%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT393-2 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 11:45:45 AM UTC 2026
% Result : Unsatisfiable 79.31s 11.80s
% Output : CNFRefutation 95.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 138
% Number of leaves : 2
% Syntax : Number of clauses : 1306 (1306 unt; 0 nHn; 4 RR)
% Number of literals : 1306 (1305 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 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 : 3684 ( 291 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(x0,f(f(x1,x2),f(x1,x2))) != f(x1,f(f(x0,x2),f(x0,x2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
cnf(c3,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(f(X2,X2),X2)),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(X3,f(f(X2,X2),X2)),X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
f(X3,X3) = f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(f(X2,X2),X2)),X))),X3),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
f(f(X3,X3),f(X3,X3)) = f(f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(f(X2,X2),X2)),X))),X3),f(X3,X3)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(f(X4,f(X3,X2)),f(X4,f(X3,X2))),f(X4,f(X3,X2)))),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
f(f(f(X4,X3),f(X3,X2)),X3) = f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,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(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(f(X2,X2),X2)),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
X4 = f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(f(X2,X2),X2)),X3))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(f(f(X2,X4),f(X2,X4)),f(X2,X4))),X))) = f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(f(X2,X2),X2)),X3))),f(f(X4,X3),f(f(f(X4,X3),f(f(f(X2,X4),f(X2,X4)),f(X2,X4))),X))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(f(X2,X2),X2)),X3))),f(f(X4,X3),f(f(f(X4,X3),f(f(f(X2,X4),f(X2,X4)),f(X2,X4))),X))) = f(X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(f(f(X2,X4),f(X2,X4)),f(X2,X4))),X))) = f(X4,X3),
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))) = f(f(X4,X3),f(X3,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,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)],[c10,c16]) ).
cnf(c18,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),X2)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),X2) = f(X2,X2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)),
inference(transitivity,[status(thm)],[c19,c22]) ).
cnf(c24,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
f(f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(f(X2,X2),X2)),X))),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
f(f(X,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c6,c27]) ).
cnf(c29,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
f(X2,X) = f(f(f(X2,X2),f(X2,X2)),X),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))) = f(f(f(f(X2,X2),f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
f(f(f(f(X2,X2),f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
X2 = f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
f(X2,X2) = f(X2,f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
f(f(X2,X),f(X2,X2)) = f(f(X2,X),f(X2,f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
X2 = f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c38,plain,
f(X2,f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2)))) = f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2)))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
f(f(X2,X),f(X2,f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))))) = f(f(X2,X),f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
f(f(f(X3,X2),f(f(f(X,X3),f(X,X3)),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(f(f(X3,X2),f(X3,X2)),f(X3,X2))),f(X3,X2)))) = f(X3,X2),
inference(substitution,[status(thm)],[c33]) ).
cnf(c41,plain,
f(X3,X2) = f(f(f(X3,X2),f(f(f(X,X3),f(X,X3)),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(f(f(X3,X2),f(X3,X2)),f(X3,X2))),f(X3,X2)))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
f(f(X3,X2),f(X3,X2)) = f(f(X3,X2),f(f(f(X3,X2),f(f(f(X,X3),f(X,X3)),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(f(f(X3,X2),f(X3,X2)),f(X3,X2))),f(X3,X2))))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
f(X3,f(f(X3,X2),f(X3,X2))) = f(X3,f(f(X3,X2),f(f(f(X3,X2),f(f(f(X,X3),f(X,X3)),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(f(f(X3,X2),f(X3,X2)),f(X3,X2))),f(X3,X2)))))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(f(f(X,X3),f(X,X3)),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(f(f(X3,X2),f(X3,X2)),f(X3,X2))),f(X3,X2)))))) = f(X3,X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c45,plain,
f(X2,f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
f(f(X2,X),f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))))) = f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
f(f(X2,X),f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))))) = X2,
inference(transitivity,[status(thm)],[c46,c33]) ).
cnf(c48,plain,
f(f(X2,X),f(X2,f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))))) = X2,
inference(transitivity,[status(thm)],[c39,c47]) ).
cnf(c49,plain,
f(f(X2,X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c36,c48]) ).
cnf(c50,plain,
f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X3,X2))) = f(X3,X2),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
f(X3,X2) = f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X3,X2))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
f(f(X3,X2),f(X2,X2)) = f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X3,X2))),f(X2,X2)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
f(X3,X3) = f(X3,f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2)))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,X3)) = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c58,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
f(X3,f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2)))) = f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2)))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))) = f(f(f(f(X4,X3),f(X3,X2)),X),f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))) = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c62,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))) = X3,
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))) = X3,
inference(transitivity,[status(thm)],[c60,c63]) ).
cnf(c65,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c56,c64]) ).
cnf(c66,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X3,X2))),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
f(f(X2,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c52,c66]) ).
cnf(c68,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
f(X2,f(f(X,X2),f(X,X2))) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X,X2))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X,X2))) = f(X,X2),
inference(substitution,[status(thm)],[c49]) ).
cnf(c72,plain,
f(X2,f(f(X,X2),f(X,X2))) = f(X,X2),
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
f(X,f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),X))) = f(f(X2,f(X,X)),X),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
f(f(X2,f(X,X)),X) = f(X,f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),X))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c76,plain,
f(X2,X) = f(f(f(X2,X2),f(X2,X2)),X),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,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)],[c76]) ).
cnf(c78,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c26]) ).
cnf(c79,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
f(X4,f(f(X4,X4),X3)) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
f(f(X4,f(f(X4,X4),X3)),f(X4,X4)) = f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),f(X4,X4)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
f(X4,f(f(X4,f(f(X4,X4),X3)),f(X4,X4))) = f(X4,f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),f(X4,X4))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c26]) ).
cnf(c84,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
f(X4,f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),f(X4,X4))) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),f(X4,X4))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),f(X4,X4))) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c87,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c26]) ).
cnf(c88,plain,
f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)) = f(X4,f(f(X4,X4),X3)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),f(X4,X4))) = f(X4,f(f(X4,X4),X3)),
inference(transitivity,[status(thm)],[c86,c88]) ).
cnf(c90,plain,
f(X4,f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(X4,X4),X3)),f(X4,X4))) = f(X4,f(f(X4,X4),X3)),
inference(transitivity,[status(thm)],[c85,c89]) ).
cnf(c91,plain,
f(X2,f(f(X2,f(f(X2,X2),X)),f(X2,X2))) = f(X2,f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c82,c90]) ).
cnf(c92,plain,
f(f(X2,X2),f(f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)),f(f(X2,X2),f(X2,X2)))) = f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)) = f(f(X2,X2),f(f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)),f(f(X2,X2),f(X2,X2)))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
f(f(X,X),f(X,X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c95,plain,
f(f(f(X2,X2),f(X2,X2)),X) = f(X2,X),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)) = f(f(X2,X2),f(X2,X)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
f(f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)),f(f(X2,X2),f(X2,X2))) = f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
f(f(X2,X2),f(f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)),f(f(X2,X2),f(X2,X2)))) = f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c49]) ).
cnf(c100,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X2)))) = f(f(X2,X2),f(X2,X2)),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X2)))) = X2,
inference(transitivity,[status(thm)],[c100,c28]) ).
cnf(c102,plain,
f(f(X2,X2),f(f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)),f(f(X2,X2),f(X2,X2)))) = X2,
inference(transitivity,[status(thm)],[c98,c101]) ).
cnf(c103,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)) = X2,
inference(transitivity,[status(thm)],[c93,c102]) ).
cnf(c104,plain,
f(f(X2,X2),f(X2,X)) = X2,
inference(transitivity,[status(thm)],[c77,c103]) ).
cnf(c105,plain,
f(f(X,X),f(X,X)) = X,
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
f(f(X2,f(X,X)),X) = f(f(X2,f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),X)) = f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c110,plain,
f(f(X2,f(X,X)),X) = f(f(X2,f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))) = f(f(f(X2,f(X,X)),f(f(X,X),f(X,X))),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c113,plain,
f(X,X) = f(f(f(X,X),f(X,X)),X),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
f(f(X,X),f(X,X)) = f(f(X,X),f(f(f(X,X),f(X,X)),X)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
f(f(X2,f(X,X)),f(f(X,X),f(X,X))) = f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
f(f(f(X2,f(X,X)),f(f(X,X),f(X,X))),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))) = f(f(f(X2,f(X,X)),f(f(X,X),f(X,X))),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c118,plain,
f(f(X,X),f(X,X)) = f(f(X,X),f(f(f(X,X),f(X,X)),X)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
f(f(X2,f(X,X)),f(f(X,X),f(X,X))) = f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
f(f(f(X2,f(X,X)),f(f(X,X),f(X,X))),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))) = f(f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X))),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c122,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)],[c121]) ).
cnf(c123,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c49]) ).
cnf(c124,plain,
f(f(f(X2,X2),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),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)],[c124]) ).
cnf(c126,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(X2,f(f(X3,X3),X3)),X))),f(f(X3,X2),f(X2,X))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c128,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),f(f(X3,X2),f(X2,X))) = f(X2,f(f(X3,X2),f(X2,X))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,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)],[c126,c128]) ).
cnf(c130,plain,
f(f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X))),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))) = f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c132,plain,
f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X))) = f(f(X2,f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))) = f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
f(f(X2,f(X,X)),f(f(X,X),f(X,X))) = f(f(X2,f(X,X)),X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c135,plain,
f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))) = f(f(X,X),f(f(X2,f(X,X)),X)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c137,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
f(X2,X2) = f(X2,f(f(X,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
f(f(X2,X2),f(X,X2)) = f(f(X2,f(f(X,X2),f(X2,X2))),f(X,X2)),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c141,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
f(X2,f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
f(f(X2,f(f(X,X2),f(X2,X2))),f(X,X2)) = f(f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))),f(X,X2)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c145,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
f(X2,X2) = f(f(f(X,X2),f(X2,X2)),X2),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
f(f(X,X2),f(X2,X2)) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
f(f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))),f(X,X2)) = f(f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),f(X,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)) = f(f(X,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c151,plain,
f(f(X,X2),f(X2,X2)) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))) = f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
f(f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),f(X,X2)) = f(f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),f(X,X2)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
X2 = f(f(X2,X),f(X2,X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c155,plain,
f(f(f(X2,X),f(X2,X)),X2) = f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X2))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X2))) = f(X2,X),
inference(substitution,[status(thm)],[c104]) ).
cnf(c157,plain,
f(f(f(X2,X),f(X2,X)),X2) = f(X2,X),
inference(transitivity,[status(thm)],[c155,c156]) ).
cnf(c158,plain,
f(f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),f(X,X2)) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)) = f(f(X,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c160,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c161,plain,
f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)) = X2,
inference(transitivity,[status(thm)],[c159,c160]) ).
cnf(c162,plain,
f(f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c158,c161]) ).
cnf(c163,plain,
f(f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c153,c162]) ).
cnf(c164,plain,
f(f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c149,c163]) ).
cnf(c165,plain,
f(f(X2,f(f(X,X2),f(X2,X2))),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c143,c164]) ).
cnf(c166,plain,
f(f(X2,X2),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c139,c165]) ).
cnf(c167,plain,
f(f(X,X),f(f(X2,f(X,X)),X)) = X,
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c135,c167]) ).
cnf(c169,plain,
f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))) = X,
inference(transitivity,[status(thm)],[c133,c168]) ).
cnf(c170,plain,
f(f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X))),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))) = X,
inference(transitivity,[status(thm)],[c130,c169]) ).
cnf(c171,plain,
f(f(f(X2,f(X,X)),f(f(X,X),f(X,X))),f(f(X2,f(X,X)),f(f(X,X),f(f(f(X,X),f(X,X)),X)))) = X,
inference(transitivity,[status(thm)],[c120,c170]) ).
cnf(c172,plain,
f(f(f(X2,f(X,X)),f(f(X,X),f(X,X))),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c116,c171]) ).
cnf(c173,plain,
f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),f(f(X,X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c111,c172]) ).
cnf(c174,plain,
f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c108,c173]) ).
cnf(c175,plain,
f(X,f(f(f(X2,f(X,X)),X),f(f(X2,f(X,X)),X))) = f(X,X),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
f(f(X2,f(X,X)),X) = f(X,X),
inference(transitivity,[status(thm)],[c74,c175]) ).
cnf(c177,plain,
f(f(X,f(X2,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
f(X2,X2) = f(f(X,f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
f(f(X2,X2),X) = f(f(f(X,f(X2,X2)),X2),X),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
f(f(f(X2,X2),X),f(X,f(X2,X2))) = f(f(f(f(X,f(X2,X2)),X2),X),f(X,f(X2,X2))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
f(f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),X2),
inference(substitution,[status(thm)],[c157]) ).
cnf(c182,plain,
f(f(X,f(X2,X2)),X2) = f(f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)) = X2,
inference(substitution,[status(thm)],[c174]) ).
cnf(c184,plain,
f(f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))) = f(X2,f(X,f(X2,X2))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
f(f(X,f(X2,X2)),X2) = f(X2,f(X,f(X2,X2))),
inference(transitivity,[status(thm)],[c182,c184]) ).
cnf(c186,plain,
f(f(f(X,f(X2,X2)),X2),X) = f(f(X2,f(X,f(X2,X2))),X),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
f(f(f(f(X,f(X2,X2)),X2),X),f(X,f(X2,X2))) = f(f(f(X2,f(X,f(X2,X2))),X),f(X,f(X2,X2))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
X2 = f(f(X2,X),f(X2,X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c189,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
f(f(f(X3,f(X2,X)),X2),f(X2,X)) = f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(X2,X)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c192,plain,
X2 = f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
f(f(f(X3,X2),f(X2,X)),X2) = 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(X2,f(f(X3,X3),X3)),X)))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
f(X2,f(f(X2,X2),X)) = f(X2,f(f(X2,f(f(X2,X2),X)),f(X2,X2))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c195,plain,
f(f(X2,f(f(X2,X2),X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c49]) ).
cnf(c196,plain,
f(X2,f(f(X2,f(f(X2,X2),X)),f(X2,X2))) = f(X2,X2),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
f(X2,f(f(X2,X2),X)) = f(X2,X2),
inference(transitivity,[status(thm)],[c194,c196]) ).
cnf(c198,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(X2,f(f(X3,X3),X3)),X)))) = f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,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(X2,f(f(X3,X3),X3)),X)))) = f(X2,f(f(X3,X2),f(X2,X))),
inference(transitivity,[status(thm)],[c198,c129]) ).
cnf(c200,plain,
f(f(f(X3,X2),f(X2,X)),X2) = f(X2,f(f(X3,X2),f(X2,X))),
inference(transitivity,[status(thm)],[c193,c199]) ).
cnf(c201,plain,
f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(X2,X)) = f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))),
inference(substitution,[status(thm)],[c200]) ).
cnf(c202,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))) = f(f(X3,f(X2,X)),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c203,plain,
f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(X2,X)) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(transitivity,[status(thm)],[c201,c203]) ).
cnf(c205,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)],[c190,c204]) ).
cnf(c206,plain,
f(f(f(X2,f(X,f(X2,X2))),X),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),f(f(X2,f(X,f(X2,X2))),X)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
f(X2,f(X,f(X2,X2))) = f(f(X,f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c208,plain,
f(f(X2,f(X,f(X2,X2))),X) = f(f(f(X,f(X2,X2)),X2),X),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
f(f(X,f(X2,X2)),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(f(X,f(X2,X2)),X2),X)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
f(f(X,f(X2,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c211,plain,
f(f(f(X,f(X2,X2)),X2),X) = f(f(X2,X2),X),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
f(f(X,f(X2,X2)),f(f(f(X,f(X2,X2)),X2),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
f(f(X,f(X2,X2)),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c209,c212]) ).
cnf(c214,plain,
f(f(f(X2,f(X,f(X2,X2))),X),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c206,c213]) ).
cnf(c215,plain,
f(f(f(f(X,f(X2,X2)),X2),X),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c187,c214]) ).
cnf(c216,plain,
f(f(f(X2,X2),X),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c180,c215]) ).
cnf(c217,plain,
f(f(f(X,X),X2),f(X2,f(X,X))) = f(f(X2,f(X,X)),f(f(X,X),X2)),
inference(substitution,[status(thm)],[c216]) ).
cnf(c218,plain,
f(f(X2,f(X,X)),f(f(X,X),X2)) = f(f(f(X,X),X2),f(X2,f(X,X))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
f(X2,f(f(X2,f(X,X)),f(f(X,X),X2))) = f(X2,f(f(f(X,X),X2),f(X2,f(X,X)))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
f(f(f(f(X,X),X2),f(X2,f(X,X))),f(f(f(X,X),X2),f(X2,f(X,X)))) = f(X2,f(f(f(X,X),X2),f(X2,f(X,X)))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c221,plain,
f(X2,f(f(f(X,X),X2),f(X2,f(X,X)))) = f(f(f(f(X,X),X2),f(X2,f(X,X))),f(f(f(X,X),X2),f(X2,f(X,X)))),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
f(f(f(X,X),X2),f(X2,f(X,X))) = f(f(X2,f(X,X)),f(f(X,X),X2)),
inference(substitution,[status(thm)],[c216]) ).
cnf(c223,plain,
f(f(f(f(X,X),X2),f(X2,f(X,X))),f(f(f(X,X),X2),f(X2,f(X,X)))) = f(f(f(X2,f(X,X)),f(f(X,X),X2)),f(f(f(X,X),X2),f(X2,f(X,X)))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
f(f(f(X,X),X2),f(X2,f(X,X))) = f(f(X2,f(X,X)),f(f(X,X),X2)),
inference(substitution,[status(thm)],[c216]) ).
cnf(c225,plain,
f(f(f(X2,f(X,X)),f(f(X,X),X2)),f(f(f(X,X),X2),f(X2,f(X,X)))) = f(f(f(X2,f(X,X)),f(f(X,X),X2)),f(f(X2,f(X,X)),f(f(X,X),X2))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
f(f(f(X2,f(X,X)),f(f(X,X),X2)),f(f(X2,f(X,X)),f(f(X,X),X2))) = f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),X2))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c227,plain,
f(f(f(X,f(X2,X2)),f(f(X2,X2),X)),f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(f(X2,X2),f(f(X,f(X2,X2)),f(f(X2,X2),X))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c228,plain,
f(f(X2,X2),f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(f(f(X,f(X2,X2)),f(f(X2,X2),X)),f(f(X,f(X2,X2)),f(f(X2,X2),X))),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
f(f(X,f(X2,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c230,plain,
f(X2,X2) = f(f(X,f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
f(f(X2,X2),X) = f(f(f(X,f(X2,X2)),X2),X),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
f(f(f(X2,X2),X),f(f(X2,X2),X)) = f(f(f(X2,X2),X),f(f(f(X,f(X2,X2)),X2),X)),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
f(f(f(X,f(X2,X2)),X2),X) = f(f(X2,f(X,f(X2,X2))),X),
inference(congruence,[status(thm)],[c185]) ).
cnf(c234,plain,
f(f(f(X2,X2),X),f(f(f(X,f(X2,X2)),X2),X)) = f(f(f(X2,X2),X),f(f(X2,f(X,f(X2,X2))),X)),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
f(f(X,f(X2,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c236,plain,
f(X2,X2) = f(f(X,f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
f(f(X2,X2),X) = f(f(f(X,f(X2,X2)),X2),X),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
f(f(f(X2,X2),X),f(f(X2,f(X,f(X2,X2))),X)) = f(f(f(f(X,f(X2,X2)),X2),X),f(f(X2,f(X,f(X2,X2))),X)),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
f(f(f(X,f(X2,X2)),X2),X) = f(f(X2,f(X,f(X2,X2))),X),
inference(congruence,[status(thm)],[c185]) ).
cnf(c240,plain,
f(f(f(f(X,f(X2,X2)),X2),X),f(f(X2,f(X,f(X2,X2))),X)) = f(f(f(X2,f(X,f(X2,X2))),X),f(f(X2,f(X,f(X2,X2))),X)),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
X2 = f(f(X2,X),f(X2,X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c242,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
f(f(f(X3,f(X2,X)),X2),f(f(X3,f(X2,X)),X2)) = f(f(f(X3,f(X2,X)),X2),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
X2 = f(f(X2,X),f(X2,X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c245,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
f(f(f(X3,f(X2,X)),X2),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))) = f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))) = f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c248,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))) = f(f(X3,f(X2,X)),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c249,plain,
f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(transitivity,[status(thm)],[c247,c249]) ).
cnf(c251,plain,
f(f(f(X3,f(X2,X)),X2),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2)))) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(transitivity,[status(thm)],[c246,c250]) ).
cnf(c252,plain,
f(f(f(X3,f(X2,X)),X2),f(f(X3,f(X2,X)),X2)) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(transitivity,[status(thm)],[c243,c251]) ).
cnf(c253,plain,
f(f(f(X2,f(X,f(X2,X2))),X),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(X2,f(X,f(X2,X2))),X)),
inference(substitution,[status(thm)],[c252]) ).
cnf(c254,plain,
f(X2,f(X,f(X2,X2))) = f(f(X,f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c255,plain,
f(f(X2,f(X,f(X2,X2))),X) = f(f(f(X,f(X2,X2)),X2),X),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
f(f(X,f(X2,X2)),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(f(X,f(X2,X2)),X2),X)),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
f(f(X,f(X2,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c258,plain,
f(f(f(X,f(X2,X2)),X2),X) = f(f(X2,X2),X),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
f(f(X,f(X2,X2)),f(f(f(X,f(X2,X2)),X2),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
f(f(X,f(X2,X2)),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c256,c259]) ).
cnf(c261,plain,
f(f(f(X2,f(X,f(X2,X2))),X),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c253,c260]) ).
cnf(c262,plain,
f(f(f(f(X,f(X2,X2)),X2),X),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c240,c261]) ).
cnf(c263,plain,
f(f(f(X2,X2),X),f(f(X2,f(X,f(X2,X2))),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c238,c262]) ).
cnf(c264,plain,
f(f(f(X2,X2),X),f(f(f(X,f(X2,X2)),X2),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c234,c263]) ).
cnf(c265,plain,
f(f(f(X2,X2),X),f(f(X2,X2),X)) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(transitivity,[status(thm)],[c232,c264]) ).
cnf(c266,plain,
f(f(X,f(X2,X2)),f(f(X2,X2),X)) = f(f(f(X2,X2),X),f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
f(f(f(X,f(X2,X2)),f(f(X2,X2),X)),f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(f(f(X,f(X2,X2)),f(f(X2,X2),X)),f(f(f(X2,X2),X),f(f(X2,X2),X))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2)) = f(f(f(X3,X3),X2),f(f(X3,X3),X2)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c269,plain,
f(f(f(X3,X3),X2),f(f(X3,X3),X2)) = f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2)),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
f(f(f(X2,f(X3,X3)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X3,X3),X2))) = f(f(f(X2,f(X3,X3)),f(f(X3,X3),X2)),f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
f(f(X,f(X2,X2)),f(f(X2,X2),X)) = f(f(f(X2,X2),X),f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c272,plain,
f(f(f(X2,f(X3,X3)),f(f(X3,X3),X2)),f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2))) = f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2))) = f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c274,plain,
f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)) = f(f(X3,X3),X2),
inference(substitution,[status(thm)],[c104]) ).
cnf(c275,plain,
f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2))) = f(f(X3,X3),X2),
inference(transitivity,[status(thm)],[c273,c274]) ).
cnf(c276,plain,
f(f(f(X2,f(X3,X3)),f(f(X3,X3),X2)),f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),X)),f(f(X3,X3),X2))) = f(f(X3,X3),X2),
inference(transitivity,[status(thm)],[c272,c275]) ).
cnf(c277,plain,
f(f(f(X,f(X2,X2)),f(f(X2,X2),X)),f(f(f(X2,X2),X),f(f(X2,X2),X))) = f(f(X2,X2),X),
inference(transitivity,[status(thm)],[c270,c276]) ).
cnf(c278,plain,
f(f(f(X,f(X2,X2)),f(f(X2,X2),X)),f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(f(X2,X2),X),
inference(transitivity,[status(thm)],[c267,c277]) ).
cnf(c279,plain,
f(f(X2,X2),f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(f(X2,X2),X),
inference(transitivity,[status(thm)],[c228,c278]) ).
cnf(c280,plain,
f(f(X,X),f(f(X2,f(X,X)),f(f(X,X),X2))) = f(f(X,X),X2),
inference(substitution,[status(thm)],[c279]) ).
cnf(c281,plain,
f(f(f(X2,f(X,X)),f(f(X,X),X2)),f(f(X2,f(X,X)),f(f(X,X),X2))) = f(f(X,X),X2),
inference(transitivity,[status(thm)],[c226,c280]) ).
cnf(c282,plain,
f(f(f(X2,f(X,X)),f(f(X,X),X2)),f(f(f(X,X),X2),f(X2,f(X,X)))) = f(f(X,X),X2),
inference(transitivity,[status(thm)],[c225,c281]) ).
cnf(c283,plain,
f(f(f(f(X,X),X2),f(X2,f(X,X))),f(f(f(X,X),X2),f(X2,f(X,X)))) = f(f(X,X),X2),
inference(transitivity,[status(thm)],[c223,c282]) ).
cnf(c284,plain,
f(X2,f(f(f(X,X),X2),f(X2,f(X,X)))) = f(f(X,X),X2),
inference(transitivity,[status(thm)],[c221,c283]) ).
cnf(c285,plain,
f(X2,f(f(X2,f(X,X)),f(f(X,X),X2))) = f(f(X,X),X2),
inference(transitivity,[status(thm)],[c219,c284]) ).
cnf(c286,plain,
f(X,f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(f(X2,X2),X),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
f(f(X2,X2),X) = f(X,f(f(X,f(X2,X2)),f(f(X2,X2),X))),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
f(f(X,X),f(f(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c166]) ).
cnf(c289,plain,
X = f(f(X,X),f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
f(X,f(X2,X2)) = f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
f(f(X,f(X2,X2)),f(f(X2,X2),X)) = f(f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),f(f(X2,X2),X)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
f(X,f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(X,f(f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),f(f(X2,X2),X))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
f(f(X,X),f(f(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c166]) ).
cnf(c294,plain,
X = f(f(X,X),f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
f(X,f(f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),f(f(X2,X2),X))) = f(f(f(X,X),f(f(X2,X2),X)),f(f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),f(f(X2,X2),X))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
X2 = f(f(X2,X),f(X2,X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c297,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
f(f(f(X3,f(X2,X)),X2),f(X2,X)) = f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(X2,X)),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),X2),f(X2,X))) = f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(X2,X))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(X2,X))) = f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c301,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))) = f(f(X3,f(X2,X)),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c302,plain,
f(f(X3,f(X2,X)),f(f(f(X3,f(X2,X)),f(f(X2,X),f(X2,X2))),f(X2,X))) = f(f(X3,f(X2,X)),X2),
inference(transitivity,[status(thm)],[c300,c301]) ).
cnf(c303,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)],[c299,c302]) ).
cnf(c304,plain,
f(f(f(X,X),f(f(X2,X2),X)),f(f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),f(f(X2,X2),X))) = f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),
inference(substitution,[status(thm)],[c303]) ).
cnf(c305,plain,
f(f(X,X),f(f(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c166]) ).
cnf(c306,plain,
f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)) = f(X,f(X2,X2)),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
f(f(f(X,X),f(f(X2,X2),X)),f(f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),f(f(X2,X2),X))) = f(X,f(X2,X2)),
inference(transitivity,[status(thm)],[c304,c306]) ).
cnf(c308,plain,
f(X,f(f(f(f(X,X),f(f(X2,X2),X)),f(X2,X2)),f(f(X2,X2),X))) = f(X,f(X2,X2)),
inference(transitivity,[status(thm)],[c295,c307]) ).
cnf(c309,plain,
f(X,f(f(X,f(X2,X2)),f(f(X2,X2),X))) = f(X,f(X2,X2)),
inference(transitivity,[status(thm)],[c292,c308]) ).
cnf(c310,plain,
f(f(X2,X2),X) = f(X,f(X2,X2)),
inference(transitivity,[status(thm)],[c287,c309]) ).
cnf(c311,plain,
f(f(f(X3,X),f(X3,X)),X2) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c310]) ).
cnf(c312,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(f(f(X3,X),f(X3,X)),X2),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(f(f(X3,X),f(X3,X)),X2),f(X3,f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c315,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(symmetry,[status(thm)],[c314]) ).
cnf(c316,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X,X)) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))),f(X,X)),
inference(congruence,[status(thm)],[c315]) ).
cnf(c317,plain,
f(f(X2,X2),f(f(X,f(X2,X2)),X2)) = X2,
inference(substitution,[status(thm)],[c166]) ).
cnf(c318,plain,
X2 = f(f(X2,X2),f(f(X,f(X2,X2)),X2)),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
f(X2,f(X,f(X2,X2))) = f(f(f(X2,X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
f(f(X,f(X2,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c321,plain,
f(X2,X2) = f(f(X,f(X2,X2)),X2),
inference(symmetry,[status(thm)],[c320]) ).
cnf(c322,plain,
f(f(X2,X2),f(f(X,f(X2,X2)),X2)) = f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
f(f(f(X2,X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))) = f(f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
f(f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),X2),
inference(substitution,[status(thm)],[c157]) ).
cnf(c325,plain,
f(f(X,f(X2,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c176]) ).
cnf(c326,plain,
f(f(f(f(X,f(X2,X2)),X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c324,c325]) ).
cnf(c327,plain,
f(f(f(X2,X2),f(f(X,f(X2,X2)),X2)),f(X,f(X2,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c323,c326]) ).
cnf(c328,plain,
f(X2,f(X,f(X2,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c319,c327]) ).
cnf(c329,plain,
f(f(X2,X),f(X,f(f(X2,X),f(X2,X)))) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c328]) ).
cnf(c330,plain,
f(f(X2,X),f(X2,X)) = f(f(X2,X),f(X,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
f(f(f(X3,X2),f(X3,X2)),X) = f(f(f(X3,X2),f(X2,f(f(X3,X2),f(X3,X2)))),X),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
f(f(f(f(X3,X2),f(X3,X2)),X),f(X2,X2)) = f(f(f(f(X3,X2),f(X2,f(f(X3,X2),f(X3,X2)))),X),f(X2,X2)),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
f(f(f(f(X3,X2),f(X2,f(f(X3,X2),f(X3,X2)))),X),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c65]) ).
cnf(c334,plain,
f(f(f(f(X3,X2),f(X3,X2)),X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c332,c333]) ).
cnf(c335,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))),f(X,X)) = X,
inference(substitution,[status(thm)],[c334]) ).
cnf(c336,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X,X)) = X,
inference(transitivity,[status(thm)],[c316,c335]) ).
cnf(c337,plain,
X = f(f(X3,f(f(X2,X),f(X2,X))),f(X,X)),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
f(X3,X) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X,X))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X,X)))),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
f(X2,f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))) = f(X2,f(f(X,X),X)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c341,plain,
f(X2,f(f(X,X),X)) = f(X2,f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
X2 = f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c343,plain,
f(X3,f(f(X,X),X)) = f(f(f(X3,X2),f(X3,f(f(X3,f(f(X3,X3),X3)),X3))),f(f(X,X),X)),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
f(f(X3,X2),f(X3,f(f(X,X),X))) = f(f(X3,X2),f(f(f(X3,X2),f(X3,f(f(X3,f(f(X3,X3),X3)),X3))),f(f(X,X),X))),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
X2 = f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c346,plain,
f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))) = f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X))))) = f(f(X2,X),f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c349,plain,
f(X,f(X,X)) = f(f(f(X,X),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
f(f(X2,X),f(X2,f(X2,X2))) = f(f(X2,X),f(f(f(X2,X2),f(X2,X2)),f(X2,X2))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
f(X2,f(f(X2,X),f(X2,f(X2,X2)))) = f(X2,f(f(X2,X),f(f(f(X2,X2),f(X2,X2)),f(X2,X2)))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
f(f(X4,X3),f(f(f(X4,X3),f(f(f(X2,X4),f(X2,X4)),f(X2,X4))),f(f(f(f(X4,X3),f(f(f(X2,X4),f(X2,X4)),f(X2,X4))),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),X5))) = f(f(X4,X3),f(f(f(X2,X4),f(X2,X4)),f(X2,X4))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c353,plain,
f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5))) = f(f(X5,X4),f(f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5))),f(f(f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5))),f(f(f(X2,f(X5,X4)),f(X2,f(X5,X4))),f(X2,f(X5,X4)))),X))),
inference(symmetry,[status(thm)],[c352]) ).
cnf(c354,plain,
f(X5,f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5)))) = f(X5,f(f(X5,X4),f(f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5))),f(f(f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5))),f(f(f(X2,f(X5,X4)),f(X2,f(X5,X4))),f(X2,f(X5,X4)))),X)))),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5))),f(f(f(f(X5,X4),f(f(f(X3,X5),f(X3,X5)),f(X3,X5))),f(f(f(X2,f(X5,X4)),f(X2,f(X5,X4))),f(X2,f(X5,X4)))),X)))) = f(X5,X4),
inference(substitution,[status(thm)],[c15]) ).
cnf(c356,plain,
f(X3,f(f(X3,X2),f(f(f(X,X3),f(X,X3)),f(X,X3)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c354,c355]) ).
cnf(c357,plain,
f(X2,f(f(X2,X),f(f(f(X2,X2),f(X2,X2)),f(X2,X2)))) = f(X2,X),
inference(substitution,[status(thm)],[c356]) ).
cnf(c358,plain,
f(X2,f(f(X2,X),f(X2,f(X2,X2)))) = f(X2,X),
inference(transitivity,[status(thm)],[c351,c357]) ).
cnf(c359,plain,
f(f(X2,X),f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(f(X2,X),f(X2,X))))) = f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(substitution,[status(thm)],[c358]) ).
cnf(c360,plain,
f(f(X2,X),f(f(f(X2,X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),f(f(X2,X),f(f(X2,X),f(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c359,c33]) ).
cnf(c361,plain,
f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c347,c360]) ).
cnf(c362,plain,
f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),
inference(substitution,[status(thm)],[c361]) ).
cnf(c363,plain,
f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X) = f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
f(f(f(f(f(X,X),X),f(f(X,X),X)),f(X,X)),f(f(X,X),X)) = f(f(f(X,X),X),f(f(X,X),X)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c365,plain,
f(f(f(X,X),X),f(f(X,X),X)) = f(f(f(f(f(X,X),X),f(f(X,X),X)),f(X,X)),f(f(X,X),X)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X) = f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),f(X2,X2)),f(f(X2,X2),X2)),X),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2) = f(f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),f(X2,X2)),f(f(X2,X2),X2)),X),X2),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c369,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X2)),X),X2) = f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X2)),X),f(f(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
f(f(f(X,X),f(f(X2,X2),X2)),X) = f(X,X),
inference(substitution,[status(thm)],[c124]) ).
cnf(c371,plain,
f(X,X) = f(f(f(X,X),f(f(X2,X2),X2)),X),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c372,plain,
f(f(X,X),f(X,X)) = f(f(X,X),f(f(f(X,X),f(f(X2,X2),X2)),X)),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X2)),X),f(f(X2,X2),f(X2,X2))) = f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(f(X2,X2),f(f(X3,X3),X3)),X2))),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(f(X2,X2),f(f(X3,X3),X3)),X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c375,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X2)),X),f(f(X2,X2),f(X2,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c373,c374]) ).
cnf(c376,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X2)),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c369,c375]) ).
cnf(c377,plain,
f(f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),f(X2,X2)),f(f(X2,X2),X2)),X),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c376]) ).
cnf(c378,plain,
f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c367,c377]) ).
cnf(c379,plain,
f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))) = f(f(X2,X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))),
inference(congruence,[status(thm)],[c378]) ).
cnf(c381,plain,
f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)))) = f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)))),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)) = f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)),
inference(congruence,[status(thm)],[c378]) ).
cnf(c384,plain,
f(f(X2,X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))) = f(f(X2,X2),f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)))) = f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)))),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)) = f(f(X2,X2),f(X2,X2)),
inference(congruence,[status(thm)],[c378]) ).
cnf(c388,plain,
f(f(X2,X2),f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))) = f(f(X2,X2),f(f(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c387]) ).
cnf(c389,plain,
f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2)))) = f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(X2,X2))))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
f(f(X,X),f(f(X,X),f(X,X))) = f(f(X,X),X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c392,plain,
f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(X2,X2)))) = f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),X2)),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(X2,X2))))) = f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),X2))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),X2)) = f(f(f(X2,X2),X2),f(f(X2,X2),X2)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c395,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),X2))) = f(f(X2,X2),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c26]) ).
cnf(c397,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)),
inference(symmetry,[status(thm)],[c396]) ).
cnf(c398,plain,
f(X3,X3) = f(X3,f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
f(f(X3,X3),X3) = f(f(X3,f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),X3),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
f(f(f(X4,X4),X3),f(f(X4,X4),X4)) = f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),X4)),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
f(f(X4,X4),f(f(f(X4,X4),X3),f(f(X4,X4),X4))) = f(f(X4,X4),f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),X4))),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c26]) ).
cnf(c403,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
f(f(X3,f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),X3) = f(f(X3,f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),X4)) = f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)))),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
f(f(X4,X4),f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),X4))) = f(f(X4,X4),f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))))),
inference(congruence,[status(thm)],[c405]) ).
cnf(c407,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c26]) ).
cnf(c408,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c409,plain,
f(X3,f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))) = f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)),f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
f(f(X3,f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))) = f(f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3)),f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,X3))),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)))) = f(f(f(X4,X4),X3),f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)))),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,plain,
f(f(X4,X4),f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))))) = f(f(X4,X4),f(f(f(X4,X4),X3),f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))))),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
f(f(X4,X4),f(f(f(X4,X4),X3),f(f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4)),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))))) = f(f(X4,X4),X3),
inference(substitution,[status(thm)],[c356]) ).
cnf(c414,plain,
f(f(X4,X4),f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))))) = f(f(X4,X4),X3),
inference(transitivity,[status(thm)],[c412,c413]) ).
cnf(c415,plain,
f(f(X4,X4),f(f(f(X4,X4),X3),f(f(X4,f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,X4))),X4))) = f(f(X4,X4),X3),
inference(transitivity,[status(thm)],[c406,c414]) ).
cnf(c416,plain,
f(f(X2,X2),f(f(f(X2,X2),X),f(f(X2,X2),X2))) = f(f(X2,X2),X),
inference(transitivity,[status(thm)],[c401,c415]) ).
cnf(c417,plain,
f(f(X,X),f(f(f(X,X),X),f(f(X,X),X))) = f(f(X,X),X),
inference(substitution,[status(thm)],[c416]) ).
cnf(c418,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),X2))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c395,c417]) ).
cnf(c419,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(X2,X2))))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c393,c418]) ).
cnf(c420,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c390,c419]) ).
cnf(c421,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(X2,X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c386,c420]) ).
cnf(c422,plain,
f(f(X2,X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c382,c421]) ).
cnf(c423,plain,
f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2),f(f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),X2))))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c379,c422]) ).
cnf(c424,plain,
f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c363,c423]) ).
cnf(c425,plain,
f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X2)) = f(f(X,X),X),
inference(substitution,[status(thm)],[c424]) ).
cnf(c426,plain,
f(f(X,X),X) = f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
f(f(X3,X2),f(f(X,X),X)) = f(f(X3,X2),f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X3))),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
f(X3,f(f(X3,X2),f(f(X,X),X))) = f(X3,f(f(X3,X2),f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X2)) = f(f(f(X,X),X),f(f(X,X),X)),
inference(substitution,[status(thm)],[c197]) ).
cnf(c430,plain,
f(f(f(X,X),X),f(f(X,X),X)) = f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X2)) = f(f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
f(f(X3,X2),f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X3))) = f(f(X3,X2),f(f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3))),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
f(X3,f(f(X3,X2),f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))) = f(X3,f(f(X3,X2),f(f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
f(f(f(f(X,X),X),f(f(X,X),X)),X2) = f(f(X,X),X),
inference(substitution,[status(thm)],[c424]) ).
cnf(c435,plain,
f(f(X,X),X) = f(f(f(f(X,X),X),f(f(X,X),X)),X2),
inference(symmetry,[status(thm)],[c434]) ).
cnf(c436,plain,
f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X2)) = f(f(f(f(f(X,X),X),f(f(X,X),X)),X2),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
f(f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),f(f(f(f(X,X),X),f(f(X,X),X)),X2)) = f(f(f(f(f(f(X,X),X),f(f(X,X),X)),X2),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),f(f(f(f(X,X),X),f(f(X,X),X)),X2)),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
f(f(X3,X2),f(f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3))) = f(f(X3,X2),f(f(f(f(f(f(X,X),X),f(f(X,X),X)),X3),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3))),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
f(X3,f(f(X3,X2),f(f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))) = f(X3,f(f(X3,X2),f(f(f(f(f(f(X,X),X),f(f(X,X),X)),X3),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
f(X3,f(f(X3,X2),f(f(f(f(f(f(X,X),X),f(f(X,X),X)),X3),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))) = f(X3,X2),
inference(substitution,[status(thm)],[c356]) ).
cnf(c441,plain,
f(X3,f(f(X3,X2),f(f(f(f(X,X),X),f(f(f(f(X,X),X),f(f(X,X),X)),X3)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c439,c440]) ).
cnf(c442,plain,
f(X3,f(f(X3,X2),f(f(f(f(X,X),X),f(f(X,X),X)),f(f(f(f(X,X),X),f(f(X,X),X)),X3)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c433,c441]) ).
cnf(c443,plain,
f(X3,f(f(X3,X2),f(f(X,X),X))) = f(X3,X2),
inference(transitivity,[status(thm)],[c428,c442]) ).
cnf(c444,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X3,f(f(X3,f(f(X3,X3),X3)),X3))),f(f(X,X),X))) = f(f(X3,X2),f(X3,f(f(X3,f(f(X3,X3),X3)),X3))),
inference(substitution,[status(thm)],[c443]) ).
cnf(c445,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X3,f(f(X3,f(f(X3,X3),X3)),X3))),f(f(X,X),X))) = X3,
inference(transitivity,[status(thm)],[c444,c33]) ).
cnf(c446,plain,
f(f(X3,X2),f(X3,f(f(X,X),X))) = X3,
inference(transitivity,[status(thm)],[c344,c445]) ).
cnf(c447,plain,
f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X))) = X2,
inference(substitution,[status(thm)],[c446]) ).
cnf(c448,plain,
f(X2,f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))) = f(X2,X2),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
f(X2,f(f(X,X),X)) = f(X2,X2),
inference(transitivity,[status(thm)],[c341,c448]) ).
cnf(c450,plain,
f(f(X4,f(f(X4,X3),X2)),f(f(X,X),X)) = f(f(X4,f(f(X4,X3),X2)),f(X4,f(f(X4,X3),X2))),
inference(substitution,[status(thm)],[c449]) ).
cnf(c451,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c452,plain,
f(X3,f(f(X3,X2),X)) = f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
f(f(X3,f(f(X3,X2),X)),f(X3,f(f(X3,X2),X))) = f(f(X3,f(f(X3,X2),X)),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c455,plain,
f(X3,f(f(X3,X2),X)) = f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
f(f(X3,f(f(X3,X2),X)),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))) = f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))) = f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c458,plain,
f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)) = f(X3,f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c459,plain,
f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))) = f(f(X3,X2),f(X3,f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c458]) ).
cnf(c460,plain,
f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))) = f(f(X3,X2),f(X3,f(f(X3,X2),X))),
inference(transitivity,[status(thm)],[c457,c459]) ).
cnf(c461,plain,
f(f(X3,f(f(X3,X2),X)),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))) = f(f(X3,X2),f(X3,f(f(X3,X2),X))),
inference(transitivity,[status(thm)],[c456,c460]) ).
cnf(c462,plain,
f(f(X3,f(f(X3,X2),X)),f(X3,f(f(X3,X2),X))) = f(f(X3,X2),f(X3,f(f(X3,X2),X))),
inference(transitivity,[status(thm)],[c453,c461]) ).
cnf(c463,plain,
f(f(X4,f(f(X4,X3),X2)),f(f(X,X),X)) = f(f(X4,X3),f(X4,f(f(X4,X3),X2))),
inference(transitivity,[status(thm)],[c450,c462]) ).
cnf(c464,plain,
f(f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X2,X2))),f(f(X,X),X)) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X2,X2)))),
inference(substitution,[status(thm)],[c463]) ).
cnf(c465,plain,
f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X2,X2)))) = f(f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X2,X2))),f(f(X,X),X)),
inference(symmetry,[status(thm)],[c464]) ).
cnf(c466,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X,X))) = f(X3,X),
inference(congruence,[status(thm)],[c336]) ).
cnf(c467,plain,
f(f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X2,X2))),f(f(X,X),X)) = f(f(X4,X2),f(f(X,X),X)),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
f(f(X3,X2),f(f(X,X),X)) = f(f(X3,X2),f(X3,X2)),
inference(substitution,[status(thm)],[c449]) ).
cnf(c469,plain,
f(f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X2,X2))),f(f(X,X),X)) = f(f(X4,X2),f(X4,X2)),
inference(transitivity,[status(thm)],[c467,c468]) ).
cnf(c470,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X,X)))) = f(f(X3,X),f(X3,X)),
inference(transitivity,[status(thm)],[c465,c469]) ).
cnf(c471,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)) = f(f(X3,X),f(X3,X)),
inference(transitivity,[status(thm)],[c339,c470]) ).
cnf(c472,plain,
f(f(X3,X),f(X3,X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),
inference(symmetry,[status(thm)],[c471]) ).
cnf(c473,plain,
f(f(f(X3,X),f(X3,X)),X2) = f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),X2),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
f(f(f(f(X3,X),f(X3,X)),X2),f(X3,f(f(X2,X),f(X2,X)))) = f(f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),X2),f(X3,f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
f(f(X3,f(f(X2,X2),X2)),f(f(X,X),X)) = f(f(X3,X3),f(f(X,X),X)),
inference(congruence,[status(thm)],[c449]) ).
cnf(c476,plain,
f(f(X2,X2),f(f(X,X),X)) = f(f(X2,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c449]) ).
cnf(c477,plain,
f(f(X2,X2),f(f(X,X),X)) = X2,
inference(transitivity,[status(thm)],[c476,c28]) ).
cnf(c478,plain,
f(f(X3,f(f(X2,X2),X2)),f(f(X,X),X)) = X3,
inference(transitivity,[status(thm)],[c475,c477]) ).
cnf(c479,plain,
f(f(f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(X2,X2),X2)),f(f(X,X),X)) = f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),
inference(substitution,[status(thm)],[c478]) ).
cnf(c480,plain,
f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))) = f(f(f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(X2,X2),X2)),f(f(X,X),X)),
inference(symmetry,[status(thm)],[c479]) ).
cnf(c481,plain,
f(f(X2,X2),X2) = f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X),
inference(symmetry,[status(thm)],[c424]) ).
cnf(c482,plain,
f(f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(X2,X2),X2)) = f(f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X)),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
f(f(f(X4,f(f(f(X3,X3),X3),f(f(X3,X3),X3))),f(f(X3,X3),X3)),f(f(X2,X2),X2)) = f(f(f(X4,f(f(f(X3,X3),X3),f(f(X3,X3),X3))),f(f(f(f(X3,X3),X3),f(f(X3,X3),X3)),X)),f(f(X2,X2),X2)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
f(f(f(X4,X3),f(X3,X2)),f(f(X,X),X)) = f(f(f(X4,X3),f(X3,X2)),f(f(X4,X3),f(X3,X2))),
inference(substitution,[status(thm)],[c449]) ).
cnf(c485,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),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)],[c124]) ).
cnf(c486,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(X2,f(f(X3,X3),X3)),X))),f(f(X3,X2),f(X2,X))),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c488,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),f(f(X3,X2),f(X2,X))) = f(X2,f(f(X3,X2),f(X2,X))),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,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)],[c486,c488]) ).
cnf(c490,plain,
f(f(f(X4,X3),f(X3,X2)),f(f(X,X),X)) = f(X3,f(f(X4,X3),f(X3,X2))),
inference(transitivity,[status(thm)],[c484,c489]) ).
cnf(c491,plain,
f(f(f(X4,f(f(f(X3,X3),X3),f(f(X3,X3),X3))),f(f(f(f(X3,X3),X3),f(f(X3,X3),X3)),X)),f(f(X2,X2),X2)) = f(f(f(f(X3,X3),X3),f(f(X3,X3),X3)),f(f(X4,f(f(f(X3,X3),X3),f(f(X3,X3),X3))),f(f(f(f(X3,X3),X3),f(f(X3,X3),X3)),X))),
inference(substitution,[status(thm)],[c490]) ).
cnf(c492,plain,
f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),f(f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(f(X2,X2),X2),f(f(X2,X2),X2)),X))) = f(f(X2,X2),X2),
inference(substitution,[status(thm)],[c424]) ).
cnf(c493,plain,
f(f(f(X4,f(f(f(X3,X3),X3),f(f(X3,X3),X3))),f(f(f(f(X3,X3),X3),f(f(X3,X3),X3)),X)),f(f(X2,X2),X2)) = f(f(X3,X3),X3),
inference(transitivity,[status(thm)],[c491,c492]) ).
cnf(c494,plain,
f(f(f(X3,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(X2,X2),X2)),f(f(X,X),X)) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c483,c493]) ).
cnf(c495,plain,
f(X2,f(f(f(X,X),X),f(f(X,X),X))) = f(f(X,X),X),
inference(transitivity,[status(thm)],[c480,c494]) ).
cnf(c496,plain,
f(f(f(X3,f(X3,X3)),f(f(X,X),X)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))) = f(f(X2,X2),X2),
inference(substitution,[status(thm)],[c495]) ).
cnf(c497,plain,
f(f(X2,X2),X2) = f(f(f(X3,f(X3,X3)),f(f(X,X),X)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
f(f(X2,f(X2,X2)),f(f(X,X),X)) = f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),
inference(substitution,[status(thm)],[c449]) ).
cnf(c499,plain,
f(f(f(X3,f(X3,X3)),f(f(X2,X2),X2)),X) = f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),
inference(substitution,[status(thm)],[c361]) ).
cnf(c501,plain,
f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X) = f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))),
inference(symmetry,[status(thm)],[c500]) ).
cnf(c502,plain,
f(f(f(f(X2,X),f(X2,X)),X2),f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c503,plain,
f(f(X2,X),f(X2,X)) = f(f(f(f(X2,X),f(X2,X)),X2),f(X2,X)),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
f(f(f(X3,X2),f(X3,X2)),X) = f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X2)),X),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)) = f(f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X2)),X),f(X3,X3)),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
f(f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X2)),X),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c65]) ).
cnf(c507,plain,
f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c505,c506]) ).
cnf(c508,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c507]) ).
cnf(c509,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c507]) ).
cnf(c511,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))) = f(X2,f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))))) = f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))))),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c507]) ).
cnf(c515,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))) = f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))),
inference(congruence,[status(thm)],[c514]) ).
cnf(c516,plain,
f(X2,f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))) = f(X2,f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))))) = f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))))),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))),
inference(congruence,[status(thm)],[c517]) ).
cnf(c519,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c507]) ).
cnf(c520,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))) = f(X2,X2),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
f(X2,f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))) = f(X2,f(X2,X2)),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2))))) = f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,X2))),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,X2))) = f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),
inference(substitution,[status(thm)],[c124]) ).
cnf(c525,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,X2)))) = f(X2,f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
f(X,f(f(X,f(X,X)),f(X,f(X,X)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c358]) ).
cnf(c527,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,X2)))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c525,c526]) ).
cnf(c528,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c523,c527]) ).
cnf(c529,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c518,c528]) ).
cnf(c530,plain,
f(X2,f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c513,c529]) ).
cnf(c531,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)),f(f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X),f(X2,X2)))))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c509,c530]) ).
cnf(c532,plain,
f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c501,c531]) ).
cnf(c533,plain,
f(f(f(X3,f(X3,X3)),f(f(X2,X2),X2)),X) = f(X3,f(X3,X3)),
inference(transitivity,[status(thm)],[c499,c532]) ).
cnf(c534,plain,
f(f(f(X3,f(X3,X3)),f(f(X,X),X)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))) = f(X3,f(X3,X3)),
inference(substitution,[status(thm)],[c533]) ).
cnf(c535,plain,
f(f(X,X),X) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c497,c534]) ).
cnf(c536,plain,
f(f(X3,X2),f(f(X,X),X)) = f(f(X3,X2),f(X2,f(X2,X2))),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
f(f(f(X3,X2),f(f(X,X),X)),X3) = f(f(f(X3,X2),f(X2,f(X2,X2))),X3),
inference(congruence,[status(thm)],[c536]) ).
cnf(c538,plain,
f(X2,f(f(X3,X2),f(X2,X))) = f(f(f(X3,X2),f(X2,X)),X2),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c539,plain,
f(f(X3,X2),f(X2,f(f(X3,X2),f(X2,X)))) = f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
f(f(f(f(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c541,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))),
inference(symmetry,[status(thm)],[c540]) ).
cnf(c542,plain,
f(f(f(X4,X3),f(X3,X2)),X3) = f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2)))),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,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(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))),
inference(congruence,[status(thm)],[c542]) ).
cnf(c544,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(f(f(X,f(X4,X3)),f(X,f(X4,X3))),f(X,f(X4,X3)))),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))))) = f(f(X4,X3),f(X3,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c545,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)],[c543,c544]) ).
cnf(c546,plain,
f(f(X3,X2),f(X2,f(f(X3,X2),f(X2,X)))) = f(f(X3,X2),f(X2,X)),
inference(transitivity,[status(thm)],[c539,c545]) ).
cnf(c547,plain,
f(f(X2,X),f(X,f(f(X2,X),f(X,f(X,X))))) = f(f(X2,X),f(X,f(X,X))),
inference(substitution,[status(thm)],[c546]) ).
cnf(c548,plain,
f(f(X2,X),f(X,f(X,X))) = f(f(X2,X),f(X,f(f(X2,X),f(X,f(X,X))))),
inference(symmetry,[status(thm)],[c547]) ).
cnf(c549,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c550,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c549]) ).
cnf(c551,plain,
f(X2,f(X2,X2)) = f(f(f(X,X2),f(X2,X2)),f(X2,X2)),
inference(congruence,[status(thm)],[c550]) ).
cnf(c552,plain,
f(f(X,X2),f(X2,f(X2,X2))) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(X2,X2))),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
f(X2,f(f(X,X2),f(X2,f(X2,X2)))) = f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(X2,X2)))),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c555,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c554]) ).
cnf(c556,plain,
f(X2,X2) = f(f(f(X,X2),f(X2,X2)),X2),
inference(congruence,[status(thm)],[c555]) ).
cnf(c557,plain,
f(f(f(X,X2),f(X2,X2)),f(X2,X2)) = f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),X2)),
inference(congruence,[status(thm)],[c556]) ).
cnf(c558,plain,
f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(X2,X2))) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),X2))),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(X2,X2)))) = f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),X2)))),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c561,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c560]) ).
cnf(c562,plain,
f(f(f(X,X2),f(X2,X2)),X2) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c561]) ).
cnf(c563,plain,
f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),X2)) = f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),X2))) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))))),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),X2)))) = f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))),
inference(congruence,[status(thm)],[c564]) ).
cnf(c566,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c567,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c566]) ).
cnf(c568,plain,
f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c570,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c569]) ).
cnf(c571,plain,
f(X2,X2) = f(f(f(X,X2),f(X2,X2)),X2),
inference(congruence,[status(thm)],[c570]) ).
cnf(c572,plain,
f(f(X,X2),f(X2,X2)) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))) = f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))))) = f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))))),
inference(congruence,[status(thm)],[c573]) ).
cnf(c575,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c577,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c576]) ).
cnf(c578,plain,
f(X2,X2) = f(f(f(X,X2),f(X2,X2)),X2),
inference(congruence,[status(thm)],[c577]) ).
cnf(c579,plain,
f(f(X,X2),f(X2,X2)) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c579]) ).
cnf(c581,plain,
f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))) = f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c580]) ).
cnf(c582,plain,
f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2))))) = f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2))))),
inference(congruence,[status(thm)],[c581]) ).
cnf(c583,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2)))))),
inference(congruence,[status(thm)],[c582]) ).
cnf(c584,plain,
f(f(X,X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c67]) ).
cnf(c585,plain,
X2 = f(f(X,X2),f(X2,X2)),
inference(symmetry,[status(thm)],[c584]) ).
cnf(c586,plain,
f(X2,X2) = f(f(f(X,X2),f(X2,X2)),X2),
inference(congruence,[status(thm)],[c585]) ).
cnf(c587,plain,
f(f(X,X2),f(X2,X2)) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(congruence,[status(thm)],[c586]) ).
cnf(c588,plain,
f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2))) = f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))),
inference(congruence,[status(thm)],[c587]) ).
cnf(c589,plain,
f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2)))) = f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)))),
inference(congruence,[status(thm)],[c588]) ).
cnf(c590,plain,
f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2))))) = f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2))))),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2)))))) = f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)))))),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)) = f(f(X,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c593,plain,
f(f(X,X2),f(X2,X2)) = f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),
inference(symmetry,[status(thm)],[c592]) ).
cnf(c594,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)))))) = f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)))))),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)))))) = f(X,X2),
inference(substitution,[status(thm)],[c361]) ).
cnf(c596,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)))))) = f(X,X2),
inference(transitivity,[status(thm)],[c594,c595]) ).
cnf(c597,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(X,X2),f(X2,X2)))))) = f(X,X2),
inference(transitivity,[status(thm)],[c591,c596]) ).
cnf(c598,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(f(f(X,X2),f(X2,X2)),X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))) = f(X,X2),
inference(transitivity,[status(thm)],[c583,c597]) ).
cnf(c599,plain,
f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))) = f(X,X2),
inference(transitivity,[status(thm)],[c575,c598]) ).
cnf(c600,plain,
f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),f(f(X,X2),f(X2,X2)))))) = f(X,X2),
inference(transitivity,[status(thm)],[c568,c599]) ).
cnf(c601,plain,
f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(f(f(X,X2),f(X2,X2)),X2)))) = f(X,X2),
inference(transitivity,[status(thm)],[c565,c600]) ).
cnf(c602,plain,
f(X2,f(f(X,X2),f(f(f(X,X2),f(X2,X2)),f(X2,X2)))) = f(X,X2),
inference(transitivity,[status(thm)],[c559,c601]) ).
cnf(c603,plain,
f(X2,f(f(X,X2),f(X2,f(X2,X2)))) = f(X,X2),
inference(transitivity,[status(thm)],[c553,c602]) ).
cnf(c604,plain,
f(X,f(f(X2,X),f(X,f(X,X)))) = f(X2,X),
inference(substitution,[status(thm)],[c603]) ).
cnf(c605,plain,
f(f(X2,X),f(X,f(f(X2,X),f(X,f(X,X))))) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c604]) ).
cnf(c606,plain,
f(f(X2,X),f(X,f(X,X))) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c548,c605]) ).
cnf(c607,plain,
f(f(f(X2,X),f(X,f(X,X))),X2) = f(f(f(X2,X),f(X2,X)),X2),
inference(congruence,[status(thm)],[c606]) ).
cnf(c608,plain,
f(f(f(X2,X),f(X,f(X,X))),X2) = f(X2,X),
inference(transitivity,[status(thm)],[c607,c157]) ).
cnf(c609,plain,
f(f(f(X3,X2),f(f(X,X),X)),X3) = f(X3,X2),
inference(transitivity,[status(thm)],[c537,c608]) ).
cnf(c610,plain,
f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),
inference(substitution,[status(thm)],[c609]) ).
cnf(c611,plain,
f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)) = f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(symmetry,[status(thm)],[c610]) ).
cnf(c612,plain,
f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),X3) = f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3),
inference(congruence,[status(thm)],[c611]) ).
cnf(c613,plain,
f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),X3),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c615,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(symmetry,[status(thm)],[c614]) ).
cnf(c616,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2)) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))),f(X2,X2)),
inference(congruence,[status(thm)],[c615]) ).
cnf(c617,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X))))),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c507]) ).
cnf(c618,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c616,c617]) ).
cnf(c619,plain,
X2 = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2)),
inference(symmetry,[status(thm)],[c618]) ).
cnf(c620,plain,
f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),X2) = f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2))),
inference(congruence,[status(thm)],[c619]) ).
cnf(c621,plain,
f(f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),X2),f(X3,f(f(X2,X),f(X2,X)))) = f(f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2))),f(X3,f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c620]) ).
cnf(c622,plain,
f(f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2)))),
inference(substitution,[status(thm)],[c200]) ).
cnf(c623,plain,
f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2))) = f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),X2),
inference(congruence,[status(thm)],[c618]) ).
cnf(c624,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),X2)),
inference(congruence,[status(thm)],[c623]) ).
cnf(c625,plain,
f(f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),X2)),
inference(transitivity,[status(thm)],[c622,c624]) ).
cnf(c626,plain,
f(f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),X2),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(X4,f(X3,f(f(X2,X),f(X2,X)))),X2)),
inference(transitivity,[status(thm)],[c621,c625]) ).
cnf(c627,plain,
f(f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3)),
inference(substitution,[status(thm)],[c626]) ).
cnf(c628,plain,
f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),
inference(substitution,[status(thm)],[c609]) ).
cnf(c629,plain,
f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3) = f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),X3),
inference(congruence,[status(thm)],[c628]) ).
cnf(c630,plain,
f(f(X4,f(f(X3,X2),f(X3,X2))),f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3)) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),X3)),
inference(congruence,[status(thm)],[c629]) ).
cnf(c631,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),X2) = f(f(f(X3,X),f(X3,X)),X2),
inference(congruence,[status(thm)],[c471]) ).
cnf(c632,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),X2)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,X),f(X3,X)),X2)),
inference(congruence,[status(thm)],[c631]) ).
cnf(c633,plain,
f(f(f(X3,X),f(X3,X)),X2) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c310]) ).
cnf(c634,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,X),f(X3,X)),X2)) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c633]) ).
cnf(c635,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),X2)) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c632,c634]) ).
cnf(c636,plain,
f(f(X4,f(f(X3,X2),f(X3,X2))),f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3)) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))),
inference(transitivity,[status(thm)],[c630,c635]) ).
cnf(c637,plain,
f(f(f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,X2)),f(f(X,X),X)),f(X4,f(f(X3,X2),f(X3,X2)))),X3),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))),
inference(transitivity,[status(thm)],[c627,c636]) ).
cnf(c638,plain,
f(f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),X2),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c613,c637]) ).
cnf(c639,plain,
f(f(f(f(X3,X),f(X3,X)),X2),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c474,c638]) ).
cnf(c640,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c313,c639]) ).
cnf(c641,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c640]) ).
cnf(c642,plain,
f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c641]) ).
cnf(c643,plain,
f(f(X3,X),f(X3,X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X)),
inference(symmetry,[status(thm)],[c471]) ).
cnf(c644,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,X),f(X3,X))) = f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X))),
inference(congruence,[status(thm)],[c643]) ).
cnf(c645,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,X))) = f(X3,f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c646,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,X),f(X3,X))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c644,c645]) ).
cnf(c647,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,X),f(X3,X))),
inference(symmetry,[status(thm)],[c646]) ).
cnf(c648,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c647]) ).
cnf(c649,plain,
f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c648]) ).
cnf(c650,plain,
f(f(X2,X2),f(f(f(X,X),X),f(f(X,X),X))) = f(f(X,X),X),
inference(substitution,[status(thm)],[c495]) ).
cnf(c651,plain,
f(f(X,X),X) = f(f(X2,X2),f(f(f(X,X),X),f(f(X,X),X))),
inference(symmetry,[status(thm)],[c650]) ).
cnf(c652,plain,
f(f(f(X,X),X),X2) = f(f(f(X2,X2),f(f(f(X,X),X),f(f(X,X),X))),X2),
inference(congruence,[status(thm)],[c651]) ).
cnf(c653,plain,
f(f(f(X2,X2),f(f(f(X,X),X),f(f(X,X),X))),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c124]) ).
cnf(c654,plain,
f(f(f(X,X),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c652,c653]) ).
cnf(c655,plain,
f(f(f(X4,X4),X4),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))) = f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c656,plain,
f(f(f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),X2),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))) = f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),
inference(substitution,[status(thm)],[c124]) ).
cnf(c657,plain,
f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))) = f(f(f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),X2),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),
inference(symmetry,[status(thm)],[c656]) ).
cnf(c658,plain,
f(f(X2,X2),f(f(X,f(X2,X2)),f(X,f(X2,X2)))) = f(X,f(X2,X2)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c659,plain,
f(X,f(X2,X2)) = f(f(X2,X2),f(f(X,f(X2,X2)),f(X,f(X2,X2)))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c660,plain,
f(f(X3,f(X2,X2)),f(X,f(X2,X2))) = f(f(X3,f(X2,X2)),f(f(X2,X2),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(congruence,[status(thm)],[c659]) ).
cnf(c661,plain,
f(f(f(X4,f(X3,X3)),f(X2,f(X3,X3))),X) = f(f(f(X4,f(X3,X3)),f(f(X3,X3),f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))),X),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
f(f(f(f(X4,f(X3,X3)),f(X2,f(X3,X3))),X),X3) = f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))),X),X3),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c664,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),X3) = f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(X3,X3))),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(X3,X3))) = f(X3,X3),
inference(substitution,[status(thm)],[c65]) ).
cnf(c666,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),X3) = f(X3,X3),
inference(transitivity,[status(thm)],[c664,c665]) ).
cnf(c667,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))),X),X3) = f(X3,X3),
inference(substitution,[status(thm)],[c666]) ).
cnf(c668,plain,
f(f(f(f(X4,f(X3,X3)),f(X2,f(X3,X3))),X),X3) = f(X3,X3),
inference(transitivity,[status(thm)],[c662,c667]) ).
cnf(c669,plain,
f(f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c668]) ).
cnf(c670,plain,
f(f(f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),X2),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))) = f(f(X2,X2),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),
inference(congruence,[status(thm)],[c669]) ).
cnf(c671,plain,
f(f(f(X3,f(X2,X2)),f(X,f(X2,X2))),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))) = f(f(X2,X2),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),
inference(transitivity,[status(thm)],[c657,c670]) ).
cnf(c672,plain,
f(f(f(X4,X4),X4),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))) = f(f(X2,X2),f(f(X3,f(X2,X2)),f(X,f(X2,X2)))),
inference(transitivity,[status(thm)],[c655,c671]) ).
cnf(c673,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),f(f(X4,X2),f(X4,X2))))) = f(f(f(X4,X2),f(X4,X2)),f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),f(f(X4,X2),f(X4,X2))))),
inference(substitution,[status(thm)],[c672]) ).
cnf(c674,plain,
f(f(f(X4,X2),f(X4,X2)),f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),f(f(X4,X2),f(X4,X2))))) = f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),f(f(X4,X2),f(X4,X2))))),
inference(symmetry,[status(thm)],[c673]) ).
cnf(c675,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c646]) ).
cnf(c676,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),f(f(X4,X2),f(X4,X2))))) = f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))),
inference(congruence,[status(thm)],[c675]) ).
cnf(c677,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c640]) ).
cnf(c678,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c677]) ).
cnf(c679,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))) = f(f(f(X,X),X),f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2))))),
inference(congruence,[status(thm)],[c678]) ).
cnf(c680,plain,
f(f(f(X5,X5),X5),f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))) = f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c681,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c618]) ).
cnf(c682,plain,
X3 = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X3)),
inference(symmetry,[status(thm)],[c681]) ).
cnf(c683,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X3)),f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c682]) ).
cnf(c684,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X3)),f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c685,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X2,f(f(X3,X),f(X3,X))),
inference(transitivity,[status(thm)],[c683,c684]) ).
cnf(c686,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(symmetry,[status(thm)],[c685]) ).
cnf(c687,plain,
f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))) = f(f(X4,X3),f(X4,f(f(X2,f(f(X4,X),f(X4,X))),f(X2,f(f(X4,X),f(X4,X)))))),
inference(congruence,[status(thm)],[c686]) ).
cnf(c688,plain,
f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))) = f(X4,f(f(X4,X3),f(X4,f(f(X2,f(f(X4,X),f(X4,X))),f(X2,f(f(X4,X),f(X4,X))))))),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X2,f(f(X4,X),f(X4,X))),f(X2,f(f(X4,X),f(X4,X)))))))),
inference(congruence,[status(thm)],[c688]) ).
cnf(c690,plain,
f(X2,X) = f(f(f(X2,X),f(X2,X)),X2),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c691,plain,
f(f(X3,X2),f(X3,X)) = f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),
inference(congruence,[status(thm)],[c690]) ).
cnf(c692,plain,
f(X3,f(f(X3,X2),f(X3,X))) = f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X))),
inference(congruence,[status(thm)],[c691]) ).
cnf(c693,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,X)))) = f(f(X3,X2),f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)))),
inference(congruence,[status(thm)],[c692]) ).
cnf(c694,plain,
f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3) = f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X))),
inference(substitution,[status(thm)],[c200]) ).
cnf(c695,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X))) = f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3),
inference(symmetry,[status(thm)],[c694]) ).
cnf(c696,plain,
f(f(X3,X2),f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)))) = f(f(X3,X2),f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3)),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
f(X2,X) = f(f(f(X2,X),f(X2,X)),X2),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c698,plain,
f(f(X3,X2),f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3)) = f(f(f(f(X3,X2),f(X3,X2)),X3),f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3)),
inference(congruence,[status(thm)],[c697]) ).
cnf(c699,plain,
f(f(f(f(X3,X2),f(X3,X2)),X3),f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3)) = f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c700,plain,
f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)) = f(f(X3,X2),f(X3,X)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c701,plain,
f(f(f(f(X3,X2),f(X3,X2)),X3),f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3)) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c699,c700]) ).
cnf(c702,plain,
f(f(X3,X2),f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3)) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c698,c701]) ).
cnf(c703,plain,
f(f(X3,X2),f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)))) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c696,c702]) ).
cnf(c704,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)],[c693,c703]) ).
cnf(c705,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X2,f(f(X4,X),f(X4,X))),f(X2,f(f(X4,X),f(X4,X)))))))) = f(f(X4,X3),f(X4,f(f(X2,f(f(X4,X),f(X4,X))),f(X2,f(f(X4,X),f(X4,X)))))),
inference(substitution,[status(thm)],[c704]) ).
cnf(c706,plain,
f(f(X4,X3),f(X4,f(f(X2,f(f(X4,X),f(X4,X))),f(X2,f(f(X4,X),f(X4,X)))))) = f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),
inference(congruence,[status(thm)],[c685]) ).
cnf(c707,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X2,f(f(X4,X),f(X4,X))),f(X2,f(f(X4,X),f(X4,X)))))))) = f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),
inference(transitivity,[status(thm)],[c705,c706]) ).
cnf(c708,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))) = f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),
inference(transitivity,[status(thm)],[c689,c707]) ).
cnf(c709,plain,
f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),
inference(symmetry,[status(thm)],[c708]) ).
cnf(c710,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))) = f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))),
inference(congruence,[status(thm)],[c709]) ).
cnf(c711,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),
inference(substitution,[status(thm)],[c704]) ).
cnf(c712,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))))),
inference(symmetry,[status(thm)],[c711]) ).
cnf(c713,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))) = f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))))),
inference(congruence,[status(thm)],[c712]) ).
cnf(c714,plain,
f(X2,X) = f(f(f(X2,X),f(X2,X)),X2),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c715,plain,
f(f(X3,X2),f(X3,X)) = f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),
inference(congruence,[status(thm)],[c714]) ).
cnf(c716,plain,
f(f(f(X3,X2),f(X3,X)),X3) = f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3),
inference(congruence,[status(thm)],[c715]) ).
cnf(c717,plain,
f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3) = f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X))),
inference(substitution,[status(thm)],[c200]) ).
cnf(c718,plain,
f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)) = f(f(X3,X2),f(X3,X)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c719,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X))) = f(X3,f(f(X3,X2),f(X3,X))),
inference(congruence,[status(thm)],[c718]) ).
cnf(c720,plain,
f(f(f(f(f(X3,X2),f(X3,X2)),X3),f(X3,X)),X3) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c717,c719]) ).
cnf(c721,plain,
f(f(f(X3,X2),f(X3,X)),X3) = f(X3,f(f(X3,X2),f(X3,X))),
inference(transitivity,[status(thm)],[c716,c720]) ).
cnf(c722,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4) = f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))),
inference(substitution,[status(thm)],[c721]) ).
cnf(c723,plain,
f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))) = f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4),
inference(symmetry,[status(thm)],[c722]) ).
cnf(c724,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))))) = f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4)),
inference(congruence,[status(thm)],[c723]) ).
cnf(c725,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))))) = f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4))),
inference(congruence,[status(thm)],[c724]) ).
cnf(c726,plain,
f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),
inference(symmetry,[status(thm)],[c708]) ).
cnf(c727,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4))) = f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4))),
inference(congruence,[status(thm)],[c726]) ).
cnf(c728,plain,
f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)) = f(f(X3,X2),X),
inference(substitution,[status(thm)],[c157]) ).
cnf(c729,plain,
f(f(X3,X2),X) = f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),
inference(symmetry,[status(thm)],[c728]) ).
cnf(c730,plain,
f(f(f(X3,X2),X),X3) = f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),
inference(congruence,[status(thm)],[c729]) ).
cnf(c731,plain,
f(f(X3,X2),f(f(f(X3,X2),X),X3)) = f(f(X3,X2),f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3)),
inference(congruence,[status(thm)],[c730]) ).
cnf(c732,plain,
f(f(f(X3,X2),X),f(f(X3,X2),f(f(f(X3,X2),X),X3))) = f(f(f(X3,X2),X),f(f(X3,X2),f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3))),
inference(congruence,[status(thm)],[c731]) ).
cnf(c733,plain,
f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2)) = f(f(X3,X2),f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c734,plain,
f(f(X3,X2),f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3)) = f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2)),
inference(symmetry,[status(thm)],[c733]) ).
cnf(c735,plain,
f(f(f(X3,X2),X),f(f(X3,X2),f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3))) = f(f(f(X3,X2),X),f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2))),
inference(congruence,[status(thm)],[c734]) ).
cnf(c736,plain,
f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)) = f(f(X3,X2),X),
inference(substitution,[status(thm)],[c157]) ).
cnf(c737,plain,
f(f(X3,X2),X) = f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),
inference(symmetry,[status(thm)],[c736]) ).
cnf(c738,plain,
f(f(f(X3,X2),X),f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2))) = f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2))),
inference(congruence,[status(thm)],[c737]) ).
cnf(c739,plain,
f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2))) = f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),
inference(substitution,[status(thm)],[c303]) ).
cnf(c740,plain,
f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)) = f(f(X3,X2),X),
inference(substitution,[status(thm)],[c157]) ).
cnf(c741,plain,
f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3) = f(f(f(X3,X2),X),X3),
inference(congruence,[status(thm)],[c740]) ).
cnf(c742,plain,
f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2))) = f(f(f(X3,X2),X),X3),
inference(transitivity,[status(thm)],[c739,c741]) ).
cnf(c743,plain,
f(f(f(X3,X2),X),f(f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3),f(X3,X2))) = f(f(f(X3,X2),X),X3),
inference(transitivity,[status(thm)],[c738,c742]) ).
cnf(c744,plain,
f(f(f(X3,X2),X),f(f(X3,X2),f(f(f(f(f(X3,X2),X),f(f(X3,X2),X)),f(X3,X2)),X3))) = f(f(f(X3,X2),X),X3),
inference(transitivity,[status(thm)],[c735,c743]) ).
cnf(c745,plain,
f(f(f(X3,X2),X),f(f(X3,X2),f(f(f(X3,X2),X),X3))) = f(f(f(X3,X2),X),X3),
inference(transitivity,[status(thm)],[c732,c744]) ).
cnf(c746,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4))) = f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4),
inference(substitution,[status(thm)],[c745]) ).
cnf(c747,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4) = f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))),
inference(substitution,[status(thm)],[c721]) ).
cnf(c748,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c749,plain,
f(X3,f(f(X3,X2),X)) = f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c748]) ).
cnf(c750,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),X))) = f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c749]) ).
cnf(c751,plain,
f(X3,f(f(X3,X2),f(X3,f(f(X3,X2),X)))) = f(X3,f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)))),
inference(congruence,[status(thm)],[c750]) ).
cnf(c752,plain,
f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2)) = f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))),
inference(substitution,[status(thm)],[c200]) ).
cnf(c753,plain,
f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X))) = f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2)),
inference(symmetry,[status(thm)],[c752]) ).
cnf(c754,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)))) = f(X3,f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2))),
inference(congruence,[status(thm)],[c753]) ).
cnf(c755,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c756,plain,
f(X3,f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2))) = f(f(f(X3,X3),f(X3,X2)),f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2))),
inference(congruence,[status(thm)],[c755]) ).
cnf(c757,plain,
f(f(f(X3,X3),f(X3,X2)),f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2))) = f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c758,plain,
f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)) = f(X3,f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c759,plain,
f(f(f(X3,X3),f(X3,X2)),f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2))) = f(X3,f(f(X3,X2),X)),
inference(transitivity,[status(thm)],[c757,c758]) ).
cnf(c760,plain,
f(X3,f(f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)),f(X3,X2))) = f(X3,f(f(X3,X2),X)),
inference(transitivity,[status(thm)],[c756,c759]) ).
cnf(c761,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X3),f(X3,X2)),f(f(X3,X2),X)))) = f(X3,f(f(X3,X2),X)),
inference(transitivity,[status(thm)],[c754,c760]) ).
cnf(c762,plain,
f(X3,f(f(X3,X2),f(X3,f(f(X3,X2),X)))) = f(X3,f(f(X3,X2),X)),
inference(transitivity,[status(thm)],[c751,c761]) ).
cnf(c763,plain,
f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(substitution,[status(thm)],[c762]) ).
cnf(c764,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(transitivity,[status(thm)],[c747,c763]) ).
cnf(c765,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4))) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(transitivity,[status(thm)],[c746,c764]) ).
cnf(c766,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))))),X4))) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(transitivity,[status(thm)],[c727,c765]) ).
cnf(c767,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))))) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(transitivity,[status(thm)],[c725,c766]) ).
cnf(c768,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))))) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(transitivity,[status(thm)],[c713,c767]) ).
cnf(c769,plain,
f(f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X)))),f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(transitivity,[status(thm)],[c710,c768]) ).
cnf(c770,plain,
f(f(f(X5,X5),X5),f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))) = f(X4,f(f(X4,X3),f(X2,f(f(X4,X),f(X4,X))))),
inference(transitivity,[status(thm)],[c680,c769]) ).
cnf(c771,plain,
f(f(f(X,X),X),f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2))))) = f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2))))),
inference(substitution,[status(thm)],[c770]) ).
cnf(c772,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))) = f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2))))),
inference(transitivity,[status(thm)],[c679,c771]) ).
cnf(c773,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),f(f(X4,X2),f(X4,X2))))) = f(X4,f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2))))),
inference(transitivity,[status(thm)],[c676,c772]) ).
cnf(c774,plain,
f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,X),f(X3,X))))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(transitivity,[status(thm)],[c674,c773]) ).
cnf(c775,plain,
f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(transitivity,[status(thm)],[c649,c774]) ).
cnf(c776,plain,
f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(transitivity,[status(thm)],[c642,c775]) ).
cnf(c777,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),
inference(substitution,[status(thm)],[c776]) ).
cnf(c778,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))) = f(X3,f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))),
inference(substitution,[status(thm)],[c770]) ).
cnf(c779,plain,
f(X3,f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))) = f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))),
inference(symmetry,[status(thm)],[c778]) ).
cnf(c780,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))) = f(f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c781,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c782,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c781]) ).
cnf(c783,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(symmetry,[status(thm)],[c685]) ).
cnf(c784,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c783]) ).
cnf(c785,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))))),
inference(congruence,[status(thm)],[c784]) ).
cnf(c786,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))))),
inference(congruence,[status(thm)],[c785]) ).
cnf(c787,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(substitution,[status(thm)],[c704]) ).
cnf(c788,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c685]) ).
cnf(c789,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c640]) ).
cnf(c790,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c788,c789]) ).
cnf(c791,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c787,c790]) ).
cnf(c792,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c786,c791]) ).
cnf(c793,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c782,c792]) ).
cnf(c794,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),
inference(symmetry,[status(thm)],[c793]) ).
cnf(c795,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))),
inference(congruence,[status(thm)],[c794]) ).
cnf(c796,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),
inference(substitution,[status(thm)],[c704]) ).
cnf(c797,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))))),
inference(symmetry,[status(thm)],[c796]) ).
cnf(c798,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))) = f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))))),
inference(congruence,[status(thm)],[c797]) ).
cnf(c799,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))),
inference(substitution,[status(thm)],[c721]) ).
cnf(c800,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))) = f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3),
inference(symmetry,[status(thm)],[c799]) ).
cnf(c801,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3)),
inference(congruence,[status(thm)],[c800]) ).
cnf(c802,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))))) = f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3))),
inference(congruence,[status(thm)],[c801]) ).
cnf(c803,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),
inference(symmetry,[status(thm)],[c793]) ).
cnf(c804,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3))) = f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3))),
inference(congruence,[status(thm)],[c803]) ).
cnf(c805,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3))) = f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3),
inference(substitution,[status(thm)],[c745]) ).
cnf(c806,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))),
inference(substitution,[status(thm)],[c721]) ).
cnf(c807,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c793]) ).
cnf(c808,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(transitivity,[status(thm)],[c806,c807]) ).
cnf(c809,plain,
f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(transitivity,[status(thm)],[c805,c808]) ).
cnf(c810,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),X3))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(transitivity,[status(thm)],[c804,c809]) ).
cnf(c811,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(transitivity,[status(thm)],[c802,c810]) ).
cnf(c812,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(transitivity,[status(thm)],[c798,c811]) ).
cnf(c813,plain,
f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(transitivity,[status(thm)],[c795,c812]) ).
cnf(c814,plain,
f(f(f(X,X),X),f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))) = f(X4,f(f(X3,f(f(X4,X2),f(X4,X2))),f(X4,f(f(X3,X2),f(X3,X2))))),
inference(transitivity,[status(thm)],[c780,c813]) ).
cnf(c815,plain,
f(X2,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(transitivity,[status(thm)],[c779,c814]) ).
cnf(c816,plain,
f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),
inference(substitution,[status(thm)],[c815]) ).
cnf(c817,plain,
f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(substitution,[status(thm)],[c640]) ).
cnf(c818,plain,
f(X,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(congruence,[status(thm)],[c817]) ).
cnf(c819,plain,
f(X,f(f(f(X2,X2),X2),f(f(X2,X2),X2))) = f(f(X2,X2),X2),
inference(substitution,[status(thm)],[c495]) ).
cnf(c820,plain,
f(f(X2,X2),X2) = f(X,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),
inference(symmetry,[status(thm)],[c819]) ).
cnf(c821,plain,
f(f(f(X2,X2),X2),f(X,X)) = f(f(X,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X,X)),
inference(congruence,[status(thm)],[c820]) ).
cnf(c822,plain,
f(f(X,f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X,X)) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c823,plain,
f(f(f(X2,X2),X2),f(X,X)) = X,
inference(transitivity,[status(thm)],[c821,c822]) ).
cnf(c824,plain,
f(f(f(X,X),X),f(f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))),f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))))) = f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))),
inference(substitution,[status(thm)],[c823]) ).
cnf(c825,plain,
f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))) = f(f(f(X,X),X),f(f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))),f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))))),
inference(symmetry,[status(thm)],[c824]) ).
cnf(c826,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c166]) ).
cnf(c827,plain,
X = f(f(X,X),f(X2,X)),
inference(symmetry,[status(thm)],[c826]) ).
cnf(c828,plain,
f(X,X2) = f(f(f(X,X),f(X2,X)),X2),
inference(congruence,[status(thm)],[c827]) ).
cnf(c829,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)],[c828]) ).
cnf(c830,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)],[c205]) ).
cnf(c831,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c166]) ).
cnf(c832,plain,
f(f(f(X,X),f(X2,X)),X2) = f(X,X2),
inference(congruence,[status(thm)],[c831]) ).
cnf(c833,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)],[c832]) ).
cnf(c834,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)],[c830,c833]) ).
cnf(c835,plain,
f(f(X,X2),f(X2,X)) = f(f(X2,X),f(X,X2)),
inference(transitivity,[status(thm)],[c829,c834]) ).
cnf(c836,plain,
f(f(X2,X),f(X,X2)) = f(f(X,X2),f(X2,X)),
inference(substitution,[status(thm)],[c835]) ).
cnf(c837,plain,
f(X2,f(f(X2,X),f(X,X2))) = f(X2,f(f(X,X2),f(X2,X))),
inference(congruence,[status(thm)],[c836]) ).
cnf(c838,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c839,plain,
f(X2,X) = f(f(f(X2,X2),f(X,X2)),X),
inference(congruence,[status(thm)],[c838]) ).
cnf(c840,plain,
f(f(X,X2),f(X2,X)) = f(f(X,X2),f(f(f(X2,X2),f(X,X2)),X)),
inference(congruence,[status(thm)],[c839]) ).
cnf(c841,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X2,f(f(X,X2),f(f(f(X2,X2),f(X,X2)),X))),
inference(congruence,[status(thm)],[c840]) ).
cnf(c842,plain,
f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2)) = f(f(X,X2),f(f(f(X2,X2),f(X,X2)),X)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c843,plain,
f(f(X,X2),f(f(f(X2,X2),f(X,X2)),X)) = f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2)),
inference(symmetry,[status(thm)],[c842]) ).
cnf(c844,plain,
f(X2,f(f(X,X2),f(f(f(X2,X2),f(X,X2)),X))) = f(X2,f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))),
inference(congruence,[status(thm)],[c843]) ).
cnf(c845,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c846,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)],[c845]) ).
cnf(c847,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)],[c303]) ).
cnf(c848,plain,
f(f(f(X2,X2),f(X,X2)),X) = f(X2,X),
inference(congruence,[status(thm)],[c166]) ).
cnf(c849,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)],[c847,c848]) ).
cnf(c850,plain,
f(X2,f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2))) = f(X2,X),
inference(transitivity,[status(thm)],[c846,c849]) ).
cnf(c851,plain,
f(X2,f(f(X,X2),f(f(f(X2,X2),f(X,X2)),X))) = f(X2,X),
inference(transitivity,[status(thm)],[c844,c850]) ).
cnf(c852,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c841,c851]) ).
cnf(c853,plain,
f(X2,f(f(X2,X),f(X,X2))) = f(X2,X),
inference(transitivity,[status(thm)],[c837,c852]) ).
cnf(c854,plain,
f(X,f(f(X,X2),f(X2,X))) = f(X,X2),
inference(substitution,[status(thm)],[c853]) ).
cnf(c855,plain,
f(X,X2) = f(X,f(f(X,X2),f(X2,X))),
inference(symmetry,[status(thm)],[c854]) ).
cnf(c856,plain,
f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c197]) ).
cnf(c857,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),X)),
inference(symmetry,[status(thm)],[c856]) ).
cnf(c858,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X2,f(f(X2,X),f(X,X2))),
inference(congruence,[status(thm)],[c835]) ).
cnf(c859,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c858,c853]) ).
cnf(c860,plain,
f(X,f(f(X2,X),f(X,X2))) = f(X,X2),
inference(substitution,[status(thm)],[c859]) ).
cnf(c861,plain,
f(X,X2) = f(X,f(f(X2,X),f(X,X2))),
inference(symmetry,[status(thm)],[c860]) ).
cnf(c862,plain,
f(f(X,X2),f(X,X2)) = f(f(X,X2),f(X,f(f(X2,X),f(X,X2)))),
inference(congruence,[status(thm)],[c861]) ).
cnf(c863,plain,
f(f(f(X2,X3),f(X2,X3)),X) = f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X),
inference(congruence,[status(thm)],[c862]) ).
cnf(c864,plain,
f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X2,X3),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)),
inference(congruence,[status(thm)],[c863]) ).
cnf(c865,plain,
f(X,f(f(X2,X),f(X,X2))) = f(X,X2),
inference(substitution,[status(thm)],[c859]) ).
cnf(c866,plain,
f(X,X2) = f(X,f(f(X2,X),f(X,X2))),
inference(symmetry,[status(thm)],[c865]) ).
cnf(c867,plain,
f(f(X2,X3),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)) = f(f(X2,f(f(X3,X2),f(X2,X3))),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)),
inference(congruence,[status(thm)],[c866]) ).
cnf(c868,plain,
f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X,X2))) = f(X,f(f(X2,X),f(X,X2))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c869,plain,
f(X,f(f(X2,X),f(X,X2))) = f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X,X2))),
inference(symmetry,[status(thm)],[c868]) ).
cnf(c870,plain,
f(f(X2,f(f(X3,X2),f(X2,X3))),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)) = f(f(f(f(X3,X2),f(X2,X3)),f(f(X3,X2),f(X2,X3))),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)),
inference(congruence,[status(thm)],[c869]) ).
cnf(c871,plain,
f(X,f(f(X2,X),f(X,X2))) = f(X,X2),
inference(substitution,[status(thm)],[c859]) ).
cnf(c872,plain,
f(X,X2) = f(X,f(f(X2,X),f(X,X2))),
inference(symmetry,[status(thm)],[c871]) ).
cnf(c873,plain,
f(f(X,X2),f(X,f(f(X2,X),f(X,X2)))) = f(f(X,f(f(X2,X),f(X,X2))),f(X,f(f(X2,X),f(X,X2)))),
inference(congruence,[status(thm)],[c872]) ).
cnf(c874,plain,
f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X) = f(f(f(X2,f(f(X3,X2),f(X2,X3))),f(X2,f(f(X3,X2),f(X2,X3)))),X),
inference(congruence,[status(thm)],[c873]) ).
cnf(c875,plain,
f(f(f(f(X3,X2),f(X2,X3)),f(f(X3,X2),f(X2,X3))),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)) = f(f(f(f(X3,X2),f(X2,X3)),f(f(X3,X2),f(X2,X3))),f(f(f(X2,f(f(X3,X2),f(X2,X3))),f(X2,f(f(X3,X2),f(X2,X3)))),X)),
inference(congruence,[status(thm)],[c874]) ).
cnf(c876,plain,
f(f(X,X2),f(X2,f(f(X,X2),f(X,X2)))) = f(f(X,X2),f(X,X2)),
inference(substitution,[status(thm)],[c328]) ).
cnf(c877,plain,
f(f(X,X2),f(X,X2)) = f(f(X,X2),f(X2,f(f(X,X2),f(X,X2)))),
inference(symmetry,[status(thm)],[c876]) ).
cnf(c878,plain,
f(f(f(X2,X3),f(X2,X3)),X) = f(f(f(X2,X3),f(X3,f(f(X2,X3),f(X2,X3)))),X),
inference(congruence,[status(thm)],[c877]) ).
cnf(c879,plain,
f(f(X3,X3),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X3,X3),f(f(f(X2,X3),f(X3,f(f(X2,X3),f(X2,X3)))),X)),
inference(congruence,[status(thm)],[c878]) ).
cnf(c880,plain,
f(X,X2) = f(X2,f(f(X,X2),f(X,X2))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c881,plain,
f(f(X,X2),f(X2,f(f(X,X2),f(X,X2)))) = f(f(X2,f(f(X,X2),f(X,X2))),f(X2,f(f(X,X2),f(X,X2)))),
inference(congruence,[status(thm)],[c880]) ).
cnf(c882,plain,
f(f(f(X2,X3),f(X3,f(f(X2,X3),f(X2,X3)))),X) = f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X3),f(X2,X3)))),X),
inference(congruence,[status(thm)],[c881]) ).
cnf(c883,plain,
f(f(X3,X3),f(f(f(X2,X3),f(X3,f(f(X2,X3),f(X2,X3)))),X)) = f(f(X3,X3),f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X3),f(X2,X3)))),X)),
inference(congruence,[status(thm)],[c882]) ).
cnf(c884,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))) = f(X3,X3),
inference(substitution,[status(thm)],[c328]) ).
cnf(c885,plain,
f(X3,X3) = f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),
inference(symmetry,[status(thm)],[c884]) ).
cnf(c886,plain,
f(f(X3,X3),f(f(f(X3,X2),f(X3,X2)),X)) = f(f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(congruence,[status(thm)],[c885]) ).
cnf(c887,plain,
X3 = f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c888,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))) = f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),
inference(congruence,[status(thm)],[c887]) ).
cnf(c889,plain,
f(f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),f(f(f(X3,X2),f(X3,X2)),X)) = f(f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(congruence,[status(thm)],[c888]) ).
cnf(c890,plain,
f(f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),f(f(f(X3,X2),f(X3,X2)),X)) = f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),
inference(substitution,[status(thm)],[c157]) ).
cnf(c891,plain,
f(f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),f(f(f(X3,X2),f(X3,X2)),X)) = X3,
inference(transitivity,[status(thm)],[c890,c507]) ).
cnf(c892,plain,
f(f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3))),f(f(f(X3,X2),f(X3,X2)),X)) = X3,
inference(transitivity,[status(thm)],[c889,c891]) ).
cnf(c893,plain,
f(f(X3,X3),f(f(f(X3,X2),f(X3,X2)),X)) = X3,
inference(transitivity,[status(thm)],[c886,c892]) ).
cnf(c894,plain,
f(f(X3,X3),f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X3),f(X2,X3)))),X)) = X3,
inference(substitution,[status(thm)],[c893]) ).
cnf(c895,plain,
f(f(X3,X3),f(f(f(X2,X3),f(X3,f(f(X2,X3),f(X2,X3)))),X)) = X3,
inference(transitivity,[status(thm)],[c883,c894]) ).
cnf(c896,plain,
f(f(X3,X3),f(f(f(X2,X3),f(X2,X3)),X)) = X3,
inference(transitivity,[status(thm)],[c879,c895]) ).
cnf(c897,plain,
f(f(f(f(X3,X2),f(X2,X3)),f(f(X3,X2),f(X2,X3))),f(f(f(X2,f(f(X3,X2),f(X2,X3))),f(X2,f(f(X3,X2),f(X2,X3)))),X)) = f(f(X3,X2),f(X2,X3)),
inference(substitution,[status(thm)],[c896]) ).
cnf(c898,plain,
f(f(f(f(X3,X2),f(X2,X3)),f(f(X3,X2),f(X2,X3))),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)) = f(f(X3,X2),f(X2,X3)),
inference(transitivity,[status(thm)],[c875,c897]) ).
cnf(c899,plain,
f(f(X2,f(f(X3,X2),f(X2,X3))),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)) = f(f(X3,X2),f(X2,X3)),
inference(transitivity,[status(thm)],[c870,c898]) ).
cnf(c900,plain,
f(f(X2,X3),f(f(f(X2,X3),f(X2,f(f(X3,X2),f(X2,X3)))),X)) = f(f(X3,X2),f(X2,X3)),
inference(transitivity,[status(thm)],[c867,c899]) ).
cnf(c901,plain,
f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X3,X2),f(X2,X3)),
inference(transitivity,[status(thm)],[c864,c900]) ).
cnf(c902,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(transitivity,[status(thm)],[c857,c901]) ).
cnf(c903,plain,
f(f(X2,X),f(X2,X)) = f(f(X,X2),f(X2,X)),
inference(substitution,[status(thm)],[c902]) ).
cnf(c904,plain,
f(f(X,X2),f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(symmetry,[status(thm)],[c903]) ).
cnf(c905,plain,
f(X,f(f(X,X2),f(X2,X))) = f(X,f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c904]) ).
cnf(c906,plain,
f(X,f(f(X2,X),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c72]) ).
cnf(c907,plain,
f(X,f(f(X,X2),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c905,c906]) ).
cnf(c908,plain,
f(X,X2) = f(X2,X),
inference(transitivity,[status(thm)],[c855,c907]) ).
cnf(c909,plain,
f(f(X3,f(X2,X2)),f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2)))),f(X3,f(X2,X2))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c910,plain,
f(f(X,f(X2,X2)),f(f(X2,X2),X2)) = f(f(X,f(X2,X2)),f(X,f(X2,X2))),
inference(substitution,[status(thm)],[c449]) ).
cnf(c911,plain,
f(f(X,f(X2,X2)),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),f(f(X2,X2),X2)),
inference(symmetry,[status(thm)],[c910]) ).
cnf(c912,plain,
f(X2,f(f(X,f(X3,X3)),f(X,f(X3,X3)))) = f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))),
inference(congruence,[status(thm)],[c911]) ).
cnf(c913,plain,
f(X3,f(X2,f(f(X,f(X3,X3)),f(X,f(X3,X3))))) = f(X3,f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3)))),
inference(congruence,[status(thm)],[c912]) ).
cnf(c914,plain,
f(f(f(X,f(X3,X3)),f(f(X3,X3),X3)),f(f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))),f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))))) = f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c915,plain,
f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))) = f(f(f(X,f(X3,X3)),f(f(X3,X3),X3)),f(f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))),f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))))),
inference(symmetry,[status(thm)],[c914]) ).
cnf(c916,plain,
f(X3,f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3)))) = f(X3,f(f(f(X,f(X3,X3)),f(f(X3,X3),X3)),f(f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))),f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3)))))),
inference(congruence,[status(thm)],[c915]) ).
cnf(c917,plain,
f(f(X3,X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)) = X3,
inference(substitution,[status(thm)],[c166]) ).
cnf(c918,plain,
X3 = f(f(X3,X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),
inference(symmetry,[status(thm)],[c917]) ).
cnf(c919,plain,
f(X3,f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)) = f(f(f(X3,X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)),
inference(congruence,[status(thm)],[c918]) ).
cnf(c920,plain,
f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3) = f(X3,X3),
inference(substitution,[status(thm)],[c376]) ).
cnf(c921,plain,
f(X3,X3) = f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3),
inference(symmetry,[status(thm)],[c920]) ).
cnf(c922,plain,
f(f(X3,X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)) = f(f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),
inference(congruence,[status(thm)],[c921]) ).
cnf(c923,plain,
f(f(f(X3,X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)) = f(f(f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)),
inference(congruence,[status(thm)],[c922]) ).
cnf(c924,plain,
f(f(f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)) = f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3),
inference(substitution,[status(thm)],[c157]) ).
cnf(c925,plain,
f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3) = f(X3,X3),
inference(substitution,[status(thm)],[c376]) ).
cnf(c926,plain,
f(f(f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)) = f(X3,X3),
inference(transitivity,[status(thm)],[c924,c925]) ).
cnf(c927,plain,
f(f(f(X3,X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X),X3)),f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)) = f(X3,X3),
inference(transitivity,[status(thm)],[c923,c926]) ).
cnf(c928,plain,
f(X3,f(f(f(X2,f(X3,X3)),f(f(X3,X3),X3)),X)) = f(X3,X3),
inference(transitivity,[status(thm)],[c919,c927]) ).
cnf(c929,plain,
f(X3,f(f(f(X,f(X3,X3)),f(f(X3,X3),X3)),f(f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3))),f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3)))))) = f(X3,X3),
inference(substitution,[status(thm)],[c928]) ).
cnf(c930,plain,
f(X3,f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X3)))) = f(X3,X3),
inference(transitivity,[status(thm)],[c916,c929]) ).
cnf(c931,plain,
f(X3,f(X2,f(f(X,f(X3,X3)),f(X,f(X3,X3))))) = f(X3,X3),
inference(transitivity,[status(thm)],[c913,c930]) ).
cnf(c932,plain,
f(X2,f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c931]) ).
cnf(c933,plain,
f(X2,X2) = f(X2,f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(symmetry,[status(thm)],[c932]) ).
cnf(c934,plain,
f(X3,f(X2,X2)) = f(X3,f(X2,f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2)))))),
inference(congruence,[status(thm)],[c933]) ).
cnf(c935,plain,
f(f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2)))),f(X3,f(X2,X2))) = f(f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2)))),f(X3,f(X2,f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2))))))),
inference(congruence,[status(thm)],[c934]) ).
cnf(c936,plain,
f(f(f(X4,X4),X4),f(X3,f(X2,f(X3,X)))) = f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c937,plain,
f(f(X3,f(X2,f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))))) = f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))),
inference(substitution,[status(thm)],[c328]) ).
cnf(c938,plain,
f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))) = f(f(X3,f(X2,f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))))),
inference(symmetry,[status(thm)],[c937]) ).
cnf(c939,plain,
f(X2,f(X4,f(X,f(X4,X3)))) = f(f(X4,f(X,f(X4,X3))),X2),
inference(substitution,[status(thm)],[c908]) ).
cnf(c940,plain,
f(f(f(X4,X3),f(X4,X3)),f(X2,f(X4,f(X,f(X4,X3))))) = f(f(f(X4,X3),f(X4,X3)),f(f(X4,f(X,f(X4,X3))),X2)),
inference(congruence,[status(thm)],[c939]) ).
cnf(c941,plain,
f(f(X3,f(f(X2,X2),X2)),X) = f(X,f(X3,f(f(X2,X2),X2))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c942,plain,
f(X3,f(f(X3,f(f(X2,X2),X2)),X)) = f(X3,f(X,f(X3,f(f(X2,X2),X2)))),
inference(congruence,[status(thm)],[c941]) ).
cnf(c943,plain,
f(X2,f(X3,f(f(X,X),X))) = f(X2,f(X3,X3)),
inference(congruence,[status(thm)],[c449]) ).
cnf(c944,plain,
f(X3,f(X2,f(X3,f(f(X,X),X)))) = f(X3,f(X2,f(X3,X3))),
inference(congruence,[status(thm)],[c943]) ).
cnf(c945,plain,
f(X3,f(X2,f(X3,f(f(X,X),X)))) = f(X3,X3),
inference(transitivity,[status(thm)],[c944,c328]) ).
cnf(c946,plain,
f(X3,f(X,f(X3,f(f(X2,X2),X2)))) = f(X3,X3),
inference(substitution,[status(thm)],[c945]) ).
cnf(c947,plain,
f(X3,f(f(X3,f(f(X2,X2),X2)),X)) = f(X3,X3),
inference(transitivity,[status(thm)],[c942,c946]) ).
cnf(c948,plain,
f(f(X4,X3),f(f(f(X4,X3),f(f(X,X),X)),f(X4,f(X2,f(X4,X3))))) = f(f(X4,X3),f(X4,X3)),
inference(substitution,[status(thm)],[c947]) ).
cnf(c949,plain,
f(f(X4,X3),f(X4,X3)) = f(f(X4,X3),f(f(f(X4,X3),f(f(X,X),X)),f(X4,f(X2,f(X4,X3))))),
inference(symmetry,[status(thm)],[c948]) ).
cnf(c950,plain,
f(f(f(X5,X4),f(X5,X4)),f(f(X5,f(X2,f(X5,X4))),X3)) = f(f(f(X5,X4),f(f(f(X5,X4),f(f(X,X),X)),f(X5,f(X2,f(X5,X4))))),f(f(X5,f(X2,f(X5,X4))),X3)),
inference(congruence,[status(thm)],[c949]) ).
cnf(c951,plain,
f(X2,f(X3,f(X2,X))) = f(f(X3,f(X2,X)),X2),
inference(substitution,[status(thm)],[c908]) ).
cnf(c952,plain,
f(f(X2,X),f(X2,f(X3,f(X2,X)))) = f(f(X2,X),f(f(X3,f(X2,X)),X2)),
inference(congruence,[status(thm)],[c951]) ).
cnf(c953,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(X3,f(X2,X))))) = f(f(X3,f(X2,X)),f(f(X2,X),f(f(X3,f(X2,X)),X2))),
inference(congruence,[status(thm)],[c952]) ).
cnf(c954,plain,
X2 = f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X))))),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c955,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))))),
inference(congruence,[status(thm)],[c954]) ).
cnf(c956,plain,
f(f(X2,X),f(f(X3,f(X2,X)),X2)) = f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X))))))),
inference(congruence,[status(thm)],[c955]) ).
cnf(c957,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(f(X3,f(X2,X)),X2))) = f(f(X3,f(X2,X)),f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))))))),
inference(congruence,[status(thm)],[c956]) ).
cnf(c958,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))))))) = f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))))),
inference(substitution,[status(thm)],[c546]) ).
cnf(c959,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))))) = f(f(X3,f(X2,X)),X2),
inference(congruence,[status(thm)],[c361]) ).
cnf(c960,plain,
f(X2,f(X3,f(X2,X))) = f(f(X3,f(X2,X)),X2),
inference(substitution,[status(thm)],[c908]) ).
cnf(c961,plain,
f(f(X3,f(X2,X)),X2) = f(X2,f(X3,f(X2,X))),
inference(symmetry,[status(thm)],[c960]) ).
cnf(c962,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c959,c961]) ).
cnf(c963,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(f(X3,f(X2,X)),f(f(X2,X),f(X2,f(f(X2,X),f(f(X2,X),f(X2,X)))))))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c958,c962]) ).
cnf(c964,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(f(X3,f(X2,X)),X2))) = f(X2,f(X3,f(X2,X))),
inference(transitivity,[status(thm)],[c957,c963]) ).
cnf(c965,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)],[c953,c964]) ).
cnf(c966,plain,
f(f(X,f(X3,X2)),f(f(X3,X2),f(X3,f(X,f(X3,X2))))) = f(X3,f(X,f(X3,X2))),
inference(substitution,[status(thm)],[c965]) ).
cnf(c967,plain,
f(X3,f(X,f(X3,X2))) = f(f(X,f(X3,X2)),f(f(X3,X2),f(X3,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c966]) ).
cnf(c968,plain,
f(f(X4,f(X,f(X4,X3))),X2) = f(f(f(X,f(X4,X3)),f(f(X4,X3),f(X4,f(X,f(X4,X3))))),X2),
inference(congruence,[status(thm)],[c967]) ).
cnf(c969,plain,
f(f(f(X5,X4),f(f(f(X5,X4),f(f(X,X),X)),f(X5,f(X2,f(X5,X4))))),f(f(X5,f(X2,f(X5,X4))),X3)) = f(f(f(X5,X4),f(f(f(X5,X4),f(f(X,X),X)),f(X5,f(X2,f(X5,X4))))),f(f(f(X2,f(X5,X4)),f(f(X5,X4),f(X5,f(X2,f(X5,X4))))),X3)),
inference(congruence,[status(thm)],[c968]) ).
cnf(c970,plain,
f(f(X5,f(f(X5,f(f(X4,X4),X4)),X3)),f(f(f(X2,X5),f(X5,X3)),X)) = f(f(f(f(X2,X5),f(X5,X3)),X),f(X5,f(f(X5,f(f(X4,X4),X4)),X3))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c971,plain,
X = f(f(X2,X),f(X,X)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c972,plain,
f(X,f(f(X2,X),f(f(X2,X),f(X2,X)))) = f(f(f(X2,X),f(X,X)),f(f(X2,X),f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c971]) ).
cnf(c973,plain,
f(f(X2,X),f(X,f(f(X2,X),f(f(X2,X),f(X2,X))))) = f(f(X2,X),f(f(f(X2,X),f(X,X)),f(f(X2,X),f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c972]) ).
cnf(c974,plain,
f(f(X2,X),f(f(f(X2,X),f(X,X)),f(f(X2,X),f(f(X2,X),f(X2,X))))) = f(f(X2,X),f(X,X)),
inference(substitution,[status(thm)],[c358]) ).
cnf(c975,plain,
f(f(X2,X),f(f(f(X2,X),f(X,X)),f(f(X2,X),f(f(X2,X),f(X2,X))))) = X,
inference(transitivity,[status(thm)],[c974,c67]) ).
cnf(c976,plain,
f(f(X2,X),f(X,f(f(X2,X),f(f(X2,X),f(X2,X))))) = X,
inference(transitivity,[status(thm)],[c973,c975]) ).
cnf(c977,plain,
f(f(X2,f(f(X,X),X)),f(f(f(X,X),X),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))))) = f(f(X,X),X),
inference(substitution,[status(thm)],[c976]) ).
cnf(c978,plain,
f(f(X,X),X) = f(f(X2,f(f(X,X),X)),f(f(f(X,X),X),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))))),
inference(symmetry,[status(thm)],[c977]) ).
cnf(c979,plain,
f(f(f(X,X),X),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X))))) = f(f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X))))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c980,plain,
f(f(X2,f(f(X,X),X)),f(f(f(X,X),X),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))))) = f(f(X2,f(f(X,X),X)),f(f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))))),
inference(congruence,[status(thm)],[c979]) ).
cnf(c981,plain,
f(f(X2,f(f(X,X),X)),f(f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))))) = f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))),
inference(substitution,[status(thm)],[c358]) ).
cnf(c982,plain,
f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X))) = X2,
inference(substitution,[status(thm)],[c446]) ).
cnf(c983,plain,
f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))) = f(f(X2,f(f(X,X),X)),X2),
inference(congruence,[status(thm)],[c982]) ).
cnf(c984,plain,
f(f(X2,f(f(X,X),X)),X2) = f(f(X2,X2),X2),
inference(congruence,[status(thm)],[c449]) ).
cnf(c985,plain,
f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c983,c984]) ).
cnf(c986,plain,
f(f(X2,f(f(X,X),X)),f(f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c981,c985]) ).
cnf(c987,plain,
f(f(X2,f(f(X,X),X)),f(f(f(X,X),X),f(f(X2,f(f(X,X),X)),f(f(X2,f(f(X,X),X)),f(X2,f(f(X,X),X)))))) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c980,c986]) ).
cnf(c988,plain,
f(f(X,X),X) = f(f(X2,X2),X2),
inference(transitivity,[status(thm)],[c978,c987]) ).
cnf(c989,plain,
f(f(X2,X2),X2) = f(f(X,X),X),
inference(substitution,[status(thm)],[c988]) ).
cnf(c990,plain,
f(X3,f(f(X2,X2),X2)) = f(X3,f(f(X,X),X)),
inference(congruence,[status(thm)],[c989]) ).
cnf(c991,plain,
f(f(X4,f(f(X3,X3),X3)),X2) = f(f(X4,f(f(X,X),X)),X2),
inference(congruence,[status(thm)],[c990]) ).
cnf(c992,plain,
f(X4,f(f(X4,f(f(X3,X3),X3)),X2)) = f(X4,f(f(X4,f(f(X,X),X)),X2)),
inference(congruence,[status(thm)],[c991]) ).
cnf(c993,plain,
f(f(f(f(X2,X5),f(X5,X3)),X),f(X5,f(f(X5,f(f(X4,X4),X4)),X3))) = f(f(f(f(X2,X5),f(X5,X3)),X),f(X5,f(f(X5,f(f(X2,X2),X2)),X3))),
inference(congruence,[status(thm)],[c992]) ).
cnf(c994,plain,
f(f(f(f(X2,X4),f(X4,X3)),X),f(X4,f(f(X4,f(f(X2,X2),X2)),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c995,plain,
f(f(f(f(X2,X5),f(X5,X3)),X),f(X5,f(f(X5,f(f(X4,X4),X4)),X3))) = X5,
inference(transitivity,[status(thm)],[c993,c994]) ).
cnf(c996,plain,
f(f(X5,f(f(X5,f(f(X4,X4),X4)),X3)),f(f(f(X2,X5),f(X5,X3)),X)) = X5,
inference(transitivity,[status(thm)],[c970,c995]) ).
cnf(c997,plain,
f(f(f(X5,X4),f(f(f(X5,X4),f(f(X,X),X)),f(X5,f(X2,f(X5,X4))))),f(f(f(X2,f(X5,X4)),f(f(X5,X4),f(X5,f(X2,f(X5,X4))))),X3)) = f(X5,X4),
inference(substitution,[status(thm)],[c996]) ).
cnf(c998,plain,
f(f(f(X5,X4),f(f(f(X5,X4),f(f(X,X),X)),f(X5,f(X2,f(X5,X4))))),f(f(X5,f(X2,f(X5,X4))),X3)) = f(X5,X4),
inference(transitivity,[status(thm)],[c969,c997]) ).
cnf(c999,plain,
f(f(f(X4,X3),f(X4,X3)),f(f(X4,f(X,f(X4,X3))),X2)) = f(X4,X3),
inference(transitivity,[status(thm)],[c950,c998]) ).
cnf(c1000,plain,
f(f(f(X4,X3),f(X4,X3)),f(X2,f(X4,f(X,f(X4,X3))))) = f(X4,X3),
inference(transitivity,[status(thm)],[c940,c999]) ).
cnf(c1001,plain,
f(f(f(X3,X),f(X3,X)),f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X))))) = f(X3,X),
inference(substitution,[status(thm)],[c1000]) ).
cnf(c1002,plain,
f(f(X3,f(X2,f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))))) = f(f(X3,f(X2,f(X3,X))),f(X3,X)),
inference(congruence,[status(thm)],[c1001]) ).
cnf(c1003,plain,
f(f(X3,X),f(X3,f(X2,f(X3,X)))) = f(f(X3,f(X2,f(X3,X))),f(X3,X)),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1004,plain,
f(f(X3,f(X2,f(X3,X))),f(X3,X)) = f(f(X3,X),f(X3,f(X2,f(X3,X)))),
inference(symmetry,[status(thm)],[c1003]) ).
cnf(c1005,plain,
f(f(X3,f(X2,f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))))) = f(f(X3,X),f(X3,f(X2,f(X3,X)))),
inference(transitivity,[status(thm)],[c1002,c1004]) ).
cnf(c1006,plain,
f(f(X3,f(X2,f(X3,X))),f(X3,f(X2,f(X3,X)))) = f(f(X3,X),f(X3,f(X2,f(X3,X)))),
inference(transitivity,[status(thm)],[c938,c1005]) ).
cnf(c1007,plain,
f(f(f(X4,X4),X4),f(X3,f(X2,f(X3,X)))) = f(f(X3,X),f(X3,f(X2,f(X3,X)))),
inference(transitivity,[status(thm)],[c936,c1006]) ).
cnf(c1008,plain,
f(f(f(X,X),X),f(X4,f(X3,f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))))) = f(f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3)))),f(X4,f(X3,f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))))),
inference(substitution,[status(thm)],[c1007]) ).
cnf(c1009,plain,
f(f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3)))),f(X4,f(X3,f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))))) = f(f(f(X,X),X),f(X4,f(X3,f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))))),
inference(symmetry,[status(thm)],[c1008]) ).
cnf(c1010,plain,
f(X2,f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c931]) ).
cnf(c1011,plain,
f(X3,f(X2,f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2)))))) = f(X3,f(X2,X2)),
inference(congruence,[status(thm)],[c1010]) ).
cnf(c1012,plain,
f(f(f(X,X),X),f(X4,f(X3,f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))))) = f(f(f(X,X),X),f(X4,f(X3,X3))),
inference(congruence,[status(thm)],[c1011]) ).
cnf(c1013,plain,
f(f(f(X2,X2),X2),X) = f(X,X),
inference(substitution,[status(thm)],[c654]) ).
cnf(c1014,plain,
f(X2,X2) = f(X2,f(f(X,X),X)),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c1015,plain,
f(f(f(X3,X3),X3),X2) = f(X2,f(f(X,X),X)),
inference(transitivity,[status(thm)],[c1013,c1014]) ).
cnf(c1016,plain,
f(f(f(X2,X2),X2),f(X4,f(X3,X3))) = f(f(X4,f(X3,X3)),f(f(X,X),X)),
inference(substitution,[status(thm)],[c1015]) ).
cnf(c1017,plain,
f(f(X3,f(X2,X2)),f(f(X,X),X)) = f(f(X3,f(X2,X2)),f(X3,f(X2,X2))),
inference(substitution,[status(thm)],[c449]) ).
cnf(c1018,plain,
f(f(f(X,X),X),f(X3,f(X2,X2))) = f(f(X3,f(X2,X2)),f(X3,f(X2,X2))),
inference(transitivity,[status(thm)],[c1016,c1017]) ).
cnf(c1019,plain,
f(f(f(X,X),X),f(X4,f(X3,f(X4,f(f(X2,f(X3,X3)),f(X2,f(X3,X3))))))) = f(f(X4,f(X3,X3)),f(X4,f(X3,X3))),
inference(transitivity,[status(thm)],[c1012,c1018]) ).
cnf(c1020,plain,
f(f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2)))),f(X3,f(X2,f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2))))))) = f(f(X3,f(X2,X2)),f(X3,f(X2,X2))),
inference(transitivity,[status(thm)],[c1009,c1019]) ).
cnf(c1021,plain,
f(f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2)))),f(X3,f(X2,X2))) = f(f(X3,f(X2,X2)),f(X3,f(X2,X2))),
inference(transitivity,[status(thm)],[c935,c1020]) ).
cnf(c1022,plain,
f(f(X3,f(X2,X2)),f(X3,f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(f(X3,f(X2,X2)),f(X3,f(X2,X2))),
inference(transitivity,[status(thm)],[c909,c1021]) ).
cnf(c1023,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))))) = f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2)))),
inference(substitution,[status(thm)],[c1022]) ).
cnf(c1024,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2)))) = f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))))),
inference(symmetry,[status(thm)],[c1023]) ).
cnf(c1025,plain,
f(f(X3,f(f(X,X2),f(X,X2))),f(X3,X2)) = f(f(X3,X2),f(X3,X2)),
inference(substitution,[status(thm)],[c471]) ).
cnf(c1026,plain,
f(f(X3,X2),f(X3,X2)) = f(f(X3,f(f(X,X2),f(X,X2))),f(X3,X2)),
inference(symmetry,[status(thm)],[c1025]) ).
cnf(c1027,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(f(f(X3,f(f(X,X2),f(X,X2))),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(congruence,[status(thm)],[c1026]) ).
cnf(c1028,plain,
f(f(f(X3,f(f(X,X2),f(X,X2))),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(X3,f(f(X,X2),f(X,X2))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c1029,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(X3,f(f(X,X2),f(X,X2))),
inference(transitivity,[status(thm)],[c1027,c1028]) ).
cnf(c1030,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))))) = f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(congruence,[status(thm)],[c1029]) ).
cnf(c1031,plain,
f(f(X3,f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2)))) = f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1032,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))) = f(f(X3,f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2)))),
inference(symmetry,[status(thm)],[c1031]) ).
cnf(c1033,plain,
f(X,X2) = f(X2,f(f(X,X2),f(X,X2))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c1034,plain,
f(f(X3,X2),f(X,X2)) = f(f(X3,X2),f(X2,f(f(X,X2),f(X,X2)))),
inference(congruence,[status(thm)],[c1033]) ).
cnf(c1035,plain,
f(X2,f(f(X3,X2),f(X,X2))) = f(X2,f(f(X3,X2),f(X2,f(f(X,X2),f(X,X2))))),
inference(congruence,[status(thm)],[c1034]) ).
cnf(c1036,plain,
f(f(X3,X2),f(X2,f(f(X3,X2),f(X,X2)))) = f(f(X3,X2),f(X2,f(f(X3,X2),f(X2,f(f(X,X2),f(X,X2)))))),
inference(congruence,[status(thm)],[c1035]) ).
cnf(c1037,plain,
f(f(X3,X2),f(X2,f(f(X3,X2),f(X2,f(f(X,X2),f(X,X2)))))) = f(f(X3,X2),f(X2,f(f(X,X2),f(X,X2)))),
inference(substitution,[status(thm)],[c546]) ).
cnf(c1038,plain,
f(f(X3,X2),f(X2,f(f(X,X2),f(X,X2)))) = f(f(X3,X2),f(X,X2)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c1039,plain,
f(f(X3,X2),f(X2,f(f(X3,X2),f(X2,f(f(X,X2),f(X,X2)))))) = f(f(X3,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c1037,c1038]) ).
cnf(c1040,plain,
f(f(X3,X2),f(X2,f(f(X3,X2),f(X,X2)))) = f(f(X3,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c1036,c1039]) ).
cnf(c1041,plain,
f(f(X3,f(X2,X2)),f(f(X2,X2),f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2))))) = f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2))),
inference(substitution,[status(thm)],[c1040]) ).
cnf(c1042,plain,
f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2))) = f(f(X3,f(X2,X2)),f(f(X2,X2),f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2))))),
inference(symmetry,[status(thm)],[c1041]) ).
cnf(c1043,plain,
f(f(f(X,X),X),f(f(X4,f(X3,X3)),f(f(f(X4,X2),f(X4,X2)),f(X3,X3)))) = f(f(X3,X3),f(f(X4,f(X3,X3)),f(f(f(X4,X2),f(X4,X2)),f(X3,X3)))),
inference(substitution,[status(thm)],[c672]) ).
cnf(c1044,plain,
f(f(X3,X3),f(f(X4,f(X3,X3)),f(f(f(X4,X2),f(X4,X2)),f(X3,X3)))) = f(f(f(X,X),X),f(f(X4,f(X3,X3)),f(f(f(X4,X2),f(X4,X2)),f(X3,X3)))),
inference(symmetry,[status(thm)],[c1043]) ).
cnf(c1045,plain,
f(f(f(X5,X5),X5),f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))) = f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c1046,plain,
X3 = f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c1047,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))),
inference(congruence,[status(thm)],[c1046]) ).
cnf(c1048,plain,
f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(X3,X2),f(X3,X2)),X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c1049,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(X3,X2),f(X3,X2)),X),
inference(transitivity,[status(thm)],[c1047,c1048]) ).
cnf(c1050,plain,
f(f(f(X3,X2),f(X3,X2)),X) = f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))),
inference(symmetry,[status(thm)],[c1049]) ).
cnf(c1051,plain,
f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)) = f(f(X4,X3),f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X)))),
inference(congruence,[status(thm)],[c1050]) ).
cnf(c1052,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))) = f(X4,f(f(X4,X3),f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X))))),
inference(congruence,[status(thm)],[c1051]) ).
cnf(c1053,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X)))))),
inference(congruence,[status(thm)],[c1052]) ).
cnf(c1054,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X)))))) = f(f(X4,X3),f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X)))),
inference(substitution,[status(thm)],[c704]) ).
cnf(c1055,plain,
f(f(X4,X3),f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X)))) = f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),
inference(congruence,[status(thm)],[c1049]) ).
cnf(c1056,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X)))))) = f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),
inference(transitivity,[status(thm)],[c1054,c1055]) ).
cnf(c1057,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))) = f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),
inference(transitivity,[status(thm)],[c1053,c1056]) ).
cnf(c1058,plain,
f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)) = f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),
inference(symmetry,[status(thm)],[c1057]) ).
cnf(c1059,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))) = f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))),
inference(congruence,[status(thm)],[c1058]) ).
cnf(c1060,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),
inference(substitution,[status(thm)],[c704]) ).
cnf(c1061,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))) = f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))))),
inference(symmetry,[status(thm)],[c1060]) ).
cnf(c1062,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))) = f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))))),
inference(congruence,[status(thm)],[c1061]) ).
cnf(c1063,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4) = f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))),
inference(substitution,[status(thm)],[c721]) ).
cnf(c1064,plain,
f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))) = f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4),
inference(symmetry,[status(thm)],[c1063]) ).
cnf(c1065,plain,
f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))))) = f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4)),
inference(congruence,[status(thm)],[c1064]) ).
cnf(c1066,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))))) = f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4))),
inference(congruence,[status(thm)],[c1065]) ).
cnf(c1067,plain,
f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)) = f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),
inference(symmetry,[status(thm)],[c1057]) ).
cnf(c1068,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4))) = f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4))),
inference(congruence,[status(thm)],[c1067]) ).
cnf(c1069,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4))) = f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4),
inference(substitution,[status(thm)],[c745]) ).
cnf(c1070,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4) = f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))),
inference(substitution,[status(thm)],[c721]) ).
cnf(c1071,plain,
f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(substitution,[status(thm)],[c762]) ).
cnf(c1072,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1070,c1071]) ).
cnf(c1073,plain,
f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4))) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1069,c1072]) ).
cnf(c1074,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)))),X4))) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1068,c1073]) ).
cnf(c1075,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(X4,f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))))) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1066,c1074]) ).
cnf(c1076,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))))) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1062,c1075]) ).
cnf(c1077,plain,
f(f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X)),f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1059,c1076]) ).
cnf(c1078,plain,
f(f(f(X5,X5),X5),f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))) = f(X4,f(f(X4,X3),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1045,c1077]) ).
cnf(c1079,plain,
f(f(f(X,X),X),f(f(X4,f(X3,X3)),f(f(f(X4,X2),f(X4,X2)),f(X3,X3)))) = f(X4,f(f(X4,f(X3,X3)),f(f(f(X4,X2),f(X4,X2)),f(X3,X3)))),
inference(substitution,[status(thm)],[c1078]) ).
cnf(c1080,plain,
f(f(X2,X2),f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2)))) = f(X3,f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2)))),
inference(transitivity,[status(thm)],[c1044,c1079]) ).
cnf(c1081,plain,
f(f(X3,X3),f(f(X2,f(X3,X3)),f(f(f(X2,X),f(X2,X)),f(X3,X3)))) = f(X2,f(f(X2,f(X3,X3)),f(f(f(X2,X),f(X2,X)),f(X3,X3)))),
inference(substitution,[status(thm)],[c1080]) ).
cnf(c1082,plain,
f(f(f(X2,X),f(X2,X)),f(X3,X3)) = f(f(X3,X3),f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1083,plain,
f(f(X2,f(X3,X3)),f(f(f(X2,X),f(X2,X)),f(X3,X3))) = f(f(X2,f(X3,X3)),f(f(X3,X3),f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c1082]) ).
cnf(c1084,plain,
f(X2,f(f(X2,f(X3,X3)),f(f(f(X2,X),f(X2,X)),f(X3,X3)))) = f(X2,f(f(X2,f(X3,X3)),f(f(X3,X3),f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c1083]) ).
cnf(c1085,plain,
f(f(X2,f(X3,X3)),f(f(X3,X3),f(f(X2,X),f(X2,X)))) = f(f(f(X3,X3),f(f(X2,X),f(X2,X))),f(X2,f(X3,X3))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1086,plain,
f(X2,f(f(X2,f(X3,X3)),f(f(X3,X3),f(f(X2,X),f(X2,X))))) = f(X2,f(f(f(X3,X3),f(f(X2,X),f(X2,X))),f(X2,f(X3,X3)))),
inference(congruence,[status(thm)],[c1085]) ).
cnf(c1087,plain,
f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c1088,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(symmetry,[status(thm)],[c1087]) ).
cnf(c1089,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,X3),f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c1088]) ).
cnf(c1090,plain,
f(f(X3,X3),f(f(f(X3,X),f(X3,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))) = X3,
inference(substitution,[status(thm)],[c893]) ).
cnf(c1091,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))) = X3,
inference(transitivity,[status(thm)],[c1089,c1090]) ).
cnf(c1092,plain,
X3 = f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c1091]) ).
cnf(c1093,plain,
f(X3,X2) = f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),
inference(congruence,[status(thm)],[c1092]) ).
cnf(c1094,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2)),
inference(congruence,[status(thm)],[c1093]) ).
cnf(c1095,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2))),
inference(congruence,[status(thm)],[c1094]) ).
cnf(c1096,plain,
f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c1097,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2)) = f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c1096]) ).
cnf(c1098,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2))) = f(X3,f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c1097]) ).
cnf(c1099,plain,
X3 = f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c1091]) ).
cnf(c1100,plain,
f(X3,f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X))))) = f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c1099]) ).
cnf(c1101,plain,
f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X))))) = f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),
inference(substitution,[status(thm)],[c303]) ).
cnf(c1102,plain,
f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2) = f(X3,X2),
inference(congruence,[status(thm)],[c1091]) ).
cnf(c1103,plain,
f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X))))) = f(X3,X2),
inference(transitivity,[status(thm)],[c1101,c1102]) ).
cnf(c1104,plain,
f(X3,f(f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2),f(X2,f(f(X3,X),f(X3,X))))) = f(X3,X2),
inference(transitivity,[status(thm)],[c1100,c1103]) ).
cnf(c1105,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),X2))) = f(X3,X2),
inference(transitivity,[status(thm)],[c1098,c1104]) ).
cnf(c1106,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))) = f(X3,X2),
inference(transitivity,[status(thm)],[c1095,c1105]) ).
cnf(c1107,plain,
f(X2,f(f(f(X3,X3),f(f(X2,X),f(X2,X))),f(X2,f(X3,X3)))) = f(X2,f(X3,X3)),
inference(substitution,[status(thm)],[c1106]) ).
cnf(c1108,plain,
f(X2,f(f(X2,f(X3,X3)),f(f(X3,X3),f(f(X2,X),f(X2,X))))) = f(X2,f(X3,X3)),
inference(transitivity,[status(thm)],[c1086,c1107]) ).
cnf(c1109,plain,
f(X2,f(f(X2,f(X3,X3)),f(f(f(X2,X),f(X2,X)),f(X3,X3)))) = f(X2,f(X3,X3)),
inference(transitivity,[status(thm)],[c1084,c1108]) ).
cnf(c1110,plain,
f(f(X3,X3),f(f(X2,f(X3,X3)),f(f(f(X2,X),f(X2,X)),f(X3,X3)))) = f(X2,f(X3,X3)),
inference(transitivity,[status(thm)],[c1081,c1109]) ).
cnf(c1111,plain,
f(f(X2,X2),f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2)))) = f(X3,f(X2,X2)),
inference(substitution,[status(thm)],[c1110]) ).
cnf(c1112,plain,
f(f(X3,f(X2,X2)),f(f(X2,X2),f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2))))) = f(f(X3,f(X2,X2)),f(X3,f(X2,X2))),
inference(congruence,[status(thm)],[c1111]) ).
cnf(c1113,plain,
f(f(X3,f(X2,X2)),f(f(f(X3,X),f(X3,X)),f(X2,X2))) = f(f(X3,f(X2,X2)),f(X3,f(X2,X2))),
inference(transitivity,[status(thm)],[c1042,c1112]) ).
cnf(c1114,plain,
f(f(X3,f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2)))) = f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(substitution,[status(thm)],[c1113]) ).
cnf(c1115,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))) = f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(transitivity,[status(thm)],[c1032,c1114]) ).
cnf(c1116,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))))) = f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(transitivity,[status(thm)],[c1030,c1115]) ).
cnf(c1117,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2)))) = f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(transitivity,[status(thm)],[c1024,c1116]) ).
cnf(c1118,plain,
f(f(f(X,X),X),f(f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))),f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))))) = f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X4,f(f(X2,X3),f(X2,X3))))),
inference(congruence,[status(thm)],[c1117]) ).
cnf(c1119,plain,
f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X4,f(f(X2,X3),f(X2,X3))))) = f(X4,f(f(X2,X3),f(X2,X3))),
inference(substitution,[status(thm)],[c823]) ).
cnf(c1120,plain,
f(f(f(X,X),X),f(f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))),f(f(f(X4,X3),f(X4,X3)),f(f(X2,X3),f(X2,X3))))) = f(X4,f(f(X2,X3),f(X2,X3))),
inference(transitivity,[status(thm)],[c1118,c1119]) ).
cnf(c1121,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))) = f(X3,f(f(X,X2),f(X,X2))),
inference(transitivity,[status(thm)],[c825,c1120]) ).
cnf(c1122,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))),
inference(symmetry,[status(thm)],[c1121]) ).
cnf(c1123,plain,
f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2)))),
inference(congruence,[status(thm)],[c1122]) ).
cnf(c1124,plain,
f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))))),
inference(congruence,[status(thm)],[c1123]) ).
cnf(c1125,plain,
f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1126,plain,
f(X3,f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X))))) = f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),
inference(congruence,[status(thm)],[c1125]) ).
cnf(c1127,plain,
f(X3,f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X))))) = f(X3,X2),
inference(transitivity,[status(thm)],[c1126,c1106]) ).
cnf(c1128,plain,
f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X,X2),f(X,X2))))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(substitution,[status(thm)],[c1127]) ).
cnf(c1129,plain,
f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c1124,c1128]) ).
cnf(c1130,plain,
f(X,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c818,c1129]) ).
cnf(c1131,plain,
f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c816,c1130]) ).
cnf(c1132,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c777,c1131]) ).
cnf(c1133,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c1132]) ).
cnf(c1134,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(symmetry,[status(thm)],[c1133]) ).
cnf(c1135,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X2,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))),
inference(substitution,[status(thm)],[c776]) ).
cnf(c1136,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c1113]) ).
cnf(c1137,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c1136]) ).
cnf(c1138,plain,
f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1139,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c1138]) ).
cnf(c1140,plain,
f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))) = f(X3,f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c1121]) ).
cnf(c1141,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))),
inference(symmetry,[status(thm)],[c1140]) ).
cnf(c1142,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c1141]) ).
cnf(c1143,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c902]) ).
cnf(c1144,plain,
f(f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c1143]) ).
cnf(c1145,plain,
f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1146,plain,
f(X2,f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3))))) = f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1147,plain,
f(f(X4,X3),f(X2,f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))))) = f(f(X4,X3),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)),
inference(congruence,[status(thm)],[c1146]) ).
cnf(c1148,plain,
f(f(f(X4,X3),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))) = f(X4,X3),
inference(substitution,[status(thm)],[c166]) ).
cnf(c1149,plain,
f(X4,X3) = f(f(f(X4,X3),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),
inference(symmetry,[status(thm)],[c1148]) ).
cnf(c1150,plain,
f(f(X4,X3),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)) = f(f(f(f(X4,X3),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)),
inference(congruence,[status(thm)],[c1149]) ).
cnf(c1151,plain,
f(f(f(X4,X4),X4),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c1152,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),
inference(substitution,[status(thm)],[c776]) ).
cnf(c1153,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))),
inference(congruence,[status(thm)],[c1152]) ).
cnf(c1154,plain,
f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))) = f(X4,f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),
inference(substitution,[status(thm)],[c770]) ).
cnf(c1155,plain,
f(X4,f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))) = f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),
inference(symmetry,[status(thm)],[c1154]) ).
cnf(c1156,plain,
f(f(f(f(X4,X3),f(X4,X3)),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(X4,f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))) = f(f(f(f(X4,X3),f(X4,X3)),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))),
inference(congruence,[status(thm)],[c1155]) ).
cnf(c1157,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),
inference(substitution,[status(thm)],[c776]) ).
cnf(c1158,plain,
f(f(f(f(X4,X3),f(X4,X3)),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))) = f(f(X4,f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))),
inference(congruence,[status(thm)],[c1157]) ).
cnf(c1159,plain,
f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))),X3),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1160,plain,
f(f(X4,f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))) = f(f(f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))),X4),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))),
inference(congruence,[status(thm)],[c1159]) ).
cnf(c1161,plain,
f(f(X3,X2),f(f(f(X,X),X),X3)) = f(f(X3,X2),f(X3,X3)),
inference(congruence,[status(thm)],[c654]) ).
cnf(c1162,plain,
f(f(X3,X2),f(f(f(X,X),X),X3)) = X3,
inference(transitivity,[status(thm)],[c1161,c49]) ).
cnf(c1163,plain,
f(f(f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))),X4),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))) = f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))),
inference(substitution,[status(thm)],[c1162]) ).
cnf(c1164,plain,
f(f(X4,f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))) = f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))),
inference(transitivity,[status(thm)],[c1160,c1163]) ).
cnf(c1165,plain,
f(f(f(f(X4,X3),f(X4,X3)),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(f(f(X,X),X),f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))) = f(f(X4,f(f(X2,X3),f(X2,X3))),f(X2,f(f(X4,X3),f(X4,X3)))),
inference(transitivity,[status(thm)],[c1158,c1164]) ).
cnf(c1166,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X3,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1156,c1165]) ).
cnf(c1167,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1153,c1166]) ).
cnf(c1168,plain,
f(f(f(X4,X4),X4),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1151,c1167]) ).
cnf(c1169,plain,
f(f(f(f(X3,X),f(X3,X)),f(X3,X)),f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c1168]) ).
cnf(c1170,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(f(f(X3,X),f(X3,X)),f(X3,X)),f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(symmetry,[status(thm)],[c1169]) ).
cnf(c1171,plain,
f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))),X) = f(f(f(f(f(X4,X2),f(X4,X2)),f(X4,X2)),f(f(f(X4,X2),f(X4,X2)),f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))))),X),
inference(congruence,[status(thm)],[c1170]) ).
cnf(c1172,plain,
f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))),X),f(X4,X2)) = f(f(f(f(f(f(X4,X2),f(X4,X2)),f(X4,X2)),f(f(f(X4,X2),f(X4,X2)),f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))))),X),f(X4,X2)),
inference(congruence,[status(thm)],[c1171]) ).
cnf(c1173,plain,
f(f(f(f(X2,X2),X),f(f(X2,X2),X)),f(X2,X2)) = f(f(X2,X2),X),
inference(substitution,[status(thm)],[c157]) ).
cnf(c1174,plain,
f(f(X2,X2),X) = f(f(f(f(X2,X2),X),f(f(X2,X2),X)),f(X2,X2)),
inference(symmetry,[status(thm)],[c1173]) ).
cnf(c1175,plain,
f(f(f(X3,X3),X2),f(f(X3,X3),X)) = f(f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),f(X3,X3)),f(f(X3,X3),X)),
inference(congruence,[status(thm)],[c1174]) ).
cnf(c1176,plain,
f(f(f(f(X4,X4),X3),f(f(X4,X4),X2)),X) = f(f(f(f(f(f(X4,X4),X3),f(f(X4,X4),X3)),f(X4,X4)),f(f(X4,X4),X2)),X),
inference(congruence,[status(thm)],[c1175]) ).
cnf(c1177,plain,
f(f(f(f(f(X4,X4),X3),f(f(X4,X4),X2)),X),X4) = f(f(f(f(f(f(f(X4,X4),X3),f(f(X4,X4),X3)),f(X4,X4)),f(f(X4,X4),X2)),X),X4),
inference(congruence,[status(thm)],[c1176]) ).
cnf(c1178,plain,
f(f(f(f(f(f(f(X4,X4),X3),f(f(X4,X4),X3)),f(X4,X4)),f(f(X4,X4),X2)),X),X4) = f(X4,X4),
inference(substitution,[status(thm)],[c666]) ).
cnf(c1179,plain,
f(f(f(f(f(X4,X4),X3),f(f(X4,X4),X2)),X),X4) = f(X4,X4),
inference(transitivity,[status(thm)],[c1177,c1178]) ).
cnf(c1180,plain,
f(f(f(f(f(f(X4,X2),f(X4,X2)),f(X4,X2)),f(f(f(X4,X2),f(X4,X2)),f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))))),X),f(X4,X2)) = f(f(X4,X2),f(X4,X2)),
inference(substitution,[status(thm)],[c1179]) ).
cnf(c1181,plain,
f(f(f(f(X4,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X4,X2),f(X4,X2)))),X),f(X4,X2)) = f(f(X4,X2),f(X4,X2)),
inference(transitivity,[status(thm)],[c1172,c1180]) ).
cnf(c1182,plain,
f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)) = f(f(X4,X3),f(X4,X3)),
inference(substitution,[status(thm)],[c1181]) ).
cnf(c1183,plain,
f(f(X4,X3),f(X4,X3)) = f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)),
inference(symmetry,[status(thm)],[c1182]) ).
cnf(c1184,plain,
f(f(f(X4,X3),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))) = f(f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),
inference(congruence,[status(thm)],[c1183]) ).
cnf(c1185,plain,
f(f(f(f(X4,X3),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)) = f(f(f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)),
inference(congruence,[status(thm)],[c1184]) ).
cnf(c1186,plain,
f(f(f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)) = f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)),
inference(substitution,[status(thm)],[c157]) ).
cnf(c1187,plain,
f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)) = f(f(X4,X3),f(X4,X3)),
inference(substitution,[status(thm)],[c1181]) ).
cnf(c1188,plain,
f(f(f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c1186,c1187]) ).
cnf(c1189,plain,
f(f(f(f(X4,X3),f(X4,X3)),f(f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2),f(X4,X3))),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c1185,c1188]) ).
cnf(c1190,plain,
f(f(X4,X3),f(f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))),X2)) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c1150,c1189]) ).
cnf(c1191,plain,
f(f(X4,X3),f(X2,f(f(X4,f(f(X,X3),f(X,X3))),f(X,f(f(X4,X3),f(X4,X3)))))) = f(f(X4,X3),f(X4,X3)),
inference(transitivity,[status(thm)],[c1147,c1190]) ).
cnf(c1192,plain,
f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X3,X2),f(X3,X2)),
inference(substitution,[status(thm)],[c1191]) ).
cnf(c1193,plain,
f(f(X3,X2),f(X3,X2)) = f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))),
inference(symmetry,[status(thm)],[c1192]) ).
cnf(c1194,plain,
f(X4,f(f(X3,X2),f(X3,X2))) = f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))))),
inference(congruence,[status(thm)],[c1193]) ).
cnf(c1195,plain,
f(f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))),
inference(congruence,[status(thm)],[c1194]) ).
cnf(c1196,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))),
inference(symmetry,[status(thm)],[c793]) ).
cnf(c1197,plain,
f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c640]) ).
cnf(c1198,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c1197]) ).
cnf(c1199,plain,
f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c1121]) ).
cnf(c1200,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),
inference(symmetry,[status(thm)],[c1199]) ).
cnf(c1201,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c1200]) ).
cnf(c1202,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c1201]) ).
cnf(c1203,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c1202]) ).
cnf(c1204,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c708]) ).
cnf(c1205,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c708]) ).
cnf(c1206,plain,
f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,X2),f(X3,f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))))),
inference(symmetry,[status(thm)],[c1205]) ).
cnf(c1207,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,X2),f(X3,X2)),
inference(congruence,[status(thm)],[c1127]) ).
cnf(c1208,plain,
f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c1206,c1207]) ).
cnf(c1209,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c1208]) ).
cnf(c1210,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c1204,c1209]) ).
cnf(c1211,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c1203,c1210]) ).
cnf(c1212,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c1198,c1211]) ).
cnf(c1213,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(transitivity,[status(thm)],[c1196,c1212]) ).
cnf(c1214,plain,
f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2)))),
inference(substitution,[status(thm)],[c1213]) ).
cnf(c1215,plain,
f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))),
inference(congruence,[status(thm)],[c1214]) ).
cnf(c1216,plain,
f(f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))) = f(f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))),
inference(congruence,[status(thm)],[c1215]) ).
cnf(c1217,plain,
f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2)))),
inference(substitution,[status(thm)],[c1213]) ).
cnf(c1218,plain,
f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))) = f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))),
inference(congruence,[status(thm)],[c1217]) ).
cnf(c1219,plain,
f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X3,X2),f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2)))))),
inference(congruence,[status(thm)],[c1218]) ).
cnf(c1220,plain,
f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))))) = f(X4,f(f(X3,X2),f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))))),
inference(congruence,[status(thm)],[c1219]) ).
cnf(c1221,plain,
f(f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))) = f(f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))),
inference(congruence,[status(thm)],[c1220]) ).
cnf(c1222,plain,
f(f(f(X,X),X),f(X5,f(f(X4,X3),f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))))) = f(f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(X5,f(f(X4,X3),f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))))),
inference(substitution,[status(thm)],[c1007]) ).
cnf(c1223,plain,
f(f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3))))),f(X5,f(f(X4,X3),f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))))) = f(f(f(X,X),X),f(X5,f(f(X4,X3),f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))))),
inference(symmetry,[status(thm)],[c1222]) ).
cnf(c1224,plain,
f(f(X3,X2),f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X3,X2),f(X3,X2)),
inference(substitution,[status(thm)],[c931]) ).
cnf(c1225,plain,
f(X4,f(f(X3,X2),f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))))) = f(X4,f(f(X3,X2),f(X3,X2))),
inference(congruence,[status(thm)],[c1224]) ).
cnf(c1226,plain,
f(f(f(X,X),X),f(X5,f(f(X4,X3),f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))))) = f(f(f(X,X),X),f(X5,f(f(X4,X3),f(X4,X3)))),
inference(congruence,[status(thm)],[c1225]) ).
cnf(c1227,plain,
f(f(f(X,X),X),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(f(X5,X5),X5)),
inference(substitution,[status(thm)],[c1015]) ).
cnf(c1228,plain,
f(f(X4,f(f(X3,X2),f(X3,X2))),f(f(X,X),X)) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(substitution,[status(thm)],[c449]) ).
cnf(c1229,plain,
f(f(f(X,X),X),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1227,c1228]) ).
cnf(c1230,plain,
f(f(f(X,X),X),f(X5,f(f(X4,X3),f(X5,f(f(X2,f(f(X4,X3),f(X4,X3))),f(X2,f(f(X4,X3),f(X4,X3)))))))) = f(f(X5,f(f(X4,X3),f(X4,X3))),f(X5,f(f(X4,X3),f(X4,X3)))),
inference(transitivity,[status(thm)],[c1226,c1229]) ).
cnf(c1231,plain,
f(f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1223,c1230]) ).
cnf(c1232,plain,
f(f(X4,f(f(X,f(f(X3,X2),f(X3,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1221,c1231]) ).
cnf(c1233,plain,
f(f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1216,c1232]) ).
cnf(c1234,plain,
f(f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2))))),f(X4,f(f(X3,X2),f(X3,X2)))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1195,c1233]) ).
cnf(c1235,plain,
f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,f(f(X,X2),f(X,X2))),f(X,f(f(X3,X2),f(X3,X2)))))) = f(f(X4,f(f(X3,X2),f(X3,X2))),f(X4,f(f(X3,X2),f(X3,X2)))),
inference(transitivity,[status(thm)],[c1145,c1234]) ).
cnf(c1236,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c1235]) ).
cnf(c1237,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(symmetry,[status(thm)],[c1236]) ).
cnf(c1238,plain,
f(f(f(X,X2),f(X,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(substitution,[status(thm)],[c776]) ).
cnf(c1239,plain,
f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(X3,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(substitution,[status(thm)],[c815]) ).
cnf(c1240,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(symmetry,[status(thm)],[c1029]) ).
cnf(c1241,plain,
f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))))),
inference(congruence,[status(thm)],[c1240]) ).
cnf(c1242,plain,
f(X3,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(X3,f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))))),
inference(congruence,[status(thm)],[c1241]) ).
cnf(c1243,plain,
f(f(f(X3,X3),X3),f(f(f(X4,X2),f(X4,X2)),X)) = f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X)),
inference(substitution,[status(thm)],[c654]) ).
cnf(c1244,plain,
f(X4,f(f(f(X3,X3),X3),f(f(f(X4,X2),f(X4,X2)),X))) = f(X4,f(f(f(f(X4,X2),f(X4,X2)),X),f(f(f(X4,X2),f(X4,X2)),X))),
inference(congruence,[status(thm)],[c1243]) ).
cnf(c1245,plain,
X3 = f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c1246,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))),
inference(congruence,[status(thm)],[c1245]) ).
cnf(c1247,plain,
f(f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)),f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(X3,X2),f(X3,X2)),X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c1248,plain,
f(X3,f(f(f(f(X3,X2),f(X3,X2)),X),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(X3,X2),f(X3,X2)),X),
inference(transitivity,[status(thm)],[c1246,c1247]) ).
cnf(c1249,plain,
f(X4,f(f(f(X3,X3),X3),f(f(f(X4,X2),f(X4,X2)),X))) = f(f(f(X4,X2),f(X4,X2)),X),
inference(transitivity,[status(thm)],[c1244,c1248]) ).
cnf(c1250,plain,
f(X5,f(f(f(X,X),X),f(f(f(X5,X3),f(X5,X3)),f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2))))) = f(f(f(X5,X3),f(X5,X3)),f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2))),
inference(substitution,[status(thm)],[c1249]) ).
cnf(c1251,plain,
f(f(f(X5,X3),f(X5,X3)),f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2))) = f(X5,f(f(f(X,X),X),f(f(f(X5,X3),f(X5,X3)),f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2))))),
inference(symmetry,[status(thm)],[c1250]) ).
cnf(c1252,plain,
f(f(f(X4,X4),X4),f(X3,f(f(X2,X3),f(X3,X)))) = f(f(X3,f(f(X2,X3),f(X3,X))),f(X3,f(f(X2,X3),f(X3,X)))),
inference(substitution,[status(thm)],[c654]) ).
cnf(c1253,plain,
f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X))) = f(X3,f(f(X2,X3),f(X3,X))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c1254,plain,
f(X3,f(f(X2,X3),f(X3,X))) = f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X))),
inference(symmetry,[status(thm)],[c1253]) ).
cnf(c1255,plain,
f(f(X3,f(f(X2,X3),f(X3,X))),f(X3,f(f(X2,X3),f(X3,X)))) = f(f(X3,f(f(X2,X3),f(X3,X))),f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X)))),
inference(congruence,[status(thm)],[c1254]) ).
cnf(c1256,plain,
f(f(f(X2,X3),f(X3,X)),X3) = f(X3,f(f(X2,X3),f(X3,X))),
inference(substitution,[status(thm)],[c200]) ).
cnf(c1257,plain,
f(X3,f(f(X2,X3),f(X3,X))) = f(f(f(X2,X3),f(X3,X)),X3),
inference(symmetry,[status(thm)],[c1256]) ).
cnf(c1258,plain,
f(f(X3,f(f(X2,X3),f(X3,X))),f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X)))) = f(f(f(f(X2,X3),f(X3,X)),X3),f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X)))),
inference(congruence,[status(thm)],[c1257]) ).
cnf(c1259,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X)))) = f(f(X2,X3),f(X3,X)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c1260,plain,
f(f(X3,f(f(X2,X3),f(X3,X))),f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X)))) = f(f(X2,X3),f(X3,X)),
inference(transitivity,[status(thm)],[c1258,c1259]) ).
cnf(c1261,plain,
f(f(X3,f(f(X2,X3),f(X3,X))),f(X3,f(f(X2,X3),f(X3,X)))) = f(f(X2,X3),f(X3,X)),
inference(transitivity,[status(thm)],[c1255,c1260]) ).
cnf(c1262,plain,
f(f(f(X4,X4),X4),f(X3,f(f(X2,X3),f(X3,X)))) = f(f(X2,X3),f(X3,X)),
inference(transitivity,[status(thm)],[c1252,c1261]) ).
cnf(c1263,plain,
f(f(f(X,X),X),f(f(f(X5,X3),f(X5,X3)),f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2)))) = f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2)),
inference(substitution,[status(thm)],[c1262]) ).
cnf(c1264,plain,
f(X5,f(f(f(X,X),X),f(f(f(X5,X3),f(X5,X3)),f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2))))) = f(X5,f(f(X4,f(f(X5,X3),f(X5,X3))),f(f(f(X5,X3),f(X5,X3)),X2))),
inference(congruence,[status(thm)],[c1263]) ).
cnf(c1265,plain,
f(f(f(X4,X2),f(X4,X2)),f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,X2),f(X4,X2)),X))) = f(X4,f(f(X3,f(f(X4,X2),f(X4,X2))),f(f(f(X4,X2),f(X4,X2)),X))),
inference(transitivity,[status(thm)],[c1251,c1264]) ).
cnf(c1266,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))))) = f(X3,f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))))),
inference(substitution,[status(thm)],[c1265]) ).
cnf(c1267,plain,
f(X3,f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))))),
inference(symmetry,[status(thm)],[c1266]) ).
cnf(c1268,plain,
f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2)))))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2)))),
inference(congruence,[status(thm)],[c1029]) ).
cnf(c1269,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(congruence,[status(thm)],[c1268]) ).
cnf(c1270,plain,
f(X3,f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),f(f(X3,f(f(X,X2),f(X,X2))),f(X3,f(f(X,X2),f(X,X2))))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(transitivity,[status(thm)],[c1267,c1269]) ).
cnf(c1271,plain,
f(X3,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(transitivity,[status(thm)],[c1242,c1270]) ).
cnf(c1272,plain,
f(X,f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(transitivity,[status(thm)],[c1239,c1271]) ).
cnf(c1273,plain,
f(f(f(X,X2),f(X,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,f(f(X3,X2),f(X3,X2))),f(X3,f(f(X,X2),f(X,X2))))),
inference(transitivity,[status(thm)],[c1238,c1272]) ).
cnf(c1274,plain,
f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(substitution,[status(thm)],[c1273]) ).
cnf(c1275,plain,
f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(symmetry,[status(thm)],[c1274]) ).
cnf(c1276,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c1275]) ).
cnf(c1277,plain,
f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c1132]) ).
cnf(c1278,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c1277]) ).
cnf(c1279,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1280,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c1279]) ).
cnf(c1281,plain,
f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c908]) ).
cnf(c1282,plain,
f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))) = f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))),
inference(symmetry,[status(thm)],[c1281]) ).
cnf(c1283,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c1282]) ).
cnf(c1284,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c1208]) ).
cnf(c1285,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c1213]) ).
cnf(c1286,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c1285]) ).
cnf(c1287,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1284,c1286]) ).
cnf(c1288,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1283,c1287]) ).
cnf(c1289,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1280,c1288]) ).
cnf(c1290,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X3,X),f(X3,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1278,c1289]) ).
cnf(c1291,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1276,c1290]) ).
cnf(c1292,plain,
f(f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1237,c1291]) ).
cnf(c1293,plain,
f(f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1144,c1292]) ).
cnf(c1294,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(X3,X),f(X3,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1142,c1293]) ).
cnf(c1295,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,X),f(X3,X)),f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1139,c1294]) ).
cnf(c1296,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(transitivity,[status(thm)],[c1137,c1295]) ).
cnf(c1297,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c1296]) ).
cnf(c1298,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c1297]) ).
cnf(c1299,plain,
f(X2,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X2,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c1298]) ).
cnf(c1300,plain,
f(X2,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X))))) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c1301,plain,
f(X2,f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X2,f(f(X3,X),f(X3,X))),
inference(transitivity,[status(thm)],[c1299,c1300]) ).
cnf(c1302,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,f(f(X2,X),f(X2,X))))) = f(X2,f(f(X3,X),f(X3,X))),
inference(transitivity,[status(thm)],[c1135,c1301]) ).
cnf(c1303,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(X2,f(f(X3,X),f(X3,X))),
inference(transitivity,[status(thm)],[c1134,c1302]) ).
cnf(c1304,plain,
f(x1,f(f(x0,x2),f(x0,x2))) = f(x0,f(f(x1,x2),f(x1,x2))),
inference(substitution,[status(thm)],[c1303]) ).
cnf(c1305,plain,
f(x0,f(f(x1,x2),f(x1,x2))) = f(x1,f(f(x0,x2),f(x0,x2))),
inference(symmetry,[status(thm)],[c1304]) ).
cnf(c1306,plain,
$false,
inference(resolution,[status(thm)],[c1,c1305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT393-2 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:19:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 79.31/11.80 Command-line arguments: --flatten --complete-subsets
% 79.31/11.80
% 79.31/11.80 % SZS status Unsatisfiable
% 79.31/11.80
% 82.12/12.23 % SZS output start CNFRefutation
% See solution above
% 95.89/14.18
% 95.89/14.18 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------