse(X),X)) = multiply(X,X,inverse(X)),
inference(substitution,[status(thm)],[c443]) ).
cnf(c450,plain,
multiply(X,X,inverse(X)) = multiply(X,inverse(X),multiply(X,inverse(X),X)),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c451,plain,
inverse(multiply(X,X,inverse(X))) = inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
multiply(inverse(X3),multiply(X7,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X7)))),multiply(X7,X7,X6)),X3) = multiply(multiply(multiply(X7,X7,X6),inverse(multiply(X5,inverse(X5),multiply(X5,inverse(X5),X5))),X5),inverse(multiply(X4,inverse(X4),multiply(X4,inverse(X4),X4))),X4),
inference(substitution,[status(thm)],[c149]) ).
cnf(c454,plain,
multiply(multiply(multiply(X7,X7,X6),inverse(multiply(X5,inverse(X5),multiply(X5,inverse(X5),X5))),X5),inverse(multiply(X4,inverse(X4),multiply(X4,inverse(X4),X4))),X4) = multiply(inverse(X3),multiply(X7,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X7)))),multiply(X7,X7,X6)),X3),
inference(symmetry,[status(thm)],[c453]) ).
cnf(c455,plain,
multiply(X4,multiply(X2,X,inverse(X4)),X3) = multiply(X4,X3,multiply(X2,X,inverse(X4))),
inference(substitution,[status(thm)],[c331]) ).
cnf(c456,plain,
multiply(X4,X3,multiply(X2,X,inverse(X4))) = multiply(X4,multiply(X2,X,inverse(X4)),X3),
inference(symmetry,[status(thm)],[c455]) ).
cnf(c457,plain,
multiply(multiply(multiply(multiply(X9,X10,inverse(X10)),X7,multiply(X9,X10,X8)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X10,multiply(X8,X7,inverse(X10)),X9),
inference(substitution,[status(thm)],[c60]) ).
cnf(c458,plain,
multiply(X10,multiply(X8,X7,inverse(X10)),X9) = multiply(multiply(multiply(multiply(X9,X10,inverse(X10)),X7,multiply(X9,X10,X8)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(symmetry,[status(thm)],[c457]) ).
cnf(c459,plain,
multiply(X,X2,inverse(X2)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c460,plain,
multiply(multiply(X3,X4,inverse(X4)),X,multiply(X3,X4,X2)) = multiply(X3,X,multiply(X3,X4,X2)),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
multiply(multiply(multiply(X6,X7,inverse(X7)),X4,multiply(X6,X7,X5)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(X6,X4,multiply(X6,X7,X5)),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
multiply(multiply(multiply(multiply(X9,X10,inverse(X10)),X7,multiply(X9,X10,X8)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(multiply(multiply(X9,X7,multiply(X9,X10,X8)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(congruence,[status(thm)],[c461]) ).
cnf(c463,plain,
multiply(inverse(X4),multiply(X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),multiply(X13,X11,multiply(X13,X14,X12))),X4) = multiply(multiply(multiply(X13,X11,multiply(X13,X14,X12)),inverse(multiply(multiply(X10,inverse(X10),X9),inverse(multiply(X10,inverse(X10),X9)),multiply(X10,inverse(X10),X8))),X8),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5),
inference(substitution,[status(thm)],[c149]) ).
cnf(c464,plain,
multiply(multiply(multiply(X13,X11,multiply(X13,X14,X12)),inverse(multiply(multiply(X10,inverse(X10),X9),inverse(multiply(X10,inverse(X10),X9)),multiply(X10,inverse(X10),X8))),X8),inverse(multiply(multiply(X7,inverse(X7),X6),inverse(multiply(X7,inverse(X7),X6)),multiply(X7,inverse(X7),X5))),X5) = multiply(inverse(X4),multiply(X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),multiply(X13,X11,multiply(X13,X14,X12))),X4),
inference(symmetry,[status(thm)],[c463]) ).
cnf(c465,plain,
multiply(inverse(X6),multiply(X5,inverse(multiply(multiply(X4,inverse(X4),X3),inverse(multiply(X4,inverse(X4),X3)),multiply(X4,inverse(X4),multiply(X6,inverse(X6),X5)))),multiply(X9,X7,multiply(X9,X10,X8))),X6) = multiply(multiply(multiply(X9,X7,multiply(X9,X10,X8)),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X),
inference(substitution,[status(thm)],[c149]) ).
cnf(c466,plain,
multiply(X,inverse(X),multiply(X,inverse(X),X)) = multiply(X,X,inverse(X)),
inference(substitution,[status(thm)],[c443]) ).
cnf(c467,plain,
inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))) = inverse(multiply(X,X,inverse(X))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
multiply(multiply(X4,X2,multiply(X4,X5,X3)),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = multiply(multiply(X4,X2,multiply(X4,X5,X3)),inverse(multiply(X,X,inverse(X))),X),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
multiply(X,inverse(X),multiply(X,inverse(X),X)) = multiply(X,X,inverse(X)),
inference(substitution,[status(thm)],[c443]) ).
cnf(c471,plain,
inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))) = inverse(multiply(X,X,inverse(X))),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,X,inverse(X))),X),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
multiply(X,X,inverse(X)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c474,plain,
inverse(multiply(X,X,inverse(X))) = inverse(X),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
multiply(multiply(X4,X2,multiply(X4,X5,X3)),inverse(multiply(X,X,inverse(X))),X) = multiply(multiply(X4,X2,multiply(X4,X5,X3)),inverse(X),X),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(X2),X2),inverse(multiply(X,X,inverse(X))),X),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
multiply(X,X,inverse(X)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c478,plain,
inverse(multiply(X,X,inverse(X))) = inverse(X),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(X2),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(X2),X2),inverse(X),X),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(X2),X2),inverse(X),X) = multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(X2),X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c481,plain,
multiply(multiply(X4,X2,multiply(X4,X5,X3)),inverse(X),X) = multiply(X4,X2,multiply(X4,X5,X3)),
inference(substitution,[status(thm)],[c186]) ).
cnf(c482,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(X2),X2),inverse(X),X) = multiply(X5,X3,multiply(X5,X6,X4)),
inference(transitivity,[status(thm)],[c480,c481]) ).
cnf(c483,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(X2),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(X5,X3,multiply(X5,X6,X4)),
inference(transitivity,[status(thm)],[c479,c482]) ).
cnf(c484,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(X5,X3,multiply(X5,X6,X4)),
inference(transitivity,[status(thm)],[c476,c483]) ).
cnf(c485,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = multiply(X5,X3,multiply(X5,X6,X4)),
inference(transitivity,[status(thm)],[c472,c484]) ).
cnf(c486,plain,
multiply(multiply(multiply(X5,X3,multiply(X5,X6,X4)),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = multiply(X5,X3,multiply(X5,X6,X4)),
inference(transitivity,[status(thm)],[c469,c485]) ).
cnf(c487,plain,
multiply(inverse(X4),multiply(X3,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X4,inverse(X4),X3)))),multiply(X7,X5,multiply(X7,X8,X6))),X4) = multiply(X7,X5,multiply(X7,X8,X6)),
inference(transitivity,[status(thm)],[c465,c486]) ).
cnf(c488,plain,
multiply(multiply(multiply(X9,X7,multiply(X9,X10,X8)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X9,X7,multiply(X9,X10,X8)),
inference(transitivity,[status(thm)],[c464,c487]) ).
cnf(c489,plain,
multiply(multiply(multiply(multiply(X9,X10,inverse(X10)),X7,multiply(X9,X10,X8)),inverse(multiply(multiply(X6,inverse(X6),X5),inverse(multiply(X6,inverse(X6),X5)),multiply(X6,inverse(X6),X4))),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X9,X7,multiply(X9,X10,X8)),
inference(transitivity,[status(thm)],[c462,c488]) ).
cnf(c490,plain,
multiply(X4,multiply(X2,X,inverse(X4)),X3) = multiply(X3,X,multiply(X3,X4,X2)),
inference(transitivity,[status(thm)],[c458,c489]) ).
cnf(c491,plain,
multiply(X4,X3,multiply(X2,X,inverse(X4))) = multiply(X3,X,multiply(X3,X4,X2)),
inference(transitivity,[status(thm)],[c456,c490]) ).
cnf(c492,plain,
multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))) = multiply(X5,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),multiply(X5,X5,X4)),
inference(substitution,[status(thm)],[c491]) ).
cnf(c493,plain,
multiply(X5,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),multiply(X5,X5,X4)) = multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))),
inference(symmetry,[status(thm)],[c492]) ).
cnf(c494,plain,
multiply(inverse(X3),multiply(X5,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),multiply(X5,X5,X4)),X3) = multiply(inverse(X3),multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))),X3),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
multiply(inverse(X3),multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))),X3) = multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))),
inference(substitution,[status(thm)],[c164]) ).
cnf(c496,plain,
multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))) = multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c497,plain,
inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4)))) = inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),
inference(congruence,[status(thm)],[c496]) ).
cnf(c498,plain,
multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5)) = multiply(X4,inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5))),inverse(X5)),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))) = multiply(X5,X5,multiply(X4,inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5))),inverse(X5))),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
multiply(X,inverse(X),multiply(X2,inverse(X2),X3)) = multiply(X2,inverse(X2),X3),
inference(substitution,[status(thm)],[c209]) ).
cnf(c501,plain,
inverse(multiply(X,inverse(X),multiply(X2,inverse(X2),X3))) = inverse(multiply(X2,inverse(X2),X3)),
inference(congruence,[status(thm)],[c500]) ).
cnf(c502,plain,
multiply(X3,inverse(multiply(X,inverse(X),multiply(X2,inverse(X2),X4))),inverse(X4)) = multiply(X3,inverse(multiply(X2,inverse(X2),X4)),inverse(X4)),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
multiply(X4,X4,multiply(X3,inverse(multiply(X,inverse(X),multiply(X2,inverse(X2),X4))),inverse(X4))) = multiply(X4,X4,multiply(X3,inverse(multiply(X2,inverse(X2),X4)),inverse(X4))),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
inverse(multiply(X,inverse(X),X2)) = inverse(X2),
inference(substitution,[status(thm)],[c174]) ).
cnf(c505,plain,
multiply(X2,inverse(multiply(X,inverse(X),X3)),inverse(X3)) = multiply(X2,inverse(X3),inverse(X3)),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
multiply(X3,X3,multiply(X2,inverse(multiply(X,inverse(X),X3)),inverse(X3))) = multiply(X3,X3,multiply(X2,inverse(X3),inverse(X3))),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
multiply(inverse(X2),X3,multiply(X2,X,inverse(X3))) = multiply(X3,inverse(X2),multiply(X2,X,inverse(X3))),
inference(substitution,[status(thm)],[c356]) ).
cnf(c508,plain,
multiply(X3,inverse(X2),multiply(X2,X,inverse(X3))) = multiply(inverse(X2),X3,multiply(X2,X,inverse(X3))),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
multiply(X,X2,inverse(X3)) = multiply(X2,X,inverse(X3)),
inference(substitution,[status(thm)],[c356]) ).
cnf(c510,plain,
multiply(X2,X,inverse(X3)) = multiply(X,X2,inverse(X3)),
inference(symmetry,[status(thm)],[c509]) ).
cnf(c511,plain,
multiply(inverse(X2),X3,multiply(X2,X,inverse(X3))) = multiply(inverse(X2),X3,multiply(X,X2,inverse(X3))),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
multiply(X,inverse(X3),X2) = multiply(X,X2,inverse(X3)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c513,plain,
multiply(X,X2,inverse(X3)) = multiply(X,inverse(X3),X2),
inference(symmetry,[status(thm)],[c512]) ).
cnf(c514,plain,
multiply(inverse(X2),X3,multiply(X,X2,inverse(X3))) = multiply(inverse(X2),X3,multiply(X,inverse(X3),X2)),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
multiply(inverse(X2),multiply(X,inverse(X3),X2),X3) = multiply(inverse(X2),X3,multiply(X,inverse(X3),X2)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c516,plain,
multiply(inverse(X2),X3,multiply(X,inverse(X3),X2)) = multiply(inverse(X2),multiply(X,inverse(X3),X2),X3),
inference(symmetry,[status(thm)],[c515]) ).
cnf(c517,plain,
X2 = multiply(X2,inverse(X),X),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c518,plain,
inverse(X2) = inverse(multiply(X2,inverse(X),X)),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
multiply(X,inverse(X3),X2) = multiply(X,inverse(multiply(X3,inverse(X2),X2)),X2),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
multiply(inverse(X2),multiply(X,inverse(X3),X2),X3) = multiply(inverse(X2),multiply(X,inverse(multiply(X3,inverse(X2),X2)),X2),X3),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
multiply(multiply(X8,inverse(X7),X6),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(inverse(X7),multiply(X6,inverse(multiply(X8,inverse(X7),X7)),X7),X8),
inference(substitution,[status(thm)],[c45]) ).
cnf(c522,plain,
multiply(inverse(X7),multiply(X6,inverse(multiply(X8,inverse(X7),X7)),X7),X8) = multiply(multiply(X8,inverse(X7),X6),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)),
inference(symmetry,[status(thm)],[c521]) ).
cnf(c523,plain,
multiply(multiply(X11,inverse(X10),X9),inverse(multiply(multiply(X8,X7,X6),X5,multiply(X8,X7,X4))),multiply(X7,multiply(X4,X5,X6),X8)) = multiply(multiply(X11,inverse(X10),X9),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X),
inference(substitution,[status(thm)],[c52]) ).
cnf(c524,plain,
multiply(multiply(X7,inverse(X6),X5),inverse(multiply(multiply(X4,inverse(X4),X3),inverse(multiply(X4,inverse(X4),X3)),multiply(X4,inverse(X4),X2))),X2) = multiply(multiply(X7,inverse(X6),X5),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X),
inference(substitution,[status(thm)],[c107]) ).
cnf(c525,plain,
multiply(X,inverse(X),multiply(X,inverse(X),X)) = multiply(X,X,inverse(X)),
inference(substitution,[status(thm)],[c443]) ).
cnf(c526,plain,
inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))) = inverse(multiply(X,X,inverse(X))),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
multiply(multiply(X4,inverse(X3),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = multiply(multiply(X4,inverse(X3),X2),inverse(multiply(X,X,inverse(X))),X),
inference(congruence,[status(thm)],[c526]) ).
cnf(c528,plain,
multiply(X,X,inverse(X)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c529,plain,
inverse(multiply(X,X,inverse(X))) = inverse(X),
inference(congruence,[status(thm)],[c528]) ).
cnf(c530,plain,
multiply(multiply(X4,inverse(X3),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(multiply(X4,inverse(X3),X2),inverse(X),X),
inference(congruence,[status(thm)],[c529]) ).
cnf(c531,plain,
multiply(multiply(X4,inverse(X3),X2),inverse(X),X) = multiply(X4,inverse(X3),X2),
inference(substitution,[status(thm)],[c186]) ).
cnf(c532,plain,
multiply(X3,inverse(X2),X) = multiply(X3,X,inverse(X2)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c533,plain,
multiply(multiply(X4,inverse(X3),X2),inverse(X),X) = multiply(X4,X2,inverse(X3)),
inference(transitivity,[status(thm)],[c531,c532]) ).
cnf(c534,plain,
multiply(multiply(X4,inverse(X3),X2),inverse(multiply(X,X,inverse(X))),X) = multiply(X4,X2,inverse(X3)),
inference(transitivity,[status(thm)],[c530,c533]) ).
cnf(c535,plain,
multiply(multiply(X4,inverse(X3),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = multiply(X4,X2,inverse(X3)),
inference(transitivity,[status(thm)],[c527,c534]) ).
cnf(c536,plain,
multiply(multiply(X6,inverse(X5),X4),inverse(multiply(multiply(X3,inverse(X3),X2),inverse(multiply(X3,inverse(X3),X2)),multiply(X3,inverse(X3),X))),X) = multiply(X6,X4,inverse(X5)),
inference(transitivity,[status(thm)],[c524,c535]) ).
cnf(c537,plain,
multiply(multiply(X8,inverse(X7),X6),inverse(multiply(multiply(X5,X4,X3),X2,multiply(X5,X4,X))),multiply(X4,multiply(X,X2,X3),X5)) = multiply(X8,X6,inverse(X7)),
inference(transitivity,[status(thm)],[c523,c536]) ).
cnf(c538,plain,
multiply(inverse(X2),multiply(X,inverse(multiply(X3,inverse(X2),X2)),X2),X3) = multiply(X3,X,inverse(X2)),
inference(transitivity,[status(thm)],[c522,c537]) ).
cnf(c539,plain,
multiply(inverse(X2),multiply(X,inverse(X3),X2),X3) = multiply(X3,X,inverse(X2)),
inference(transitivity,[status(thm)],[c520,c538]) ).
cnf(c540,plain,
multiply(inverse(X2),X3,multiply(X,inverse(X3),X2)) = multiply(X3,X,inverse(X2)),
inference(transitivity,[status(thm)],[c516,c539]) ).
cnf(c541,plain,
multiply(inverse(X2),X3,multiply(X,X2,inverse(X3))) = multiply(X3,X,inverse(X2)),
inference(transitivity,[status(thm)],[c514,c540]) ).
cnf(c542,plain,
multiply(inverse(X2),X3,multiply(X2,X,inverse(X3))) = multiply(X3,X,inverse(X2)),
inference(transitivity,[status(thm)],[c511,c541]) ).
cnf(c543,plain,
multiply(X3,inverse(X2),multiply(X2,X,inverse(X3))) = multiply(X3,X,inverse(X2)),
inference(transitivity,[status(thm)],[c508,c542]) ).
cnf(c544,plain,
multiply(X2,inverse(X),multiply(X,inverse(X),inverse(X2))) = multiply(X2,inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c543]) ).
cnf(c545,plain,
multiply(X2,inverse(X),inverse(X)) = multiply(X2,inverse(X),multiply(X,inverse(X),inverse(X2))),
inference(symmetry,[status(thm)],[c544]) ).
cnf(c546,plain,
multiply(X,inverse(X),inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c209]) ).
cnf(c547,plain,
multiply(X2,inverse(X),multiply(X,inverse(X),inverse(X2))) = multiply(X2,inverse(X),inverse(X2)),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
X2 = multiply(X2,inverse(X),X),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c549,plain,
multiply(X3,X2,inverse(X3)) = multiply(X3,multiply(X2,inverse(X),X),inverse(X3)),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
inverse(multiply(inverse(X2),inverse(inverse(X2)),X)) = inverse(X),
inference(substitution,[status(thm)],[c174]) ).
cnf(c551,plain,
inverse(X) = inverse(multiply(inverse(X2),inverse(inverse(X2)),X)),
inference(symmetry,[status(thm)],[c550]) ).
cnf(c552,plain,
multiply(X2,inverse(X),X) = multiply(X2,inverse(multiply(inverse(X3),inverse(inverse(X3)),X)),X),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
multiply(X3,multiply(X2,inverse(X),X),inverse(X3)) = multiply(X3,multiply(X2,inverse(multiply(inverse(X3),inverse(inverse(X3)),X)),X),inverse(X3)),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c555,plain,
multiply(X3,multiply(X2,inverse(multiply(inverse(X3),inverse(inverse(X3)),X)),X),inverse(X3)) = multiply(inverse(inverse(X3)),multiply(X2,inverse(multiply(inverse(X3),inverse(inverse(X3)),X)),X),inverse(X3)),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
multiply(inverse(inverse(X3)),multiply(X2,inverse(multiply(inverse(X3),inverse(inverse(X3)),X)),X),inverse(X3)) = X2,
inference(substitution,[status(thm)],[c49]) ).
cnf(c557,plain,
multiply(X3,multiply(X2,inverse(multiply(inverse(X3),inverse(inverse(X3)),X)),X),inverse(X3)) = X2,
inference(transitivity,[status(thm)],[c555,c556]) ).
cnf(c558,plain,
multiply(X3,multiply(X2,inverse(X),X),inverse(X3)) = X2,
inference(transitivity,[status(thm)],[c553,c557]) ).
cnf(c559,plain,
multiply(X2,X,inverse(X2)) = X,
inference(transitivity,[status(thm)],[c549,c558]) ).
cnf(c560,plain,
multiply(X2,inverse(X),inverse(X2)) = inverse(X),
inference(substitution,[status(thm)],[c559]) ).
cnf(c561,plain,
multiply(X2,inverse(X),multiply(X,inverse(X),inverse(X2))) = inverse(X),
inference(transitivity,[status(thm)],[c547,c560]) ).
cnf(c562,plain,
multiply(X2,inverse(X),inverse(X)) = inverse(X),
inference(transitivity,[status(thm)],[c545,c561]) ).
cnf(c563,plain,
multiply(X,inverse(X2),inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c562]) ).
cnf(c564,plain,
multiply(X2,X2,multiply(X,inverse(X2),inverse(X2))) = multiply(X2,X2,inverse(X2)),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
multiply(X,X,inverse(X)) = X,
inference(substitution,[status(thm)],[c312]) ).
cnf(c566,plain,
multiply(X2,X2,multiply(X,inverse(X2),inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c564,c565]) ).
cnf(c567,plain,
multiply(X3,X3,multiply(X2,inverse(multiply(X,inverse(X),X3)),inverse(X3))) = X3,
inference(transitivity,[status(thm)],[c506,c566]) ).
cnf(c568,plain,
multiply(X4,X4,multiply(X3,inverse(multiply(X,inverse(X),multiply(X2,inverse(X2),X4))),inverse(X4))) = X4,
inference(transitivity,[status(thm)],[c503,c567]) ).
cnf(c569,plain,
multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))) = X5,
inference(transitivity,[status(thm)],[c499,c568]) ).
cnf(c570,plain,
multiply(inverse(X3),multiply(X5,X5,multiply(X4,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),inverse(X5))),X3) = X5,
inference(transitivity,[status(thm)],[c495,c569]) ).
cnf(c571,plain,
multiply(inverse(X3),multiply(X5,inverse(multiply(multiply(X2,inverse(X2),X),inverse(multiply(X2,inverse(X2),X)),multiply(X2,inverse(X2),multiply(X3,inverse(X3),X5)))),multiply(X5,X5,X4)),X3) = X5,
inference(transitivity,[status(thm)],[c494,c570]) ).
cnf(c572,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,inverse(X),multiply(X,inverse(X),X))),X) = X4,
inference(transitivity,[status(thm)],[c454,c571]) ).
cnf(c573,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,inverse(X2),multiply(X2,inverse(X2),X2))),X2),inverse(multiply(X,X,inverse(X))),X) = X4,
inference(transitivity,[status(thm)],[c452,c572]) ).
cnf(c574,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(multiply(X,X,inverse(X))),X) = X4,
inference(transitivity,[status(thm)],[c448,c573]) ).
cnf(c575,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(multiply(X2,X2,inverse(X2))),X2),inverse(X),X) = X4,
inference(transitivity,[status(thm)],[c430,c574]) ).
cnf(c576,plain,
multiply(multiply(multiply(X4,X4,X3),inverse(X2),X2),inverse(X),X) = X4,
inference(transitivity,[status(thm)],[c426,c575]) ).
cnf(c577,plain,
multiply(multiply(X3,X3,X2),inverse(X),X) = X3,
inference(transitivity,[status(thm)],[c421,c576]) ).
cnf(c578,plain,
multiply(X2,X2,X) = X2,
inference(transitivity,[status(thm)],[c419,c577]) ).
cnf(c579,plain,
multiply(X,X,X2) = X,
inference(substitution,[status(thm)],[c578]) ).
cnf(c580,plain,
multiply(X2,inverse(X),multiply(X,X,X3)) = multiply(X2,inverse(X),X),
inference(congruence,[status(thm)],[c579]) ).
cnf(c581,plain,
multiply(X2,inverse(X),multiply(X,X,X3)) = X2,
inference(transitivity,[status(thm)],[c580,c186]) ).
cnf(c582,plain,
multiply(X2,X,X) = X,
inference(transitivity,[status(thm)],[c417,c581]) ).
cnf(c583,plain,
multiply(b,a,a) = a,
inference(substitution,[status(thm)],[c582]) ).
cnf(c584,plain,
$false,
inference(resolution,[status(thm)],[c1,c583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO068-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:10:45 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.23/0.90 Command-line arguments: --no-flatten-goal
% 5.23/0.90
% 5.23/0.90 % SZS status Unsatisfiable
% 5.23/0.90
% 5.23/1.01 % SZS output start CNFRefutation
% See solution above
% 10.76/1.60
% 10.76/1.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------