%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT072-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 11:42:57 AM UTC 2026
% Result : Unsatisfiable 18.76s 2.91s
% Output : CNFRefutation 25.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 86
% Number of leaves : 2
% Syntax : Number of clauses : 421 ( 421 unt; 0 nHn; 4 RR)
% Number of literals : 421 ( 420 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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 : 1250 ( 162 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(a,f(f(b,c),f(b,c))) != f(c,f(f(b,a),f(b,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c2,axiom,
f(f(f(f(B,A),f(A,C)),D),f(A,f(f(C,f(f(A,A),C)),C))) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oml_23A) ).
cnf(c3,plain,
f(f(f(f(X,X4),f(X4,X3)),f(f(X4,X3),X2)),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X4 = f(f(f(f(X,X4),f(X4,X3)),f(f(X4,X3),X2)),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
f(X4,f(f(X4,X3),f(f(X2,f(f(f(X4,X3),f(X4,X3)),X2)),X2))) = f(f(f(f(f(X,X4),f(X4,X3)),f(f(X4,X3),X2)),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(X4,X3),f(f(X2,f(f(f(X4,X3),f(X4,X3)),X2)),X2))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
f(f(f(f(f(X,X4),f(X4,X3)),f(f(X4,X3),X2)),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(X4,X3),f(f(X2,f(f(f(X4,X3),f(X4,X3)),X2)),X2))) = f(X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
f(X3,f(f(X3,X2),f(f(X,f(f(f(X3,X2),f(X3,X2)),X)),X))) = f(X3,X2),
inference(transitivity,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
f(f(X2,X),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
f(f(X2,X),f(X2,X)) = f(f(X2,X),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
f(X2,f(f(X2,X),f(X2,X))) = f(X2,f(f(X2,X),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X)))))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
f(f(f(f(X,X3),f(X3,X2)),X3),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
X3 = f(f(f(f(X,X3),f(X3,X2)),X3),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
f(X4,X3) = f(f(f(f(f(X,X4),f(X4,X2)),X4),f(X4,f(f(X2,f(f(X4,X4),X2)),X2))),X3),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
f(f(X4,X3),f(X4,f(f(f(f(X2,f(f(X4,X4),X2)),X2),f(f(X4,X4),f(f(X2,f(f(X4,X4),X2)),X2))),f(f(X2,f(f(X4,X4),X2)),X2)))) = f(f(f(f(f(f(X,X4),f(X4,X2)),X4),f(X4,f(f(X2,f(f(X4,X4),X2)),X2))),X3),f(X4,f(f(f(f(X2,f(f(X4,X4),X2)),X2),f(f(X4,X4),f(f(X2,f(f(X4,X4),X2)),X2))),f(f(X2,f(f(X4,X4),X2)),X2)))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
f(f(f(f(f(f(X,X4),f(X4,X2)),X4),f(X4,f(f(X2,f(f(X4,X4),X2)),X2))),X3),f(X4,f(f(f(f(X2,f(f(X4,X4),X2)),X2),f(f(X4,X4),f(f(X2,f(f(X4,X4),X2)),X2))),f(f(X2,f(f(X4,X4),X2)),X2)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))) = X3,
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
f(f(f(X4,X3),f(X3,X2)),f(f(X4,X3),f(f(f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X),f(f(f(X4,X3),f(X4,X3)),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X))),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X)))) = f(X4,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
f(X4,X3) = f(f(f(X4,X3),f(X3,X2)),f(f(X4,X3),f(f(f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X),f(f(f(X4,X3),f(X4,X3)),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X))),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X)))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
f(f(X4,X3),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))) = f(f(f(f(X4,X3),f(X3,X2)),f(f(X4,X3),f(f(f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X),f(f(f(X4,X3),f(X4,X3)),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X))),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X)))),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
f(f(f(f(X4,X3),f(X3,X2)),f(f(X4,X3),f(f(f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X),f(f(f(X4,X3),f(X4,X3)),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X))),f(f(X,f(f(f(X4,X3),f(X4,X3)),X)),X)))),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
f(f(X3,X2),f(X2,f(f(X,f(f(X2,X2),X)),X))) = X2,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
f(f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
f(f(X2,X),f(X2,X)) = f(f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X)))) = f(f(f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
f(f(X2,X),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))) = f(f(X2,X),f(f(f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
f(X2,f(f(X2,X),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X)))))) = f(X2,f(f(X2,X),f(f(f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X)))))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
f(X2,f(f(X2,X),f(f(f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X))))),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X)))))) = f(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c28,plain,
f(X2,f(f(X2,X),f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),f(f(X2,X),f(X2,X)))),f(f(X2,X),f(X2,X)))))) = f(X2,X),
inference(transitivity,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
f(X2,f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c10,c28]) ).
cnf(c30,plain,
f(X2,f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X)))) = f(X2,f(f(X2,X2),X)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
f(X2,f(f(X2,X2),X)) = f(X2,f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X)))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c33,plain,
X2 = f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
f(X2,X2) = f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
f(f(X3,X2),f(X2,X2)) = f(f(X3,X2),f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
f(f(X2,X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))) = X2,
inference(substitution,[status(thm)],[c16]) ).
cnf(c37,plain,
X2 = f(f(X2,X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2) = f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),f(f(X2,X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))) = f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),f(f(X2,X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))) = f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),f(f(X2,X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
f(f(X3,X2),f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))))) = f(f(X3,X2),f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),f(f(X2,X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
f(f(X3,X2),f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),f(f(X2,X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))))),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))))) = X2,
inference(substitution,[status(thm)],[c21]) ).
cnf(c43,plain,
f(f(X3,X2),f(X2,f(f(f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X))),X2),f(X2,f(f(f(f(X,f(f(X2,X2),X)),X),f(f(X2,X2),f(f(X,f(f(X2,X2),X)),X))),f(f(X,f(f(X2,X2),X)),X)))))) = X2,
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
f(f(X2,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c35,c43]) ).
cnf(c45,plain,
f(f(X,X),f(X,X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,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)],[c46]) ).
cnf(c48,plain,
X3 = f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c49,plain,
f(X3,X3) = f(X3,f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
f(f(X3,X2),f(X3,X3)) = f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
X3 = f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c52,plain,
f(X3,f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))) = f(f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = f(f(X3,X2),f(f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c55,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = X3,
inference(transitivity,[status(thm)],[c54,c16]) ).
cnf(c56,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = X3,
inference(transitivity,[status(thm)],[c53,c55]) ).
cnf(c57,plain,
f(f(X2,X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c50,c56]) ).
cnf(c58,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
f(f(f(X2,X2),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c47,c58]) ).
cnf(c60,plain,
f(f(f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X))),X2),f(X2,f(f(X2,X2),X))) = f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X))) = f(f(f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X))),X2),f(X2,f(f(X2,X2),X))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))) = f(f(X3,X3),X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c63,plain,
f(f(X3,X3),X2) = f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
f(X3,f(f(X3,X3),X2)) = f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
f(f(X4,X3),f(X3,f(f(X3,X3),X2))) = f(f(X4,X3),f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
f(f(X3,X3),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))) = f(f(X3,X3),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c67,plain,
f(f(X3,X3),X2) = f(f(X3,X3),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)) = f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))) = f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))) = f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
f(f(X4,X3),f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))))) = f(f(X4,X3),f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
f(f(X4,X3),f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)))),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))))) = X3,
inference(substitution,[status(thm)],[c21]) ).
cnf(c73,plain,
f(f(X4,X3),f(X3,f(f(f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X)),f(f(X3,X3),X2)),f(f(f(X3,X3),X2),f(f(X,f(f(f(f(X3,X3),X2),f(f(X3,X3),X2)),X)),X))))) = X3,
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
f(f(X3,X2),f(X2,f(f(X2,X2),X))) = X2,
inference(transitivity,[status(thm)],[c65,c73]) ).
cnf(c75,plain,
f(f(f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X))),X2),f(X2,f(f(X2,X2),X))) = X2,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X))) = X2,
inference(transitivity,[status(thm)],[c61,c75]) ).
cnf(c77,plain,
f(X2,f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X)))) = f(X2,X2),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
f(X2,f(f(X2,X2),X)) = f(X2,X2),
inference(transitivity,[status(thm)],[c31,c77]) ).
cnf(c79,plain,
f(X2,X2) = f(X2,f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
f(f(X3,X3),f(X3,X2)) = f(f(X3,f(f(X3,X3),X)),f(X3,X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
X2 = f(f(X2,f(f(X2,X2),X)),f(X2,f(f(X2,X2),X))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c82,plain,
f(X3,X2) = f(f(f(X3,f(f(X3,X3),X)),f(X3,f(f(X3,X3),X))),X2),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
f(f(X3,f(f(X3,X3),X)),f(X3,X2)) = f(f(X3,f(f(X3,X3),X)),f(f(f(X3,f(f(X3,X3),X)),f(X3,f(f(X3,X3),X))),X2)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
f(f(X3,f(f(X3,X3),X)),f(f(f(X3,f(f(X3,X3),X)),f(X3,f(f(X3,X3),X))),X2)) = f(f(X3,f(f(X3,X3),X)),f(X3,f(f(X3,X3),X))),
inference(substitution,[status(thm)],[c78]) ).
cnf(c85,plain,
f(f(X3,f(f(X3,X3),X)),f(f(f(X3,f(f(X3,X3),X)),f(X3,f(f(X3,X3),X))),X2)) = X3,
inference(transitivity,[status(thm)],[c84,c76]) ).
cnf(c86,plain,
f(f(X3,f(f(X3,X3),X)),f(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c83,c85]) ).
cnf(c87,plain,
f(f(X2,X2),f(X2,X)) = X2,
inference(transitivity,[status(thm)],[c80,c86]) ).
cnf(c88,plain,
f(f(f(X,X2),f(X,X2)),f(f(X,X2),f(X2,X))) = f(X,X2),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
f(X,X2) = f(f(f(X,X2),f(X,X2)),f(f(X,X2),f(X2,X))),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
f(f(X,X),f(X,X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c91,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
f(X,X2) = f(X,f(f(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
f(f(X2,X2),f(X,X2)) = f(f(X2,X2),f(X,f(f(X2,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
f(f(X2,X3),f(X3,f(f(X,f(f(X3,X3),X)),X))) = X3,
inference(substitution,[status(thm)],[c21]) ).
cnf(c95,plain,
X3 = f(f(X2,X3),f(X3,f(f(X,f(f(X3,X3),X)),X))),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
f(X3,f(f(X2,X3),f(X2,X3))) = f(f(f(X2,X3),f(X3,f(f(X,f(f(X3,X3),X)),X))),f(f(X2,X3),f(X2,X3))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
f(f(f(X2,X3),f(X3,f(f(X,f(f(X3,X3),X)),X))),f(f(X2,X3),f(X2,X3))) = f(X2,X3),
inference(substitution,[status(thm)],[c57]) ).
cnf(c98,plain,
f(X2,f(f(X,X2),f(X,X2))) = f(X,X2),
inference(transitivity,[status(thm)],[c96,c97]) ).
cnf(c99,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)],[c98]) ).
cnf(c100,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)],[c99]) ).
cnf(c101,plain,
f(X2,f(X,f(X2,X2))) = f(X2,f(f(X2,X2),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
f(X2,f(f(X2,X2),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c78]) ).
cnf(c103,plain,
f(X2,f(X,f(X2,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
f(f(X2,X2),f(X,f(f(X2,X2),f(X2,X2)))) = f(f(X2,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
f(f(X,X),f(X,X)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c106,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
f(X2,X) = f(f(f(X2,X2),f(X2,X2)),X),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,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)],[c107]) ).
cnf(c109,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X2)),X)) = f(f(X2,X2),f(X2,X2)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c110,plain,
f(f(X2,X2),f(X2,X)) = f(f(X2,X2),f(X2,X2)),
inference(transitivity,[status(thm)],[c108,c109]) ).
cnf(c111,plain,
f(f(X2,X2),f(X2,X2)) = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
f(f(X,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c111,c87]) ).
cnf(c113,plain,
f(f(X2,X2),f(X,f(f(X2,X2),f(X2,X2)))) = X2,
inference(transitivity,[status(thm)],[c104,c112]) ).
cnf(c114,plain,
f(f(X2,X2),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c93,c113]) ).
cnf(c115,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
X = f(f(X,X),f(X2,X)),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
f(X,X2) = f(f(f(X,X),f(X2,X)),X2),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
f(f(X,X2),f(X,X2)) = f(f(X,X2),f(f(f(X,X),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c114]) ).
cnf(c120,plain,
X = f(f(X,X),f(X2,X)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
f(X,X2) = f(f(f(X,X),f(X2,X)),X2),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
f(f(X,X2),f(f(f(X,X),f(X2,X)),X2)) = f(f(f(f(X,X),f(X2,X)),X2),f(f(f(X,X),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
X3 = f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c124,plain,
f(f(X4,f(X3,X2)),X3) = f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
f(f(f(X4,f(X3,X2)),X3),f(f(X4,f(X3,X2)),X3)) = f(f(f(X4,f(X3,X2)),X3),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
X3 = f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c127,plain,
f(f(X4,f(X3,X2)),X3) = f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
f(f(f(X4,f(X3,X2)),X3),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = f(f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X,f(f(X2,X2),X)),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)],[c59]) ).
cnf(c130,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(X,f(f(X2,X2),X)),X))),f(f(X3,X2),f(X2,X))),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X,f(f(X2,X2),X)),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c132,plain,
f(f(f(f(f(X3,X2),f(X2,X)),f(f(X3,X2),f(X2,X))),f(X2,f(f(X,f(f(X2,X2),X)),X))),f(f(X3,X2),f(X2,X))) = f(X2,f(f(X3,X2),f(X2,X))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,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)],[c130,c132]) ).
cnf(c134,plain,
f(f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = f(f(X3,X2),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))) = f(f(X4,f(X3,X2)),X3),
inference(congruence,[status(thm)],[c16]) ).
cnf(c136,plain,
f(f(X3,X2),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = f(f(X3,X2),f(f(X4,f(X3,X2)),X3)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
f(f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X))))),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = f(f(X3,X2),f(f(X4,f(X3,X2)),X3)),
inference(transitivity,[status(thm)],[c134,c136]) ).
cnf(c138,plain,
f(f(f(X4,f(X3,X2)),X3),f(f(X4,f(X3,X2)),f(f(X3,X2),f(X3,f(f(f(f(X,f(f(X3,X3),X)),X),f(f(X3,X3),f(f(X,f(f(X3,X3),X)),X))),f(f(X,f(f(X3,X3),X)),X)))))) = f(f(X3,X2),f(f(X4,f(X3,X2)),X3)),
inference(transitivity,[status(thm)],[c128,c137]) ).
cnf(c139,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)],[c125,c138]) ).
cnf(c140,plain,
f(f(f(f(X,X),f(X2,X)),X2),f(f(f(X,X),f(X2,X)),X2)) = f(f(X2,X),f(f(f(X,X),f(X2,X)),X2)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c114]) ).
cnf(c142,plain,
f(f(f(X,X),f(X2,X)),X2) = f(X,X2),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,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)],[c142]) ).
cnf(c144,plain,
f(f(f(f(X,X),f(X2,X)),X2),f(f(f(X,X),f(X2,X)),X2)) = f(f(X2,X),f(X,X2)),
inference(transitivity,[status(thm)],[c140,c143]) ).
cnf(c145,plain,
f(f(X,X2),f(f(f(X,X),f(X2,X)),X2)) = f(f(X2,X),f(X,X2)),
inference(transitivity,[status(thm)],[c122,c144]) ).
cnf(c146,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(transitivity,[status(thm)],[c118,c145]) ).
cnf(c147,plain,
f(f(X2,X),f(X2,X)) = f(f(X,X2),f(X2,X)),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
f(f(X,X2),f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
f(f(f(X,X2),f(X,X2)),f(f(X,X2),f(X2,X))) = f(f(f(X,X2),f(X,X2)),f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
f(f(f(X,X2),f(X,X2)),f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c151,plain,
f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c152,plain,
f(f(f(X,X2),f(X,X2)),f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
f(f(f(X,X2),f(X,X2)),f(f(X,X2),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c149,c152]) ).
cnf(c154,plain,
f(X,X2) = f(X2,X),
inference(transitivity,[status(thm)],[c89,c153]) ).
cnf(c155,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),X3),
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))) = f(X3,X2),
inference(substitution,[status(thm)],[c114]) ).
cnf(c157,plain,
f(X3,X2) = f(f(f(X3,X2),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
f(f(X3,X2),f(X2,f(f(X3,X),f(X3,X)))) = f(f(f(f(X3,X2),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,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)],[c98]) ).
cnf(c160,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)],[c159]) ).
cnf(c161,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)],[c160]) ).
cnf(c162,plain,
f(f(X,X),f(X,X)) = X,
inference(substitution,[status(thm)],[c57]) ).
cnf(c163,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,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)],[c163]) ).
cnf(c165,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c166,plain,
f(f(X,X),f(X,X)) = f(f(X,X),f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(X3,X3))) = f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3)))))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
f(f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))),f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c169,plain,
f(f(X,X),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))),f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X)))) = f(f(f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))),f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X)))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))) = f(f(X,X),f(f(f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))),f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))),f(f(f(f(X,X),f(X,X)),f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(f(X,X),f(X,X)))),f(f(X,X),f(X,X))))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3)))))) = f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(f(f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3))),f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3))))),f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3)))))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c174,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
f(X3,X3) = f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),X3),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
f(f(X3,X3),X5) = f(f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),X3),X5),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
f(X,f(f(X4,X4),X)) = f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
f(f(X,f(f(X4,X4),X)),X) = f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),X),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
f(X4,f(f(X,f(f(X4,X4),X)),X)) = f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),X)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(X4,X4),X)),X))) = f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),X))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c182,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),X3) = f(f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2)))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X) = f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)) = f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),X) = f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),X)) = f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),X))) = f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c190,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X)) = f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X)),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X))) = f(f(f(f(X5,X4),f(X4,X3)),X2),f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X))) = f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c194,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X2,f(f(X3,X3),X2)),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c195,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X))) = X4,
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3)))),X)),X))) = X4,
inference(transitivity,[status(thm)],[c192,c195]) ).
cnf(c197,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X3,f(f(X4,X4),X3)),X3))),X4),X)),X))) = X4,
inference(transitivity,[status(thm)],[c188,c196]) ).
cnf(c198,plain,
f(f(f(f(X5,X4),f(X4,X3)),X2),f(X4,f(f(X,f(f(X4,X4),X)),X))) = X4,
inference(transitivity,[status(thm)],[c180,c197]) ).
cnf(c199,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(f(f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3))),f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3))))),f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3)))))) = f(X3,X3),
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(f(f(X3,X3),f(X3,X3)),f(f(X3,X3),f(X3,X3))),f(f(X3,X3),f(X3,X3)))),f(f(X3,X3),f(X3,X3)))))) = f(X3,X3),
inference(transitivity,[status(thm)],[c172,c199]) ).
cnf(c201,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(transitivity,[status(thm)],[c167,c200]) ).
cnf(c202,plain,
f(f(f(f(X4,f(X3,X3)),f(f(X3,X3),X2)),X),X3) = f(X3,X3),
inference(transitivity,[status(thm)],[c164,c201]) ).
cnf(c203,plain,
f(f(f(f(X2,f(f(X4,X3),f(X4,X3))),f(f(f(X4,X3),f(X4,X3)),X)),X4),f(X4,X3)) = f(f(X4,X3),f(X4,X3)),
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
f(f(X4,X3),f(X4,X3)) = f(f(f(f(X2,f(f(X4,X3),f(X4,X3))),f(f(f(X4,X3),f(X4,X3)),X)),X4),f(X4,X3)),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
f(f(f(X5,X4),f(X5,X4)),X3) = f(f(f(f(f(X2,f(f(X5,X4),f(X5,X4))),f(f(f(X5,X4),f(X5,X4)),X)),X5),f(X5,X4)),X3),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
f(f(f(f(X5,X4),f(X5,X4)),X3),f(X5,X5)) = f(f(f(f(f(f(X2,f(f(X5,X4),f(X5,X4))),f(f(f(X5,X4),f(X5,X4)),X)),X5),f(X5,X4)),X3),f(X5,X5)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
f(X,f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))) = f(X,X),
inference(substitution,[status(thm)],[c78]) ).
cnf(c208,plain,
f(X,X) = f(X,f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,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(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))) = f(X,X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c211,plain,
f(X,X) = f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X))) = f(f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
f(X,f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))) = f(X,f(f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))) = f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)),f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)))),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)),f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)))),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))) = X3,
inference(substitution,[status(thm)],[c198]) ).
cnf(c216,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))) = X3,
inference(transitivity,[status(thm)],[c214,c215]) ).
cnf(c217,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c209,c216]) ).
cnf(c218,plain,
f(f(f(f(f(f(X2,f(f(X5,X4),f(X5,X4))),f(f(f(X5,X4),f(X5,X4)),X)),X5),f(X5,X4)),X3),f(X5,X5)) = X5,
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
f(f(f(f(X3,X2),f(X3,X2)),X),f(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c206,c218]) ).
cnf(c220,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)],[c219]) ).
cnf(c221,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c161,c220]) ).
cnf(c222,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X3)) = X3,
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
X3 = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X3)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,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)],[c223]) ).
cnf(c225,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)],[c57]) ).
cnf(c226,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)],[c224,c225]) ).
cnf(c227,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)],[c226]) ).
cnf(c228,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,X3),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)],[c227]) ).
cnf(c229,plain,
f(f(X3,X3),f(X3,f(f(X2,f(f(X3,X),f(X3,X))),f(X2,f(f(X3,X),f(X3,X)))))) = X3,
inference(substitution,[status(thm)],[c87]) ).
cnf(c230,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))) = X3,
inference(transitivity,[status(thm)],[c228,c229]) ).
cnf(c231,plain,
f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))) = X2,
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
X2 = f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
f(X2,X3) = f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X3)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
f(f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c236,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)) = f(f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))) = X2,
inference(substitution,[status(thm)],[c230]) ).
cnf(c238,plain,
f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3) = f(X2,X3),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
f(f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)) = f(f(X2,X3),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))) = X2,
inference(substitution,[status(thm)],[c230]) ).
cnf(c241,plain,
f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3) = f(X2,X3),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
f(f(X2,X3),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)) = f(f(X2,X3),f(X2,X3)),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
f(f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)) = f(f(X2,X3),f(X2,X3)),
inference(transitivity,[status(thm)],[c239,c242]) ).
cnf(c244,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X2),f(X3,f(f(X2,X),f(X2,X)))),X3)) = f(f(X2,X3),f(X2,X3)),
inference(transitivity,[status(thm)],[c236,c243]) ).
cnf(c245,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(X2,X3)) = f(f(X2,X3),f(X2,X3)),
inference(transitivity,[status(thm)],[c234,c244]) ).
cnf(c246,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)) = f(f(X3,X2),f(X3,X2)),
inference(substitution,[status(thm)],[c245]) ).
cnf(c247,plain,
f(f(X3,X2),f(X3,X2)) = f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))) = f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c251,plain,
f(f(f(X2,X),f(X2,X)),X2) = f(f(f(X2,X),f(X2,X)),f(f(X2,X2),f(X2,X))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,X2),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c114]) ).
cnf(c253,plain,
f(f(f(X2,X),f(X2,X)),X2) = f(X2,X),
inference(transitivity,[status(thm)],[c251,c252]) ).
cnf(c254,plain,
f(f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),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)],[c253]) ).
cnf(c255,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)) = f(f(X3,X2),f(X3,X2)),
inference(substitution,[status(thm)],[c245]) ).
cnf(c256,plain,
f(f(f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c254,c255]) ).
cnf(c257,plain,
f(f(f(f(X3,X2),f(X3,X2)),f(f(X2,f(f(X3,X),f(X3,X))),f(X3,X2))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c249,c256]) ).
cnf(c258,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)],[c158,c257]) ).
cnf(c259,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c260,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
f(f(f(X2,X3),f(X2,X3)),X) = f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X))) = f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
f(f(f(X3,X2),f(X,X2)),f(f(X4,f(f(X3,X2),f(X,X2))),f(X4,f(f(X3,X2),f(X,X2))))) = f(X4,f(f(X3,X2),f(X,X2))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c265,plain,
f(X4,f(f(X3,X2),f(X,X2))) = f(f(f(X3,X2),f(X,X2)),f(f(X4,f(f(X3,X2),f(X,X2))),f(X4,f(f(X3,X2),f(X,X2))))),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)) = f(f(f(f(X3,X2),f(X,X2)),f(f(X4,f(f(X3,X2),f(X,X2))),f(X4,f(f(X3,X2),f(X,X2))))),f(X2,X2)),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
f(X,f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))) = f(X,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c268,plain,
f(X,X) = f(X,f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
f(f(f(f(X4,X3),f(X2,X3)),X),f(X3,X3)) = f(f(f(f(X4,X3),f(X2,X3)),X),f(X3,f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))) = f(X,X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c271,plain,
f(X,X) = f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X))) = f(f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
f(X,f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))) = f(X,f(f(f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)),f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),f(f(f(X,X),f(f(f(X,X),f(X,X)),f(X,X))),f(X,X)))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
f(f(f(f(X4,X3),f(X2,X3)),X),f(X3,f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))) = f(f(f(f(X4,X3),f(X2,X3)),X),f(X3,f(f(f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)),f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)))),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
f(f(X2,X3),f(X3,f(f(X,f(f(X3,X3),X)),X))) = X3,
inference(substitution,[status(thm)],[c21]) ).
cnf(c276,plain,
X3 = f(f(X2,X3),f(X3,f(f(X,f(f(X3,X3),X)),X))),
inference(symmetry,[status(thm)],[c275]) ).
cnf(c277,plain,
f(X4,f(f(X3,X4),f(f(X2,f(f(f(X3,X4),f(X3,X4)),X2)),X2))) = f(f(f(X3,X4),f(X4,f(f(X,f(f(X4,X4),X)),X))),f(f(X3,X4),f(f(X2,f(f(f(X3,X4),f(X3,X4)),X2)),X2))),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X,f(f(X3,X3),X)),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c279,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X,f(f(X3,X3),X)),X))),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
f(X4,X3) = f(f(f(f(f(X2,X4),f(X4,X)),X4),f(X4,f(f(X,f(f(X4,X4),X)),X))),X3),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
f(f(X5,X4),f(X5,f(f(X3,f(f(X5,X5),X3)),X3))) = f(f(f(f(f(f(X2,X5),f(X5,X)),X5),f(X5,f(f(X,f(f(X5,X5),X)),X))),X4),f(X5,f(f(X3,f(f(X5,X5),X3)),X3))),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
f(f(f(f(f(f(X2,X5),f(X5,X)),X5),f(X5,f(f(X,f(f(X5,X5),X)),X))),X4),f(X5,f(f(X3,f(f(X5,X5),X3)),X3))) = X5,
inference(substitution,[status(thm)],[c198]) ).
cnf(c283,plain,
f(f(X3,X2),f(X3,f(f(X,f(f(X3,X3),X)),X))) = X3,
inference(transitivity,[status(thm)],[c281,c282]) ).
cnf(c284,plain,
f(f(f(X3,X4),f(X4,f(f(X,f(f(X4,X4),X)),X))),f(f(X3,X4),f(f(X2,f(f(f(X3,X4),f(X3,X4)),X2)),X2))) = f(X3,X4),
inference(substitution,[status(thm)],[c283]) ).
cnf(c285,plain,
f(X2,f(f(X,X2),f(f(X3,f(f(f(X,X2),f(X,X2)),X3)),X3))) = f(X,X2),
inference(transitivity,[status(thm)],[c277,c284]) ).
cnf(c286,plain,
f(X2,X3) = f(X3,f(f(X2,X3),f(f(X,f(f(f(X2,X3),f(X2,X3)),X)),X))),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c287,plain,
f(f(X4,X3),f(X2,X3)) = f(f(X4,X3),f(X3,f(f(X2,X3),f(f(X,f(f(f(X2,X3),f(X2,X3)),X)),X)))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
f(f(f(X5,X4),f(X3,X4)),X2) = f(f(f(X5,X4),f(X4,f(f(X3,X4),f(f(X,f(f(f(X3,X4),f(X3,X4)),X)),X)))),X2),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
f(f(f(f(X6,X5),f(X4,X5)),X3),f(X5,f(f(X2,f(f(X5,X5),X2)),X2))) = f(f(f(f(X6,X5),f(X5,f(f(X4,X5),f(f(X,f(f(f(X4,X5),f(X4,X5)),X)),X)))),X3),f(X5,f(f(X2,f(f(X5,X5),X2)),X2))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
f(f(f(f(X6,X5),f(X5,f(f(X4,X5),f(f(X,f(f(f(X4,X5),f(X4,X5)),X)),X)))),X3),f(X5,f(f(X2,f(f(X5,X5),X2)),X2))) = X5,
inference(substitution,[status(thm)],[c198]) ).
cnf(c291,plain,
f(f(f(f(X5,X4),f(X3,X4)),X2),f(X4,f(f(X,f(f(X4,X4),X)),X))) = X4,
inference(transitivity,[status(thm)],[c289,c290]) ).
cnf(c292,plain,
f(f(f(f(X4,X3),f(X2,X3)),X),f(X3,f(f(f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)),f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3)))),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))) = X3,
inference(substitution,[status(thm)],[c291]) ).
cnf(c293,plain,
f(f(f(f(X4,X3),f(X2,X3)),X),f(X3,f(f(X3,X3),f(f(f(X3,X3),f(f(f(X3,X3),f(X3,X3)),f(X3,X3))),f(X3,X3))))) = X3,
inference(transitivity,[status(thm)],[c274,c292]) ).
cnf(c294,plain,
f(f(f(f(X4,X3),f(X2,X3)),X),f(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c269,c293]) ).
cnf(c295,plain,
f(f(f(f(X3,X2),f(X,X2)),f(f(X4,f(f(X3,X2),f(X,X2))),f(X4,f(f(X3,X2),f(X,X2))))),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c294]) ).
cnf(c296,plain,
f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c266,c295]) ).
cnf(c297,plain,
X2 = f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2) = f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2)) = f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
X2 = f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c301,plain,
f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2) = f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2))),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))) = f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))) = f(f(X4,f(f(X3,X2),f(X,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))),
inference(substitution,[status(thm)],[c133]) ).
cnf(c304,plain,
f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2))) = f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2),
inference(congruence,[status(thm)],[c296]) ).
cnf(c305,plain,
f(f(X4,f(f(X3,X2),f(X,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))) = f(f(X4,f(f(X3,X2),f(X,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2)),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))) = f(f(X4,f(f(X3,X2),f(X,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2)),
inference(transitivity,[status(thm)],[c303,c305]) ).
cnf(c307,plain,
f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,X2)))) = f(f(X4,f(f(X3,X2),f(X,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2)),
inference(transitivity,[status(thm)],[c302,c306]) ).
cnf(c308,plain,
f(f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2)) = f(f(X4,f(f(X3,X2),f(X,X2))),f(f(X5,f(X4,f(f(X3,X2),f(X,X2)))),X2)),
inference(transitivity,[status(thm)],[c299,c307]) ).
cnf(c309,plain,
f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(substitution,[status(thm)],[c308]) ).
cnf(c310,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(symmetry,[status(thm)],[c309]) ).
cnf(c311,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X))) = f(X3,f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X))),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
f(f(f(f(X3,X4),f(X4,X2)),X),f(X4,f(f(X2,f(f(X4,X4),X2)),X2))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c313,plain,
X4 = f(f(f(f(X3,X4),f(X4,X2)),X),f(X4,f(f(X2,f(f(X4,X4),X2)),X2))),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
f(X4,f(f(f(f(X3,X4),f(X4,X2)),X),f(f(f(X3,X4),f(X4,X2)),X))) = f(f(f(f(f(X3,X4),f(X4,X2)),X),f(X4,f(f(X2,f(f(X4,X4),X2)),X2))),f(f(f(f(X3,X4),f(X4,X2)),X),f(f(f(X3,X4),f(X4,X2)),X))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
f(f(f(f(f(X3,X4),f(X4,X2)),X),f(X4,f(f(X2,f(f(X4,X4),X2)),X2))),f(f(f(f(X3,X4),f(X4,X2)),X),f(f(f(X3,X4),f(X4,X2)),X))) = f(f(f(X3,X4),f(X4,X2)),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c316,plain,
f(X4,f(f(f(f(X3,X4),f(X4,X2)),X),f(f(f(X3,X4),f(X4,X2)),X))) = f(f(f(X3,X4),f(X4,X2)),X),
inference(transitivity,[status(thm)],[c314,c315]) ).
cnf(c317,plain,
f(X3,f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X))) = f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(substitution,[status(thm)],[c316]) ).
cnf(c318,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c319,plain,
f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X) = f(f(f(X2,X3),f(X2,X3)),X),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
f(X3,f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X))) = f(f(f(X2,X3),f(X2,X3)),X),
inference(transitivity,[status(thm)],[c317,c319]) ).
cnf(c321,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X))) = f(f(f(X2,X3),f(X2,X3)),X),
inference(transitivity,[status(thm)],[c311,c320]) ).
cnf(c322,plain,
f(X3,f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X))) = f(f(f(X2,X3),f(X2,X3)),X),
inference(transitivity,[status(thm)],[c263,c321]) ).
cnf(c323,plain,
f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X),f(X2,X)),X3))) = f(f(f(X2,X),f(X2,X)),X3),
inference(substitution,[status(thm)],[c322]) ).
cnf(c324,plain,
f(f(f(X2,X),f(X2,X)),X3) = f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X),f(X2,X)),X3))),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),X3),
inference(substitution,[status(thm)],[c154]) ).
cnf(c326,plain,
f(f(f(X2,X),f(X2,X)),X3) = f(X3,f(f(X2,X),f(X2,X))),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X),f(X2,X)),X3)) = f(f(X,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X),f(X2,X)),X3))) = f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),X3),
inference(substitution,[status(thm)],[c154]) ).
cnf(c330,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(X2,X),f(X2,X)),X3)),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
f(f(X2,X),f(X2,X)) = f(f(X,X2),f(X2,X)),
inference(substitution,[status(thm)],[c146]) ).
cnf(c332,plain,
f(f(X,X2),f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(symmetry,[status(thm)],[c331]) ).
cnf(c333,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X2,f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c332]) ).
cnf(c334,plain,
f(X2,f(f(X,X2),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c333,c29]) ).
cnf(c335,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)),X))) = f(f(f(X3,X2),f(X3,X2)),X),
inference(substitution,[status(thm)],[c334]) ).
cnf(c336,plain,
f(f(f(X3,X2),f(X3,X2)),X) = 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)),X))),
inference(symmetry,[status(thm)],[c335]) ).
cnf(c337,plain,
f(f(f(f(X3,X2),f(X3,X2)),X),f(X2,f(f(X3,X),f(X3,X)))) = f(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)),X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X))) = 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)),X))),
inference(substitution,[status(thm)],[c133]) ).
cnf(c339,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)),X))) = f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X))),
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
f(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)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(substitution,[status(thm)],[c146]) ).
cnf(c342,plain,
f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X2,X3),f(X2,X3)),X)),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c344,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
f(f(f(X2,X3),f(X2,X3)),X) = f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
f(X,X2) = f(X2,f(f(X,X2),f(X,X2))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c348,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X) = f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c352,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
f(X3,f(f(X2,X3),f(X2,X3))) = f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),X) = f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c358,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
f(f(f(X2,X3),f(X2,X3)),X) = f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,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)],[c133]) ).
cnf(c362,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)],[c361]) ).
cnf(c363,plain,
f(f(X3,f(f(X2,X3),f(X3,X))),f(X3,X)) = f(f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X))),f(X3,X)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c114]) ).
cnf(c365,plain,
X = f(f(X,X),f(X2,X)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
f(f(f(X2,X),f(X2,X)),X) = f(f(f(X2,X),f(X2,X)),f(f(X,X),f(X2,X))),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
f(f(f(X2,X),f(X2,X)),f(f(X,X),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c114]) ).
cnf(c368,plain,
f(f(f(X2,X),f(X2,X)),X) = f(X2,X),
inference(transitivity,[status(thm)],[c366,c367]) ).
cnf(c369,plain,
f(f(f(f(X2,X3),f(X3,X)),f(f(X2,X3),f(X3,X))),f(X3,X)) = f(f(X2,X3),f(X3,X)),
inference(substitution,[status(thm)],[c368]) ).
cnf(c370,plain,
f(f(X3,f(f(X2,X3),f(X3,X))),f(X3,X)) = f(f(X2,X3),f(X3,X)),
inference(transitivity,[status(thm)],[c363,c369]) ).
cnf(c371,plain,
f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c370]) ).
cnf(c372,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c371]) ).
cnf(c373,plain,
f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X) = f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(congruence,[status(thm)],[c372]) ).
cnf(c374,plain,
f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
f(f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(substitution,[status(thm)],[c308]) ).
cnf(c376,plain,
f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c370]) ).
cnf(c377,plain,
f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X) = f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c380,plain,
f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X) = f(f(f(X2,X3),f(X2,X3)),X),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c378,c381]) ).
cnf(c383,plain,
f(f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c375,c382]) ).
cnf(c384,plain,
f(f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c374,c383]) ).
cnf(c385,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X3,f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X))))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c360,c384]) ).
cnf(c386,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X3,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c356,c385]) ).
cnf(c387,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X2,X3),f(X3,f(f(X2,X),f(X2,X)))),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c350,c386]) ).
cnf(c388,plain,
f(f(f(f(X2,X3),f(X2,X3)),X),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c346,c387]) ).
cnf(c389,plain,
f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X3),f(X2,X3)),X)) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X3),f(X2,X3)),X)),
inference(transitivity,[status(thm)],[c342,c388]) ).
cnf(c390,plain,
f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c391,plain,
f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
f(f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c394,plain,
f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))) = f(f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
f(f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
f(f(f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c397,plain,
f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(substitution,[status(thm)],[c389]) ).
cnf(c398,plain,
f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
f(f(f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(transitivity,[status(thm)],[c396,c398]) ).
cnf(c400,plain,
f(f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X2,f(f(X3,X),f(X3,X))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(transitivity,[status(thm)],[c395,c399]) ).
cnf(c401,plain,
f(f(f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(transitivity,[status(thm)],[c392,c400]) ).
cnf(c402,plain,
f(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)),X))),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(transitivity,[status(thm)],[c340,c401]) ).
cnf(c403,plain,
f(f(f(f(X3,X2),f(X3,X2)),X),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X,f(f(X3,X2),f(X3,X2))),f(f(f(X3,X2),f(X3,X2)),X)),
inference(transitivity,[status(thm)],[c337,c402]) ).
cnf(c404,plain,
f(f(f(f(X2,X),f(X2,X)),X3),f(X,f(f(X2,X3),f(X2,X3)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),X3)),
inference(substitution,[status(thm)],[c403]) ).
cnf(c405,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),X3)) = f(f(f(f(X2,X),f(X2,X)),X3),f(X,f(f(X2,X3),f(X2,X3)))),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c406,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),X3),
inference(substitution,[status(thm)],[c154]) ).
cnf(c407,plain,
f(f(f(X2,X),f(X2,X)),X3) = f(X3,f(f(X2,X),f(X2,X))),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
f(f(f(f(X2,X),f(X2,X)),X3),f(X,f(f(X2,X3),f(X2,X3)))) = f(f(X3,f(f(X2,X),f(X2,X))),f(X,f(f(X2,X3),f(X2,X3)))),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
f(f(X3,f(f(X2,X),f(X2,X))),f(f(f(X2,X),f(X2,X)),X3)) = f(f(X3,f(f(X2,X),f(X2,X))),f(X,f(f(X2,X3),f(X2,X3)))),
inference(transitivity,[status(thm)],[c405,c408]) ).
cnf(c410,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(X,f(f(X2,X3),f(X2,X3)))),
inference(transitivity,[status(thm)],[c330,c409]) ).
cnf(c411,plain,
f(f(X,f(f(X2,X3),f(X2,X3))),f(X,f(f(X2,X3),f(X2,X3)))) = f(f(X,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))),
inference(substitution,[status(thm)],[c410]) ).
cnf(c412,plain,
f(f(X,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X)))) = f(f(X,f(f(X2,X3),f(X2,X3))),f(X,f(f(X2,X3),f(X2,X3)))),
inference(symmetry,[status(thm)],[c411]) ).
cnf(c413,plain,
f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X))))) = f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(X,f(f(X2,X3),f(X2,X3))))),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(X,f(f(X2,X3),f(X2,X3))))) = f(X,f(f(X2,X3),f(X2,X3))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c415,plain,
f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(X3,f(f(X2,X),f(X2,X))))) = f(X,f(f(X2,X3),f(X2,X3))),
inference(transitivity,[status(thm)],[c413,c414]) ).
cnf(c416,plain,
f(X,f(f(X,f(f(X2,X3),f(X2,X3))),f(f(f(X2,X),f(X2,X)),X3))) = f(X,f(f(X2,X3),f(X2,X3))),
inference(transitivity,[status(thm)],[c328,c415]) ).
cnf(c417,plain,
f(f(f(X2,X),f(X2,X)),X3) = f(X,f(f(X2,X3),f(X2,X3))),
inference(transitivity,[status(thm)],[c324,c416]) ).
cnf(c418,plain,
f(X3,f(f(X2,X),f(X2,X))) = f(X,f(f(X2,X3),f(X2,X3))),
inference(transitivity,[status(thm)],[c155,c417]) ).
cnf(c419,plain,
f(c,f(f(b,a),f(b,a))) = f(a,f(f(b,c),f(b,c))),
inference(substitution,[status(thm)],[c418]) ).
cnf(c420,plain,
f(a,f(f(b,c),f(b,c))) = f(c,f(f(b,a),f(b,a))),
inference(symmetry,[status(thm)],[c419]) ).
cnf(c421,plain,
$false,
inference(resolution,[status(thm)],[c1,c420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT072-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n004.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 13:59:06 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.76/2.91 Command-line arguments: --flatten --complete-subsets
% 18.76/2.91
% 18.76/2.91 % SZS status Unsatisfiable
% 18.76/2.91
% 19.49/3.07 % SZS output start CNFRefutation
% See solution above
% 25.87/3.81
% 25.87/3.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------