%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT078-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 11:43:07 AM UTC 2026
% Result : Unsatisfiable 187.23s 27.27s
% Output : CNFRefutation 203.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 167
% Number of leaves : 2
% Syntax : Number of clauses : 1116 (1116 unt; 0 nHn; 14 RR)
% Number of literals : 1116 (1115 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 3967 ( 226 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(a,f(f(b,c),f(b,c))) != f(c,f(f(b,a),f(b,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c2,axiom,
f(f(f(f(B,A),f(A,C)),D),f(A,f(f(f(B,f(B,f(f(C,C),A))),A),C))) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mol_27B2) ).
cnf(c3,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
f(X3,X4) = f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),X4),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
f(X5,f(X4,X3)) = f(X5,f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,f(f(f(X2,f(X2,f(f(X,X),X4))),X4),X))),X3)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
f(f(X3,f(X5,X4)),f(f(X3,f(X5,X4)),f(f(X6,X6),X5))) = f(f(X3,f(f(f(f(f(X2,X5),f(X5,X)),X5),f(X5,f(f(f(X2,f(X2,f(f(X,X),X5))),X5),X))),X4)),f(f(X3,f(X5,X4)),f(f(X6,X6),X5))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
f(f(f(X4,f(X6,X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6) = f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
f(f(f(f(X4,f(X6,X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3) = f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
f(X6,f(f(f(f(X4,f(X6,X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3)) = f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
f(f(X6,X5),f(X6,f(f(f(f(X4,f(X6,X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3))) = f(f(X6,X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
f(X4,X3) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,f(f(f(X2,f(X2,f(f(X,X),X4))),X4),X))),X3),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
f(X3,f(X5,X4)) = f(X3,f(f(f(f(f(X2,X5),f(X5,X)),X5),f(X5,f(f(f(X2,f(X2,f(f(X,X),X5))),X5),X))),X4)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
f(f(X4,f(X6,X5)),f(f(X3,X3),X6)) = f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))) = f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6) = f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3) = f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),X3),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3)) = f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),X3)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
f(f(X6,X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3))) = f(f(X6,X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),X3))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
f(X4,X3) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,f(f(f(X2,f(X2,f(f(X,X),X4))),X4),X))),X3),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
f(f(X6,X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),X3))) = f(f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),X3))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
f(f(X,X),X4) = f(f(X,X),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(f(X5,f(X5,f(f(X3,X3),X4))),X4),X3)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),X5)) = f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4))))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),X5))) = f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),X5))),X5) = f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),X5))),X5),X) = f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),X),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),X5))),X5),X)) = f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),X)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),X5))),X5),X))) = f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),X))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5) = f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),X) = f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),X)) = f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),X))) = f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c42,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X)) = f(f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4))),f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X))) = f(f(f(f(X6,X5),f(X5,X4)),X3),f(f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4))),f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
X4 = f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
f(X4,f(f(X4,X3),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))) = f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),f(f(X4,X3),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),f(f(X4,X3),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))) = f(X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
f(X4,f(f(X4,X3),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))) = f(X4,X3),
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4))),f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X))) = f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4))),f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X))) = X5,
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))),X))) = X5,
inference(transitivity,[status(thm)],[c44,c52]) ).
cnf(c54,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(X6,f(X6,f(f(X4,X4),X5))),X5),X4)))))),X5),X))) = X5,
inference(transitivity,[status(thm)],[c40,c53]) ).
cnf(c55,plain,
f(f(f(f(X6,X5),f(X5,X4)),X3),f(X5,f(f(f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X2,f(f(f(X6,X5),f(X5,X4)),X3)),f(f(X,X),X5))),X5),X))) = X5,
inference(transitivity,[status(thm)],[c34,c54]) ).
cnf(c56,plain,
f(f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),X3))) = X6,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
f(f(X6,X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,X3),X6))),X6),X3))) = X6,
inference(transitivity,[status(thm)],[c25,c56]) ).
cnf(c58,plain,
f(f(X6,X5),f(X6,f(f(f(f(X4,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,f(X6,X5)),f(f(X3,X3),X6))),X6),X3))) = X6,
inference(transitivity,[status(thm)],[c21,c57]) ).
cnf(c59,plain,
f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X))) = X4,
inference(transitivity,[status(thm)],[c11,c58]) ).
cnf(c60,plain,
f(f(f(X5,X4),f(X4,X3)),f(f(X5,X4),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X5,X4)))),f(X5,X4)),X))) = f(X5,X4),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
f(X5,X4) = f(f(f(X5,X4),f(X4,X3)),f(f(X5,X4),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X5,X4)))),f(X5,X4)),X))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
f(f(X5,X4),f(X4,f(f(f(X5,f(X5,f(f(X3,X3),X4))),X4),X3))) = f(f(f(f(X5,X4),f(X4,X3)),f(f(X5,X4),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X5,X4)))),f(X5,X4)),X))),f(X4,f(f(f(X5,f(X5,f(f(X3,X3),X4))),X4),X3))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
f(f(f(f(X5,X4),f(X4,X3)),f(f(X5,X4),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X5,X4)))),f(X5,X4)),X))),f(X4,f(f(f(X5,f(X5,f(f(X3,X3),X4))),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))) = X2,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
f(f(X2,X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
X3 = f(f(X2,X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
f(X2,X4) = f(X2,f(f(X3,X4),f(X4,f(f(f(X3,f(X3,f(f(X,X),X4))),X4),X)))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
f(f(X3,X5),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))) = f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
f(f(f(X3,X5),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)) = f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
f(f(f(f(X3,X5),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2) = f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
f(f(X4,X5),f(f(f(f(X3,X5),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2)) = f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
f(X5,f(f(X4,X5),f(f(f(f(X3,X5),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))) = f(X5,f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
f(f(X2,X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c64]) ).
cnf(c74,plain,
X3 = f(f(X2,X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
f(X2,X4) = f(X2,f(f(X3,X4),f(X4,f(f(f(X3,f(X3,f(f(X,X),X4))),X4),X)))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
f(f(X3,X5),f(f(X2,X2),f(X4,X5))) = f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))) = f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)) = f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2) = f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2)) = f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
f(X5,f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))) = f(X5,f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
f(f(X2,X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c64]) ).
cnf(c83,plain,
X3 = f(f(X2,X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
f(X5,f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))) = f(f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X))),f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
f(f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X))),f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))) = f(X4,X5),
inference(substitution,[status(thm)],[c59]) ).
cnf(c86,plain,
f(X5,f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))) = f(X4,X5),
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
f(X5,f(f(X4,X5),f(f(f(f(X3,f(f(X4,X5),f(X5,f(f(f(X4,f(X4,f(f(X,X),X5))),X5),X)))),f(f(X3,X5),f(f(X2,X2),f(X4,X5)))),f(X4,X5)),X2))) = f(X4,X5),
inference(transitivity,[status(thm)],[c81,c86]) ).
cnf(c88,plain,
f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))) = f(X3,X4),
inference(transitivity,[status(thm)],[c72,c87]) ).
cnf(c89,plain,
f(X3,X4) = f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
f(f(X4,X4),f(X3,X4)) = f(f(X4,X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
f(f(f(X5,X4),f(X4,X3)),f(f(X6,f(f(X5,X4),f(X4,X3))),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X6,f(f(X5,X4),f(X4,X3)))))),f(X6,f(f(X5,X4),f(X4,X3)))),X))) = f(X6,f(f(X5,X4),f(X4,X3))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c92,plain,
f(X6,f(f(X5,X4),f(X4,X3))) = f(f(f(X5,X4),f(X4,X3)),f(f(X6,f(f(X5,X4),f(X4,X3))),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X6,f(f(X5,X4),f(X4,X3)))))),f(X6,f(f(X5,X4),f(X4,X3)))),X))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
f(f(X6,f(f(X5,X4),f(X4,X3))),f(X4,f(f(f(X5,f(X5,f(f(X3,X3),X4))),X4),X3))) = f(f(f(f(X5,X4),f(X4,X3)),f(f(X6,f(f(X5,X4),f(X4,X3))),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X6,f(f(X5,X4),f(X4,X3)))))),f(X6,f(f(X5,X4),f(X4,X3)))),X))),f(X4,f(f(f(X5,f(X5,f(f(X3,X3),X4))),X4),X3))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
f(f(f(f(X5,X4),f(X4,X3)),f(f(X6,f(f(X5,X4),f(X4,X3))),f(f(f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X2,f(f(X5,X4),f(X4,X3))),f(f(X,X),f(X6,f(f(X5,X4),f(X4,X3)))))),f(X6,f(f(X5,X4),f(X4,X3)))),X))),f(X4,f(f(f(X5,f(X5,f(f(X3,X3),X4))),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c95,plain,
f(f(X4,f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))) = X2,
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2)),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),f(f(X4,X3),f(X3,X2))))),f(f(X4,X3),f(X3,X2))),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))) = X3,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
X3 = f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2)),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),f(f(X4,X3),f(X3,X2))))),f(f(X4,X3),f(X3,X2))),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
f(f(f(X4,X3),f(X3,X2)),X3) = f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2)),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),f(f(X4,X3),f(X3,X2))))),f(f(X4,X3),f(X3,X2))),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2)))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),X3)) = f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2)),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),f(f(X4,X3),f(X3,X2))))),f(f(X4,X3),f(X3,X2))),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2)),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))),f(f(X4,X3),f(X3,X2))))),f(f(X4,X3),f(X3,X2))),f(X3,f(f(f(X4,f(X4,f(f(X2,X2),X3))),X3),X2))))) = f(f(X4,X3),f(X3,X2)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c101,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2)) = f(f(X3,X2),f(X2,X)),
inference(transitivity,[status(thm)],[c99,c100]) ).
cnf(c102,plain,
f(f(X3,X3),f(f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))),X3)) = f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))) = f(f(X3,X3),f(f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))),X3)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c59]) ).
cnf(c105,plain,
f(f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))),X3) = f(X3,X3),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
f(f(X3,X3),f(f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))),X3)) = f(f(X3,X3),f(X3,X3)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))) = f(f(X3,X3),f(X3,X3)),
inference(transitivity,[status(thm)],[c103,c106]) ).
cnf(c108,plain,
f(f(X3,X3),f(X3,X3)) = f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
f(f(X3,X3),f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X2,f(X3,X3)),f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c59]) ).
cnf(c110,plain,
f(f(X,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c108,c109]) ).
cnf(c111,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
f(X2,X) = f(f(f(X2,X2),f(X2,X2)),X),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
f(f(X2,X2),f(X2,X)) = f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
X2 = f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c115,plain,
f(X2,X2) = f(f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),X2),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
f(f(X3,X2),f(X2,X2)) = f(f(X3,X2),f(f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),X2)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),X2)) = f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c118,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),X2)) = X2,
inference(transitivity,[status(thm)],[c117,c64]) ).
cnf(c119,plain,
f(f(X2,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c116,c118]) ).
cnf(c120,plain,
f(f(f(f(X,f(X3,X2)),f(f(X,f(X3,X2)),f(f(f(X3,X3),f(X3,X3)),X3))),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
X3 = f(f(f(f(X,f(X3,X2)),f(f(X,f(X3,X2)),f(f(f(X3,X3),f(X3,X3)),X3))),X3),f(X3,X3)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
f(X3,X3) = f(X3,f(f(f(f(X,f(X3,X2)),f(f(X,f(X3,X2)),f(f(f(X3,X3),f(X3,X3)),X3))),X3),f(X3,X3))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
f(f(X3,X2),f(X3,X3)) = f(f(X3,X2),f(X3,f(f(f(f(X,f(X3,X2)),f(f(X,f(X3,X2)),f(f(f(X3,X3),f(X3,X3)),X3))),X3),f(X3,X3)))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
f(f(X3,X2),f(X3,f(f(f(f(X,f(X3,X2)),f(f(X,f(X3,X2)),f(f(f(X3,X3),f(X3,X3)),X3))),X3),f(X3,X3)))) = X3,
inference(substitution,[status(thm)],[c59]) ).
cnf(c125,plain,
f(f(X2,X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
X2 = f(f(X2,X),f(X2,X2)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
f(X3,f(f(X3,X3),X2)) = f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
f(f(f(X3,X),f(X3,X3)),f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3))) = f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),
inference(substitution,[status(thm)],[c101]) ).
cnf(c129,plain,
f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)) = f(f(f(X3,X),f(X3,X3)),f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3))),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
f(f(f(X3,X),f(X3,X3)),f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3))) = f(X3,f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c131,plain,
f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)) = f(X3,f(f(X3,X3),X2)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c132,plain,
f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3)) = f(f(X3,f(f(X3,X3),X2)),f(X3,X3)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
f(X3,f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3))) = f(X3,f(f(X3,f(f(X3,X3),X2)),f(X3,X3))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
f(f(X2,f(f(X2,X2),X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c125]) ).
cnf(c135,plain,
f(X2,f(f(X2,f(f(X2,X2),X)),f(X2,X2))) = f(X2,X2),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
f(X3,f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3))) = f(X3,X3),
inference(transitivity,[status(thm)],[c133,c135]) ).
cnf(c137,plain,
f(f(f(X3,X),f(X3,X3)),f(f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)),f(X3,X3))) = f(X3,X3),
inference(transitivity,[status(thm)],[c130,c136]) ).
cnf(c138,plain,
f(f(f(X3,X),f(X3,X3)),f(f(X3,X3),X2)) = f(X3,X3),
inference(transitivity,[status(thm)],[c129,c137]) ).
cnf(c139,plain,
f(X2,f(f(X2,X2),X)) = f(X2,X2),
inference(transitivity,[status(thm)],[c127,c138]) ).
cnf(c140,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)) = f(f(X2,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)) = X2,
inference(transitivity,[status(thm)],[c140,c110]) ).
cnf(c142,plain,
f(f(X2,X2),f(X2,X)) = X2,
inference(transitivity,[status(thm)],[c113,c141]) ).
cnf(c143,plain,
f(f(X4,X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))) = X4,
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
f(f(X2,X2),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c90,c143]) ).
cnf(c145,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
X = f(f(X,X),f(X2,X)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
f(X,X2) = f(f(f(X,X),f(X2,X)),X2),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
f(f(X,X2),f(X2,X)) = f(f(f(f(X,X),f(X2,X)),X2),f(X2,X)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X2,f(f(f(f(X,X),f(X2,X)),X2),f(X2,X))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
X4 = f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c151,plain,
f(f(X4,f(X5,X3)),X5) = f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
f(f(f(X4,f(X5,X3)),X5),f(X5,X3)) = f(f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),f(X5,X3)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
f(X5,f(f(f(X4,f(X5,X3)),X5),f(X5,X3))) = f(X5,f(f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),f(X5,X3))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
X4 = f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c155,plain,
f(X5,f(f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),f(X5,X3))) = f(f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X))),f(f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),f(X5,X3))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),f(f(X2,X4),f(X4,X3))))),f(f(X2,X4),f(X4,X3))),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))) = X4,
inference(substitution,[status(thm)],[c95]) ).
cnf(c157,plain,
X4 = f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),f(f(X2,X4),f(X4,X3))))),f(f(X2,X4),f(X4,X3))),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
f(f(f(X2,X4),f(X4,X3)),X4) = f(f(f(X2,X4),f(X4,X3)),f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),f(f(X2,X4),f(X4,X3))))),f(f(X2,X4),f(X4,X3))),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3)))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
f(f(X4,X3),f(f(f(X2,X4),f(X4,X3)),X4)) = f(f(X4,X3),f(f(f(X2,X4),f(X4,X3)),f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),f(f(X2,X4),f(X4,X3))))),f(f(X2,X4),f(X4,X3))),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
f(f(X4,X3),f(f(f(X2,X4),f(X4,X3)),f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3)),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))),f(f(X2,X4),f(X4,X3))))),f(f(X2,X4),f(X4,X3))),f(X4,f(f(f(X2,f(X2,f(f(X3,X3),X4))),X4),X3))))) = f(f(X2,X4),f(X4,X3)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c161,plain,
f(f(X3,X2),f(f(f(X,X3),f(X3,X2)),X3)) = f(f(X,X3),f(X3,X2)),
inference(transitivity,[status(thm)],[c159,c160]) ).
cnf(c162,plain,
f(f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X))),f(f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),f(X5,X3))) = f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))) = f(f(X4,f(X5,X3)),X5),
inference(congruence,[status(thm)],[c59]) ).
cnf(c164,plain,
f(f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X))),f(f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),f(X5,X3))) = f(f(X4,f(X5,X3)),X5),
inference(transitivity,[status(thm)],[c162,c163]) ).
cnf(c165,plain,
f(X5,f(f(f(X4,f(X5,X3)),f(f(X5,X3),f(X5,f(f(f(f(X2,f(X5,X3)),f(f(X2,f(X5,X3)),f(f(X,X),X5))),X5),X)))),f(X5,X3))) = f(f(X4,f(X5,X3)),X5),
inference(transitivity,[status(thm)],[c155,c164]) ).
cnf(c166,plain,
f(X3,f(f(f(X2,f(X3,X)),X3),f(X3,X))) = f(f(X2,f(X3,X)),X3),
inference(transitivity,[status(thm)],[c153,c165]) ).
cnf(c167,plain,
f(X2,f(f(f(f(X,X),f(X2,X)),X2),f(X2,X))) = f(f(f(X,X),f(X2,X)),X2),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c144]) ).
cnf(c169,plain,
f(f(f(X,X),f(X2,X)),X2) = f(X,X2),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
f(X2,f(f(f(f(X,X),f(X2,X)),X2),f(X2,X))) = f(X,X2),
inference(transitivity,[status(thm)],[c167,c169]) ).
cnf(c171,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X,X2),
inference(transitivity,[status(thm)],[c149,c170]) ).
cnf(c172,plain,
f(X,f(f(X2,X),f(X,X2))) = f(X2,X),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
f(X2,X) = f(X,f(f(X2,X),f(X,X2))),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c144]) ).
cnf(c175,plain,
X = f(f(X,X),f(X2,X)),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
f(X,X2) = f(f(f(X,X),f(X2,X)),X2),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
f(f(X,X2),f(X2,X)) = f(f(f(f(X,X),f(X2,X)),X2),f(X2,X)),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
X4 = f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c179,plain,
f(f(X5,f(X4,X3)),X4) = f(f(X5,f(X4,X3)),f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X)))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
f(f(f(X5,f(X4,X3)),X4),f(X4,X3)) = f(f(f(X5,f(X4,X3)),f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X)))),f(X4,X3)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
f(f(X5,f(X4,X3)),f(f(f(X5,f(X4,X3)),X4),f(X4,X3))) = f(f(X5,f(X4,X3)),f(f(f(X5,f(X4,X3)),f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X)))),f(X4,X3))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
f(f(X5,f(X4,X3)),f(f(f(X5,f(X4,X3)),f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X)))),f(X4,X3))) = f(f(X5,f(X4,X3)),f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X)))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c183,plain,
f(f(X5,f(X4,X3)),f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X)))) = f(f(X5,f(X4,X3)),X4),
inference(congruence,[status(thm)],[c59]) ).
cnf(c184,plain,
f(f(X5,f(X4,X3)),f(f(f(X5,f(X4,X3)),f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X)))),f(X4,X3))) = f(f(X5,f(X4,X3)),X4),
inference(transitivity,[status(thm)],[c182,c183]) ).
cnf(c185,plain,
f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X))) = f(f(X3,f(X2,X)),X2),
inference(transitivity,[status(thm)],[c181,c184]) ).
cnf(c186,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X))),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
f(f(f(X3,f(X2,X)),X2),f(X2,X)) = f(f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X))),f(X2,X)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c119]) ).
cnf(c189,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
f(f(X,f(X2,X3)),X3) = f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
f(f(X2,X3),f(f(X,f(X2,X3)),X3)) = f(f(X2,X3),f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3)))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
f(X3,f(f(X2,X3),f(f(X,f(X2,X3)),X3))) = f(X3,f(f(X2,X3),f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
f(f(f(X3,X2),f(X2,X)),f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))) = f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c194,plain,
f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))) = f(f(f(X3,X2),f(X2,X)),f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c196,plain,
f(f(f(X3,X2),f(X2,X)),f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))) = f(f(f(X3,X2),f(X2,X)),X2),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))) = f(f(f(X3,X2),f(X2,X)),X2),
inference(transitivity,[status(thm)],[c194,c196]) ).
cnf(c198,plain,
f(f(f(X3,X2),f(X2,X)),X2) = f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c200,plain,
f(f(f(X2,X2),X),X2) = f(f(f(X2,X2),X),f(f(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c125]) ).
cnf(c202,plain,
f(f(f(X2,X2),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c200,c201]) ).
cnf(c203,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),f(f(X3,X2),f(X2,X))) = f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))) = f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),f(f(X3,X2),f(X2,X))),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c206,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),f(f(X3,X2),f(X2,X))) = f(X2,f(f(X3,X2),f(X2,X))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))) = f(X2,f(f(X3,X2),f(X2,X))),
inference(transitivity,[status(thm)],[c204,c206]) ).
cnf(c208,plain,
f(f(f(X3,X2),f(X2,X)),X2) = f(X2,f(f(X3,X2),f(X2,X))),
inference(transitivity,[status(thm)],[c198,c207]) ).
cnf(c209,plain,
f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3)) = f(f(X2,X3),f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3)))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c210,plain,
f(f(X2,X3),f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3)))) = f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3)),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
f(X3,f(f(X2,X3),f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))))) = f(X3,f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3))),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c119]) ).
cnf(c213,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
f(X3,f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3))) = f(f(f(X2,X3),f(X3,X3)),f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
f(f(f(X2,X3),f(X3,X3)),f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3))) = f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c216,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c119]) ).
cnf(c217,plain,
f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))) = f(f(X,f(X2,X3)),X3),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
f(f(f(X2,X3),f(X3,X3)),f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3))) = f(f(X,f(X2,X3)),X3),
inference(transitivity,[status(thm)],[c215,c217]) ).
cnf(c219,plain,
f(X3,f(f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))),f(X2,X3))) = f(f(X,f(X2,X3)),X3),
inference(transitivity,[status(thm)],[c214,c218]) ).
cnf(c220,plain,
f(X3,f(f(X2,X3),f(f(X,f(X2,X3)),f(f(X2,X3),f(X3,X3))))) = f(f(X,f(X2,X3)),X3),
inference(transitivity,[status(thm)],[c211,c219]) ).
cnf(c221,plain,
f(X3,f(f(X2,X3),f(f(X,f(X2,X3)),X3))) = f(f(X,f(X2,X3)),X3),
inference(transitivity,[status(thm)],[c192,c220]) ).
cnf(c222,plain,
f(X2,f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2))) = f(f(f(X3,X2),f(X,X2)),X2),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
f(f(f(X3,X2),f(X,X2)),X2) = f(X2,f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2))),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
f(X3,f(f(X4,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))) = f(X4,X3),
inference(substitution,[status(thm)],[c88]) ).
cnf(c225,plain,
f(X4,X3) = f(X3,f(f(X4,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
f(f(X3,X4),f(X5,X4)) = f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
f(f(f(X3,X4),f(X5,X4)),X4) = f(f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),X4),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
f(f(X5,X4),f(f(f(X3,X4),f(X5,X4)),X4)) = f(f(X5,X4),f(f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),X4)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
f(X3,f(f(X4,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))) = f(X4,X3),
inference(substitution,[status(thm)],[c88]) ).
cnf(c230,plain,
f(X4,X3) = f(X3,f(f(X4,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
f(f(X5,X4),f(f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),X4)) = f(f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X))),f(f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),X4)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
f(f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X))),f(f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),X4)) = f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c233,plain,
f(X3,f(f(X4,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(f(X,X),f(X4,X3)))),f(X4,X3)),X))) = f(X4,X3),
inference(substitution,[status(thm)],[c88]) ).
cnf(c234,plain,
f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))) = f(f(X3,X4),f(X5,X4)),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
f(f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X))),f(f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),X4)) = f(f(X3,X4),f(X5,X4)),
inference(transitivity,[status(thm)],[c232,c234]) ).
cnf(c236,plain,
f(f(X5,X4),f(f(f(X3,X4),f(X4,f(f(X5,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X5,X4)))),f(X5,X4)),X)))),X4)) = f(f(X3,X4),f(X5,X4)),
inference(transitivity,[status(thm)],[c231,c235]) ).
cnf(c237,plain,
f(f(X3,X2),f(f(f(X,X2),f(X3,X2)),X2)) = f(f(X,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c228,c236]) ).
cnf(c238,plain,
f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)) = f(f(X3,X2),f(X,X2)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
f(X2,f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2))) = f(X2,f(f(X3,X2),f(X,X2))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
f(f(f(X3,X2),f(X,X2)),X2) = f(X2,f(f(X3,X2),f(X,X2))),
inference(transitivity,[status(thm)],[c223,c239]) ).
cnf(c241,plain,
f(f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X))),f(X2,X)) = f(f(X2,X),f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X)))),
inference(substitution,[status(thm)],[c240]) ).
cnf(c242,plain,
f(f(X2,X),f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X)))) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(congruence,[status(thm)],[c185]) ).
cnf(c243,plain,
f(f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X))),f(X2,X)) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(transitivity,[status(thm)],[c241,c242]) ).
cnf(c244,plain,
f(f(f(X3,f(X2,X)),X2),f(X2,X)) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(transitivity,[status(thm)],[c187,c243]) ).
cnf(c245,plain,
f(f(f(f(X,X),f(X2,X)),X2),f(X2,X)) = f(f(X2,X),f(f(f(X,X),f(X2,X)),X2)),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c144]) ).
cnf(c247,plain,
f(f(f(X,X),f(X2,X)),X2) = f(X,X2),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
f(f(X2,X),f(f(f(X,X),f(X2,X)),X2)) = f(f(X2,X),f(X,X2)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
f(f(f(f(X,X),f(X2,X)),X2),f(X2,X)) = f(f(X2,X),f(X,X2)),
inference(transitivity,[status(thm)],[c245,c248]) ).
cnf(c250,plain,
f(f(X,X2),f(X2,X)) = f(f(X2,X),f(X,X2)),
inference(transitivity,[status(thm)],[c177,c249]) ).
cnf(c251,plain,
f(f(X2,X),f(X,X2)) = f(f(X,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
f(X,f(f(X2,X),f(X,X2))) = f(X,f(f(X,X2),f(X2,X))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c254,plain,
f(X2,X) = f(f(f(X2,X2),f(X,X2)),X),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
f(f(X2,X),f(X,X2)) = f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
f(X2,f(f(X2,X),f(X,X2))) = f(X2,f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c258,plain,
f(X2,f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))) = f(f(f(X2,X2),f(X,X2)),f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
f(f(f(X2,X2),f(X,X2)),f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))) = f(f(f(X2,X2),f(X,X2)),X),
inference(substitution,[status(thm)],[c185]) ).
cnf(c260,plain,
f(f(f(X2,X2),f(X,X2)),X) = f(X2,X),
inference(congruence,[status(thm)],[c144]) ).
cnf(c261,plain,
f(f(f(X2,X2),f(X,X2)),f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))) = f(X2,X),
inference(transitivity,[status(thm)],[c259,c260]) ).
cnf(c262,plain,
f(X2,f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))) = f(X2,X),
inference(transitivity,[status(thm)],[c258,c261]) ).
cnf(c263,plain,
f(X2,f(f(X2,X),f(X,X2))) = f(X2,X),
inference(transitivity,[status(thm)],[c256,c262]) ).
cnf(c264,plain,
f(X,f(f(X,X2),f(X2,X))) = f(X,X2),
inference(substitution,[status(thm)],[c263]) ).
cnf(c265,plain,
f(X,f(f(X2,X),f(X,X2))) = f(X,X2),
inference(transitivity,[status(thm)],[c252,c264]) ).
cnf(c266,plain,
f(X2,X) = f(X,X2),
inference(transitivity,[status(thm)],[c173,c265]) ).
cnf(c267,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
f(f(X2,X),f(X2,X)) = f(f(X2,X),f(X,X2)),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
f(X,f(f(X3,X2),f(X3,X2))) = f(X,f(f(X3,X2),f(X2,X3))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c272,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
f(f(X2,X),f(X,X2)) = f(f(X,X2),f(X,X2)),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
f(X,f(f(X3,X2),f(X2,X3))) = f(X,f(f(X2,X3),f(X2,X3))),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c276,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,plain,
f(f(X2,X),f(X2,X)) = f(f(X,X2),f(X2,X)),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X2,X),f(X2,X))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X2,X))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c280,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c281,plain,
f(f(X,X2),f(X2,X)) = f(f(X,X2),f(X,X2)),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X2,X))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
f(f(f(X,X2),f(X,X2)),f(f(X3,X2),f(X3,X2))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c284,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))) = f(f(f(X,X2),f(X,X2)),f(f(X3,X2),f(X3,X2))),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
f(f(X,X),f(X2,f(X2,X2))) = f(f(X2,f(X2,X2)),f(X,X)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c286,plain,
f(f(X2,f(X2,X2)),f(X,X)) = f(f(X,X),f(X2,f(X2,X2))),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c288,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c287]) ).
cnf(c289,plain,
f(f(X3,X2),f(X3,f(X,f(X3,X2)))) = f(f(X2,X3),f(X3,f(X,f(X3,X2)))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
f(X3,f(f(X3,X2),f(X3,f(X,f(X3,X2))))) = f(X3,f(f(X2,X3),f(X3,f(X,f(X3,X2))))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c292,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c291]) ).
cnf(c293,plain,
f(X,f(X3,X2)) = f(X,f(X2,X3)),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
f(X3,f(X,f(X3,X2))) = f(X3,f(X,f(X2,X3))),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
f(f(X2,X3),f(X3,f(X,f(X3,X2)))) = f(f(X2,X3),f(X3,f(X,f(X2,X3)))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
f(X3,f(f(X2,X3),f(X3,f(X,f(X3,X2))))) = f(X3,f(f(X2,X3),f(X3,f(X,f(X2,X3))))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
f(f(f(X2,X3),f(X3,f(X,f(X2,X3)))),f(f(X2,X3),f(X3,f(X,f(X2,X3))))) = f(X3,f(f(X2,X3),f(X3,f(X,f(X2,X3))))),
inference(substitution,[status(thm)],[c207]) ).
cnf(c298,plain,
f(X3,f(f(X2,X3),f(X3,f(X,f(X2,X3))))) = f(f(f(X2,X3),f(X3,f(X,f(X2,X3)))),f(f(X2,X3),f(X3,f(X,f(X2,X3))))),
inference(symmetry,[status(thm)],[c297]) ).
cnf(c299,plain,
f(f(X,f(X2,X3)),X3) = f(X3,f(X,f(X2,X3))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c300,plain,
f(X3,f(X,f(X2,X3))) = f(f(X,f(X2,X3)),X3),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
f(f(X2,X3),f(X3,f(X,f(X2,X3)))) = f(f(X2,X3),f(f(X,f(X2,X3)),X3)),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
f(f(f(X2,X3),f(X3,f(X,f(X2,X3)))),f(f(X2,X3),f(X3,f(X,f(X2,X3))))) = f(f(f(X2,X3),f(f(X,f(X2,X3)),X3)),f(f(X2,X3),f(X3,f(X,f(X2,X3))))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
f(f(X,f(X2,X3)),X3) = f(X3,f(X,f(X2,X3))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c304,plain,
f(X3,f(X,f(X2,X3))) = f(f(X,f(X2,X3)),X3),
inference(symmetry,[status(thm)],[c303]) ).
cnf(c305,plain,
f(f(X2,X3),f(X3,f(X,f(X2,X3)))) = f(f(X2,X3),f(f(X,f(X2,X3)),X3)),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
f(f(f(X2,X3),f(f(X,f(X2,X3)),X3)),f(f(X2,X3),f(X3,f(X,f(X2,X3))))) = f(f(f(X2,X3),f(f(X,f(X2,X3)),X3)),f(f(X2,X3),f(f(X,f(X2,X3)),X3))),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
f(f(f(X,f(X2,X3)),X3),f(X2,X3)) = f(f(X2,X3),f(f(X,f(X2,X3)),X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c308,plain,
f(f(X2,X3),f(f(X,f(X2,X3)),X3)) = f(f(f(X,f(X2,X3)),X3),f(X2,X3)),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
f(f(f(X2,X3),f(f(X,f(X2,X3)),X3)),f(f(X2,X3),f(f(X,f(X2,X3)),X3))) = f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(X2,X3),f(f(X,f(X2,X3)),X3))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
f(f(f(X,f(X2,X3)),X3),f(X2,X3)) = f(f(X2,X3),f(f(X,f(X2,X3)),X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c311,plain,
f(f(X2,X3),f(f(X,f(X2,X3)),X3)) = f(f(f(X,f(X2,X3)),X3),f(X2,X3)),
inference(symmetry,[status(thm)],[c310]) ).
cnf(c312,plain,
f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(X2,X3),f(f(X,f(X2,X3)),X3))) = f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
X2 = f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c314,plain,
f(f(X4,f(X3,X2)),X2) = f(f(X4,f(X3,X2)),f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
f(f(f(X4,f(X3,X2)),X2),f(X3,X2)) = f(f(f(X4,f(X3,X2)),f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))),f(X3,X2)),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
f(f(X4,f(X3,X2)),f(f(f(X4,f(X3,X2)),X2),f(X3,X2))) = f(f(X4,f(X3,X2)),f(f(f(X4,f(X3,X2)),f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))),f(X3,X2))),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
f(f(X4,f(X3,X2)),f(f(f(X4,f(X3,X2)),f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))),f(X3,X2))) = f(f(X4,f(X3,X2)),f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c318,plain,
f(f(X4,f(X3,X2)),f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))) = f(f(X4,f(X3,X2)),X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c319,plain,
f(f(X4,f(X3,X2)),f(f(f(X4,f(X3,X2)),f(f(X3,X2),f(X2,f(f(f(X3,f(X3,f(f(X,X),X2))),X2),X)))),f(X3,X2))) = f(f(X4,f(X3,X2)),X2),
inference(transitivity,[status(thm)],[c317,c318]) ).
cnf(c320,plain,
f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X),f(X2,X))) = f(f(X3,f(X2,X)),X),
inference(transitivity,[status(thm)],[c316,c319]) ).
cnf(c321,plain,
f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))) = f(f(X,f(X2,X3)),X3),
inference(substitution,[status(thm)],[c320]) ).
cnf(c322,plain,
f(f(X,f(X2,X3)),X3) = f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c323,plain,
f(f(f(X,f(X2,X3)),X3),f(X2,X3)) = f(f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))),f(X2,X3)),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))) = f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))),f(X2,X3))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))),f(X2,X3))) = f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))),
inference(substitution,[status(thm)],[c237]) ).
cnf(c326,plain,
f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))) = f(f(X,f(X2,X3)),X3),
inference(substitution,[status(thm)],[c320]) ).
cnf(c327,plain,
f(f(X,f(X2,X3)),X3) = f(X3,f(X,f(X2,X3))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c328,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c329,plain,
f(X,f(X2,X3)) = f(X,f(X3,X2)),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
f(X3,f(X,f(X2,X3))) = f(X3,f(X,f(X3,X2))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
f(f(X,f(X2,X3)),X3) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c327,c330]) ).
cnf(c332,plain,
f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c326,c331]) ).
cnf(c333,plain,
f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(f(X,f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))),f(X2,X3))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c325,c332]) ).
cnf(c334,plain,
f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(f(X,f(X2,X3)),X3),f(X2,X3))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c324,c333]) ).
cnf(c335,plain,
f(f(f(f(X,f(X2,X3)),X3),f(X2,X3)),f(f(X2,X3),f(f(X,f(X2,X3)),X3))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c312,c334]) ).
cnf(c336,plain,
f(f(f(X2,X3),f(f(X,f(X2,X3)),X3)),f(f(X2,X3),f(f(X,f(X2,X3)),X3))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c309,c335]) ).
cnf(c337,plain,
f(f(f(X2,X3),f(f(X,f(X2,X3)),X3)),f(f(X2,X3),f(X3,f(X,f(X2,X3))))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c306,c336]) ).
cnf(c338,plain,
f(f(f(X2,X3),f(X3,f(X,f(X2,X3)))),f(f(X2,X3),f(X3,f(X,f(X2,X3))))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c302,c337]) ).
cnf(c339,plain,
f(X3,f(f(X2,X3),f(X3,f(X,f(X2,X3))))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c298,c338]) ).
cnf(c340,plain,
f(X3,f(f(X2,X3),f(X3,f(X,f(X3,X2))))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c296,c339]) ).
cnf(c341,plain,
f(X3,f(f(X3,X2),f(X3,f(X,f(X3,X2))))) = f(X3,f(X,f(X3,X2))),
inference(transitivity,[status(thm)],[c290,c340]) ).
cnf(c342,plain,
f(X2,f(f(X2,X),f(X2,f(X2,f(X2,X))))) = f(X2,f(X2,f(X2,X))),
inference(substitution,[status(thm)],[c341]) ).
cnf(c343,plain,
f(X2,f(X2,f(X2,X))) = f(X2,f(f(X2,X),f(X2,f(X2,f(X2,X))))),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
f(f(X2,f(X2,X)),X2) = f(X2,f(X2,f(X2,X))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c345,plain,
f(X2,f(X2,f(X2,X))) = f(f(X2,f(X2,X)),X2),
inference(symmetry,[status(thm)],[c344]) ).
cnf(c346,plain,
f(f(X2,X),f(X2,f(X2,f(X2,X)))) = f(f(X2,X),f(f(X2,f(X2,X)),X2)),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
f(X2,f(f(X2,X),f(X2,f(X2,f(X2,X))))) = f(X2,f(f(X2,X),f(f(X2,f(X2,X)),X2))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c349,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c348]) ).
cnf(c350,plain,
f(f(X3,X2),f(X3,X)) = f(f(X3,X2),f(X,X3)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
f(X3,f(f(X4,X2),f(X4,X))) = f(X3,f(f(X4,X2),f(X,X4))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
f(f(X4,X4),f(X3,f(f(X4,X2),f(X4,X)))) = f(f(X4,X4),f(X3,f(f(X4,X2),f(X,X4)))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
f(f(X,X3),f(X3,X2)) = f(f(X3,X2),f(X,X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c354,plain,
f(f(X3,X2),f(X,X3)) = f(f(X,X3),f(X3,X2)),
inference(symmetry,[status(thm)],[c353]) ).
cnf(c355,plain,
f(X3,f(f(X4,X2),f(X,X4))) = f(X3,f(f(X,X4),f(X4,X2))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
f(f(X4,X4),f(X3,f(f(X4,X2),f(X,X4)))) = f(f(X4,X4),f(X3,f(f(X,X4),f(X4,X2)))),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
f(f(f(X,X4),f(X4,X2)),X3) = f(X3,f(f(X,X4),f(X4,X2))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c358,plain,
f(X3,f(f(X,X4),f(X4,X2))) = f(f(f(X,X4),f(X4,X2)),X3),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
f(f(X4,X4),f(X3,f(f(X,X4),f(X4,X2)))) = f(f(X4,X4),f(f(f(X,X4),f(X4,X2)),X3)),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
f(f(f(f(X,X4),f(X4,X2)),X3),f(X4,X4)) = f(f(X4,X4),f(f(f(X,X4),f(X4,X2)),X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c361,plain,
f(f(X4,X4),f(f(f(X,X4),f(X4,X2)),X3)) = f(f(f(f(X,X4),f(X4,X2)),X3),f(X4,X4)),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
f(f(f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(f(X5,X5),f(X5,X5)),X5))),X5),f(X5,X5)) = X5,
inference(substitution,[status(thm)],[c119]) ).
cnf(c363,plain,
X5 = f(f(f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(f(X5,X5),f(X5,X5)),X5))),X5),f(X5,X5)),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
f(X5,X5) = f(X5,f(f(f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(f(X5,X5),f(X5,X5)),X5))),X5),f(X5,X5))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
f(f(f(f(X2,X5),f(X5,X3)),X4),f(X5,X5)) = f(f(f(f(X2,X5),f(X5,X3)),X4),f(X5,f(f(f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(f(X5,X5),f(X5,X5)),X5))),X5),f(X5,X5)))),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
f(f(f(f(X2,X5),f(X5,X3)),X4),f(X5,f(f(f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(X,f(f(f(X2,X5),f(X5,X3)),X4)),f(f(f(X5,X5),f(X5,X5)),X5))),X5),f(X5,X5)))) = X5,
inference(substitution,[status(thm)],[c55]) ).
cnf(c367,plain,
f(f(f(f(X,X4),f(X4,X2)),X3),f(X4,X4)) = X4,
inference(transitivity,[status(thm)],[c365,c366]) ).
cnf(c368,plain,
f(f(X4,X4),f(f(f(X,X4),f(X4,X2)),X3)) = X4,
inference(transitivity,[status(thm)],[c361,c367]) ).
cnf(c369,plain,
f(f(X4,X4),f(X3,f(f(X,X4),f(X4,X2)))) = X4,
inference(transitivity,[status(thm)],[c359,c368]) ).
cnf(c370,plain,
f(f(X4,X4),f(X3,f(f(X4,X2),f(X,X4)))) = X4,
inference(transitivity,[status(thm)],[c356,c369]) ).
cnf(c371,plain,
f(f(X4,X4),f(X3,f(f(X4,X2),f(X4,X)))) = X4,
inference(transitivity,[status(thm)],[c352,c370]) ).
cnf(c372,plain,
f(f(X2,X2),f(f(X2,X2),f(f(X2,X2),f(X2,X)))) = X2,
inference(substitution,[status(thm)],[c371]) ).
cnf(c373,plain,
X2 = f(f(X2,X2),f(f(X2,X2),f(f(X2,X2),f(X2,X)))),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
f(X2,f(X2,X)) = f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X2),f(X2,X)))),f(X2,X)),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
f(f(X2,f(X2,X)),X2) = f(f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X2),f(X2,X)))),f(X2,X)),X2),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
f(f(X2,X),f(f(X2,f(X2,X)),X2)) = f(f(X2,X),f(f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X2),f(X2,X)))),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
f(X2,f(f(X2,X),f(f(X2,f(X2,X)),X2))) = f(X2,f(f(X2,X),f(f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X2),f(X2,X)))),f(X2,X)),X2))),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
f(X2,f(f(X2,X),f(f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X2),f(X2,X)))),f(X2,X)),X2))) = f(X2,X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c379,plain,
f(X2,f(f(X2,X),f(f(X2,f(X2,X)),X2))) = f(X2,X),
inference(transitivity,[status(thm)],[c377,c378]) ).
cnf(c380,plain,
f(X2,f(f(X2,X),f(X2,f(X2,f(X2,X))))) = f(X2,X),
inference(transitivity,[status(thm)],[c347,c379]) ).
cnf(c381,plain,
f(X2,f(X2,f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c343,c380]) ).
cnf(c382,plain,
f(f(X3,X3),f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X))))) = f(f(X3,X3),f(f(X3,X2),f(X3,X))),
inference(substitution,[status(thm)],[c381]) ).
cnf(c383,plain,
f(f(X3,X3),f(f(X3,X2),f(X3,X))) = f(f(X3,X3),f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X))))),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X)))) = X3,
inference(substitution,[status(thm)],[c371]) ).
cnf(c385,plain,
f(f(X3,X3),f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X))))) = f(f(X3,X3),X3),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
f(f(X,X),X) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c387,plain,
f(f(X3,X3),f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X))))) = f(X3,f(X3,X3)),
inference(transitivity,[status(thm)],[c385,c386]) ).
cnf(c388,plain,
f(f(X3,X3),f(f(X3,X2),f(X3,X))) = f(X3,f(X3,X3)),
inference(transitivity,[status(thm)],[c383,c387]) ).
cnf(c389,plain,
f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c388]) ).
cnf(c390,plain,
f(X,f(X,X)) = f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))),
inference(symmetry,[status(thm)],[c389]) ).
cnf(c391,plain,
f(X2,f(X,f(X,X))) = f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
f(f(X2,X2),X) = f(X,f(X2,X2)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c393,plain,
f(X,f(X2,X2)) = f(f(X2,X2),X),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
f(f(X2,f(X3,X3)),f(X,f(X3,X3))) = f(f(X2,f(X3,X3)),f(f(X3,X3),X)),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
f(X3,f(f(X2,f(X4,X4)),f(X,f(X4,X4)))) = f(X3,f(f(X2,f(X4,X4)),f(f(X4,X4),X))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
f(X4,f(X3,f(f(X2,f(X4,X4)),f(X,f(X4,X4))))) = f(X4,f(X3,f(f(X2,f(X4,X4)),f(f(X4,X4),X)))),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3) = f(X3,f(f(X2,f(X4,X4)),f(f(X4,X4),X))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c398,plain,
f(X3,f(f(X2,f(X4,X4)),f(f(X4,X4),X))) = f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
f(X4,f(X3,f(f(X2,f(X4,X4)),f(f(X4,X4),X)))) = f(X4,f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3)),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
f(f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3),X4) = f(X4,f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c401,plain,
f(X4,f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3)) = f(f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3),X4),
inference(symmetry,[status(thm)],[c400]) ).
cnf(c402,plain,
f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)) = X6,
inference(substitution,[status(thm)],[c144]) ).
cnf(c403,plain,
X6 = f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
f(f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5),X6) = f(f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
f(f(X4,X4),f(f(X3,f(X4,X4)),f(f(f(f(X2,f(X4,X4)),f(f(X2,f(X4,X4)),f(f(X,X),f(X3,f(X4,X4))))),f(X3,f(X4,X4))),X))) = f(X3,f(X4,X4)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c406,plain,
f(X3,f(X4,X4)) = f(f(X4,X4),f(f(X3,f(X4,X4)),f(f(f(f(X2,f(X4,X4)),f(f(X2,f(X4,X4)),f(f(X,X),f(X3,f(X4,X4))))),f(X3,f(X4,X4))),X))),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
f(X4,f(X3,f(X4,X4))) = f(X4,f(f(X4,X4),f(f(X3,f(X4,X4)),f(f(f(f(X2,f(X4,X4)),f(f(X2,f(X4,X4)),f(f(X,X),f(X3,f(X4,X4))))),f(X3,f(X4,X4))),X)))),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
f(X4,f(f(X4,X4),f(f(X3,f(X4,X4)),f(f(f(f(X2,f(X4,X4)),f(f(X2,f(X4,X4)),f(f(X,X),f(X3,f(X4,X4))))),f(X3,f(X4,X4))),X)))) = f(X4,X4),
inference(substitution,[status(thm)],[c139]) ).
cnf(c409,plain,
f(X2,f(X,f(X2,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c407,c408]) ).
cnf(c410,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c411,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c412,plain,
f(X2,f(X3,X3)) = f(X2,f(X3,f(f(X,X3),f(X3,X3)))),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
f(f(X3,f(X4,X4)),f(f(X4,X4),X2)) = f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,X4),X2)),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
f(f(f(X3,f(X5,X5)),f(f(X5,X5),X2)),X4) = f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,X5),X2)),X4),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
f(f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c417,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c416]) ).
cnf(c418,plain,
f(f(X3,X3),X2) = f(f(X3,f(f(X,X3),f(X3,X3))),X2),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,X4),X2)) = f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,f(f(X,X4),f(X4,X4))),X2)),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,X5),X2)),X4) = f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c423,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c424,plain,
f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)) = f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c427,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c426]) ).
cnf(c428,plain,
f(X2,f(X3,X3)) = f(X2,f(X3,f(f(X,X3),f(X3,X3)))),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
f(f(X3,f(X4,X4)),f(f(X4,X4),X2)) = f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,X4),X2)),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
f(f(f(X3,f(X5,X5)),f(f(X5,X5),X2)),X4) = f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,X5),X2)),X4),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)) = f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)) = f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6) = f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)) = f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c438,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
f(f(X3,X3),X2) = f(f(X3,f(f(X,X3),f(X3,X3))),X2),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,X4),X2)) = f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,f(f(X,X4),f(X4,X4))),X2)),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,X5),X2)),X4) = f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4),
inference(congruence,[status(thm)],[c440]) ).
cnf(c442,plain,
f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)) = f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),
inference(congruence,[status(thm)],[c441]) ).
cnf(c443,plain,
f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)) = f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),
inference(congruence,[status(thm)],[c443]) ).
cnf(c445,plain,
f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6) = f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6),
inference(congruence,[status(thm)],[c444]) ).
cnf(c446,plain,
f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)) = f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c446]) ).
cnf(c448,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c449,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c448]) ).
cnf(c450,plain,
f(X2,f(X3,X3)) = f(X2,f(X3,f(f(X,X3),f(X3,X3)))),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
f(f(X3,f(X4,X4)),f(f(X4,X4),X2)) = f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,X4),X2)),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
f(f(f(X3,f(X5,X5)),f(f(X5,X5),X2)),X4) = f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,X5),X2)),X4),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)) = f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6))) = f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6))),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)) = f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6) = f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)) = f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c458]) ).
cnf(c460,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c461,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c460]) ).
cnf(c462,plain,
f(f(X3,X3),X2) = f(f(X3,f(f(X,X3),f(X3,X3))),X2),
inference(congruence,[status(thm)],[c461]) ).
cnf(c463,plain,
f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,X4),X2)) = f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,f(f(X,X4),f(X4,X4))),X2)),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,X5),X2)),X4) = f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)) = f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6))) = f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6))),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)) = f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6) = f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)) = f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c473,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(symmetry,[status(thm)],[c472]) ).
cnf(c474,plain,
f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)) = f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6) = f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6)) = f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c479,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c478]) ).
cnf(c480,plain,
f(X2,f(X3,f(f(X,X3),f(X3,X3)))) = f(X2,f(f(f(X,X3),f(X3,X3)),X3)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,f(f(X,X4),f(X4,X4))),X2)) = f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(X4,f(f(X,X4),f(X4,X4))),X2)),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4) = f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c485,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c484]) ).
cnf(c486,plain,
f(f(X3,f(f(X,X3),f(X3,X3))),X2) = f(f(f(f(X,X3),f(X3,X3)),X3),X2),
inference(congruence,[status(thm)],[c485]) ).
cnf(c487,plain,
f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(X4,f(f(X,X4),f(X4,X4))),X2)) = f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(f(f(X,X4),f(X4,X4)),X4),X2)),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4) = f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(f(f(X,X5),f(X5,X5)),X5),X2)),X4),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c491,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c490]) ).
cnf(c492,plain,
f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)) = f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)),
inference(congruence,[status(thm)],[c491]) ).
cnf(c493,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c495,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c494]) ).
cnf(c496,plain,
f(X2,f(X3,f(f(X,X3),f(X3,X3)))) = f(X2,f(f(f(X,X3),f(X3,X3)),X3)),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,f(f(X,X4),f(X4,X4))),X2)) = f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(X4,f(f(X,X4),f(X4,X4))),X2)),
inference(congruence,[status(thm)],[c496]) ).
cnf(c498,plain,
f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4) = f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)) = f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c499]) ).
cnf(c501,plain,
f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))) = f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c500]) ).
cnf(c502,plain,
f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6) = f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)) = f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c506,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c505]) ).
cnf(c507,plain,
f(f(X3,f(f(X,X3),f(X3,X3))),X2) = f(f(f(f(X,X3),f(X3,X3)),X3),X2),
inference(congruence,[status(thm)],[c506]) ).
cnf(c508,plain,
f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(X4,f(f(X,X4),f(X4,X4))),X2)) = f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(f(f(X,X4),f(X4,X4)),X4),X2)),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4) = f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(f(f(X,X5),f(X5,X5)),X5),X2)),X4),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)) = f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),
inference(congruence,[status(thm)],[c509]) ).
cnf(c511,plain,
f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))) = f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6) = f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)) = f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c514]) ).
cnf(c516,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c517,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c516]) ).
cnf(c518,plain,
f(X2,f(X3,f(f(X,X3),f(X3,X3)))) = f(X2,f(f(f(X,X3),f(X3,X3)),X3)),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
f(f(X3,f(X4,f(f(X,X4),f(X4,X4)))),f(f(X4,f(f(X,X4),f(X4,X4))),X2)) = f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(X4,f(f(X,X4),f(X4,X4))),X2)),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
f(f(f(X3,f(X5,f(f(X,X5),f(X5,X5)))),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4) = f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)) = f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6))),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))) = f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c523]) ).
cnf(c525,plain,
f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6) = f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)) = f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c526]) ).
cnf(c528,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c529,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c528]) ).
cnf(c530,plain,
f(f(X3,f(f(X,X3),f(X3,X3))),X2) = f(f(f(f(X,X3),f(X3,X3)),X3),X2),
inference(congruence,[status(thm)],[c529]) ).
cnf(c531,plain,
f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(X4,f(f(X,X4),f(X4,X4))),X2)) = f(f(X3,f(f(f(X,X4),f(X4,X4)),X4)),f(f(f(f(X,X4),f(X4,X4)),X4),X2)),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(X5,f(f(X,X5),f(X5,X5))),X2)),X4) = f(f(f(X3,f(f(f(X,X5),f(X5,X5)),X5)),f(f(f(f(X,X5),f(X5,X5)),X5),X2)),X4),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)) = f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),
inference(congruence,[status(thm)],[c532]) ).
cnf(c534,plain,
f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6))),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c534]) ).
cnf(c536,plain,
f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))) = f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6) = f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)) = f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)),
inference(congruence,[status(thm)],[c537]) ).
cnf(c539,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c541,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c540]) ).
cnf(c542,plain,
f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))) = f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6) = f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6),
inference(congruence,[status(thm)],[c542]) ).
cnf(c544,plain,
f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6)) = f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6)),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6))),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
f(f(X2,X2),f(f(f(X,X2),f(X2,X2)),X2)) = f(f(X,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c547,plain,
f(f(X,X2),f(X2,X2)) = f(f(X2,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(symmetry,[status(thm)],[c546]) ).
cnf(c548,plain,
f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6))),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))) = f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6)))),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)) = f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6)))),f(f(f(X,X6),f(X6,X6)),X6)),
inference(congruence,[status(thm)],[c549]) ).
cnf(c551,plain,
f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6) = f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6)) = f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6)),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6))) = f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6))),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6))) = f(f(f(X,X6),f(X6,X6)),X6),
inference(substitution,[status(thm)],[c55]) ).
cnf(c555,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c556,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c409]) ).
cnf(c557,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c555,c556]) ).
cnf(c558,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X6,X6),f(f(f(X,X6),f(X6,X6)),X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c554,c557]) ).
cnf(c559,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(f(f(X,X6),f(X6,X6)),X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c553,c558]) ).
cnf(c560,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c545,c559]) ).
cnf(c561,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c539,c560]) ).
cnf(c562,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c527,c561]) ).
cnf(c563,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c515,c562]) ).
cnf(c564,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(f(f(X,X6),f(X6,X6)),X6),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c504,c563]) ).
cnf(c565,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(f(f(X,X6),f(X6,X6)),X6),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c493,c564]) ).
cnf(c566,plain,
f(f(f(f(X4,f(f(f(X,X6),f(X6,X6)),X6)),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c489,c565]) ).
cnf(c567,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,f(f(X,X6),f(X6,X6)))),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c483,c566]) ).
cnf(c568,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c477,c567]) ).
cnf(c569,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c471,c568]) ).
cnf(c570,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c459,c569]) ).
cnf(c571,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c447,c570]) ).
cnf(c572,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,f(f(X,X6),f(X6,X6))),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c436,c571]) ).
cnf(c573,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,f(f(X,X6),f(X6,X6))),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c425,c572]) ).
cnf(c574,plain,
f(f(f(f(X4,f(X6,f(f(X,X6),f(X6,X6)))),f(f(X6,X6),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c421,c573]) ).
cnf(c575,plain,
f(f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5),f(f(X6,X6),f(f(f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X2,f(f(f(X4,f(X6,X6)),f(f(X6,X6),X3)),X5)),f(f(X,X6),f(X6,X6)))),f(X6,X6)),X6))) = f(X6,X6),
inference(transitivity,[status(thm)],[c415,c574]) ).
cnf(c576,plain,
f(f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3),X4) = f(X4,X4),
inference(transitivity,[status(thm)],[c404,c575]) ).
cnf(c577,plain,
f(X4,f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),X3)) = f(X4,X4),
inference(transitivity,[status(thm)],[c401,c576]) ).
cnf(c578,plain,
f(X4,f(X3,f(f(X2,f(X4,X4)),f(f(X4,X4),X)))) = f(X4,X4),
inference(transitivity,[status(thm)],[c399,c577]) ).
cnf(c579,plain,
f(X4,f(X3,f(f(X2,f(X4,X4)),f(X,f(X4,X4))))) = f(X4,X4),
inference(transitivity,[status(thm)],[c396,c578]) ).
cnf(c580,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c579]) ).
cnf(c581,plain,
f(X2,f(X,f(X,X))) = f(X2,X2),
inference(transitivity,[status(thm)],[c391,c580]) ).
cnf(c582,plain,
f(f(X2,X2),f(X,f(X,X))) = f(f(X2,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c581]) ).
cnf(c583,plain,
f(f(X2,X2),f(X,f(X,X))) = X2,
inference(transitivity,[status(thm)],[c582,c110]) ).
cnf(c584,plain,
f(f(X,X),f(X2,f(X2,X2))) = X,
inference(substitution,[status(thm)],[c583]) ).
cnf(c585,plain,
f(f(X2,f(X2,X2)),f(X,X)) = X,
inference(transitivity,[status(thm)],[c286,c584]) ).
cnf(c586,plain,
f(f(X,f(X,X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c585]) ).
cnf(c587,plain,
X2 = f(f(X,f(X,X)),f(X2,X2)),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
f(X3,X2) = f(X3,f(f(X,f(X,X)),f(X2,X2))),
inference(congruence,[status(thm)],[c587]) ).
cnf(c589,plain,
f(f(X4,X3),f(X4,f(f(X2,X3),f(X2,X3)))) = f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X2,X3),f(X2,X3)))),
inference(congruence,[status(thm)],[c588]) ).
cnf(c590,plain,
f(f(X,f(X,X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c585]) ).
cnf(c591,plain,
X2 = f(f(X,f(X,X)),f(X2,X2)),
inference(symmetry,[status(thm)],[c590]) ).
cnf(c592,plain,
f(X2,X3) = f(X2,f(f(X,f(X,X)),f(X3,X3))),
inference(congruence,[status(thm)],[c591]) ).
cnf(c593,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3)))),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
f(X4,f(f(X2,X3),f(X2,X3))) = f(X4,f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3))))),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X2,X3),f(X2,X3)))) = f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3)))))),
inference(congruence,[status(thm)],[c594]) ).
cnf(c596,plain,
f(X,f(X2,f(X2,X2))) = f(f(X2,f(X2,X2)),X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c597,plain,
f(f(X2,f(X2,X2)),X) = f(X,f(X2,f(X2,X2))),
inference(symmetry,[status(thm)],[c596]) ).
cnf(c598,plain,
f(X,f(X2,f(X2,X2))) = f(X,X),
inference(substitution,[status(thm)],[c581]) ).
cnf(c599,plain,
f(f(X2,f(X2,X2)),X) = f(X,X),
inference(transitivity,[status(thm)],[c597,c598]) ).
cnf(c600,plain,
f(f(X,f(X,X)),f(X4,f(X2,f(X3,X3)))) = f(f(X4,f(X2,f(X3,X3))),f(X4,f(X2,f(X3,X3)))),
inference(substitution,[status(thm)],[c599]) ).
cnf(c601,plain,
f(X2,f(X,f(X,X))) = f(f(X,f(X,X)),X2),
inference(substitution,[status(thm)],[c266]) ).
cnf(c602,plain,
f(f(X,f(X,X)),X2) = f(X2,f(X,f(X,X))),
inference(symmetry,[status(thm)],[c601]) ).
cnf(c603,plain,
f(X2,f(f(X,f(X,X)),X3)) = f(X2,f(X3,f(X,f(X,X)))),
inference(congruence,[status(thm)],[c602]) ).
cnf(c604,plain,
f(X3,f(X2,f(f(X,f(X,X)),X3))) = f(X3,f(X2,f(X3,f(X,f(X,X))))),
inference(congruence,[status(thm)],[c603]) ).
cnf(c605,plain,
f(X2,f(X3,f(X,f(X,X)))) = f(X2,f(X3,X3)),
inference(congruence,[status(thm)],[c581]) ).
cnf(c606,plain,
f(X3,f(X2,f(X3,f(X,f(X,X))))) = f(X3,f(X2,f(X3,X3))),
inference(congruence,[status(thm)],[c605]) ).
cnf(c607,plain,
f(X3,f(X2,f(X3,f(X,f(X,X))))) = f(X3,X3),
inference(transitivity,[status(thm)],[c606,c409]) ).
cnf(c608,plain,
f(X3,f(X2,f(f(X,f(X,X)),X3))) = f(X3,X3),
inference(transitivity,[status(thm)],[c604,c607]) ).
cnf(c609,plain,
f(f(X5,f(X3,f(X4,X4))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))) = f(f(X5,f(X3,f(X4,X4))),f(X5,f(X3,f(X4,X4)))),
inference(substitution,[status(thm)],[c608]) ).
cnf(c610,plain,
f(f(X5,f(X3,f(X4,X4))),f(X5,f(X3,f(X4,X4)))) = f(f(X5,f(X3,f(X4,X4))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))),
inference(symmetry,[status(thm)],[c609]) ).
cnf(c611,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c612,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c611]) ).
cnf(c613,plain,
f(f(X3,X2),f(X4,f(X,f(X2,X2)))) = f(f(X2,X3),f(X4,f(X,f(X2,X2)))),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
f(X4,f(f(X3,X2),f(X4,f(X,f(X2,X2))))) = f(X4,f(f(X2,X3),f(X4,f(X,f(X2,X2))))),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
f(f(X4,f(X,f(X2,X2))),f(X2,X3)) = f(f(X2,X3),f(X4,f(X,f(X2,X2)))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c616,plain,
f(f(X2,X3),f(X4,f(X,f(X2,X2)))) = f(f(X4,f(X,f(X2,X2))),f(X2,X3)),
inference(symmetry,[status(thm)],[c615]) ).
cnf(c617,plain,
f(X4,f(f(X2,X3),f(X4,f(X,f(X2,X2))))) = f(X4,f(f(X4,f(X,f(X2,X2))),f(X2,X3))),
inference(congruence,[status(thm)],[c616]) ).
cnf(c618,plain,
f(f(X2,X2),X) = f(X,f(X2,X2)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c619,plain,
f(X,f(X2,X2)) = f(f(X2,X2),X),
inference(symmetry,[status(thm)],[c618]) ).
cnf(c620,plain,
f(f(X2,f(X2,X2)),f(X,f(X3,X3))) = f(f(X2,f(X2,X2)),f(f(X3,X3),X)),
inference(congruence,[status(thm)],[c619]) ).
cnf(c621,plain,
f(f(X4,X3),f(f(X2,f(X2,X2)),f(X,f(X4,X4)))) = f(f(X4,X3),f(f(X2,f(X2,X2)),f(f(X4,X4),X))),
inference(congruence,[status(thm)],[c620]) ).
cnf(c622,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c623,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c622]) ).
cnf(c624,plain,
f(f(X4,X3),f(f(X2,f(X2,X2)),f(f(X4,X4),X))) = f(f(X3,X4),f(f(X2,f(X2,X2)),f(f(X4,X4),X))),
inference(congruence,[status(thm)],[c623]) ).
cnf(c625,plain,
f(f(f(X2,f(X2,X2)),f(f(X4,X4),X)),f(X3,X4)) = f(f(X3,X4),f(f(X2,f(X2,X2)),f(f(X4,X4),X))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c626,plain,
f(f(X3,X4),f(f(X2,f(X2,X2)),f(f(X4,X4),X))) = f(f(f(X2,f(X2,X2)),f(f(X4,X4),X)),f(X3,X4)),
inference(symmetry,[status(thm)],[c625]) ).
cnf(c627,plain,
f(f(X2,f(X2,X2)),f(f(X3,X3),X)) = f(f(f(X3,X3),X),f(f(X3,X3),X)),
inference(substitution,[status(thm)],[c599]) ).
cnf(c628,plain,
f(f(f(X2,f(X2,X2)),f(f(X4,X4),X)),f(X3,X4)) = f(f(f(f(X4,X4),X),f(f(X4,X4),X)),f(X3,X4)),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
f(f(X,f(X,X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c585]) ).
cnf(c630,plain,
X2 = f(f(X,f(X,X)),f(X2,X2)),
inference(symmetry,[status(thm)],[c629]) ).
cnf(c631,plain,
f(X2,X3) = f(X2,f(f(X,f(X,X)),f(X3,X3))),
inference(congruence,[status(thm)],[c630]) ).
cnf(c632,plain,
f(f(f(f(X4,X4),X2),f(f(X4,X4),X2)),f(X3,X4)) = f(f(f(f(X4,X4),X2),f(f(X4,X4),X2)),f(X3,f(f(X,f(X,X)),f(X4,X4)))),
inference(congruence,[status(thm)],[c631]) ).
cnf(c633,plain,
f(X2,X2) = f(X2,f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c634,plain,
f(f(X,f(X,X)),f(X3,X3)) = f(f(X,f(X,X)),f(X3,f(f(X3,X3),X2))),
inference(congruence,[status(thm)],[c633]) ).
cnf(c635,plain,
f(X3,f(f(X,f(X,X)),f(X4,X4))) = f(X3,f(f(X,f(X,X)),f(X4,f(f(X4,X4),X2)))),
inference(congruence,[status(thm)],[c634]) ).
cnf(c636,plain,
f(f(f(f(X4,X4),X2),f(f(X4,X4),X2)),f(X3,f(f(X,f(X,X)),f(X4,X4)))) = f(f(f(f(X4,X4),X2),f(f(X4,X4),X2)),f(X3,f(f(X,f(X,X)),f(X4,f(f(X4,X4),X2))))),
inference(congruence,[status(thm)],[c635]) ).
cnf(c637,plain,
f(X2,f(X,f(X,X))) = f(f(X,f(X,X)),X2),
inference(substitution,[status(thm)],[c266]) ).
cnf(c638,plain,
f(f(X,f(X,X)),X2) = f(X2,f(X,f(X,X))),
inference(symmetry,[status(thm)],[c637]) ).
cnf(c639,plain,
f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c388]) ).
cnf(c640,plain,
f(X,f(X,X)) = f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))),
inference(symmetry,[status(thm)],[c639]) ).
cnf(c641,plain,
f(X2,f(X,f(X,X))) = f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c642,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c579]) ).
cnf(c643,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c579]) ).
cnf(c644,plain,
f(X2,X2) = f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(symmetry,[status(thm)],[c643]) ).
cnf(c645,plain,
f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c388]) ).
cnf(c646,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,f(X,f(X,X))),
inference(congruence,[status(thm)],[c645]) ).
cnf(c647,plain,
f(X2,X2) = f(X2,f(X,f(X,X))),
inference(transitivity,[status(thm)],[c644,c646]) ).
cnf(c648,plain,
f(X3,f(f(X,X),f(f(X,f(X3,X3)),f(X,f(X3,X3))))) = f(X3,f(X2,f(X2,X2))),
inference(transitivity,[status(thm)],[c642,c647]) ).
cnf(c649,plain,
f(X3,f(X,f(X,X))) = f(X3,f(X2,f(X2,X2))),
inference(transitivity,[status(thm)],[c641,c648]) ).
cnf(c650,plain,
f(X2,f(X,f(X,X))) = f(X2,f(X3,f(X3,X3))),
inference(substitution,[status(thm)],[c649]) ).
cnf(c651,plain,
f(X,f(X2,f(X2,X2))) = f(f(X2,f(X2,X2)),X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c652,plain,
f(X2,f(X,f(X,X))) = f(f(X3,f(X3,X3)),X2),
inference(transitivity,[status(thm)],[c650,c651]) ).
cnf(c653,plain,
f(f(X,f(X,X)),X2) = f(f(X3,f(X3,X3)),X2),
inference(transitivity,[status(thm)],[c638,c652]) ).
cnf(c654,plain,
f(f(X2,f(X2,X2)),f(X,X3)) = f(f(X3,f(X3,X3)),f(X,X3)),
inference(substitution,[status(thm)],[c653]) ).
cnf(c655,plain,
f(X3,f(f(X2,f(X2,X2)),f(X,X4))) = f(X3,f(f(X4,f(X4,X4)),f(X,X4))),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
f(f(X4,X4),f(X3,f(f(X2,f(X2,X2)),f(X,X4)))) = f(f(X4,X4),f(X3,f(f(X4,f(X4,X4)),f(X,X4)))),
inference(congruence,[status(thm)],[c655]) ).
cnf(c657,plain,
f(f(X,X),X) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c658,plain,
f(X,f(X,X)) = f(f(X,X),X),
inference(symmetry,[status(thm)],[c657]) ).
cnf(c659,plain,
f(f(X2,f(X2,X2)),f(X,X2)) = f(f(f(X2,X2),X2),f(X,X2)),
inference(congruence,[status(thm)],[c658]) ).
cnf(c660,plain,
f(X2,f(f(X3,f(X3,X3)),f(X,X3))) = f(X2,f(f(f(X3,X3),X3),f(X,X3))),
inference(congruence,[status(thm)],[c659]) ).
cnf(c661,plain,
f(f(X3,X3),f(X2,f(f(X3,f(X3,X3)),f(X,X3)))) = f(f(X3,X3),f(X2,f(f(f(X3,X3),X3),f(X,X3)))),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c663,plain,
f(X,X2) = f(X,f(f(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c662]) ).
cnf(c664,plain,
f(f(f(X2,X2),X2),f(X,X2)) = f(f(f(X2,X2),X2),f(X,f(f(X2,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
f(X2,f(f(f(X3,X3),X3),f(X,X3))) = f(X2,f(f(f(X3,X3),X3),f(X,f(f(X3,X3),f(X3,X3))))),
inference(congruence,[status(thm)],[c664]) ).
cnf(c666,plain,
f(f(X3,X3),f(X2,f(f(f(X3,X3),X3),f(X,X3)))) = f(f(X3,X3),f(X2,f(f(f(X3,X3),X3),f(X,f(f(X3,X3),f(X3,X3)))))),
inference(congruence,[status(thm)],[c665]) ).
cnf(c667,plain,
f(f(X,X),f(X,X)) = X,
inference(substitution,[status(thm)],[c119]) ).
cnf(c668,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c667]) ).
cnf(c669,plain,
f(f(X,X),X) = f(f(X,X),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c668]) ).
cnf(c670,plain,
f(f(f(X2,X2),X2),f(X,f(f(X2,X2),f(X2,X2)))) = f(f(f(X2,X2),f(f(X2,X2),f(X2,X2))),f(X,f(f(X2,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
f(X2,f(f(f(X3,X3),X3),f(X,f(f(X3,X3),f(X3,X3))))) = f(X2,f(f(f(X3,X3),f(f(X3,X3),f(X3,X3))),f(X,f(f(X3,X3),f(X3,X3))))),
inference(congruence,[status(thm)],[c670]) ).
cnf(c672,plain,
f(f(X3,X3),f(X2,f(f(f(X3,X3),X3),f(X,f(f(X3,X3),f(X3,X3)))))) = f(f(X3,X3),f(X2,f(f(f(X3,X3),f(f(X3,X3),f(X3,X3))),f(X,f(f(X3,X3),f(X3,X3)))))),
inference(congruence,[status(thm)],[c671]) ).
cnf(c673,plain,
f(f(X3,X3),f(X2,f(f(f(X3,X3),f(f(X3,X3),f(X3,X3))),f(X,f(f(X3,X3),f(X3,X3)))))) = f(f(X3,X3),f(X3,X3)),
inference(substitution,[status(thm)],[c579]) ).
cnf(c674,plain,
f(f(X3,X3),f(X2,f(f(f(X3,X3),f(f(X3,X3),f(X3,X3))),f(X,f(f(X3,X3),f(X3,X3)))))) = X3,
inference(transitivity,[status(thm)],[c673,c110]) ).
cnf(c675,plain,
f(f(X3,X3),f(X2,f(f(f(X3,X3),X3),f(X,f(f(X3,X3),f(X3,X3)))))) = X3,
inference(transitivity,[status(thm)],[c672,c674]) ).
cnf(c676,plain,
f(f(X3,X3),f(X2,f(f(f(X3,X3),X3),f(X,X3)))) = X3,
inference(transitivity,[status(thm)],[c666,c675]) ).
cnf(c677,plain,
f(f(X3,X3),f(X2,f(f(X3,f(X3,X3)),f(X,X3)))) = X3,
inference(transitivity,[status(thm)],[c661,c676]) ).
cnf(c678,plain,
f(f(X4,X4),f(X3,f(f(X2,f(X2,X2)),f(X,X4)))) = X4,
inference(transitivity,[status(thm)],[c656,c677]) ).
cnf(c679,plain,
f(f(f(f(X4,X4),X2),f(f(X4,X4),X2)),f(X3,f(f(X,f(X,X)),f(X4,f(f(X4,X4),X2))))) = f(f(X4,X4),X2),
inference(substitution,[status(thm)],[c678]) ).
cnf(c680,plain,
f(f(X2,X2),X) = f(X,f(X2,X2)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c681,plain,
f(f(f(f(X4,X4),X2),f(f(X4,X4),X2)),f(X3,f(f(X,f(X,X)),f(X4,f(f(X4,X4),X2))))) = f(X2,f(X4,X4)),
inference(transitivity,[status(thm)],[c679,c680]) ).
cnf(c682,plain,
f(f(f(f(X4,X4),X2),f(f(X4,X4),X2)),f(X3,f(f(X,f(X,X)),f(X4,X4)))) = f(X2,f(X4,X4)),
inference(transitivity,[status(thm)],[c636,c681]) ).
cnf(c683,plain,
f(f(f(f(X3,X3),X),f(f(X3,X3),X)),f(X2,X3)) = f(X,f(X3,X3)),
inference(transitivity,[status(thm)],[c632,c682]) ).
cnf(c684,plain,
f(f(f(X2,f(X2,X2)),f(f(X4,X4),X)),f(X3,X4)) = f(X,f(X4,X4)),
inference(transitivity,[status(thm)],[c628,c683]) ).
cnf(c685,plain,
f(f(X3,X4),f(f(X2,f(X2,X2)),f(f(X4,X4),X))) = f(X,f(X4,X4)),
inference(transitivity,[status(thm)],[c626,c684]) ).
cnf(c686,plain,
f(f(X4,X3),f(f(X2,f(X2,X2)),f(f(X4,X4),X))) = f(X,f(X4,X4)),
inference(transitivity,[status(thm)],[c624,c685]) ).
cnf(c687,plain,
f(f(X4,X3),f(f(X2,f(X2,X2)),f(X,f(X4,X4)))) = f(X,f(X4,X4)),
inference(transitivity,[status(thm)],[c621,c686]) ).
cnf(c688,plain,
f(f(X3,X2),f(f(X,f(X,X)),f(X4,f(X3,X3)))) = f(X4,f(X3,X3)),
inference(substitution,[status(thm)],[c687]) ).
cnf(c689,plain,
f(X4,f(X3,X3)) = f(f(X3,X2),f(f(X,f(X,X)),f(X4,f(X3,X3)))),
inference(symmetry,[status(thm)],[c688]) ).
cnf(c690,plain,
f(f(X4,f(X3,X3)),f(f(X3,X2),f(X3,X2))) = f(f(f(X3,X2),f(f(X,f(X,X)),f(X4,f(X3,X3)))),f(f(X3,X2),f(X3,X2))),
inference(congruence,[status(thm)],[c689]) ).
cnf(c691,plain,
f(f(f(X3,X2),f(f(X,f(X,X)),f(X4,f(X3,X3)))),f(f(X3,X2),f(X3,X2))) = f(X3,X2),
inference(substitution,[status(thm)],[c125]) ).
cnf(c692,plain,
f(f(X3,f(X2,X2)),f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c690,c691]) ).
cnf(c693,plain,
f(f(X,f(X2,X2)),f(f(X2,X3),f(X2,X3))) = f(X2,X3),
inference(substitution,[status(thm)],[c692]) ).
cnf(c694,plain,
f(X2,X3) = f(f(X,f(X2,X2)),f(f(X2,X3),f(X2,X3))),
inference(symmetry,[status(thm)],[c693]) ).
cnf(c695,plain,
f(f(X4,f(X,f(X2,X2))),f(X2,X3)) = f(f(X4,f(X,f(X2,X2))),f(f(X,f(X2,X2)),f(f(X2,X3),f(X2,X3)))),
inference(congruence,[status(thm)],[c694]) ).
cnf(c696,plain,
f(X4,f(f(X4,f(X,f(X2,X2))),f(X2,X3))) = f(X4,f(f(X4,f(X,f(X2,X2))),f(f(X,f(X2,X2)),f(f(X2,X3),f(X2,X3))))),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
f(f(X2,X),f(X3,X2)) = f(f(X3,X2),f(X2,X)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c698,plain,
f(f(X3,X2),f(X2,X)) = f(f(X2,X),f(X3,X2)),
inference(symmetry,[status(thm)],[c697]) ).
cnf(c699,plain,
f(X3,f(f(X3,X2),f(X2,X))) = f(X3,f(f(X2,X),f(X3,X2))),
inference(congruence,[status(thm)],[c698]) ).
cnf(c700,plain,
f(f(X,f(X4,X3)),f(X4,f(X2,X2))) = f(f(X4,f(X2,X2)),f(X,f(X4,X3))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c701,plain,
f(f(X4,f(X2,X2)),f(X,f(X4,X3))) = f(f(X,f(X4,X3)),f(X4,f(X2,X2))),
inference(symmetry,[status(thm)],[c700]) ).
cnf(c702,plain,
f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3)))) = f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2)))),
inference(congruence,[status(thm)],[c701]) ).
cnf(c703,plain,
f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))) = f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2))))),
inference(congruence,[status(thm)],[c702]) ).
cnf(c704,plain,
f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3)))))) = f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2)))))),
inference(congruence,[status(thm)],[c703]) ).
cnf(c705,plain,
f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))))) = f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2))))))),
inference(congruence,[status(thm)],[c704]) ).
cnf(c706,plain,
f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3)))))))) = f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2)))))))),
inference(congruence,[status(thm)],[c705]) ).
cnf(c707,plain,
f(f(X,X),X2) = f(X2,f(X,X)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c708,plain,
f(X2,f(X,X)) = f(f(X,X),X2),
inference(symmetry,[status(thm)],[c707]) ).
cnf(c709,plain,
f(f(X,f(X4,X3)),f(X4,f(X2,X2))) = f(f(X,f(X4,X3)),f(f(X2,X2),X4)),
inference(congruence,[status(thm)],[c708]) ).
cnf(c710,plain,
f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2)))) = f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),
inference(congruence,[status(thm)],[c709]) ).
cnf(c711,plain,
f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2))))) = f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4)))),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2)))))) = f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))))),
inference(congruence,[status(thm)],[c711]) ).
cnf(c713,plain,
f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2))))))) = f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4)))))),
inference(congruence,[status(thm)],[c712]) ).
cnf(c714,plain,
f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2)))))))) = f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))))))),
inference(congruence,[status(thm)],[c713]) ).
cnf(c715,plain,
f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4) = f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4)))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c716,plain,
f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4)))) = f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4),
inference(symmetry,[status(thm)],[c715]) ).
cnf(c717,plain,
f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))))) = f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4)),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4)))))) = f(X4,f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4))),
inference(congruence,[status(thm)],[c717]) ).
cnf(c719,plain,
f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))))))) = f(f(X4,X3),f(X4,f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4)))),
inference(congruence,[status(thm)],[c718]) ).
cnf(c720,plain,
f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4),X2) = f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c721,plain,
f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4)) = f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4),X2),
inference(symmetry,[status(thm)],[c720]) ).
cnf(c722,plain,
f(X4,f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4))) = f(X4,f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4),X2)),
inference(congruence,[status(thm)],[c721]) ).
cnf(c723,plain,
f(f(X4,X3),f(X4,f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4)))) = f(f(X4,X3),f(X4,f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4),X2))),
inference(congruence,[status(thm)],[c722]) ).
cnf(c724,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c725,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c724]) ).
cnf(c726,plain,
f(X4,X3) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,f(f(f(X2,f(X2,f(f(X,X),X4))),X4),X))),X3),
inference(congruence,[status(thm)],[c725]) ).
cnf(c727,plain,
f(X3,f(X5,X4)) = f(X3,f(f(f(f(f(X2,X5),f(X5,X)),X5),f(X5,f(f(f(X2,f(X2,f(f(X,X),X5))),X5),X))),X4)),
inference(congruence,[status(thm)],[c726]) ).
cnf(c728,plain,
f(f(X3,f(X6,X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))) = f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),
inference(congruence,[status(thm)],[c727]) ).
cnf(c729,plain,
f(f(f(X3,f(X6,X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6) = f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),
inference(congruence,[status(thm)],[c728]) ).
cnf(c730,plain,
f(f(f(f(X3,f(X6,X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4) = f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4),
inference(congruence,[status(thm)],[c729]) ).
cnf(c731,plain,
f(X6,f(f(f(f(X3,f(X6,X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4)) = f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4)),
inference(congruence,[status(thm)],[c730]) ).
cnf(c732,plain,
f(f(X6,X5),f(X6,f(f(f(f(X3,f(X6,X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4))) = f(f(X6,X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4))),
inference(congruence,[status(thm)],[c731]) ).
cnf(c733,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c734,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c733]) ).
cnf(c735,plain,
f(X4,X3) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,f(f(f(X2,f(X2,f(f(X,X),X4))),X4),X))),X3),
inference(congruence,[status(thm)],[c734]) ).
cnf(c736,plain,
f(X3,f(X5,X4)) = f(X3,f(f(f(f(f(X2,X5),f(X5,X)),X5),f(X5,f(f(f(X2,f(X2,f(f(X,X),X5))),X5),X))),X4)),
inference(congruence,[status(thm)],[c735]) ).
cnf(c737,plain,
f(f(X3,f(X6,X5)),f(f(X4,X4),X6)) = f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6)),
inference(congruence,[status(thm)],[c736]) ).
cnf(c738,plain,
f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))) = f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),
inference(congruence,[status(thm)],[c737]) ).
cnf(c739,plain,
f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6) = f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),
inference(congruence,[status(thm)],[c738]) ).
cnf(c740,plain,
f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4) = f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),X4),
inference(congruence,[status(thm)],[c739]) ).
cnf(c741,plain,
f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4)) = f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),X4)),
inference(congruence,[status(thm)],[c740]) ).
cnf(c742,plain,
f(f(X6,X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4))) = f(f(X6,X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),X4))),
inference(congruence,[status(thm)],[c741]) ).
cnf(c743,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c744,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(f(X2,f(X2,f(f(X,X),X3))),X3),X))),
inference(symmetry,[status(thm)],[c743]) ).
cnf(c745,plain,
f(X4,X3) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,f(f(f(X2,f(X2,f(f(X,X),X4))),X4),X))),X3),
inference(congruence,[status(thm)],[c744]) ).
cnf(c746,plain,
f(f(X6,X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),X4))) = f(f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),X4))),
inference(congruence,[status(thm)],[c745]) ).
cnf(c747,plain,
f(f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),X4))) = X6,
inference(substitution,[status(thm)],[c55]) ).
cnf(c748,plain,
f(f(X6,X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X4,X4),X6))),X6),X4))) = X6,
inference(transitivity,[status(thm)],[c746,c747]) ).
cnf(c749,plain,
f(f(X6,X5),f(X6,f(f(f(f(X3,f(f(f(f(f(X2,X6),f(X6,X)),X6),f(X6,f(f(f(X2,f(X2,f(f(X,X),X6))),X6),X))),X5)),f(f(X3,f(X6,X5)),f(f(X4,X4),X6))),X6),X4))) = X6,
inference(transitivity,[status(thm)],[c742,c748]) ).
cnf(c750,plain,
f(f(X4,X3),f(X4,f(f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4),X2))) = X4,
inference(transitivity,[status(thm)],[c732,c749]) ).
cnf(c751,plain,
f(f(X4,X3),f(X4,f(X2,f(f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))),X4)))) = X4,
inference(transitivity,[status(thm)],[c723,c750]) ).
cnf(c752,plain,
f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(f(X2,X2),X4))))))) = X4,
inference(transitivity,[status(thm)],[c719,c751]) ).
cnf(c753,plain,
f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X,f(X4,X3)),f(X4,f(X2,X2)))))))) = X4,
inference(transitivity,[status(thm)],[c714,c752]) ).
cnf(c754,plain,
f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3)))))))) = X4,
inference(transitivity,[status(thm)],[c706,c753]) ).
cnf(c755,plain,
X4 = f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3)))))))),
inference(symmetry,[status(thm)],[c754]) ).
cnf(c756,plain,
f(X5,X4) = f(X5,f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))))))),
inference(congruence,[status(thm)],[c755]) ).
cnf(c757,plain,
f(f(X4,X3),f(X5,X4)) = f(f(X4,X3),f(X5,f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3)))))))))),
inference(congruence,[status(thm)],[c756]) ).
cnf(c758,plain,
f(X5,f(f(X4,X3),f(X5,X4))) = f(X5,f(f(X4,X3),f(X5,f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))))))))),
inference(congruence,[status(thm)],[c757]) ).
cnf(c759,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c760,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c759]) ).
cnf(c761,plain,
f(X3,f(X2,X)) = f(X3,f(X,X2)),
inference(congruence,[status(thm)],[c760]) ).
cnf(c762,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(X3,f(X2,X))))) = f(f(X3,f(X,X2)),f(f(X2,X),f(X2,f(X3,f(X2,X))))),
inference(congruence,[status(thm)],[c761]) ).
cnf(c763,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c764,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c763]) ).
cnf(c765,plain,
f(f(X2,X),f(X2,f(X3,f(X2,X)))) = f(f(X,X2),f(X2,f(X3,f(X2,X)))),
inference(congruence,[status(thm)],[c764]) ).
cnf(c766,plain,
f(f(X3,f(X,X2)),f(f(X2,X),f(X2,f(X3,f(X2,X))))) = f(f(X3,f(X,X2)),f(f(X,X2),f(X2,f(X3,f(X2,X))))),
inference(congruence,[status(thm)],[c765]) ).
cnf(c767,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c768,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c767]) ).
cnf(c769,plain,
f(X3,f(X2,X)) = f(X3,f(X,X2)),
inference(congruence,[status(thm)],[c768]) ).
cnf(c770,plain,
f(X2,f(X3,f(X2,X))) = f(X2,f(X3,f(X,X2))),
inference(congruence,[status(thm)],[c769]) ).
cnf(c771,plain,
f(f(X,X2),f(X2,f(X3,f(X2,X)))) = f(f(X,X2),f(X2,f(X3,f(X,X2)))),
inference(congruence,[status(thm)],[c770]) ).
cnf(c772,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(X2,f(X3,f(X2,X))))) = f(f(X3,f(X,X2)),f(f(X,X2),f(X2,f(X3,f(X,X2))))),
inference(congruence,[status(thm)],[c771]) ).
cnf(c773,plain,
f(f(X3,f(X,X2)),X2) = f(X2,f(X3,f(X,X2))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c774,plain,
f(X2,f(X3,f(X,X2))) = f(f(X3,f(X,X2)),X2),
inference(symmetry,[status(thm)],[c773]) ).
cnf(c775,plain,
f(f(X,X2),f(X2,f(X3,f(X,X2)))) = f(f(X,X2),f(f(X3,f(X,X2)),X2)),
inference(congruence,[status(thm)],[c774]) ).
cnf(c776,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(X2,f(X3,f(X,X2))))) = f(f(X3,f(X,X2)),f(f(X,X2),f(f(X3,f(X,X2)),X2))),
inference(congruence,[status(thm)],[c775]) ).
cnf(c777,plain,
f(X3,X4) = f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c778,plain,
f(f(X3,X4),f(f(X5,f(X3,X4)),X4)) = f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X3,X4)),X4)),
inference(congruence,[status(thm)],[c777]) ).
cnf(c779,plain,
f(f(X5,f(X3,X4)),f(f(X3,X4),f(f(X5,f(X3,X4)),X4))) = f(f(X5,f(X3,X4)),f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X3,X4)),X4))),
inference(congruence,[status(thm)],[c778]) ).
cnf(c780,plain,
f(X3,X4) = f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c781,plain,
f(X5,f(X3,X4)) = f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),
inference(congruence,[status(thm)],[c780]) ).
cnf(c782,plain,
f(f(X5,f(X3,X4)),X4) = f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),
inference(congruence,[status(thm)],[c781]) ).
cnf(c783,plain,
f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X3,X4)),X4)) = f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4)),
inference(congruence,[status(thm)],[c782]) ).
cnf(c784,plain,
f(f(X5,f(X3,X4)),f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X3,X4)),X4))) = f(f(X5,f(X3,X4)),f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4))),
inference(congruence,[status(thm)],[c783]) ).
cnf(c785,plain,
f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))) = f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4)),
inference(substitution,[status(thm)],[c244]) ).
cnf(c786,plain,
f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4)) = f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),
inference(symmetry,[status(thm)],[c785]) ).
cnf(c787,plain,
f(f(X5,f(X3,X4)),f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4))) = f(f(X5,f(X3,X4)),f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))))),
inference(congruence,[status(thm)],[c786]) ).
cnf(c788,plain,
f(X3,X4) = f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c789,plain,
f(X5,f(X3,X4)) = f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),
inference(congruence,[status(thm)],[c788]) ).
cnf(c790,plain,
f(f(X5,f(X3,X4)),f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))))) = f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))))),
inference(congruence,[status(thm)],[c789]) ).
cnf(c791,plain,
f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))))) = f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),
inference(substitution,[status(thm)],[c185]) ).
cnf(c792,plain,
f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))) = f(X5,f(X3,X4)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c793,plain,
f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4) = f(f(X5,f(X3,X4)),X4),
inference(congruence,[status(thm)],[c792]) ).
cnf(c794,plain,
f(f(X3,f(X,X2)),X2) = f(X2,f(X3,f(X,X2))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c795,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c796,plain,
f(X3,f(X,X2)) = f(X3,f(X2,X)),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
f(X2,f(X3,f(X,X2))) = f(X2,f(X3,f(X2,X))),
inference(congruence,[status(thm)],[c796]) ).
cnf(c798,plain,
f(f(X3,f(X,X2)),X2) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c794,c797]) ).
cnf(c799,plain,
f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4) = f(X4,f(X5,f(X4,X3))),
inference(transitivity,[status(thm)],[c793,c798]) ).
cnf(c800,plain,
f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))))) = f(X4,f(X5,f(X4,X3))),
inference(transitivity,[status(thm)],[c791,c799]) ).
cnf(c801,plain,
f(f(X5,f(X3,X4)),f(f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4),f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))))) = f(X4,f(X5,f(X4,X3))),
inference(transitivity,[status(thm)],[c790,c800]) ).
cnf(c802,plain,
f(f(X5,f(X3,X4)),f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X)))),X4))) = f(X4,f(X5,f(X4,X3))),
inference(transitivity,[status(thm)],[c787,c801]) ).
cnf(c803,plain,
f(f(X5,f(X3,X4)),f(f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),f(f(X5,f(X3,X4)),X4))) = f(X4,f(X5,f(X4,X3))),
inference(transitivity,[status(thm)],[c784,c802]) ).
cnf(c804,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(f(X3,f(X,X2)),X2))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c779,c803]) ).
cnf(c805,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(X2,f(X3,f(X,X2))))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c776,c804]) ).
cnf(c806,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(X2,f(X3,f(X2,X))))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c772,c805]) ).
cnf(c807,plain,
f(f(X3,f(X,X2)),f(f(X2,X),f(X2,f(X3,f(X2,X))))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c766,c806]) ).
cnf(c808,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(X3,f(X2,X))))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c762,c807]) ).
cnf(c809,plain,
f(f(X2,f(X3,f(X2,X))),f(f(X3,f(X2,X)),f(X3,f(X2,f(X3,f(X2,X)))))) = f(X3,f(X2,f(X3,f(X2,X)))),
inference(substitution,[status(thm)],[c808]) ).
cnf(c810,plain,
f(X3,f(X2,f(X3,f(X2,X)))) = f(f(X2,f(X3,f(X2,X))),f(f(X3,f(X2,X)),f(X3,f(X2,f(X3,f(X2,X)))))),
inference(symmetry,[status(thm)],[c809]) ).
cnf(c811,plain,
f(f(X3,X2),X) = f(X,f(X3,X2)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c812,plain,
f(X,f(X3,X2)) = f(f(X3,X2),X),
inference(symmetry,[status(thm)],[c811]) ).
cnf(c813,plain,
f(X3,f(X,f(X3,X2))) = f(X3,f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c812]) ).
cnf(c814,plain,
f(X4,f(X3,f(X,f(X3,X2)))) = f(X4,f(X3,f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c813]) ).
cnf(c815,plain,
f(f(X4,f(X3,X2)),f(X4,f(X3,f(X,f(X3,X2))))) = f(f(X4,f(X3,X2)),f(X4,f(X3,f(f(X3,X2),X)))),
inference(congruence,[status(thm)],[c814]) ).
cnf(c816,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X3,f(f(X4,f(X3,X2)),f(f(X3,f(X,X)),f(X4,f(X3,X2)))))))),
inference(symmetry,[status(thm)],[c754]) ).
cnf(c817,plain,
f(X5,f(f(X5,X4),X3)) = f(f(f(X5,X4),f(X5,f(X2,f(X5,f(f(X,f(X5,X4)),f(f(X5,f(X2,X2)),f(X,f(X5,X4)))))))),f(f(X5,X4),X3)),
inference(congruence,[status(thm)],[c816]) ).
cnf(c818,plain,
f(X6,f(X5,f(f(X5,X4),X3))) = f(X6,f(f(f(X5,X4),f(X5,f(X2,f(X5,f(f(X,f(X5,X4)),f(f(X5,f(X2,X2)),f(X,f(X5,X4)))))))),f(f(X5,X4),X3))),
inference(congruence,[status(thm)],[c817]) ).
cnf(c819,plain,
f(f(X6,f(X5,X4)),f(X6,f(X5,f(f(X5,X4),X3)))) = f(f(X6,f(X5,X4)),f(X6,f(f(f(X5,X4),f(X5,f(X2,f(X5,f(f(X,f(X5,X4)),f(f(X5,f(X2,X2)),f(X,f(X5,X4)))))))),f(f(X5,X4),X3)))),
inference(congruence,[status(thm)],[c818]) ).
cnf(c820,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c821,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c820]) ).
cnf(c822,plain,
f(f(X3,X2),f(X3,X)) = f(f(X3,X2),f(X,X3)),
inference(congruence,[status(thm)],[c821]) ).
cnf(c823,plain,
f(X3,f(f(X3,X2),f(X3,X))) = f(X3,f(f(X3,X2),f(X,X3))),
inference(congruence,[status(thm)],[c822]) ).
cnf(c824,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,X)))) = f(f(X3,X2),f(X3,f(f(X3,X2),f(X,X3)))),
inference(congruence,[status(thm)],[c823]) ).
cnf(c825,plain,
X4 = f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c826,plain,
f(X3,X5) = f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X)))),
inference(congruence,[status(thm)],[c825]) ).
cnf(c827,plain,
f(f(X5,X4),f(X3,X5)) = f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))),
inference(congruence,[status(thm)],[c826]) ).
cnf(c828,plain,
f(X5,f(f(X5,X4),f(X3,X5))) = f(X5,f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X)))))),
inference(congruence,[status(thm)],[c827]) ).
cnf(c829,plain,
f(f(X5,X4),f(X5,f(f(X5,X4),f(X3,X5)))) = f(f(X5,X4),f(X5,f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))))),
inference(congruence,[status(thm)],[c828]) ).
cnf(c830,plain,
X4 = f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X3)),f(f(X2,f(X4,X3)),f(f(X,X),X4))),X4),X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c831,plain,
f(X5,f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X)))))) = f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))),f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X)))))),
inference(congruence,[status(thm)],[c830]) ).
cnf(c832,plain,
f(f(X5,X4),f(X5,f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))))) = f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))),f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))))),
inference(congruence,[status(thm)],[c831]) ).
cnf(c833,plain,
f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))),f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))))) = f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))),
inference(substitution,[status(thm)],[c341]) ).
cnf(c834,plain,
f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X)))) = f(X3,X5),
inference(congruence,[status(thm)],[c59]) ).
cnf(c835,plain,
f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))) = f(f(X5,X4),f(X3,X5)),
inference(congruence,[status(thm)],[c834]) ).
cnf(c836,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c837,plain,
f(f(X3,X2),f(X,X3)) = f(f(X3,X2),f(X3,X)),
inference(congruence,[status(thm)],[c836]) ).
cnf(c838,plain,
f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))) = f(f(X5,X4),f(X5,X3)),
inference(transitivity,[status(thm)],[c835,c837]) ).
cnf(c839,plain,
f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))),f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))))) = f(f(X5,X4),f(X5,X3)),
inference(transitivity,[status(thm)],[c833,c838]) ).
cnf(c840,plain,
f(f(X5,X4),f(X5,f(f(X5,X4),f(X3,f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X4)),f(f(X2,f(X5,X4)),f(f(X,X),X5))),X5),X))))))) = f(f(X5,X4),f(X5,X3)),
inference(transitivity,[status(thm)],[c832,c839]) ).
cnf(c841,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X,X3)))) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c829,c840]) ).
cnf(c842,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,X)))) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c824,c841]) ).
cnf(c843,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))) = f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),
inference(substitution,[status(thm)],[c842]) ).
cnf(c844,plain,
f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))),
inference(symmetry,[status(thm)],[c843]) ).
cnf(c845,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))),
inference(substitution,[status(thm)],[c341]) ).
cnf(c846,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))) = f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))))),
inference(symmetry,[status(thm)],[c845]) ).
cnf(c847,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,X3)) = f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c848,plain,
f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))) = f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,X3)),
inference(symmetry,[status(thm)],[c847]) ).
cnf(c849,plain,
f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X))))) = f(X4,f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,X3))),
inference(congruence,[status(thm)],[c848]) ).
cnf(c850,plain,
f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X)))) = X3,
inference(substitution,[status(thm)],[c371]) ).
cnf(c851,plain,
X3 = f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X)))),
inference(symmetry,[status(thm)],[c850]) ).
cnf(c852,plain,
f(X4,X3) = f(X4,f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X))))),
inference(congruence,[status(thm)],[c851]) ).
cnf(c853,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,X3)) = f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X)))))),
inference(congruence,[status(thm)],[c852]) ).
cnf(c854,plain,
f(X4,f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,X3))) = f(X4,f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X))))))),
inference(congruence,[status(thm)],[c853]) ).
cnf(c855,plain,
f(X4,f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X))))))) = f(X4,f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X))))),
inference(substitution,[status(thm)],[c341]) ).
cnf(c856,plain,
f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X)))) = X3,
inference(substitution,[status(thm)],[c371]) ).
cnf(c857,plain,
f(X4,f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X))))) = f(X4,X3),
inference(congruence,[status(thm)],[c856]) ).
cnf(c858,plain,
f(X4,f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,f(f(X3,X3),f(X4,f(f(X3,X2),f(X3,X))))))) = f(X4,X3),
inference(transitivity,[status(thm)],[c855,c857]) ).
cnf(c859,plain,
f(X4,f(f(X4,f(f(X3,X2),f(X3,X))),f(X4,X3))) = f(X4,X3),
inference(transitivity,[status(thm)],[c854,c858]) ).
cnf(c860,plain,
f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X))))) = f(X4,X3),
inference(transitivity,[status(thm)],[c849,c859]) ).
cnf(c861,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))) = f(f(X4,X3),f(X4,X3)),
inference(congruence,[status(thm)],[c860]) ).
cnf(c862,plain,
f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X))))))) = f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,X3))),
inference(congruence,[status(thm)],[c861]) ).
cnf(c863,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))))) = f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,X3)))),
inference(congruence,[status(thm)],[c862]) ).
cnf(c864,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,X3)))) = f(f(X4,X3),f(X4,X3)),
inference(substitution,[status(thm)],[c409]) ).
cnf(c865,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c863,c864]) ).
cnf(c866,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c846,c865]) ).
cnf(c867,plain,
f(f(X4,X3),f(X4,f(f(X3,X2),f(X3,X)))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c844,c866]) ).
cnf(c868,plain,
f(f(X6,f(X5,X4)),f(X6,f(f(f(X5,X4),f(X5,f(X2,f(X5,f(f(X,f(X5,X4)),f(f(X5,f(X2,X2)),f(X,f(X5,X4)))))))),f(f(X5,X4),X3)))) = f(f(X6,f(X5,X4)),f(X6,f(X5,X4))),
inference(substitution,[status(thm)],[c867]) ).
cnf(c869,plain,
f(f(X,f(X,X)),f(X4,f(X3,X2))) = f(f(X4,f(X3,X2)),f(X4,f(X3,X2))),
inference(substitution,[status(thm)],[c599]) ).
cnf(c870,plain,
f(f(X4,f(X3,X2)),f(X4,f(X3,X2))) = f(f(X,f(X,X)),f(X4,f(X3,X2))),
inference(symmetry,[status(thm)],[c869]) ).
cnf(c871,plain,
f(f(X7,f(X6,X5)),f(X7,f(f(f(X6,X5),f(X6,f(X2,f(X6,f(f(X,f(X6,X5)),f(f(X6,f(X2,X2)),f(X,f(X6,X5)))))))),f(f(X6,X5),X4)))) = f(f(X3,f(X3,X3)),f(X7,f(X6,X5))),
inference(transitivity,[status(thm)],[c868,c870]) ).
cnf(c872,plain,
f(f(X5,f(X4,X3)),f(X5,f(X4,f(f(X4,X3),X2)))) = f(f(X,f(X,X)),f(X5,f(X4,X3))),
inference(transitivity,[status(thm)],[c819,c871]) ).
cnf(c873,plain,
f(f(X5,f(X4,X3)),f(X5,f(X4,f(X2,f(X4,X3))))) = f(f(X,f(X,X)),f(X5,f(X4,X3))),
inference(transitivity,[status(thm)],[c815,c872]) ).
cnf(c874,plain,
f(f(X4,f(X3,X2)),f(X4,f(X3,f(X4,f(X3,X2))))) = f(f(X,f(X,X)),f(X4,f(X3,X2))),
inference(substitution,[status(thm)],[c873]) ).
cnf(c875,plain,
f(f(X3,f(X4,f(X3,X2))),f(f(X4,f(X3,X2)),f(X4,f(X3,f(X4,f(X3,X2)))))) = f(f(X3,f(X4,f(X3,X2))),f(f(X,f(X,X)),f(X4,f(X3,X2)))),
inference(congruence,[status(thm)],[c874]) ).
cnf(c876,plain,
f(X2,f(X,f(X,X))) = f(f(X,f(X,X)),X2),
inference(substitution,[status(thm)],[c266]) ).
cnf(c877,plain,
f(f(X,f(X,X)),X2) = f(X2,f(X,f(X,X))),
inference(symmetry,[status(thm)],[c876]) ).
cnf(c878,plain,
f(f(X3,X2),f(f(X,f(X,X)),X2)) = f(f(X3,X2),f(X2,f(X,f(X,X)))),
inference(congruence,[status(thm)],[c877]) ).
cnf(c879,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c880,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c879]) ).
cnf(c881,plain,
f(f(X3,X2),f(X2,f(X,f(X,X)))) = f(f(X2,X3),f(X2,f(X,f(X,X)))),
inference(congruence,[status(thm)],[c880]) ).
cnf(c882,plain,
f(X,f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))) = f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c883,plain,
f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X) = f(X,f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),
inference(symmetry,[status(thm)],[c882]) ).
cnf(c884,plain,
f(f(f(X,f(X,X)),f(X,f(X,X))),X2) = f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c885,plain,
f(X2,f(f(X,f(X,X)),f(X,f(X,X)))) = f(f(f(X,f(X,X)),f(X,f(X,X))),X2),
inference(symmetry,[status(thm)],[c884]) ).
cnf(c886,plain,
f(f(X4,X4),f(f(f(X3,f(X3,X3)),X2),f(f(X3,f(X3,X3)),f(X,X4)))) = X4,
inference(substitution,[status(thm)],[c678]) ).
cnf(c887,plain,
X4 = f(f(X4,X4),f(f(f(X3,f(X3,X3)),X2),f(f(X3,f(X3,X3)),f(X,X4)))),
inference(symmetry,[status(thm)],[c886]) ).
cnf(c888,plain,
f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X4) = f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),f(f(X4,X4),f(f(f(X3,f(X3,X3)),X2),f(f(X3,f(X3,X3)),f(X,X4))))),
inference(congruence,[status(thm)],[c887]) ).
cnf(c889,plain,
f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),f(f(X4,X4),f(f(f(X3,f(X3,X3)),X2),f(f(X3,f(X3,X3)),f(X,X4))))) = f(X3,f(X3,X3)),
inference(substitution,[status(thm)],[c371]) ).
cnf(c890,plain,
f(f(f(X,f(X,X)),f(X,f(X,X))),X2) = f(X,f(X,X)),
inference(transitivity,[status(thm)],[c888,c889]) ).
cnf(c891,plain,
f(X2,f(f(X,f(X,X)),f(X,f(X,X)))) = f(X,f(X,X)),
inference(transitivity,[status(thm)],[c885,c890]) ).
cnf(c892,plain,
f(X,f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))) = f(X2,f(X2,X2)),
inference(substitution,[status(thm)],[c891]) ).
cnf(c893,plain,
f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c883,c892]) ).
cnf(c894,plain,
f(f(f(X,f(X,X)),f(X,f(X,X))),f(X3,X2)) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c893]) ).
cnf(c895,plain,
f(X,f(X,X)) = f(f(f(X,f(X,X)),f(X,f(X,X))),f(X3,X2)),
inference(symmetry,[status(thm)],[c894]) ).
cnf(c896,plain,
f(X3,f(X,f(X,X))) = f(X3,f(f(f(X,f(X,X)),f(X,f(X,X))),f(X3,X2))),
inference(congruence,[status(thm)],[c895]) ).
cnf(c897,plain,
f(f(X3,X2),f(X3,f(X,f(X,X)))) = f(f(X3,X2),f(X3,f(f(f(X,f(X,X)),f(X,f(X,X))),f(X3,X2)))),
inference(congruence,[status(thm)],[c896]) ).
cnf(c898,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c899,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c898]) ).
cnf(c900,plain,
f(X,f(X3,X2)) = f(X,f(X2,X3)),
inference(congruence,[status(thm)],[c899]) ).
cnf(c901,plain,
f(X3,f(X,f(X3,X2))) = f(X3,f(X,f(X2,X3))),
inference(congruence,[status(thm)],[c900]) ).
cnf(c902,plain,
f(f(X,f(X,X)),f(X4,f(X2,f(X4,X3)))) = f(f(X,f(X,X)),f(X4,f(X2,f(X3,X4)))),
inference(congruence,[status(thm)],[c901]) ).
cnf(c903,plain,
f(f(X2,X3),X) = f(X,f(X2,X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c904,plain,
f(X,f(X2,X3)) = f(f(X2,X3),X),
inference(symmetry,[status(thm)],[c903]) ).
cnf(c905,plain,
f(X3,f(X,f(X2,X3))) = f(X3,f(f(X2,X3),X)),
inference(congruence,[status(thm)],[c904]) ).
cnf(c906,plain,
f(f(X,f(X,X)),f(X4,f(X2,f(X3,X4)))) = f(f(X,f(X,X)),f(X4,f(f(X3,X4),X2))),
inference(congruence,[status(thm)],[c905]) ).
cnf(c907,plain,
f(f(X,f(X,X)),f(X4,f(f(X3,X4),X2))) = f(f(X4,f(f(X3,X4),X2)),f(X4,f(f(X3,X4),X2))),
inference(substitution,[status(thm)],[c599]) ).
cnf(c908,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c909,plain,
f(X3,f(f(X2,X3),X)) = f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),
inference(congruence,[status(thm)],[c908]) ).
cnf(c910,plain,
f(f(X3,f(f(X2,X3),X)),f(X3,f(f(X2,X3),X))) = f(f(X3,f(f(X2,X3),X)),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))),
inference(congruence,[status(thm)],[c909]) ).
cnf(c911,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c912,plain,
f(X3,f(f(X2,X3),X)) = f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),
inference(congruence,[status(thm)],[c911]) ).
cnf(c913,plain,
f(f(X3,f(f(X2,X3),X)),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))) = f(f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))),
inference(congruence,[status(thm)],[c912]) ).
cnf(c914,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))) = f(f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),f(X2,X3)),
inference(substitution,[status(thm)],[c197]) ).
cnf(c915,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),f(X2,X3)) = f(f(X2,X3),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))),
inference(substitution,[status(thm)],[c208]) ).
cnf(c916,plain,
f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)) = f(X3,f(f(X2,X3),X)),
inference(congruence,[status(thm)],[c144]) ).
cnf(c917,plain,
f(f(X2,X3),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))) = f(f(X2,X3),f(X3,f(f(X2,X3),X))),
inference(congruence,[status(thm)],[c916]) ).
cnf(c918,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c919,plain,
f(f(X2,X3),X) = f(f(X3,X2),X),
inference(congruence,[status(thm)],[c918]) ).
cnf(c920,plain,
f(X3,f(f(X2,X3),X)) = f(X3,f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c919]) ).
cnf(c921,plain,
f(f(X2,X3),f(X3,f(f(X2,X3),X))) = f(f(X2,X3),f(X3,f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c920]) ).
cnf(c922,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c923,plain,
f(f(X2,X3),f(X3,f(f(X3,X2),X))) = f(f(X3,X2),f(X3,f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c922]) ).
cnf(c924,plain,
f(f(X3,X2),X) = f(X,f(X3,X2)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c925,plain,
f(X3,f(f(X3,X2),X)) = f(X3,f(X,f(X3,X2))),
inference(congruence,[status(thm)],[c924]) ).
cnf(c926,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),X))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(congruence,[status(thm)],[c925]) ).
cnf(c927,plain,
f(f(X2,X3),f(X3,f(f(X3,X2),X))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c923,c926]) ).
cnf(c928,plain,
f(f(X2,X3),f(X3,f(f(X2,X3),X))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c921,c927]) ).
cnf(c929,plain,
f(f(X2,X3),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c917,c928]) ).
cnf(c930,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),f(X2,X3)) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c915,c929]) ).
cnf(c931,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X)),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c914,c930]) ).
cnf(c932,plain,
f(f(X3,f(f(X2,X3),X)),f(f(f(X3,X3),f(X2,X3)),f(f(X2,X3),X))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c913,c931]) ).
cnf(c933,plain,
f(f(X3,f(f(X2,X3),X)),f(X3,f(f(X2,X3),X))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c910,c932]) ).
cnf(c934,plain,
f(f(X,f(X,X)),f(X4,f(f(X3,X4),X2))) = f(f(X4,X3),f(X4,f(X2,f(X4,X3)))),
inference(transitivity,[status(thm)],[c907,c933]) ).
cnf(c935,plain,
f(f(X,f(X,X)),f(X4,f(X2,f(X3,X4)))) = f(f(X4,X3),f(X4,f(X2,f(X4,X3)))),
inference(transitivity,[status(thm)],[c906,c934]) ).
cnf(c936,plain,
f(f(X,f(X,X)),f(X4,f(X2,f(X4,X3)))) = f(f(X4,X3),f(X4,f(X2,f(X4,X3)))),
inference(transitivity,[status(thm)],[c902,c935]) ).
cnf(c937,plain,
f(f(X,f(X,X)),f(X4,f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),f(X4,X3)))) = f(f(X4,X3),f(X4,f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),f(X4,X3)))),
inference(substitution,[status(thm)],[c936]) ).
cnf(c938,plain,
f(f(X4,X3),f(X4,f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),f(X4,X3)))) = f(f(X,f(X,X)),f(X4,f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),f(X4,X3)))),
inference(symmetry,[status(thm)],[c937]) ).
cnf(c939,plain,
f(f(f(X,f(X,X)),f(X,f(X,X))),f(X3,X2)) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c893]) ).
cnf(c940,plain,
f(X3,f(f(f(X,f(X,X)),f(X,f(X,X))),f(X3,X2))) = f(X3,f(X,f(X,X))),
inference(congruence,[status(thm)],[c939]) ).
cnf(c941,plain,
f(f(X,f(X,X)),f(X4,f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),f(X4,X3)))) = f(f(X,f(X,X)),f(X4,f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c940]) ).
cnf(c942,plain,
f(f(X2,f(X,f(X,X))),f(X3,f(X3,X3))) = f(f(X3,f(X3,X3)),f(X2,f(X,f(X,X)))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c943,plain,
f(f(X3,f(X3,X3)),f(X2,f(X,f(X,X)))) = f(f(X2,f(X,f(X,X))),f(X3,f(X3,X3))),
inference(symmetry,[status(thm)],[c942]) ).
cnf(c944,plain,
f(f(X2,f(X,f(X,X))),f(X3,f(X3,X3))) = f(f(X2,X2),f(X3,f(X3,X3))),
inference(congruence,[status(thm)],[c581]) ).
cnf(c945,plain,
f(f(X,X),f(X2,f(X2,X2))) = X,
inference(substitution,[status(thm)],[c583]) ).
cnf(c946,plain,
f(f(X2,f(X,f(X,X))),f(X3,f(X3,X3))) = X2,
inference(transitivity,[status(thm)],[c944,c945]) ).
cnf(c947,plain,
f(f(X3,f(X3,X3)),f(X2,f(X,f(X,X)))) = X2,
inference(transitivity,[status(thm)],[c943,c946]) ).
cnf(c948,plain,
f(f(X,f(X,X)),f(X3,f(X2,f(X2,X2)))) = X3,
inference(substitution,[status(thm)],[c947]) ).
cnf(c949,plain,
f(f(X,f(X,X)),f(X4,f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),f(X4,X3)))) = X4,
inference(transitivity,[status(thm)],[c941,c948]) ).
cnf(c950,plain,
f(f(X3,X2),f(X3,f(f(f(X,f(X,X)),f(X,f(X,X))),f(X3,X2)))) = X3,
inference(transitivity,[status(thm)],[c938,c949]) ).
cnf(c951,plain,
f(f(X3,X2),f(X3,f(X,f(X,X)))) = X3,
inference(transitivity,[status(thm)],[c897,c950]) ).
cnf(c952,plain,
f(f(X2,X3),f(X2,f(X,f(X,X)))) = X2,
inference(substitution,[status(thm)],[c951]) ).
cnf(c953,plain,
f(f(X3,X2),f(X2,f(X,f(X,X)))) = X2,
inference(transitivity,[status(thm)],[c881,c952]) ).
cnf(c954,plain,
f(f(X3,X2),f(f(X,f(X,X)),X2)) = X2,
inference(transitivity,[status(thm)],[c878,c953]) ).
cnf(c955,plain,
f(f(X3,f(X4,f(X3,X2))),f(f(X,f(X,X)),f(X4,f(X3,X2)))) = f(X4,f(X3,X2)),
inference(substitution,[status(thm)],[c954]) ).
cnf(c956,plain,
f(f(X2,f(X3,f(X2,X))),f(f(X3,f(X2,X)),f(X3,f(X2,f(X3,f(X2,X)))))) = f(X3,f(X2,X)),
inference(transitivity,[status(thm)],[c875,c955]) ).
cnf(c957,plain,
f(X3,f(X2,f(X3,f(X2,X)))) = f(X3,f(X2,X)),
inference(transitivity,[status(thm)],[c810,c956]) ).
cnf(c958,plain,
f(X5,f(f(X4,X3),f(X5,f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))))))))) = f(X5,f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))))))),
inference(substitution,[status(thm)],[c957]) ).
cnf(c959,plain,
f(X5,f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))))))) = f(X5,X4),
inference(congruence,[status(thm)],[c754]) ).
cnf(c960,plain,
f(X5,f(f(X4,X3),f(X5,f(f(X4,X3),f(X4,f(X2,f(X4,f(f(X,f(X4,X3)),f(f(X4,f(X2,X2)),f(X,f(X4,X3))))))))))) = f(X5,X4),
inference(transitivity,[status(thm)],[c958,c959]) ).
cnf(c961,plain,
f(X3,f(f(X2,X),f(X3,X2))) = f(X3,X2),
inference(transitivity,[status(thm)],[c758,c960]) ).
cnf(c962,plain,
f(X3,f(f(X3,X2),f(X2,X))) = f(X3,X2),
inference(transitivity,[status(thm)],[c699,c961]) ).
cnf(c963,plain,
f(X4,f(f(X4,f(X,f(X2,X2))),f(f(X,f(X2,X2)),f(f(X2,X3),f(X2,X3))))) = f(X4,f(X,f(X2,X2))),
inference(substitution,[status(thm)],[c962]) ).
cnf(c964,plain,
f(X4,f(f(X4,f(X,f(X2,X2))),f(X2,X3))) = f(X4,f(X,f(X2,X2))),
inference(transitivity,[status(thm)],[c696,c963]) ).
cnf(c965,plain,
f(X4,f(f(X2,X3),f(X4,f(X,f(X2,X2))))) = f(X4,f(X,f(X2,X2))),
inference(transitivity,[status(thm)],[c617,c964]) ).
cnf(c966,plain,
f(X4,f(f(X3,X2),f(X4,f(X,f(X2,X2))))) = f(X4,f(X,f(X2,X2))),
inference(transitivity,[status(thm)],[c614,c965]) ).
cnf(c967,plain,
f(X3,f(f(X3,X2),f(X3,f(X,f(X2,X2))))) = f(X3,f(X,f(X2,X2))),
inference(substitution,[status(thm)],[c966]) ).
cnf(c968,plain,
f(X3,f(X,f(X2,X2))) = f(X3,f(f(X3,X2),f(X3,f(X,f(X2,X2))))),
inference(symmetry,[status(thm)],[c967]) ).
cnf(c969,plain,
f(f(X5,f(X3,f(X4,X4))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))) = f(f(X5,f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))),
inference(congruence,[status(thm)],[c968]) ).
cnf(c970,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c971,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c970]) ).
cnf(c972,plain,
f(f(X3,X2),f(X3,X)) = f(f(X3,X2),f(X,X3)),
inference(congruence,[status(thm)],[c971]) ).
cnf(c973,plain,
f(f(f(X3,X2),f(X3,X)),f(f(X3,X2),f(X3,X))) = f(f(f(X3,X2),f(X,X3)),f(f(X3,X2),f(X3,X))),
inference(congruence,[status(thm)],[c972]) ).
cnf(c974,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c975,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c974]) ).
cnf(c976,plain,
f(f(X3,X2),f(X3,X)) = f(f(X3,X2),f(X,X3)),
inference(congruence,[status(thm)],[c975]) ).
cnf(c977,plain,
f(f(f(X3,X2),f(X,X3)),f(f(X3,X2),f(X3,X))) = f(f(f(X3,X2),f(X,X3)),f(f(X3,X2),f(X,X3))),
inference(congruence,[status(thm)],[c976]) ).
cnf(c978,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c979,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c978]) ).
cnf(c980,plain,
f(f(X3,X2),f(X,X3)) = f(f(X2,X3),f(X,X3)),
inference(congruence,[status(thm)],[c979]) ).
cnf(c981,plain,
f(f(f(X3,X2),f(X,X3)),f(f(X3,X2),f(X,X3))) = f(f(f(X2,X3),f(X,X3)),f(f(X3,X2),f(X,X3))),
inference(congruence,[status(thm)],[c980]) ).
cnf(c982,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c983,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c982]) ).
cnf(c984,plain,
f(f(X3,X2),f(X,X3)) = f(f(X2,X3),f(X,X3)),
inference(congruence,[status(thm)],[c983]) ).
cnf(c985,plain,
f(f(f(X2,X3),f(X,X3)),f(f(X3,X2),f(X,X3))) = f(f(f(X2,X3),f(X,X3)),f(f(X2,X3),f(X,X3))),
inference(congruence,[status(thm)],[c984]) ).
cnf(c986,plain,
f(X3,X4) = f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c987,plain,
f(f(X4,X5),f(X3,X5)) = f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X)))),
inference(congruence,[status(thm)],[c986]) ).
cnf(c988,plain,
f(f(f(X4,X5),f(X3,X5)),f(f(X4,X5),f(X3,X5))) = f(f(f(X4,X5),f(X3,X5)),f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))),
inference(congruence,[status(thm)],[c987]) ).
cnf(c989,plain,
f(X3,X4) = f(X4,f(f(X3,X4),f(f(f(f(X2,X4),f(f(X2,X4),f(f(X,X),f(X3,X4)))),f(X3,X4)),X))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c990,plain,
f(f(X4,X5),f(X3,X5)) = f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X)))),
inference(congruence,[status(thm)],[c989]) ).
cnf(c991,plain,
f(f(f(X4,X5),f(X3,X5)),f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))) = f(f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X)))),f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))),
inference(congruence,[status(thm)],[c990]) ).
cnf(c992,plain,
f(f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X)))),f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))) = f(X5,f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))),
inference(substitution,[status(thm)],[c207]) ).
cnf(c993,plain,
f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X)))) = f(f(X4,X5),f(X3,X5)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c994,plain,
f(X5,f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))) = f(X5,f(f(X4,X5),f(X3,X5))),
inference(congruence,[status(thm)],[c993]) ).
cnf(c995,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c996,plain,
f(f(X2,X3),f(X,X3)) = f(f(X3,X2),f(X,X3)),
inference(congruence,[status(thm)],[c995]) ).
cnf(c997,plain,
f(X3,f(f(X2,X3),f(X,X3))) = f(X3,f(f(X3,X2),f(X,X3))),
inference(congruence,[status(thm)],[c996]) ).
cnf(c998,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c999,plain,
f(f(X3,X2),f(X,X3)) = f(f(X3,X2),f(X3,X)),
inference(congruence,[status(thm)],[c998]) ).
cnf(c1000,plain,
f(X3,f(f(X3,X2),f(X,X3))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(congruence,[status(thm)],[c999]) ).
cnf(c1001,plain,
f(X3,f(f(X2,X3),f(X,X3))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c997,c1000]) ).
cnf(c1002,plain,
f(X5,f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))) = f(X5,f(f(X5,X4),f(X5,X3))),
inference(transitivity,[status(thm)],[c994,c1001]) ).
cnf(c1003,plain,
f(f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X)))),f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))) = f(X5,f(f(X5,X4),f(X5,X3))),
inference(transitivity,[status(thm)],[c992,c1002]) ).
cnf(c1004,plain,
f(f(f(X4,X5),f(X3,X5)),f(f(X4,X5),f(X5,f(f(X3,X5),f(f(f(f(X2,X5),f(f(X2,X5),f(f(X,X),f(X3,X5)))),f(X3,X5)),X))))) = f(X5,f(f(X5,X4),f(X5,X3))),
inference(transitivity,[status(thm)],[c991,c1003]) ).
cnf(c1005,plain,
f(f(f(X2,X3),f(X,X3)),f(f(X2,X3),f(X,X3))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c988,c1004]) ).
cnf(c1006,plain,
f(f(f(X2,X3),f(X,X3)),f(f(X3,X2),f(X,X3))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c985,c1005]) ).
cnf(c1007,plain,
f(f(f(X3,X2),f(X,X3)),f(f(X3,X2),f(X,X3))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c981,c1006]) ).
cnf(c1008,plain,
f(f(f(X3,X2),f(X,X3)),f(f(X3,X2),f(X3,X))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c977,c1007]) ).
cnf(c1009,plain,
f(f(f(X3,X2),f(X3,X)),f(f(X3,X2),f(X3,X))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c973,c1008]) ).
cnf(c1010,plain,
f(f(f(X3,X2),f(X3,f(X,f(X2,X2)))),f(f(X3,X2),f(X3,f(X,f(X2,X2))))) = f(X3,f(f(X3,X2),f(X3,f(X,f(X2,X2))))),
inference(substitution,[status(thm)],[c1009]) ).
cnf(c1011,plain,
f(X3,f(f(X3,X2),f(X3,f(X,f(X2,X2))))) = f(f(f(X3,X2),f(X3,f(X,f(X2,X2)))),f(f(X3,X2),f(X3,f(X,f(X2,X2))))),
inference(symmetry,[status(thm)],[c1010]) ).
cnf(c1012,plain,
f(f(X5,f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))) = f(f(f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))),
inference(congruence,[status(thm)],[c1011]) ).
cnf(c1013,plain,
f(X3,f(f(X3,X2),f(X3,f(X,f(X2,X2))))) = f(X3,f(X,f(X2,X2))),
inference(substitution,[status(thm)],[c966]) ).
cnf(c1014,plain,
f(X3,f(X,f(X2,X2))) = f(X3,f(f(X3,X2),f(X3,f(X,f(X2,X2))))),
inference(symmetry,[status(thm)],[c1013]) ).
cnf(c1015,plain,
f(f(X,f(X,X)),f(X4,f(X2,f(X3,X3)))) = f(f(X,f(X,X)),f(X4,f(f(X4,X3),f(X4,f(X2,f(X3,X3)))))),
inference(congruence,[status(thm)],[c1014]) ).
cnf(c1016,plain,
f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4))))) = f(X2,f(f(X,f(X,X)),f(X5,f(f(X5,X4),f(X5,f(X3,f(X4,X4))))))),
inference(congruence,[status(thm)],[c1015]) ).
cnf(c1017,plain,
f(f(f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))) = f(f(f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(f(X5,X4),f(X5,f(X3,f(X4,X4)))))))),
inference(congruence,[status(thm)],[c1016]) ).
cnf(c1018,plain,
f(f(f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(f(X5,X4),f(X5,f(X3,f(X4,X4)))))))) = f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),
inference(substitution,[status(thm)],[c678]) ).
cnf(c1019,plain,
f(f(f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))) = f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),
inference(transitivity,[status(thm)],[c1017,c1018]) ).
cnf(c1020,plain,
f(f(X5,f(f(X5,X4),f(X5,f(X3,f(X4,X4))))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))) = f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),
inference(transitivity,[status(thm)],[c1012,c1019]) ).
cnf(c1021,plain,
f(f(X5,f(X3,f(X4,X4))),f(X2,f(f(X,f(X,X)),f(X5,f(X3,f(X4,X4)))))) = f(f(X5,X4),f(X5,f(X3,f(X4,X4)))),
inference(transitivity,[status(thm)],[c969,c1020]) ).
cnf(c1022,plain,
f(f(X3,f(X,f(X2,X2))),f(X3,f(X,f(X2,X2)))) = f(f(X3,X2),f(X3,f(X,f(X2,X2)))),
inference(transitivity,[status(thm)],[c610,c1021]) ).
cnf(c1023,plain,
f(f(X,f(X,X)),f(X4,f(X2,f(X3,X3)))) = f(f(X4,X3),f(X4,f(X2,f(X3,X3)))),
inference(transitivity,[status(thm)],[c600,c1022]) ).
cnf(c1024,plain,
f(f(X,f(X,X)),f(X2,f(f(X,f(X,X)),f(X3,X3)))) = f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3)))),
inference(substitution,[status(thm)],[c1023]) ).
cnf(c1025,plain,
f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3)))) = f(f(X,f(X,X)),f(X2,f(f(X,f(X,X)),f(X3,X3)))),
inference(symmetry,[status(thm)],[c1024]) ).
cnf(c1026,plain,
f(X4,f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3))))) = f(X4,f(f(X,f(X,X)),f(X2,f(f(X,f(X,X)),f(X3,X3))))),
inference(congruence,[status(thm)],[c1025]) ).
cnf(c1027,plain,
f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3)))))) = f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X,f(X,X)),f(X2,f(f(X,f(X,X)),f(X3,X3)))))),
inference(congruence,[status(thm)],[c1026]) ).
cnf(c1028,plain,
f(f(X5,f(f(X2,f(X2,X2)),f(X4,X4))),f(X5,f(f(X2,f(X2,X2)),f(X3,f(f(X2,f(X2,X2)),f(X4,X4)))))) = f(f(X,f(X,X)),f(X5,f(f(X2,f(X2,X2)),f(X4,X4)))),
inference(substitution,[status(thm)],[c873]) ).
cnf(c1029,plain,
f(f(X,f(X,X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c585]) ).
cnf(c1030,plain,
f(X3,f(f(X,f(X,X)),f(X2,X2))) = f(X3,X2),
inference(congruence,[status(thm)],[c1029]) ).
cnf(c1031,plain,
f(f(X,f(X,X)),f(X4,f(f(X2,f(X2,X2)),f(X3,X3)))) = f(f(X,f(X,X)),f(X4,X3)),
inference(congruence,[status(thm)],[c1030]) ).
cnf(c1032,plain,
f(f(X,f(X,X)),f(X3,X2)) = f(f(X3,X2),f(X3,X2)),
inference(substitution,[status(thm)],[c599]) ).
cnf(c1033,plain,
f(f(X,f(X,X)),f(X4,f(f(X2,f(X2,X2)),f(X3,X3)))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c1031,c1032]) ).
cnf(c1034,plain,
f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X,f(X,X)),f(X2,f(f(X,f(X,X)),f(X3,X3)))))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c1028,c1033]) ).
cnf(c1035,plain,
f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X2,X3),f(X2,f(f(X,f(X,X)),f(X3,X3)))))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c1027,c1034]) ).
cnf(c1036,plain,
f(f(X4,f(f(X,f(X,X)),f(X3,X3))),f(X4,f(f(X2,X3),f(X2,X3)))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c595,c1035]) ).
cnf(c1037,plain,
f(f(X3,X2),f(X3,f(f(X,X2),f(X,X2)))) = f(f(X3,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c589,c1036]) ).
cnf(c1038,plain,
f(f(X3,X2),f(X3,X2)) = f(f(X3,X2),f(X3,f(f(X,X2),f(X,X2)))),
inference(symmetry,[status(thm)],[c1037]) ).
cnf(c1039,plain,
f(f(f(X,X2),f(X,X2)),f(f(X3,X2),f(X3,X2))) = f(f(f(X,X2),f(X,X2)),f(f(X3,X2),f(X3,f(f(X,X2),f(X,X2))))),
inference(congruence,[status(thm)],[c1038]) ).
cnf(c1040,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c1041,plain,
f(f(X2,X),f(X2,X3)) = f(f(X2,X),f(X3,X2)),
inference(congruence,[status(thm)],[c1040]) ).
cnf(c1042,plain,
f(X3,f(f(X2,X),f(X2,X3))) = f(X3,f(f(X2,X),f(X3,X2))),
inference(congruence,[status(thm)],[c1041]) ).
cnf(c1043,plain,
f(f(X3,X2),f(X2,X)) = f(f(X2,X),f(X3,X2)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1044,plain,
f(f(X2,X),f(X3,X2)) = f(f(X3,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c1043]) ).
cnf(c1045,plain,
f(X3,f(f(X2,X),f(X3,X2))) = f(X3,f(f(X3,X2),f(X2,X))),
inference(congruence,[status(thm)],[c1044]) ).
cnf(c1046,plain,
f(X3,f(f(X2,X),f(X3,X2))) = f(X3,X2),
inference(transitivity,[status(thm)],[c1045,c962]) ).
cnf(c1047,plain,
f(X3,f(f(X2,X),f(X2,X3))) = f(X3,X2),
inference(transitivity,[status(thm)],[c1042,c1046]) ).
cnf(c1048,plain,
f(f(f(X,X2),f(X,X2)),f(f(X3,X2),f(X3,f(f(X,X2),f(X,X2))))) = f(f(f(X,X2),f(X,X2)),X3),
inference(substitution,[status(thm)],[c1047]) ).
cnf(c1049,plain,
f(f(f(X,X2),f(X,X2)),X3) = f(X3,f(f(X,X2),f(X,X2))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1050,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1051,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(congruence,[status(thm)],[c1050]) ).
cnf(c1052,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(X3,f(f(X2,X),f(X,X2))),
inference(congruence,[status(thm)],[c1051]) ).
cnf(c1053,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1054,plain,
f(f(X2,X),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c1053]) ).
cnf(c1055,plain,
f(X3,f(f(X2,X),f(X,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c1054]) ).
cnf(c1056,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1052,c1055]) ).
cnf(c1057,plain,
f(f(f(X,X2),f(X,X2)),X3) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1049,c1056]) ).
cnf(c1058,plain,
f(f(f(X,X2),f(X,X2)),f(f(X3,X2),f(X3,f(f(X,X2),f(X,X2))))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1048,c1057]) ).
cnf(c1059,plain,
f(f(f(X,X2),f(X,X2)),f(f(X3,X2),f(X3,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1039,c1058]) ).
cnf(c1060,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c284,c1059]) ).
cnf(c1061,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X2,X))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c282,c1060]) ).
cnf(c1062,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X2,X),f(X2,X))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c278,c1061]) ).
cnf(c1063,plain,
f(f(f(X,X2),f(X,X2)),f(f(X2,X3),f(X2,X3))) = f(X,f(f(X2,X3),f(X2,X3))),
inference(substitution,[status(thm)],[c1062]) ).
cnf(c1064,plain,
f(X,f(f(X2,X3),f(X2,X3))) = f(f(f(X,X2),f(X,X2)),f(f(X2,X3),f(X2,X3))),
inference(symmetry,[status(thm)],[c1063]) ).
cnf(c1065,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1066,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c1065]) ).
cnf(c1067,plain,
f(f(X3,X2),f(X2,f(f(X,X3),f(X,X3)))) = f(f(X2,X3),f(X2,f(f(X,X3),f(X,X3)))),
inference(congruence,[status(thm)],[c1066]) ).
cnf(c1068,plain,
f(f(X2,X3),f(X2,f(f(X,X3),f(X,X3)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c1037]) ).
cnf(c1069,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1070,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(congruence,[status(thm)],[c1069]) ).
cnf(c1071,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1072,plain,
f(f(X2,X),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c1071]) ).
cnf(c1073,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c1070,c1072]) ).
cnf(c1074,plain,
f(f(X2,X3),f(X2,f(f(X,X3),f(X,X3)))) = f(f(X3,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c1068,c1073]) ).
cnf(c1075,plain,
f(f(X3,X2),f(X2,f(f(X,X3),f(X,X3)))) = f(f(X3,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c1067,c1074]) ).
cnf(c1076,plain,
f(f(X2,X3),f(X3,f(f(X,X2),f(X,X2)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c1075]) ).
cnf(c1077,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(X3,f(f(X,X2),f(X,X2)))),
inference(symmetry,[status(thm)],[c1076]) ).
cnf(c1078,plain,
f(f(f(X,X2),f(X,X2)),f(f(X2,X3),f(X2,X3))) = f(f(f(X,X2),f(X,X2)),f(f(X2,X3),f(X3,f(f(X,X2),f(X,X2))))),
inference(congruence,[status(thm)],[c1077]) ).
cnf(c1079,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c1080,plain,
f(f(X2,X),f(X,X3)) = f(f(X2,X),f(X3,X)),
inference(congruence,[status(thm)],[c1079]) ).
cnf(c1081,plain,
f(X3,f(f(X2,X),f(X,X3))) = f(X3,f(f(X2,X),f(X3,X))),
inference(congruence,[status(thm)],[c1080]) ).
cnf(c1082,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1083,plain,
f(X2,X) = f(X,X2),
inference(symmetry,[status(thm)],[c1082]) ).
cnf(c1084,plain,
f(f(X2,X),f(X3,X)) = f(f(X,X2),f(X3,X)),
inference(congruence,[status(thm)],[c1083]) ).
cnf(c1085,plain,
f(X3,f(f(X2,X),f(X3,X))) = f(X3,f(f(X,X2),f(X3,X))),
inference(congruence,[status(thm)],[c1084]) ).
cnf(c1086,plain,
f(X3,f(f(X,X2),f(X3,X))) = f(X3,X),
inference(substitution,[status(thm)],[c1046]) ).
cnf(c1087,plain,
f(X3,f(f(X2,X),f(X3,X))) = f(X3,X),
inference(transitivity,[status(thm)],[c1085,c1086]) ).
cnf(c1088,plain,
f(X3,f(f(X2,X),f(X,X3))) = f(X3,X),
inference(transitivity,[status(thm)],[c1081,c1087]) ).
cnf(c1089,plain,
f(f(f(X,X2),f(X,X2)),f(f(X2,X3),f(X3,f(f(X,X2),f(X,X2))))) = f(f(f(X,X2),f(X,X2)),X3),
inference(substitution,[status(thm)],[c1088]) ).
cnf(c1090,plain,
f(f(f(X,X2),f(X,X2)),X3) = f(X3,f(f(X,X2),f(X,X2))),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1091,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1092,plain,
f(f(X,X2),f(X,X2)) = f(f(X,X2),f(X2,X)),
inference(congruence,[status(thm)],[c1091]) ).
cnf(c1093,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(X3,f(f(X,X2),f(X2,X))),
inference(congruence,[status(thm)],[c1092]) ).
cnf(c1094,plain,
f(X,X2) = f(X2,X),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1095,plain,
f(f(X,X2),f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c1094]) ).
cnf(c1096,plain,
f(X3,f(f(X,X2),f(X2,X))) = f(X3,f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c1095]) ).
cnf(c1097,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1093,c1096]) ).
cnf(c1098,plain,
f(f(f(X,X2),f(X,X2)),X3) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1090,c1097]) ).
cnf(c1099,plain,
f(f(f(X,X2),f(X,X2)),f(f(X2,X3),f(X3,f(f(X,X2),f(X,X2))))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1089,c1098]) ).
cnf(c1100,plain,
f(f(f(X,X2),f(X,X2)),f(f(X2,X3),f(X2,X3))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1078,c1099]) ).
cnf(c1101,plain,
f(X,f(f(X2,X3),f(X2,X3))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c1064,c1100]) ).
cnf(c1102,plain,
f(X,f(f(X3,X2),f(X2,X3))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c274,c1101]) ).
cnf(c1103,plain,
f(X,f(f(X3,X2),f(X3,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c270,c1102]) ).
cnf(c1104,plain,
f(c,f(f(a,b),f(a,b))) = f(a,f(f(b,c),f(b,c))),
inference(substitution,[status(thm)],[c1103]) ).
cnf(c1105,plain,
f(a,f(f(b,c),f(b,c))) = f(c,f(f(a,b),f(a,b))),
inference(symmetry,[status(thm)],[c1104]) ).
cnf(c1106,plain,
f(b,a) = f(a,b),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1107,plain,
f(a,b) = f(b,a),
inference(symmetry,[status(thm)],[c1106]) ).
cnf(c1108,plain,
f(f(a,b),f(a,b)) = f(f(b,a),f(a,b)),
inference(congruence,[status(thm)],[c1107]) ).
cnf(c1109,plain,
f(c,f(f(a,b),f(a,b))) = f(c,f(f(b,a),f(a,b))),
inference(congruence,[status(thm)],[c1108]) ).
cnf(c1110,plain,
f(b,a) = f(a,b),
inference(substitution,[status(thm)],[c266]) ).
cnf(c1111,plain,
f(a,b) = f(b,a),
inference(symmetry,[status(thm)],[c1110]) ).
cnf(c1112,plain,
f(f(b,a),f(a,b)) = f(f(b,a),f(b,a)),
inference(congruence,[status(thm)],[c1111]) ).
cnf(c1113,plain,
f(c,f(f(b,a),f(a,b))) = f(c,f(f(b,a),f(b,a))),
inference(congruence,[status(thm)],[c1112]) ).
cnf(c1114,plain,
f(c,f(f(a,b),f(a,b))) = f(c,f(f(b,a),f(b,a))),
inference(transitivity,[status(thm)],[c1109,c1113]) ).
cnf(c1115,plain,
f(a,f(f(b,c),f(b,c))) = f(c,f(f(b,a),f(b,a))),
inference(transitivity,[status(thm)],[c1105,c1114]) ).
cnf(c1116,plain,
$false,
inference(resolution,[status(thm)],[c1,c1115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT078-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 14:00:16 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 187.23/27.27 Command-line arguments: --no-flatten-goal
% 187.23/27.27
% 187.23/27.27 % SZS status Unsatisfiable
% 187.23/27.27
% 189.82/27.61 % SZS output start CNFRefutation
% See solution above
% 203.16/29.59
% 203.16/29.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------