%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT076-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 253.60s 32.49s
% Output : CNFRefutation 233.54s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% 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(C,A)),D),f(A,f(f(f(f(f(f(B,B),A),C),C),A),B))) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mol_27B1) ).
cnf(c3,plain,
f(f(f(f(X2,X4),f(X3,X4)),f(X,f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X4 = f(f(f(f(X2,X4),f(X3,X4)),f(X,f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
f(X4,f(f(X3,X4),f(f(f(f(f(f(f(X2,X4),f(X2,X4)),f(X3,X4)),X),X),f(X3,X4)),f(X2,X4)))) = f(f(f(f(f(X2,X4),f(X3,X4)),f(X,f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X3,X4),f(f(f(f(f(f(f(X2,X4),f(X2,X4)),f(X3,X4)),X),X),f(X3,X4)),f(X2,X4)))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
f(f(f(f(f(X2,X4),f(X3,X4)),f(X,f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X3,X4),f(f(f(f(f(f(f(X2,X4),f(X2,X4)),f(X3,X4)),X),X),f(X3,X4)),f(X2,X4)))) = f(X3,X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
f(X4,f(f(X3,X4),f(f(f(f(f(f(f(X2,X4),f(X2,X4)),f(X3,X4)),X),X),f(X3,X4)),f(X2,X4)))) = f(X3,X4),
inference(transitivity,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
f(X3,X4) = f(X4,f(f(X3,X4),f(f(f(f(f(f(f(X2,X4),f(X2,X4)),f(X3,X4)),X),X),f(X3,X4)),f(X2,X4)))),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
f(f(X4,X4),f(X3,X4)) = f(f(X4,X4),f(X4,f(f(X3,X4),f(f(f(f(f(f(f(X2,X4),f(X2,X4)),f(X3,X4)),X),X),f(X3,X4)),f(X2,X4))))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
f(f(f(X3,X2),f(X,X2)),f(f(X4,f(f(X3,X2),f(X,X2))),f(f(f(f(f(f(f(X6,f(f(X3,X2),f(X,X2))),f(X6,f(f(X3,X2),f(X,X2)))),f(X4,f(f(X3,X2),f(X,X2)))),X5),X5),f(X4,f(f(X3,X2),f(X,X2)))),f(X6,f(f(X3,X2),f(X,X2)))))) = f(X4,f(f(X3,X2),f(X,X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c11,plain,
f(X6,f(f(X5,X4),f(X3,X4))) = f(f(f(X5,X4),f(X3,X4)),f(f(X6,f(f(X5,X4),f(X3,X4))),f(f(f(f(f(f(f(X2,f(f(X5,X4),f(X3,X4))),f(X2,f(f(X5,X4),f(X3,X4)))),f(X6,f(f(X5,X4),f(X3,X4)))),X),X),f(X6,f(f(X5,X4),f(X3,X4)))),f(X2,f(f(X5,X4),f(X3,X4)))))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
f(f(X6,f(f(X5,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X5,X5),X4),X3),X3),X4),X5))) = f(f(f(f(X5,X4),f(X3,X4)),f(f(X6,f(f(X5,X4),f(X3,X4))),f(f(f(f(f(f(f(X2,f(f(X5,X4),f(X3,X4))),f(X2,f(f(X5,X4),f(X3,X4)))),f(X6,f(f(X5,X4),f(X3,X4)))),X),X),f(X6,f(f(X5,X4),f(X3,X4)))),f(X2,f(f(X5,X4),f(X3,X4)))))),f(X4,f(f(f(f(f(f(X5,X5),X4),X3),X3),X4),X5))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
f(f(f(f(X5,X4),f(X3,X4)),f(f(X6,f(f(X5,X4),f(X3,X4))),f(f(f(f(f(f(f(X2,f(f(X5,X4),f(X3,X4))),f(X2,f(f(X5,X4),f(X3,X4)))),f(X6,f(f(X5,X4),f(X3,X4)))),X),X),f(X6,f(f(X5,X4),f(X3,X4)))),f(X2,f(f(X5,X4),f(X3,X4)))))),f(X4,f(f(f(f(f(f(X5,X5),X4),X3),X3),X4),X5))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
f(f(X4,f(f(X3,X2),f(X,X2))),f(X2,f(f(f(f(f(f(X3,X3),X2),X),X),X2),X3))) = X2,
inference(transitivity,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
f(f(f(f(f(f(f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))),f(f(X2,X3),f(X4,X3))),f(X,f(X4,X3))),f(X,f(X4,X3))),f(f(X2,X3),f(X4,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))) = X3,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
X3 = f(f(f(f(f(f(f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))),f(f(X2,X3),f(X4,X3))),f(X,f(X4,X3))),f(X,f(X4,X3))),f(f(X2,X3),f(X4,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
f(f(f(X2,X3),f(X4,X3)),X3) = f(f(f(X2,X3),f(X4,X3)),f(f(f(f(f(f(f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))),f(f(X2,X3),f(X4,X3))),f(X,f(X4,X3))),f(X,f(X4,X3))),f(f(X2,X3),f(X4,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
f(f(X4,X3),f(f(f(X2,X3),f(X4,X3)),X3)) = f(f(X4,X3),f(f(f(X2,X3),f(X4,X3)),f(f(f(f(f(f(f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))),f(f(X2,X3),f(X4,X3))),f(X,f(X4,X3))),f(X,f(X4,X3))),f(f(X2,X3),f(X4,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
f(f(f(X2,f(X3,X4)),f(f(X,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X,X),X4),X3),X3),X4),X))) = X4,
inference(substitution,[status(thm)],[c14]) ).
cnf(c20,plain,
X4 = f(f(f(X2,f(X3,X4)),f(f(X,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X,X),X4),X3),X3),X4),X))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
f(X4,f(f(X3,X4),f(f(f(f(f(f(X2,X2),f(X3,X4)),f(X,X4)),f(X,X4)),f(X3,X4)),X2))) = f(f(f(f(X2,f(X3,X4)),f(f(X,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X,X),X4),X3),X3),X4),X))),f(f(X3,X4),f(f(f(f(f(f(X2,X2),f(X3,X4)),f(X,X4)),f(X,X4)),f(X3,X4)),X2))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
f(f(f(f(X2,f(X3,X4)),f(f(X,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X,X),X4),X3),X3),X4),X))),f(f(X3,X4),f(f(f(f(f(f(X2,X2),f(X3,X4)),f(X,X4)),f(X,X4)),f(X3,X4)),X2))) = f(X3,X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
f(X4,f(f(X3,X4),f(f(f(f(f(f(X2,X2),f(X3,X4)),f(X,X4)),f(X,X4)),f(X3,X4)),X2))) = f(X3,X4),
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
f(f(X4,X3),f(f(f(X2,X3),f(X4,X3)),f(f(f(f(f(f(f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))),f(f(X2,X3),f(X4,X3))),f(X,f(X4,X3))),f(X,f(X4,X3))),f(f(X2,X3),f(X4,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X4),X4),X3),X2))))) = f(f(X2,X3),f(X4,X3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
f(f(X3,X2),f(f(f(X,X2),f(X3,X2)),X2)) = f(f(X,X2),f(X3,X2)),
inference(transitivity,[status(thm)],[c18,c24]) ).
cnf(c26,plain,
f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2)) = f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)) = f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2))) = f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2)) = f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c30,plain,
f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)) = f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2))) = f(f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2)),f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
X3 = f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)) = f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c37,plain,
f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(transitivity,[status(thm)],[c35,c38]) ).
cnf(c40,plain,
f(f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2)),f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2))) = f(X,X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),X2))) = f(X,X2),
inference(transitivity,[status(thm)],[c31,c40]) ).
cnf(c42,plain,
f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2))) = f(X,X2),
inference(transitivity,[status(thm)],[c28,c41]) ).
cnf(c43,plain,
f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
f(X2,X) = f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
f(f(X2,X),f(X2,X)) = f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
f(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(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c48,plain,
f(X2,X) = f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
f(f(X2,X),f(X2,X)) = f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
f(f(f(X2,X),f(X2,X)),f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X))) = f(f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X)),f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)) = f(f(X3,X2),f(X,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c52,plain,
f(f(X3,X2),f(X,X2)) = f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
f(f(f(X3,X2),f(X,X2)),X2) = f(f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)),X2),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2)) = f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)),X2)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)),X2)) = f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c56,plain,
f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)) = f(f(X3,X2),f(X,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c57,plain,
f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X,X2),f(f(f(X3,X2),f(X,X2)),X2)),X2)) = f(f(X3,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2)) = f(f(X3,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c54,c57]) ).
cnf(c59,plain,
f(f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X)),f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X))) = f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c42]) ).
cnf(c61,plain,
f(f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X)),f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
f(f(f(X2,X),f(X2,X)),f(f(f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X)),f(f(f(f(f(X,X),f(X2,X)),X),X),f(X2,X))),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c50,c61]) ).
cnf(c63,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c46,c62]) ).
cnf(c64,plain,
f(f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X))),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X)))) = f(f(X2,X2),f(X2,X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
f(f(X2,X2),f(X2,X)) = f(f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X))),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X)))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c67,plain,
X4 = f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
f(X4,X4) = f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
f(f(X4,X4),f(X4,X4)) = f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(X4,X4)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
X4 = f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
f(X4,X4) = f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),X4),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(X4,X4)) = f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),X4)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
X4 = f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),X4) = f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),X4)) = f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c79,plain,
X4 = f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))) = f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))))) = f(f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
f(f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))))) = f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c83,plain,
f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c84,plain,
f(f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))))) = X4,
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))))) = X4,
inference(transitivity,[status(thm)],[c81,c84]) ).
cnf(c86,plain,
f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3))),X4)) = X4,
inference(transitivity,[status(thm)],[c77,c85]) ).
cnf(c87,plain,
f(f(X4,f(f(f(f(X3,X4),f(X2,X4)),X),f(X4,f(f(f(f(f(f(X3,X3),X4),X2),X2),X4),X3)))),f(X4,X4)) = X4,
inference(transitivity,[status(thm)],[c73,c86]) ).
cnf(c88,plain,
f(f(X,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c69,c87]) ).
cnf(c89,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
f(X,X) = f(X,f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,X)) = f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(X,X),f(X,X)))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
f(f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X)),f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X))) = f(f(X,f(X,X)),X),
inference(substitution,[status(thm)],[c63]) ).
cnf(c93,plain,
f(f(X,f(X,X)),X) = f(f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X)),f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c95,plain,
f(X,f(X,X)) = f(f(f(X,X),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
f(f(X,f(X,X)),X) = f(f(f(f(X,X),f(X,X)),f(X,X)),X),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X)) = f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(f(X,f(X,X)),X)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c99,plain,
f(X,f(X,X)) = f(f(f(X,X),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
f(f(X,f(X,X)),X) = f(f(f(f(X,X),f(X,X)),f(X,X)),X),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(f(X,f(X,X)),X)) = f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(f(f(f(X,X),f(X,X)),f(X,X)),X)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c103,plain,
f(X,X) = f(f(f(X,X),f(X,X)),X),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
f(f(X,X),f(X,X)) = f(f(f(f(X,X),f(X,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
f(f(f(X,X),f(X,X)),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
f(f(f(f(X,X),f(X,X)),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(f(f(f(X,X),f(X,X)),f(X,X)),X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(f(f(f(X,X),f(X,X)),f(X,X)),X)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c109,plain,
f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(f(f(f(X,X),f(X,X)),f(X,X)),X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),f(f(f(f(X,X),f(X,X)),f(X,X)),X)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c112,plain,
f(X,X) = f(f(f(X,X),f(X,X)),X),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
f(f(X,X),f(X,X)) = f(f(f(f(X,X),f(X,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
f(f(f(X,X),f(X,X)),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
f(f(f(f(X,X),f(X,X)),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),f(f(f(f(X,X),f(X,X)),f(X,X)),X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c118,plain,
f(f(f(X,X),f(X,X)),X) = f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
f(f(f(f(X,X),f(X,X)),X),f(X,X)) = f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(X,X)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(X,X)),f(X,X)),X),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),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(X,X),f(X,X))),f(X,X)),f(X,X)),X)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c124,plain,
f(f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(X,X)),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),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(X,X),f(X,X))),f(X,X)),f(X,X)),X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),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(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X)))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c127,plain,
f(f(f(X,X),f(X,X)),X) = f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
f(f(f(f(X,X),f(X,X)),X),f(X,X)) = f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(X,X)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
f(f(f(f(f(f(X,X),f(X,X)),X),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(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),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(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X)))) = f(f(f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),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(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X)))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),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(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X)))) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c133,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),f(f(X,X),f(X,X))),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(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c132,c88]) ).
cnf(c134,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),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(X,X),f(X,X))),f(X,X)),f(X,X)),f(f(X,X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c131,c133]) ).
cnf(c135,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),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(X,X),f(X,X))),f(X,X)),f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c125,c134]) ).
cnf(c136,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c122,c135]) ).
cnf(c137,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),f(f(X,X),f(X,X))),f(f(f(f(X,X),f(X,X)),f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c116,c136]) ).
cnf(c138,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(f(f(f(X,X),f(X,X)),f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c110,c137]) ).
cnf(c139,plain,
f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(f(f(f(X,X),f(X,X)),f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c107,c138]) ).
cnf(c140,plain,
f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(f(X,f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c101,c139]) ).
cnf(c141,plain,
f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c97,c140]) ).
cnf(c142,plain,
f(f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X)),f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X))) = f(X,f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
f(X,f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X))) = f(X,X),
inference(congruence,[status(thm)],[c141]) ).
cnf(c144,plain,
f(f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X)),f(f(f(X,f(X,X)),X),f(f(X,f(X,X)),X))) = f(X,X),
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
f(f(X,f(X,X)),X) = f(X,X),
inference(transitivity,[status(thm)],[c93,c144]) ).
cnf(c146,plain,
f(X,X) = f(f(X,f(X,X)),X),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
f(f(X,X),f(X,X)) = f(f(f(X,f(X,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
f(X,f(f(X,X),f(X,X))) = f(X,f(f(f(X,f(X,X)),X),f(X,X))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(X,X),f(X,X)))) = f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(f(X,f(X,X)),X),f(X,X)))),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c151,plain,
f(X,f(X,X)) = f(f(f(X,X),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
f(f(X,f(X,X)),X) = f(f(f(f(X,X),f(X,X)),f(X,X)),X),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
f(f(f(X,f(X,X)),X),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
f(X,f(f(f(X,f(X,X)),X),f(X,X))) = f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(f(X,f(X,X)),X),f(X,X)))) = f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
f(f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))),f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X)))) = f(f(X2,X),f(f(X,f(X2,X)),X)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c157,plain,
f(f(X2,X),f(f(X,f(X2,X)),X)) = f(f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))),f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X)))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c159,plain,
X = f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
f(X,f(X2,X)) = f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
f(f(X,f(X2,X)),X) = f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
f(f(X2,X),f(f(X,f(X2,X)),X)) = f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X)),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))) = f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c165,plain,
X = f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
f(X,f(X2,X)) = f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
f(f(X,f(X2,X)),X) = f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
f(f(X2,X),f(f(X,f(X2,X)),X)) = f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X))) = f(f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X)),f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
f(f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X)),f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X))) = f(X2,X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c171,plain,
f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(f(f(f(f(X,X),f(X2,X)),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X,f(f(f(f(f(f(X,X),X),X2),X2),X),X))),f(X2,X)),X))) = f(X2,X),
inference(transitivity,[status(thm)],[c169,c170]) ).
cnf(c172,plain,
f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))) = f(X2,X),
inference(transitivity,[status(thm)],[c163,c171]) ).
cnf(c173,plain,
f(f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))),f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X)))) = f(f(X2,X),f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X)))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
f(f(X2,X),f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X)))) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c175,plain,
f(f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))),f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X)))) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c173,c174]) ).
cnf(c176,plain,
f(f(X2,X),f(f(X,f(X2,X)),X)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c157,c175]) ).
cnf(c177,plain,
f(f(X2,X),f(X2,X)) = f(f(X2,X),f(f(X,f(X2,X)),X)),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
f(f(f(X2,X),f(X2,X)),X) = f(f(f(X2,X),f(f(X,f(X2,X)),X)),X),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
f(f(X3,X2),f(X,X2)) = f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c180,plain,
f(f(f(X3,X2),f(X,X2)),f(f(X3,X2),f(X,X2))) = f(f(f(X3,X2),f(X,X2)),f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
f(f(X3,X2),f(X,X2)) = f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c182,plain,
f(f(f(X3,X2),f(X,X2)),f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2))) = f(f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2)),f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
f(f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2)),f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2))) = f(f(f(X3,X2),f(X,X2)),X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c184,plain,
f(f(f(X3,X2),f(X,X2)),f(f(f(f(X3,X2),f(X,X2)),X2),f(f(f(X3,X2),f(X,X2)),X2))) = f(f(f(X3,X2),f(X,X2)),X2),
inference(transitivity,[status(thm)],[c182,c183]) ).
cnf(c185,plain,
f(f(f(X3,X2),f(X,X2)),f(f(X3,X2),f(X,X2))) = f(f(f(X3,X2),f(X,X2)),X2),
inference(transitivity,[status(thm)],[c180,c184]) ).
cnf(c186,plain,
f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))) = f(f(f(X2,X),f(f(X,f(X2,X)),X)),X),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
f(f(f(X2,X),f(f(X,f(X2,X)),X)),X) = f(f(f(X2,X),f(f(X,f(X2,X)),X)),f(f(X2,X),f(f(X,f(X2,X)),X))),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
f(f(f(X2,X),f(f(X,f(X2,X)),X)),X) = f(X2,X),
inference(transitivity,[status(thm)],[c187,c172]) ).
cnf(c189,plain,
f(f(f(X2,X),f(X2,X)),X) = f(X2,X),
inference(transitivity,[status(thm)],[c178,c188]) ).
cnf(c190,plain,
f(f(f(X,X),f(X,X)),X) = f(X,X),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
f(X,X) = f(f(f(X,X),f(X,X)),X),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
f(f(X,X),X) = f(f(f(f(X,X),f(X,X)),X),X),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
f(f(f(X,X),X),f(f(X,X),X)) = f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
f(X2,f(f(f(X,X),X),f(f(X,X),X))) = f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)))) = f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)))),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
f(f(f(X,X),f(X,X)),X) = f(X,X),
inference(substitution,[status(thm)],[c189]) ).
cnf(c197,plain,
f(X,X) = f(f(f(X,X),f(X,X)),X),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
f(f(X,X),f(X,X)) = f(f(f(f(X,X),f(X,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
f(f(f(X,X),f(X,X)),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
f(f(f(f(X,X),f(X,X)),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X))) = f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(X,X))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)))) = f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(X,X)))),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
f(f(f(X,X),f(X,X)),X) = f(X,X),
inference(substitution,[status(thm)],[c189]) ).
cnf(c205,plain,
f(X,X) = f(f(f(X,X),f(X,X)),X),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(X,X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(X,X))) = f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(X,X)))) = f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c212,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)],[c211]) ).
cnf(c213,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)],[c212]) ).
cnf(c214,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c215,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)],[c214]) ).
cnf(c216,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)],[c215]) ).
cnf(c217,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(X,X)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c218,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)],[c88]) ).
cnf(c219,plain,
f(f(f(X2,f(X,X)),f(f(X,X),f(X,X))),f(X,X)) = f(f(f(X2,f(X,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,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)),X),f(X,X)),
inference(transitivity,[status(thm)],[c217,c219]) ).
cnf(c221,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)),X),f(X,X)),
inference(transitivity,[status(thm)],[c216,c220]) ).
cnf(c222,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(X,X)),
inference(transitivity,[status(thm)],[c213,c221]) ).
cnf(c223,plain,
f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)) = f(f(f(f(X,X),f(X,X)),X),f(X,X)),
inference(substitution,[status(thm)],[c222]) ).
cnf(c224,plain,
f(f(f(f(X,X),f(X,X)),X),f(X,X)) = f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)) = f(f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)),f(f(f(X,X),f(X,X)),X)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X) = f(f(f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)),f(f(f(X,X),f(X,X)),X)),X),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)) = f(f(f(f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X))) = f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)))) = f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)))),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(f(f(X,X),f(X,X)),X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)))) = X,
inference(substitution,[status(thm)],[c14]) ).
cnf(c231,plain,
f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(f(f(X,X),f(X,X)),X)),X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c229,c230]) ).
cnf(c232,plain,
f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(f(f(X,X),f(X,X)),X),f(X,X)),f(X,X)),X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c210,c231]) ).
cnf(c233,plain,
f(f(X2,f(f(f(X,X),X),f(f(f(f(X,X),f(X,X)),X),X))),f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c203,c232]) ).
cnf(c234,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(f(f(f(X,X),f(X,X)),f(X,X)),X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c195,c233]) ).
cnf(c235,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(f(X,f(X,X)),X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c155,c234]) ).
cnf(c236,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,f(f(X,X),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c149,c235]) ).
cnf(c237,plain,
f(f(X2,f(f(f(X,X),X),f(f(X,X),X))),f(X,X)) = X,
inference(transitivity,[status(thm)],[c91,c236]) ).
cnf(c238,plain,
f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
X2 = f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
f(X2,X) = f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
f(f(X2,X2),f(X2,X)) = f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X)),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X))) = f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c237]) ).
cnf(c244,plain,
X2 = f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
f(X2,X) = f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
f(f(X2,X2),f(X2,X)) = f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X)),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X))) = f(f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X)),f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X))),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
f(f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X)),f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X))) = f(X2,X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c249,plain,
f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(f(f(f(f(f(X,X),f(X2,X2)),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(f(f(X2,X2),X2),f(f(X2,X2),X2))),f(X2,X2)),X))) = f(X2,X2),
inference(transitivity,[status(thm)],[c247,c248]) ).
cnf(c250,plain,
f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X))) = f(X2,X2),
inference(transitivity,[status(thm)],[c242,c249]) ).
cnf(c251,plain,
f(f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X))),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X)))) = f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X)))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X)))) = f(f(X2,X2),f(X2,X2)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c253,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c252,c88]) ).
cnf(c254,plain,
f(f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X))),f(f(f(X2,X2),f(X2,X)),f(f(X2,X2),f(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c251,c253]) ).
cnf(c255,plain,
f(f(X2,X2),f(X2,X)) = X2,
inference(transitivity,[status(thm)],[c65,c254]) ).
cnf(c256,plain,
f(f(X4,X4),f(X4,f(f(X3,X4),f(f(f(f(f(f(f(X2,X4),f(X2,X4)),f(X3,X4)),X),X),f(X3,X4)),f(X2,X4))))) = X4,
inference(substitution,[status(thm)],[c255]) ).
cnf(c257,plain,
f(f(X2,X2),f(X,X2)) = X2,
inference(transitivity,[status(thm)],[c9,c256]) ).
cnf(c258,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c259,plain,
f(X2,X) = f(f(f(X2,X2),f(X,X2)),X),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
f(f(X2,X),f(X,X2)) = f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2)),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c262,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,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,X2),f(X2,X)))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c265,plain,
f(f(X3,f(X2,X)),X2) = f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
f(f(f(X3,f(X2,X)),X2),f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X)))) = f(f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))),f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X)))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
f(f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))),f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X)))) = f(f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))),f(X2,X)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c268,plain,
f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))) = f(f(X3,f(X2,X)),X2),
inference(congruence,[status(thm)],[c255]) ).
cnf(c269,plain,
f(f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))),f(X2,X)) = f(f(f(X3,f(X2,X)),X2),f(X2,X)),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
f(f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X))),f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X)))) = f(f(f(X3,f(X2,X)),X2),f(X2,X)),
inference(transitivity,[status(thm)],[c267,c269]) ).
cnf(c271,plain,
f(f(f(X3,f(X2,X)),X2),f(f(X3,f(X2,X)),f(f(X2,X2),f(X2,X)))) = f(f(f(X3,f(X2,X)),X2),f(X2,X)),
inference(transitivity,[status(thm)],[c266,c270]) ).
cnf(c272,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(X2,X)),
inference(transitivity,[status(thm)],[c263,c271]) ).
cnf(c273,plain,
f(f(f(f(X2,X2),f(X,X2)),X),f(f(f(X2,X2),f(X,X2)),X)) = f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2)),
inference(substitution,[status(thm)],[c272]) ).
cnf(c274,plain,
f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2)) = f(f(f(f(X2,X2),f(X,X2)),X),f(f(f(X2,X2),f(X,X2)),X)),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
f(f(f(X2,X2),f(X,X2)),X) = f(X2,X),
inference(congruence,[status(thm)],[c257]) ).
cnf(c276,plain,
f(f(f(f(X2,X2),f(X,X2)),X),f(f(f(X2,X2),f(X,X2)),X)) = f(f(X2,X),f(f(f(X2,X2),f(X,X2)),X)),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
f(f(f(X2,X2),f(X,X2)),X) = f(X2,X),
inference(congruence,[status(thm)],[c257]) ).
cnf(c278,plain,
f(f(X2,X),f(f(f(X2,X2),f(X,X2)),X)) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
f(f(f(f(X2,X2),f(X,X2)),X),f(f(f(X2,X2),f(X,X2)),X)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c276,c278]) ).
cnf(c280,plain,
f(f(f(f(X2,X2),f(X,X2)),X),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c274,c279]) ).
cnf(c281,plain,
f(f(X2,X),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c260,c280]) ).
cnf(c282,plain,
f(f(b,c),f(c,b)) = f(f(b,c),f(b,c)),
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
f(f(b,c),f(b,c)) = f(f(b,c),f(c,b)),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
f(a,f(f(b,c),f(b,c))) = f(a,f(f(b,c),f(c,b))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c286,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)],[c285]) ).
cnf(c287,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,X2),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c257]) ).
cnf(c288,plain,
f(f(f(X2,X),f(X2,X)),X2) = f(X2,X),
inference(transitivity,[status(thm)],[c286,c287]) ).
cnf(c289,plain,
f(f(f(X,X2),f(X,X2)),X) = f(X,X2),
inference(substitution,[status(thm)],[c288]) ).
cnf(c290,plain,
f(X,X2) = f(f(f(X,X2),f(X,X2)),X),
inference(symmetry,[status(thm)],[c289]) ).
cnf(c291,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c292,plain,
f(X2,f(f(X2,X2),X)) = f(f(f(X2,X2),f(X2,X2)),f(f(X2,X2),X)),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
f(f(f(X2,X2),f(X2,X2)),f(f(X2,X2),X)) = f(X2,X2),
inference(substitution,[status(thm)],[c255]) ).
cnf(c294,plain,
f(X2,f(f(X2,X2),X)) = f(X2,X2),
inference(transitivity,[status(thm)],[c292,c293]) ).
cnf(c295,plain,
f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),f(X,X3))) = f(f(X2,X3),f(X2,X3)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c296,plain,
f(f(X2,X3),f(X2,X3)) = f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),f(X,X3))),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
f(X3,f(f(X2,X3),f(X2,X3))) = f(X3,f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),f(X,X3)))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
f(f(f(X,X2),f(f(X,X2),f(X,X2))),f(X,X2)) = f(f(X,X2),f(X,X2)),
inference(substitution,[status(thm)],[c145]) ).
cnf(c299,plain,
f(f(X,X2),f(X,X2)) = f(f(f(X,X2),f(f(X,X2),f(X,X2))),f(X,X2)),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
f(f(f(X2,X3),f(X2,X3)),f(X,X3)) = f(f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),f(X,X3))) = f(f(X2,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3))),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
f(X3,f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),f(X,X3)))) = f(X3,f(f(X2,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
f(f(X,X),f(f(f(X2,X),f(X,X)),X)) = f(f(X2,X),f(X,X)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c304,plain,
f(f(X2,X),f(X,X)) = f(f(X,X),f(f(f(X2,X),f(X,X)),X)),
inference(symmetry,[status(thm)],[c303]) ).
cnf(c305,plain,
f(f(X,X),f(f(f(X2,X),f(X,X)),X)) = X,
inference(substitution,[status(thm)],[c257]) ).
cnf(c306,plain,
f(f(X2,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c304,c305]) ).
cnf(c307,plain,
f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))) = f(X2,X3),
inference(substitution,[status(thm)],[c306]) ).
cnf(c308,plain,
f(X2,X3) = f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
f(f(X2,X3),f(f(X2,X3),f(X2,X3))) = f(f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))),f(f(X2,X3),f(X2,X3))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)) = f(f(f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))),f(f(X2,X3),f(X2,X3))),f(X2,X3)),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
f(f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)) = f(f(f(f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
f(f(X2,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3))) = f(f(X2,X3),f(f(f(f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
f(X3,f(f(X2,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)))) = f(X3,f(f(X2,X3),f(f(f(f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
f(X3,f(f(X2,X3),f(f(f(f(f(f(f(X,X3),f(X,X3)),f(X2,X3)),f(f(X2,X3),f(X2,X3))),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)))) = f(X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c315,plain,
f(X3,f(f(X2,X3),f(f(f(f(X2,X3),f(f(X2,X3),f(X2,X3))),f(X2,X3)),f(X,X3)))) = f(X2,X3),
inference(transitivity,[status(thm)],[c313,c314]) ).
cnf(c316,plain,
f(X3,f(f(X2,X3),f(f(f(X2,X3),f(X2,X3)),f(X,X3)))) = f(X2,X3),
inference(transitivity,[status(thm)],[c302,c315]) ).
cnf(c317,plain,
f(X2,f(f(X,X2),f(X,X2))) = f(X,X2),
inference(transitivity,[status(thm)],[c297,c316]) ).
cnf(c318,plain,
f(f(X,X2),f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X,X2)))) = f(f(X2,X),f(X,X2)),
inference(substitution,[status(thm)],[c317]) ).
cnf(c319,plain,
f(f(X2,X),f(X,X2)) = f(f(X,X2),f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X,X2)))),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X,X2))) = f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X,X2))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c321,plain,
f(f(X,X2),f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X,X2)))) = f(f(X,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X,X2)))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X,X2))) = f(X2,X),
inference(substitution,[status(thm)],[c255]) ).
cnf(c323,plain,
f(f(X,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X,X2)))) = f(f(X,X2),f(X2,X)),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
f(f(X,X2),f(X2,X)) = f(f(X,X2),f(X,X2)),
inference(substitution,[status(thm)],[c281]) ).
cnf(c325,plain,
f(f(X,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X,X2)))) = f(f(X,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c323,c324]) ).
cnf(c326,plain,
f(f(X,X2),f(f(f(X2,X),f(X,X2)),f(f(X2,X),f(X,X2)))) = f(f(X,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c321,c325]) ).
cnf(c327,plain,
f(f(X2,X),f(X,X2)) = f(f(X,X2),f(X,X2)),
inference(transitivity,[status(thm)],[c319,c326]) ).
cnf(c328,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
f(f(f(X,X2),f(X,X2)),X) = f(f(f(X2,X),f(X,X2)),X),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
f(f(f(X2,X),f(X,X2)),X) = f(f(f(X2,X),f(X2,X)),X),
inference(congruence,[status(thm)],[c281]) ).
cnf(c331,plain,
f(f(f(X2,X),f(X,X2)),X) = f(X2,X),
inference(transitivity,[status(thm)],[c330,c189]) ).
cnf(c332,plain,
f(f(f(X,X2),f(X,X2)),X) = f(X2,X),
inference(transitivity,[status(thm)],[c329,c331]) ).
cnf(c333,plain,
f(X,X2) = f(X2,X),
inference(transitivity,[status(thm)],[c290,c332]) ).
cnf(c334,plain,
f(f(c,b),f(b,c)) = f(f(b,c),f(c,b)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
f(f(b,c),f(c,b)) = f(f(c,b),f(b,c)),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
f(a,f(f(b,c),f(c,b))) = f(a,f(f(c,b),f(b,c))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
f(c,b) = f(b,c),
inference(substitution,[status(thm)],[c333]) ).
cnf(c338,plain,
f(b,c) = f(c,b),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
f(f(c,b),f(b,c)) = f(f(c,b),f(c,b)),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
f(a,f(f(c,b),f(b,c))) = f(a,f(f(c,b),f(c,b))),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
f(f(X2,X),f(X2,X)) = f(f(X2,X),f(X,X2)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c342,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(X2,f(f(X3,X),f(X,X3))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
f(X2,f(f(X3,X),f(X,X3))) = f(X2,f(f(X,X3),f(X,X3))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c344,plain,
f(X2,f(f(X,X3),f(X,X3))) = f(f(f(X,X3),f(X,X3)),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c345,plain,
f(f(X2,X3),f(X,f(X3,X))) = f(f(X3,X2),f(X,f(X3,X))),
inference(congruence,[status(thm)],[c333]) ).
cnf(c346,plain,
f(X3,f(f(X2,X3),f(X,f(X3,X)))) = f(X3,f(f(X3,X2),f(X,f(X3,X)))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c348,plain,
f(X,f(X2,X)) = f(X,f(X,X2)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
f(f(X3,X2),f(X,f(X3,X))) = f(f(X3,X2),f(X,f(X,X3))),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
f(X3,f(f(X3,X2),f(X,f(X3,X)))) = f(X3,f(f(X3,X2),f(X,f(X,X3)))),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c352,plain,
f(X2,f(f(X2,X),f(X2,X))) = f(f(f(X2,X2),f(X2,X)),f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
f(f(f(X2,X2),f(X2,X)),f(f(X2,X),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c306]) ).
cnf(c354,plain,
f(X2,f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c352,c353]) ).
cnf(c355,plain,
f(X2,X) = f(X2,f(f(X2,X),f(X2,X))),
inference(symmetry,[status(thm)],[c354]) ).
cnf(c356,plain,
f(X,f(X3,X2)) = f(X,f(X3,f(f(X3,X2),f(X3,X2)))),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
f(X,f(X,f(X3,X2))) = f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
f(X3,f(X,f(X,f(X3,X2)))) = f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2)))))),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))) = f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))),
inference(congruence,[status(thm)],[c358]) ).
cnf(c360,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c361,plain,
f(f(X3,X2),f(X3,X)) = f(f(X3,X2),f(X,X3)),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
f(X3,f(f(X3,X2),f(X3,X))) = f(X3,f(f(X3,X2),f(X,X3))),
inference(congruence,[status(thm)],[c361]) ).
cnf(c363,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,X)))) = f(f(X3,X2),f(X3,f(f(X3,X2),f(X,X3)))),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
f(f(X3,X2),f(X,X3)) = f(f(X,X3),f(X3,X2)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c365,plain,
f(X3,f(f(X3,X2),f(X,X3))) = f(X3,f(f(X,X3),f(X3,X2))),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X,X3)))) = f(f(X3,X2),f(X3,f(f(X,X3),f(X3,X2)))),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c368,plain,
f(f(X3,X2),f(X3,f(f(X,X3),f(X3,X2)))) = f(f(X2,X3),f(X3,f(f(X,X3),f(X3,X2)))),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c370,plain,
f(f(X,X3),f(X3,X2)) = f(f(X,X3),f(X2,X3)),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
f(X3,f(f(X,X3),f(X3,X2))) = f(X3,f(f(X,X3),f(X2,X3))),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
f(f(X2,X3),f(X3,f(f(X,X3),f(X3,X2)))) = f(f(X2,X3),f(X3,f(f(X,X3),f(X2,X3)))),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
f(X3,f(f(X,X3),f(X2,X3))) = f(f(f(X,X3),f(X2,X3)),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c374,plain,
f(f(X2,X3),f(X3,f(f(X,X3),f(X2,X3)))) = f(f(X2,X3),f(f(f(X,X3),f(X2,X3)),X3)),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
f(f(f(f(f(f(f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2)),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X2,X4),f(X3,X4))),f(X,f(X3,X4))),f(X,f(X3,X4))),f(f(X2,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))) = X4,
inference(substitution,[status(thm)],[c14]) ).
cnf(c376,plain,
X4 = f(f(f(f(f(f(f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2)),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X2,X4),f(X3,X4))),f(X,f(X3,X4))),f(X,f(X3,X4))),f(f(X2,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
f(f(f(X2,X4),f(X3,X4)),X4) = f(f(f(X2,X4),f(X3,X4)),f(f(f(f(f(f(f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2)),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X2,X4),f(X3,X4))),f(X,f(X3,X4))),f(X,f(X3,X4))),f(f(X2,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2)))),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
f(f(X3,X4),f(f(f(X2,X4),f(X3,X4)),X4)) = f(f(X3,X4),f(f(f(X2,X4),f(X3,X4)),f(f(f(f(f(f(f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2)),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X2,X4),f(X3,X4))),f(X,f(X3,X4))),f(X,f(X3,X4))),f(f(X2,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))))),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
f(f(X3,X4),f(f(f(X2,X4),f(X3,X4)),f(f(f(f(f(f(f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2)),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X2,X4),f(X3,X4))),f(X,f(X3,X4))),f(X,f(X3,X4))),f(f(X2,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))))) = f(f(X2,X4),f(X3,X4)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c380,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c381,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c380]) ).
cnf(c382,plain,
f(f(X,X3),f(X2,X3)) = f(f(X,X3),f(X3,X2)),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
f(f(X3,X2),f(X,X3)) = f(f(X,X3),f(X3,X2)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c384,plain,
f(f(X,X3),f(X3,X2)) = f(f(X3,X2),f(X,X3)),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c386,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c385]) ).
cnf(c387,plain,
f(f(X3,X2),f(X,X3)) = f(f(X3,X2),f(X3,X)),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
f(f(X,X3),f(X3,X2)) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c384,c387]) ).
cnf(c389,plain,
f(f(X,X3),f(X2,X3)) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c382,c388]) ).
cnf(c390,plain,
f(f(X3,X4),f(f(f(X2,X4),f(X3,X4)),f(f(f(f(f(f(f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2)),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))),f(f(X2,X4),f(X3,X4))),f(X,f(X3,X4))),f(X,f(X3,X4))),f(f(X2,X4),f(X3,X4))),f(X4,f(f(f(f(f(f(X2,X2),X4),X3),X3),X4),X2))))) = f(f(X4,X3),f(X4,X2)),
inference(transitivity,[status(thm)],[c379,c389]) ).
cnf(c391,plain,
f(f(X2,X3),f(f(f(X,X3),f(X2,X3)),X3)) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c378,c390]) ).
cnf(c392,plain,
f(f(X2,X3),f(X3,f(f(X,X3),f(X2,X3)))) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c374,c391]) ).
cnf(c393,plain,
f(f(X2,X3),f(X3,f(f(X,X3),f(X3,X2)))) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c372,c392]) ).
cnf(c394,plain,
f(f(X3,X2),f(X3,f(f(X,X3),f(X3,X2)))) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c368,c393]) ).
cnf(c395,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X,X3)))) = f(f(X3,X2),f(X3,X)),
inference(transitivity,[status(thm)],[c366,c394]) ).
cnf(c396,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)],[c363,c395]) ).
cnf(c397,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))))) = f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))),
inference(substitution,[status(thm)],[c396]) ).
cnf(c398,plain,
f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))) = f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))))),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
f(X2,f(X,X)) = f(f(X,X),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c400,plain,
f(X,f(X3,f(X2,X2))) = f(X,f(f(X2,X2),X3)),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
f(X,f(X,f(X3,f(X2,X2)))) = f(X,f(X,f(f(X2,X2),X3))),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
f(X3,f(X,f(X,f(X3,f(X2,X2))))) = f(X3,f(X,f(X,f(f(X2,X2),X3)))),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))) = f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))) = f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3)))))),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))))) = f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))))),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
f(X,f(f(X2,X2),X3)) = f(f(f(X2,X2),X3),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c407,plain,
f(X,f(X,f(f(X2,X2),X3))) = f(X,f(f(f(X2,X2),X3),X)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
f(X3,f(X,f(X,f(f(X2,X2),X3)))) = f(X3,f(X,f(f(f(X2,X2),X3),X))),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))) = f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))),
inference(congruence,[status(thm)],[c408]) ).
cnf(c410,plain,
f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3)))))) = f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X))))),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))))) = f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))),
inference(congruence,[status(thm)],[c410]) ).
cnf(c412,plain,
f(X,f(f(f(X2,X2),X3),X)) = f(f(f(f(X2,X2),X3),X),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c413,plain,
f(X3,f(X,f(f(f(X2,X2),X3),X))) = f(X3,f(f(f(f(X2,X2),X3),X),X)),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))) = f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X))))) = f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X)))),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))))),
inference(congruence,[status(thm)],[c415]) ).
cnf(c417,plain,
f(X3,f(f(f(f(X2,X2),X3),X),X)) = f(f(f(f(f(X2,X2),X3),X),X),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c418,plain,
f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))) = f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X)))) = f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3))),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))))) = f(f(X4,f(X4,X4)),f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)))),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)) = f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c422,plain,
f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3))) = f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),
inference(congruence,[status(thm)],[c421]) ).
cnf(c423,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)))) = f(f(X4,f(X4,X4)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
f(f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))),f(X,f(f(f(X2,X),X),f(X2,X)))) = f(f(f(X2,X),X),f(X2,X)),
inference(substitution,[status(thm)],[c257]) ).
cnf(c425,plain,
f(f(f(X2,X),X),f(X2,X)) = f(f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))),f(X,f(f(f(X2,X),X),f(X2,X)))),
inference(symmetry,[status(thm)],[c424]) ).
cnf(c426,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c427,plain,
f(f(X,X2),X2) = f(f(X,X2),f(f(X2,X2),f(X,X2))),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
f(f(f(X,X2),X2),f(X,X2)) = f(f(f(X,X2),f(f(X2,X2),f(X,X2))),f(X,X2)),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
f(X2,f(f(f(X,X2),X2),f(X,X2))) = f(X2,f(f(f(X,X2),f(f(X2,X2),f(X,X2))),f(X,X2))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c431,plain,
f(X2,f(f(f(X,X2),f(f(X2,X2),f(X,X2))),f(X,X2))) = f(f(f(X2,X2),f(X,X2)),f(f(f(X,X2),f(f(X2,X2),f(X,X2))),f(X,X2))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
f(f(f(X2,X2),f(X,X2)),f(f(f(X,X2),f(f(X2,X2),f(X,X2))),f(X,X2))) = f(f(f(X2,X2),f(X,X2)),f(f(X2,X2),f(X,X2))),
inference(substitution,[status(thm)],[c176]) ).
cnf(c433,plain,
f(f(f(X2,X2),f(X,X2)),f(f(X2,X2),f(X,X2))) = f(f(f(X2,X2),f(X,X2)),X2),
inference(substitution,[status(thm)],[c185]) ).
cnf(c434,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c435,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)],[c434]) ).
cnf(c436,plain,
f(X2,X) = f(f(f(X2,X),f(X2,X)),X2),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c437,plain,
f(f(X2,X),f(X2,X2)) = f(f(f(f(X2,X),f(X2,X)),X2),f(X2,X2)),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
f(f(f(f(X2,X),f(X2,X)),X2),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c306]) ).
cnf(c439,plain,
f(f(X2,X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c437,c438]) ).
cnf(c440,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c439]) ).
cnf(c441,plain,
f(f(f(X2,X2),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c435,c440]) ).
cnf(c442,plain,
f(f(f(X2,X2),f(X,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c441]) ).
cnf(c443,plain,
f(f(f(X2,X2),f(X,X2)),f(f(X2,X2),f(X,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c433,c442]) ).
cnf(c444,plain,
f(f(f(X2,X2),f(X,X2)),f(f(f(X,X2),f(f(X2,X2),f(X,X2))),f(X,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c432,c443]) ).
cnf(c445,plain,
f(X2,f(f(f(X,X2),f(f(X2,X2),f(X,X2))),f(X,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c431,c444]) ).
cnf(c446,plain,
f(X2,f(f(f(X,X2),X2),f(X,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c429,c445]) ).
cnf(c447,plain,
f(X,f(f(f(X2,X),X),f(X2,X))) = f(X,X),
inference(substitution,[status(thm)],[c446]) ).
cnf(c448,plain,
f(f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))),f(X,f(f(f(X2,X),X),f(X2,X)))) = f(f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))),f(X,X)),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))) = f(f(f(f(X2,X),X),f(X2,X)),X),
inference(substitution,[status(thm)],[c185]) ).
cnf(c450,plain,
f(f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))),f(X,X)) = f(f(f(f(f(X2,X),X),f(X2,X)),X),f(X,X)),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
f(f(f(f(f(X2,X),X),f(X2,X)),X),f(X,X)) = X,
inference(substitution,[status(thm)],[c306]) ).
cnf(c452,plain,
f(f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))),f(X,X)) = X,
inference(transitivity,[status(thm)],[c450,c451]) ).
cnf(c453,plain,
f(f(f(f(f(X2,X),X),f(X2,X)),f(f(f(X2,X),X),f(X2,X))),f(X,f(f(f(X2,X),X),f(X2,X)))) = X,
inference(transitivity,[status(thm)],[c448,c452]) ).
cnf(c454,plain,
f(f(f(X2,X),X),f(X2,X)) = X,
inference(transitivity,[status(thm)],[c425,c453]) ).
cnf(c455,plain,
f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))),f(f(X2,f(X2,X2)),f(X,f(X,X)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c454]) ).
cnf(c456,plain,
f(X,f(X,X)) = f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))),f(f(X2,f(X2,X2)),f(X,f(X,X)))),
inference(symmetry,[status(thm)],[c455]) ).
cnf(c457,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c458,plain,
f(f(X2,f(X2,X)),X2) = f(f(X2,f(X2,X)),f(f(X2,X2),f(X2,X))),
inference(congruence,[status(thm)],[c457]) ).
cnf(c459,plain,
X2 = f(f(X2,X2),f(X2,X)),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c460,plain,
f(X2,f(X2,X)) = f(f(f(X2,X2),f(X2,X)),f(X2,X)),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
f(f(X2,f(X2,X)),f(f(X2,X2),f(X2,X))) = f(f(f(f(X2,X2),f(X2,X)),f(X2,X)),f(f(X2,X2),f(X2,X))),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
f(f(f(f(X2,X2),f(X2,X)),f(X2,X)),f(f(X2,X2),f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c454]) ).
cnf(c463,plain,
f(f(X2,f(X2,X)),f(f(X2,X2),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c461,c462]) ).
cnf(c464,plain,
f(f(X2,f(X2,X)),X2) = f(X2,X),
inference(transitivity,[status(thm)],[c458,c463]) ).
cnf(c465,plain,
f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X),f(X2,X)))),f(X2,X2)) = f(f(X2,X2),f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c464]) ).
cnf(c466,plain,
f(f(X2,X2),f(f(X2,X),f(X2,X))) = f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X),f(X2,X)))),f(X2,X2)),
inference(symmetry,[status(thm)],[c465]) ).
cnf(c467,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c468,plain,
f(f(X2,X),f(X2,f(X2,X2))) = f(f(X,X2),f(X2,f(X2,X2))),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
f(f(X,X2),f(X2,f(X2,X2))) = f(f(X2,f(X2,X2)),f(X,X2)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c470,plain,
f(X,f(X,X)) = f(f(X,X),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c471,plain,
f(f(X2,f(X2,X2)),f(X,X2)) = f(f(f(X2,X2),X2),f(X,X2)),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
f(f(f(X2,X2),f(X,X2)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c441]) ).
cnf(c473,plain,
f(X2,X2) = f(f(f(X2,X2),f(X,X2)),X2),
inference(symmetry,[status(thm)],[c472]) ).
cnf(c474,plain,
f(f(X2,X2),X2) = f(f(f(f(X2,X2),f(X,X2)),X2),X2),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
f(f(f(X2,X2),X2),f(X,X2)) = f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)))) = f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),
inference(substitution,[status(thm)],[c317]) ).
cnf(c477,plain,
f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)) = f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)))),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c478,plain,
f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)))) = f(f(X,X2),f(X,X2)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c479,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c480,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c479,c281]) ).
cnf(c481,plain,
f(f(X,X2),f(f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)),f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)))) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c478,c480]) ).
cnf(c482,plain,
f(f(f(f(f(X2,X2),f(X,X2)),X2),X2),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c477,c481]) ).
cnf(c483,plain,
f(f(f(X2,X2),X2),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c475,c482]) ).
cnf(c484,plain,
f(f(X2,f(X2,X2)),f(X,X2)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c471,c483]) ).
cnf(c485,plain,
f(f(X,X2),f(X2,f(X2,X2))) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c469,c484]) ).
cnf(c486,plain,
f(f(X2,X),f(X2,f(X2,X2))) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c468,c485]) ).
cnf(c487,plain,
f(f(X2,X),f(X2,X)) = f(f(X2,X),f(X2,f(X2,X2))),
inference(symmetry,[status(thm)],[c486]) ).
cnf(c488,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(X2,f(f(X3,X),f(X3,f(X3,X3)))),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))) = f(f(X3,X3),f(X2,f(f(X3,X),f(X3,f(X3,X3))))),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c491,plain,
f(f(X2,X),f(X2,f(X2,X2))) = f(f(X,X2),f(X2,f(X2,X2))),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
f(X2,f(f(X3,X),f(X3,f(X3,X3)))) = f(X2,f(f(X,X3),f(X3,f(X3,X3)))),
inference(congruence,[status(thm)],[c491]) ).
cnf(c493,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,f(X3,X3))))) = f(f(X3,X3),f(X2,f(f(X,X3),f(X3,f(X3,X3))))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
f(X2,f(f(X,X3),f(X3,f(X3,X3)))) = f(f(f(X,X3),f(X3,f(X3,X3))),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c495,plain,
f(f(X3,X3),f(X2,f(f(X,X3),f(X3,f(X3,X3))))) = f(f(X3,X3),f(f(f(X,X3),f(X3,f(X3,X3))),X2)),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
f(f(X3,X3),f(f(f(X,X3),f(X3,f(X3,X3))),X2)) = f(f(f(f(X,X3),f(X3,f(X3,X3))),X2),f(X3,X3)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c497,plain,
f(X2,X2) = f(X2,f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c498,plain,
f(f(f(f(X,X3),f(X3,f(X3,X3))),X2),f(X3,X3)) = f(f(f(f(X,X3),f(X3,f(X3,X3))),X2),f(X3,f(f(X3,X3),X))),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
f(f(f(X,f(X,X)),f(X,f(X,X))),X) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c288]) ).
cnf(c500,plain,
f(X,f(X,X)) = f(f(f(X,f(X,X)),f(X,f(X,X))),X),
inference(symmetry,[status(thm)],[c499]) ).
cnf(c501,plain,
f(f(X,X2),f(X2,f(X2,X2))) = f(f(X,X2),f(f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),X2)),
inference(congruence,[status(thm)],[c500]) ).
cnf(c502,plain,
f(f(f(X,X3),f(X3,f(X3,X3))),X2) = f(f(f(X,X3),f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X3)),X2),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
f(f(f(f(X,X3),f(X3,f(X3,X3))),X2),f(X3,f(f(X3,X3),X))) = f(f(f(f(X,X3),f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X3)),X2),f(X3,f(f(X3,X3),X))),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
f(f(X,X),f(f(f(f(X,X),X),f(X,X)),X)) = X,
inference(substitution,[status(thm)],[c257]) ).
cnf(c505,plain,
X = f(f(X,X),f(f(f(f(X,X),X),f(X,X)),X)),
inference(symmetry,[status(thm)],[c504]) ).
cnf(c506,plain,
f(f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),X) = f(f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),f(f(X,X),f(f(f(f(X,X),X),f(X,X)),X))),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
f(f(f(X,X),f(X,X)),X) = f(X,X),
inference(substitution,[status(thm)],[c189]) ).
cnf(c508,plain,
f(X,X) = f(f(f(X,X),f(X,X)),X),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
f(f(X,X),X) = f(f(f(f(X,X),f(X,X)),X),X),
inference(congruence,[status(thm)],[c508]) ).
cnf(c510,plain,
f(f(f(X,X),X),f(X,X)) = f(f(f(f(f(X,X),f(X,X)),X),X),f(X,X)),
inference(congruence,[status(thm)],[c509]) ).
cnf(c511,plain,
f(f(f(f(X,X),X),f(X,X)),X) = f(f(f(f(f(f(X,X),f(X,X)),X),X),f(X,X)),X),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
f(f(X,X),f(f(f(f(X,X),X),f(X,X)),X)) = f(f(X,X),f(f(f(f(f(f(X,X),f(X,X)),X),X),f(X,X)),X)),
inference(congruence,[status(thm)],[c511]) ).
cnf(c513,plain,
f(f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),f(f(X,X),f(f(f(f(X,X),X),f(X,X)),X))) = f(f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),f(f(X,X),f(f(f(f(f(f(X,X),f(X,X)),X),X),f(X,X)),X))),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
f(f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),f(f(X,X),f(f(f(f(f(f(X,X),f(X,X)),X),X),f(X,X)),X))) = f(X,X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c515,plain,
f(f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),f(f(X,X),f(f(f(f(X,X),X),f(X,X)),X))) = f(X,X),
inference(transitivity,[status(thm)],[c513,c514]) ).
cnf(c516,plain,
f(f(X2,f(f(X,f(X,X)),f(X,f(X,X)))),X) = f(X,X),
inference(transitivity,[status(thm)],[c506,c515]) ).
cnf(c517,plain,
f(f(f(f(f(X,X),X2),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c516]) ).
cnf(c518,plain,
f(X2,X2) = f(f(f(f(f(X,X),X2),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),X2),
inference(symmetry,[status(thm)],[c517]) ).
cnf(c519,plain,
f(f(X2,X2),X) = f(f(f(f(f(f(X,X),X2),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),X2),X),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
f(X2,f(f(X2,X2),X)) = f(X2,f(f(f(f(f(f(X,X),X2),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),X2),X)),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
f(f(f(f(X,X3),f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X3)),X2),f(X3,f(f(X3,X3),X))) = f(f(f(f(X,X3),f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X3)),X2),f(X3,f(f(f(f(f(f(X,X),X3),f(f(X3,f(X3,X3)),f(X3,f(X3,X3)))),f(f(X3,f(X3,X3)),f(X3,f(X3,X3)))),X3),X))),
inference(congruence,[status(thm)],[c520]) ).
cnf(c522,plain,
f(f(f(f(X,X3),f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X3)),X2),f(X3,f(f(f(f(f(f(X,X),X3),f(f(X3,f(X3,X3)),f(X3,f(X3,X3)))),f(f(X3,f(X3,X3)),f(X3,f(X3,X3)))),X3),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c523,plain,
f(f(f(f(X,X3),f(f(f(X3,f(X3,X3)),f(X3,f(X3,X3))),X3)),X2),f(X3,f(f(X3,X3),X))) = X3,
inference(transitivity,[status(thm)],[c521,c522]) ).
cnf(c524,plain,
f(f(f(f(X,X3),f(X3,f(X3,X3))),X2),f(X3,f(f(X3,X3),X))) = X3,
inference(transitivity,[status(thm)],[c503,c523]) ).
cnf(c525,plain,
f(f(f(f(X,X3),f(X3,f(X3,X3))),X2),f(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c498,c524]) ).
cnf(c526,plain,
f(f(X3,X3),f(f(f(X,X3),f(X3,f(X3,X3))),X2)) = X3,
inference(transitivity,[status(thm)],[c496,c525]) ).
cnf(c527,plain,
f(f(X3,X3),f(X2,f(f(X,X3),f(X3,f(X3,X3))))) = X3,
inference(transitivity,[status(thm)],[c495,c526]) ).
cnf(c528,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,f(X3,X3))))) = X3,
inference(transitivity,[status(thm)],[c493,c527]) ).
cnf(c529,plain,
f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))) = X3,
inference(transitivity,[status(thm)],[c489,c528]) ).
cnf(c530,plain,
f(f(X2,X2),f(f(X2,X2),f(f(X2,X),f(X2,X)))) = X2,
inference(substitution,[status(thm)],[c529]) ).
cnf(c531,plain,
f(f(f(X2,X2),f(f(X2,X2),f(f(X2,X),f(X2,X)))),f(X2,X2)) = f(X2,f(X2,X2)),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
f(f(X2,X2),f(f(X2,X),f(X2,X))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c466,c531]) ).
cnf(c533,plain,
f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c532]) ).
cnf(c534,plain,
f(X,f(X,X)) = f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))),
inference(symmetry,[status(thm)],[c533]) ).
cnf(c535,plain,
f(X2,f(X,f(X,X))) = f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(congruence,[status(thm)],[c534]) ).
cnf(c536,plain,
f(f(X,f(X2,X2)),f(f(X2,X2),X)) = f(f(X,f(X2,X2)),f(X,f(X2,X2))),
inference(substitution,[status(thm)],[c281]) ).
cnf(c537,plain,
f(f(X,f(X2,X2)),f(X,f(X2,X2))) = f(f(X,f(X2,X2)),f(f(X2,X2),X)),
inference(symmetry,[status(thm)],[c536]) ).
cnf(c538,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),X))),
inference(congruence,[status(thm)],[c537]) ).
cnf(c539,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),X)))),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
f(f(X,f(X2,X2)),f(f(X2,X2),X)) = f(f(f(X2,X2),X),f(f(X2,X2),X)),
inference(substitution,[status(thm)],[c327]) ).
cnf(c541,plain,
f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X))) = f(X2,f(f(f(X3,X3),X),f(f(X3,X3),X))),
inference(congruence,[status(thm)],[c540]) ).
cnf(c542,plain,
f(X3,f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X)))) = f(X3,f(X2,f(f(f(X3,X3),X),f(f(X3,X3),X)))),
inference(congruence,[status(thm)],[c541]) ).
cnf(c543,plain,
X = f(f(X,X),f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c544,plain,
f(X3,f(X2,f(f(f(X3,X3),X),f(f(X3,X3),X)))) = f(f(f(X3,X3),f(X3,X3)),f(X2,f(f(f(X3,X3),X),f(f(X3,X3),X)))),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
f(f(f(X3,X3),f(X3,X3)),f(X2,f(f(f(X3,X3),X),f(f(X3,X3),X)))) = f(X3,X3),
inference(substitution,[status(thm)],[c529]) ).
cnf(c546,plain,
f(X3,f(X2,f(f(f(X3,X3),X),f(f(X3,X3),X)))) = f(X3,X3),
inference(transitivity,[status(thm)],[c544,c545]) ).
cnf(c547,plain,
f(X3,f(X2,f(f(X,f(X3,X3)),f(f(X3,X3),X)))) = f(X3,X3),
inference(transitivity,[status(thm)],[c542,c546]) ).
cnf(c548,plain,
f(X3,f(X2,f(f(X,f(X3,X3)),f(X,f(X3,X3))))) = f(X3,X3),
inference(transitivity,[status(thm)],[c539,c547]) ).
cnf(c549,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c548]) ).
cnf(c550,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c548]) ).
cnf(c551,plain,
f(X2,X2) = f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(symmetry,[status(thm)],[c550]) ).
cnf(c552,plain,
f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c532]) ).
cnf(c553,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,f(X,f(X,X))),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
f(X2,X2) = f(X2,f(X,f(X,X))),
inference(transitivity,[status(thm)],[c551,c553]) ).
cnf(c555,plain,
f(X3,f(f(X,X),f(f(X,f(X3,X3)),f(X,f(X3,X3))))) = f(X3,f(X2,f(X2,X2))),
inference(transitivity,[status(thm)],[c549,c554]) ).
cnf(c556,plain,
f(X3,f(X,f(X,X))) = f(X3,f(X2,f(X2,X2))),
inference(transitivity,[status(thm)],[c535,c555]) ).
cnf(c557,plain,
f(f(X2,f(X2,X2)),f(X,f(X,X))) = f(f(X2,f(X2,X2)),f(X2,f(X2,X2))),
inference(substitution,[status(thm)],[c556]) ).
cnf(c558,plain,
f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))),f(f(X2,f(X2,X2)),f(X,f(X,X)))) = f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))) = f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X2,f(X2,X2))),
inference(substitution,[status(thm)],[c556]) ).
cnf(c560,plain,
f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))) = f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X2,f(X2,X2))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X2,f(X2,X2))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))) = f(X2,f(X2,X2)),
inference(substitution,[status(thm)],[c306]) ).
cnf(c562,plain,
f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))),f(f(X2,f(X2,X2)),f(X2,f(X2,X2)))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c560,c561]) ).
cnf(c563,plain,
f(f(f(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,f(X,X))),f(f(X2,f(X2,X2)),f(X,f(X,X)))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c558,c562]) ).
cnf(c564,plain,
f(X,f(X,X)) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c456,c563]) ).
cnf(c565,plain,
f(X2,f(X2,X2)) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c564]) ).
cnf(c566,plain,
f(f(X4,f(X4,X4)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = f(f(X3,f(X3,X3)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(congruence,[status(thm)],[c565]) ).
cnf(c567,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c257]) ).
cnf(c568,plain,
X = f(f(X,X),f(X2,X)),
inference(symmetry,[status(thm)],[c567]) ).
cnf(c569,plain,
f(X2,X) = f(X2,f(f(X,X),f(X2,X))),
inference(congruence,[status(thm)],[c568]) ).
cnf(c570,plain,
f(f(X2,f(X2,X2)),f(X2,X)) = f(f(X2,f(X2,X2)),f(X2,f(f(X,X),f(X2,X)))),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c572,plain,
f(X,f(X3,X2)) = f(X,f(X2,X3)),
inference(congruence,[status(thm)],[c571]) ).
cnf(c573,plain,
f(X3,f(X,f(X3,X2))) = f(X3,f(X,f(X2,X3))),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
f(f(X3,f(X3,X3)),f(X3,f(X,f(X3,X2)))) = f(f(X3,f(X3,X3)),f(X3,f(X,f(X2,X3)))),
inference(congruence,[status(thm)],[c573]) ).
cnf(c575,plain,
f(f(X3,f(X3,X3)),f(X3,f(X,f(X2,X3)))) = f(f(X3,f(X,f(X2,X3))),f(X3,f(X3,X3))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c576,plain,
f(f(X3,f(X,f(X2,X3))),f(X3,f(X3,X3))) = f(f(X3,f(X,f(X2,X3))),f(X3,f(X,f(X2,X3)))),
inference(substitution,[status(thm)],[c486]) ).
cnf(c577,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c578,plain,
f(X3,f(X,f(X2,X3))) = f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),
inference(congruence,[status(thm)],[c577]) ).
cnf(c579,plain,
f(f(X3,f(X,f(X2,X3))),f(X3,f(X,f(X2,X3)))) = f(f(X3,f(X,f(X2,X3))),f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3)))),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
X2 = f(f(X2,X2),f(X,X2)),
inference(symmetry,[status(thm)],[c257]) ).
cnf(c581,plain,
f(X3,f(X,f(X2,X3))) = f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),
inference(congruence,[status(thm)],[c580]) ).
cnf(c582,plain,
f(f(X3,f(X,f(X2,X3))),f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3)))) = f(f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3)))),
inference(congruence,[status(thm)],[c581]) ).
cnf(c583,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3)))) = f(f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),f(X2,X3)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c584,plain,
f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))) = f(X3,f(X,f(X2,X3))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c585,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),f(X2,X3)) = f(f(X3,f(X,f(X2,X3))),f(X2,X3)),
inference(congruence,[status(thm)],[c584]) ).
cnf(c586,plain,
f(f(X2,X3),f(X3,f(X,f(X2,X3)))) = f(f(X3,f(X,f(X2,X3))),f(X2,X3)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c587,plain,
f(f(X3,f(X,f(X2,X3))),f(X2,X3)) = f(f(X2,X3),f(X3,f(X,f(X2,X3)))),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c589,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c588]) ).
cnf(c590,plain,
f(X,f(X2,X3)) = f(X,f(X3,X2)),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
f(X3,f(X,f(X2,X3))) = f(X3,f(X,f(X3,X2))),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
f(f(X2,X3),f(X3,f(X,f(X2,X3)))) = f(f(X2,X3),f(X3,f(X,f(X3,X2)))),
inference(congruence,[status(thm)],[c591]) ).
cnf(c593,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c594,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c593]) ).
cnf(c595,plain,
f(f(X2,X3),f(X3,f(X,f(X3,X2)))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(congruence,[status(thm)],[c594]) ).
cnf(c596,plain,
f(f(X2,X3),f(X3,f(X,f(X2,X3)))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c592,c595]) ).
cnf(c597,plain,
f(f(X3,f(X,f(X2,X3))),f(X2,X3)) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c587,c596]) ).
cnf(c598,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),f(X2,X3)) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c585,c597]) ).
cnf(c599,plain,
f(f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3))),f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3)))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c583,c598]) ).
cnf(c600,plain,
f(f(X3,f(X,f(X2,X3))),f(f(f(X3,X3),f(X2,X3)),f(X,f(X2,X3)))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c582,c599]) ).
cnf(c601,plain,
f(f(X3,f(X,f(X2,X3))),f(X3,f(X,f(X2,X3)))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c579,c600]) ).
cnf(c602,plain,
f(f(X3,f(X,f(X2,X3))),f(X3,f(X3,X3))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c576,c601]) ).
cnf(c603,plain,
f(f(X3,f(X3,X3)),f(X3,f(X,f(X2,X3)))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c575,c602]) ).
cnf(c604,plain,
f(f(X3,f(X3,X3)),f(X3,f(X,f(X3,X2)))) = f(f(X3,X2),f(X3,f(X,f(X3,X2)))),
inference(transitivity,[status(thm)],[c574,c603]) ).
cnf(c605,plain,
f(f(X2,f(X2,X2)),f(X2,f(f(X,X),f(X2,X)))) = f(f(X2,X),f(X2,f(f(X,X),f(X2,X)))),
inference(substitution,[status(thm)],[c604]) ).
cnf(c606,plain,
f(f(X,X),f(X2,X)) = X,
inference(substitution,[status(thm)],[c257]) ).
cnf(c607,plain,
f(X2,f(f(X,X),f(X2,X))) = f(X2,X),
inference(congruence,[status(thm)],[c606]) ).
cnf(c608,plain,
f(f(X2,X),f(X2,f(f(X,X),f(X2,X)))) = f(f(X2,X),f(X2,X)),
inference(congruence,[status(thm)],[c607]) ).
cnf(c609,plain,
f(f(X2,f(X2,X2)),f(X2,f(f(X,X),f(X2,X)))) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c605,c608]) ).
cnf(c610,plain,
f(f(X2,f(X2,X2)),f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(transitivity,[status(thm)],[c570,c609]) ).
cnf(c611,plain,
f(f(X3,f(X3,X3)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(substitution,[status(thm)],[c610]) ).
cnf(c612,plain,
f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c613,plain,
X3 = f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(symmetry,[status(thm)],[c612]) ).
cnf(c614,plain,
f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)) = f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(congruence,[status(thm)],[c614]) ).
cnf(c616,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c617,plain,
f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c618,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(f(f(f(f(X2,X3),f(X,X3)),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(transitivity,[status(thm)],[c616,c617]) ).
cnf(c619,plain,
f(f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(transitivity,[status(thm)],[c615,c618]) ).
cnf(c620,plain,
f(f(X3,f(X3,X3)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(transitivity,[status(thm)],[c611,c619]) ).
cnf(c621,plain,
f(f(X4,f(X4,X4)),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(transitivity,[status(thm)],[c566,c620]) ).
cnf(c622,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)))) = X3,
inference(transitivity,[status(thm)],[c423,c621]) ).
cnf(c623,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))))) = X3,
inference(transitivity,[status(thm)],[c420,c622]) ).
cnf(c624,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = X3,
inference(transitivity,[status(thm)],[c416,c623]) ).
cnf(c625,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))))) = X3,
inference(transitivity,[status(thm)],[c411,c624]) ).
cnf(c626,plain,
f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))))) = X3,
inference(transitivity,[status(thm)],[c405,c625]) ).
cnf(c627,plain,
X3 = f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))))),
inference(symmetry,[status(thm)],[c626]) ).
cnf(c628,plain,
f(X5,X3) = f(X5,f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))))),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
f(f(X4,f(X4,X4)),f(X5,X3)) = f(f(X4,f(X4,X4)),f(X5,f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))))))),
inference(congruence,[status(thm)],[c628]) ).
cnf(c630,plain,
f(X5,f(f(X4,f(X4,X4)),f(X5,X3))) = f(X5,f(f(X4,f(X4,X4)),f(X5,f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))))))),
inference(congruence,[status(thm)],[c629]) ).
cnf(c631,plain,
f(f(X3,f(X3,X3)),f(X4,f(X2,f(X4,f(X,f(X,f(X4,f(X2,X2)))))))) = X4,
inference(substitution,[status(thm)],[c626]) ).
cnf(c632,plain,
X4 = f(f(X3,f(X3,X3)),f(X4,f(X2,f(X4,f(X,f(X,f(X4,f(X2,X2)))))))),
inference(symmetry,[status(thm)],[c631]) ).
cnf(c633,plain,
f(X5,f(f(X4,f(X4,X4)),X3)) = f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)),
inference(congruence,[status(thm)],[c632]) ).
cnf(c634,plain,
f(f(X4,f(X4,X4)),f(X5,f(f(X4,f(X4,X4)),X3))) = f(f(X4,f(X4,X4)),f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3))),
inference(congruence,[status(thm)],[c633]) ).
cnf(c635,plain,
f(X5,f(f(X4,f(X4,X4)),f(X5,f(f(X4,f(X4,X4)),X3)))) = f(X5,f(f(X4,f(X4,X4)),f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)))),
inference(congruence,[status(thm)],[c634]) ).
cnf(c636,plain,
f(f(X3,f(X3,X3)),f(X4,f(X2,f(X4,f(X,f(X,f(X4,f(X2,X2)))))))) = X4,
inference(substitution,[status(thm)],[c626]) ).
cnf(c637,plain,
X4 = f(f(X3,f(X3,X3)),f(X4,f(X2,f(X4,f(X,f(X,f(X4,f(X2,X2)))))))),
inference(symmetry,[status(thm)],[c636]) ).
cnf(c638,plain,
f(X5,f(f(X4,f(X4,X4)),f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)))) = f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)))),
inference(congruence,[status(thm)],[c637]) ).
cnf(c639,plain,
f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)))) = f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)),
inference(substitution,[status(thm)],[c396]) ).
cnf(c640,plain,
f(f(X3,f(X3,X3)),f(X4,f(X2,f(X4,f(X,f(X,f(X4,f(X2,X2)))))))) = X4,
inference(substitution,[status(thm)],[c626]) ).
cnf(c641,plain,
f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)) = f(X5,f(f(X4,f(X4,X4)),X3)),
inference(congruence,[status(thm)],[c640]) ).
cnf(c642,plain,
f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)))) = f(X5,f(f(X4,f(X4,X4)),X3)),
inference(transitivity,[status(thm)],[c639,c641]) ).
cnf(c643,plain,
f(X5,f(f(X4,f(X4,X4)),f(f(f(X4,f(X4,X4)),f(X5,f(X2,f(X5,f(X,f(X,f(X5,f(X2,X2)))))))),f(f(X4,f(X4,X4)),X3)))) = f(X5,f(f(X4,f(X4,X4)),X3)),
inference(transitivity,[status(thm)],[c638,c642]) ).
cnf(c644,plain,
f(X3,f(f(X2,f(X2,X2)),f(X3,f(f(X2,f(X2,X2)),X)))) = f(X3,f(f(X2,f(X2,X2)),X)),
inference(transitivity,[status(thm)],[c635,c643]) ).
cnf(c645,plain,
f(X5,f(f(X4,f(X4,X4)),f(X5,f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))))))) = f(X5,f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))))),
inference(substitution,[status(thm)],[c644]) ).
cnf(c646,plain,
f(X5,f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))))) = f(X5,X3),
inference(congruence,[status(thm)],[c626]) ).
cnf(c647,plain,
f(X5,f(f(X4,f(X4,X4)),f(X5,f(f(X4,f(X4,X4)),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))))))) = f(X5,X3),
inference(transitivity,[status(thm)],[c645,c646]) ).
cnf(c648,plain,
f(X3,f(f(X2,f(X2,X2)),f(X3,X))) = f(X3,X),
inference(transitivity,[status(thm)],[c630,c647]) ).
cnf(c649,plain,
f(X4,f(f(X,f(X,X)),f(X4,f(X3,f(X4,f(X2,f(X2,f(X4,f(X3,X3))))))))) = f(X4,f(X3,f(X4,f(X2,f(X2,f(X4,f(X3,X3))))))),
inference(substitution,[status(thm)],[c648]) ).
cnf(c650,plain,
f(X4,f(X3,f(X4,f(X2,f(X2,f(X4,f(X3,X3))))))) = f(X4,f(f(X,f(X,X)),f(X4,f(X3,f(X4,f(X2,f(X2,f(X4,f(X3,X3))))))))),
inference(symmetry,[status(thm)],[c649]) ).
cnf(c651,plain,
f(f(X,f(X,X)),f(X4,f(X3,f(X4,f(X2,f(X2,f(X4,f(X3,X3)))))))) = X4,
inference(substitution,[status(thm)],[c626]) ).
cnf(c652,plain,
f(X4,f(f(X,f(X,X)),f(X4,f(X3,f(X4,f(X2,f(X2,f(X4,f(X3,X3))))))))) = f(X4,X4),
inference(congruence,[status(thm)],[c651]) ).
cnf(c653,plain,
f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))) = f(X3,X3),
inference(transitivity,[status(thm)],[c650,c652]) ).
cnf(c654,plain,
f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2)))))))) = f(X3,X3),
inference(substitution,[status(thm)],[c653]) ).
cnf(c655,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))))) = f(f(X3,X2),f(X3,X3)),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
f(f(X3,X2),f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))))) = X3,
inference(transitivity,[status(thm)],[c655,c439]) ).
cnf(c657,plain,
f(f(X3,X2),f(X3,f(X,f(X,f(X3,f(f(X3,X2),f(X3,X2))))))) = X3,
inference(transitivity,[status(thm)],[c398,c656]) ).
cnf(c658,plain,
f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))) = X3,
inference(transitivity,[status(thm)],[c359,c657]) ).
cnf(c659,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c660,plain,
f(X2,X4) = f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3)))))),
inference(congruence,[status(thm)],[c659]) ).
cnf(c661,plain,
f(X2,f(X2,X4)) = f(X2,f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))))),
inference(congruence,[status(thm)],[c660]) ).
cnf(c662,plain,
f(f(X4,X3),f(X2,f(X2,X4))) = f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3)))))))),
inference(congruence,[status(thm)],[c661]) ).
cnf(c663,plain,
f(X4,f(f(X4,X3),f(X2,f(X2,X4)))) = f(X4,f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))))))),
inference(congruence,[status(thm)],[c662]) ).
cnf(c664,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c665,plain,
f(X4,f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))))))) = f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))))))),
inference(congruence,[status(thm)],[c664]) ).
cnf(c666,plain,
f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))))))) = f(X4,X3),
inference(substitution,[status(thm)],[c658]) ).
cnf(c667,plain,
f(X4,f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))))))) = f(X4,X3),
inference(transitivity,[status(thm)],[c665,c666]) ).
cnf(c668,plain,
f(X3,f(f(X3,X2),f(X,f(X,X3)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c663,c667]) ).
cnf(c669,plain,
f(X3,f(f(X3,X2),f(X,f(X3,X)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c350,c668]) ).
cnf(c670,plain,
f(X3,f(f(X2,X3),f(X,f(X3,X)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c346,c669]) ).
cnf(c671,plain,
f(f(f(X2,X4),f(X2,X4)),f(f(X3,f(f(X2,X4),f(X2,X4))),f(X,f(f(f(X2,X4),f(X2,X4)),X)))) = f(f(f(X2,X4),f(X2,X4)),X3),
inference(substitution,[status(thm)],[c670]) ).
cnf(c672,plain,
f(f(f(X2,X4),f(X2,X4)),X3) = f(f(f(X2,X4),f(X2,X4)),f(f(X3,f(f(X2,X4),f(X2,X4))),f(X,f(f(f(X2,X4),f(X2,X4)),X)))),
inference(symmetry,[status(thm)],[c671]) ).
cnf(c673,plain,
f(f(X2,X),f(X2,X)) = f(f(X2,X),f(X,X2)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c674,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,X),f(X3,X))) = f(f(f(X3,X2),f(X3,X2)),f(f(X3,X),f(X,X3))),
inference(congruence,[status(thm)],[c673]) ).
cnf(c675,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,X),f(X,X3))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,X3))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c676,plain,
f(X3,f(X2,f(X3,f(X2,X)))) = f(f(X2,f(X3,f(X2,X))),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c677,plain,
f(f(X4,f(X3,X2)),f(X4,f(X4,f(X3,f(X,f(X3,X2)))))) = f(f(X4,f(X4,f(X3,f(X,f(X3,X2))))),f(X4,f(X3,X2))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c678,plain,
f(X,f(X3,X2)) = f(f(X3,X2),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c679,plain,
f(X3,f(X,f(X3,X2))) = f(X3,f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c678]) ).
cnf(c680,plain,
f(X2,f(X4,f(X,f(X4,X3)))) = f(X2,f(X4,f(f(X4,X3),X))),
inference(congruence,[status(thm)],[c679]) ).
cnf(c681,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(X2,f(X4,f(f(X4,X3),X)))),
inference(congruence,[status(thm)],[c680]) ).
cnf(c682,plain,
f(f(f(X4,X3),f(X4,X3)),f(X2,f(X4,f(f(X4,X3),X)))) = f(f(X2,f(X4,f(f(X4,X3),X))),f(f(X4,X3),f(X4,X3))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c683,plain,
f(f(X4,X3),f(f(X4,f(X,f(X,f(X4,X3)))),f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(f(X4,f(X,f(X,f(X4,X3)))),f(X4,f(X,f(X,f(X4,X3))))))))))) = f(f(X4,X3),f(X4,X3)),
inference(substitution,[status(thm)],[c653]) ).
cnf(c684,plain,
f(f(X4,X3),f(X4,X3)) = f(f(X4,X3),f(f(X4,f(X,f(X,f(X4,X3)))),f(f(X4,X3),f(X2,f(X2,f(f(X4,X3),f(f(X4,f(X,f(X,f(X4,X3)))),f(X4,f(X,f(X,f(X4,X3))))))))))),
inference(symmetry,[status(thm)],[c683]) ).
cnf(c685,plain,
f(f(X3,f(X5,f(f(X5,X4),X2))),f(f(X5,X4),f(X5,X4))) = f(f(X3,f(X5,f(f(X5,X4),X2))),f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(f(X5,X4),f(X2,f(X2,f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(X5,f(X,f(X,f(X5,X4)))))))))))),
inference(congruence,[status(thm)],[c684]) ).
cnf(c686,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c687,plain,
f(X4,f(f(X4,X3),X2)) = f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2)),
inference(congruence,[status(thm)],[c686]) ).
cnf(c688,plain,
f(X3,f(X5,f(f(X5,X4),X2))) = f(X3,f(f(f(X5,X4),f(X5,f(X,f(X,f(X5,X4))))),f(f(X5,X4),X2))),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
f(f(X3,f(X5,f(f(X5,X4),X2))),f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(f(X5,X4),f(X2,f(X2,f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(X5,f(X,f(X,f(X5,X4)))))))))))) = f(f(X3,f(f(f(X5,X4),f(X5,f(X,f(X,f(X5,X4))))),f(f(X5,X4),X2))),f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(f(X5,X4),f(X2,f(X2,f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(X5,f(X,f(X,f(X5,X4)))))))))))),
inference(congruence,[status(thm)],[c688]) ).
cnf(c690,plain,
f(X2,f(X,X)) = f(f(X,X),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c691,plain,
f(X,f(X3,f(X2,X2))) = f(X,f(f(X2,X2),X3)),
inference(congruence,[status(thm)],[c690]) ).
cnf(c692,plain,
f(X,f(X,f(X3,f(X2,X2)))) = f(X,f(X,f(f(X2,X2),X3))),
inference(congruence,[status(thm)],[c691]) ).
cnf(c693,plain,
f(X3,f(X,f(X,f(X3,f(X2,X2))))) = f(X3,f(X,f(X,f(f(X2,X2),X3)))),
inference(congruence,[status(thm)],[c692]) ).
cnf(c694,plain,
f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))) = f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))),
inference(congruence,[status(thm)],[c693]) ).
cnf(c695,plain,
f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))) = f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3)))))),
inference(congruence,[status(thm)],[c694]) ).
cnf(c696,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))))) = f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))))),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
f(X,f(f(X2,X2),X3)) = f(f(f(X2,X2),X3),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c698,plain,
f(X,f(X,f(f(X2,X2),X3))) = f(X,f(f(f(X2,X2),X3),X)),
inference(congruence,[status(thm)],[c697]) ).
cnf(c699,plain,
f(X3,f(X,f(X,f(f(X2,X2),X3)))) = f(X3,f(X,f(f(f(X2,X2),X3),X))),
inference(congruence,[status(thm)],[c698]) ).
cnf(c700,plain,
f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))) = f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))),
inference(congruence,[status(thm)],[c699]) ).
cnf(c701,plain,
f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3)))))) = f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X))))),
inference(congruence,[status(thm)],[c700]) ).
cnf(c702,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))))) = f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))),
inference(congruence,[status(thm)],[c701]) ).
cnf(c703,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c704,plain,
f(f(X3,X2),f(X3,X)) = f(f(X3,X2),f(X,X3)),
inference(congruence,[status(thm)],[c703]) ).
cnf(c705,plain,
f(X4,f(f(X3,X2),f(X3,X))) = f(X4,f(f(X3,X2),f(X,X3))),
inference(congruence,[status(thm)],[c704]) ).
cnf(c706,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = f(f(X4,f(f(X3,X2),f(X,X3))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))),
inference(congruence,[status(thm)],[c705]) ).
cnf(c707,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c708,plain,
f(f(X3,X2),f(X,X3)) = f(f(X2,X3),f(X,X3)),
inference(congruence,[status(thm)],[c707]) ).
cnf(c709,plain,
f(X4,f(f(X3,X2),f(X,X3))) = f(X4,f(f(X2,X3),f(X,X3))),
inference(congruence,[status(thm)],[c708]) ).
cnf(c710,plain,
f(f(X4,f(f(X3,X2),f(X,X3))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))),
inference(congruence,[status(thm)],[c709]) ).
cnf(c711,plain,
f(X,f(f(f(X2,X2),X3),X)) = f(f(f(f(X2,X2),X3),X),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c712,plain,
f(X3,f(X,f(f(f(X2,X2),X3),X))) = f(X3,f(f(f(f(X2,X2),X3),X),X)),
inference(congruence,[status(thm)],[c711]) ).
cnf(c713,plain,
f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))) = f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))),
inference(congruence,[status(thm)],[c712]) ).
cnf(c714,plain,
f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X))))) = f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X)))),
inference(congruence,[status(thm)],[c713]) ).
cnf(c715,plain,
f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))))),
inference(congruence,[status(thm)],[c714]) ).
cnf(c716,plain,
f(X3,f(f(f(f(X2,X2),X3),X),X)) = f(f(f(f(f(X2,X2),X3),X),X),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c717,plain,
f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))) = f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)),
inference(congruence,[status(thm)],[c716]) ).
cnf(c718,plain,
f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X)))) = f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3))),
inference(congruence,[status(thm)],[c717]) ).
cnf(c719,plain,
f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))))) = f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)))),
inference(congruence,[status(thm)],[c718]) ).
cnf(c720,plain,
f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)) = f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c721,plain,
f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3))) = f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2)),
inference(congruence,[status(thm)],[c720]) ).
cnf(c722,plain,
f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)))) = f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))),
inference(congruence,[status(thm)],[c721]) ).
cnf(c723,plain,
f(f(f(X4,X5),f(X3,X5)),f(f(X6,f(f(X4,X5),f(X3,X5))),f(f(f(f(f(f(f(X2,f(f(X4,X5),f(X3,X5))),f(X2,f(f(X4,X5),f(X3,X5)))),f(X6,f(f(X4,X5),f(X3,X5)))),X),X),f(X6,f(f(X4,X5),f(X3,X5)))),f(X2,f(f(X4,X5),f(X3,X5)))))) = f(X6,f(f(X4,X5),f(X3,X5))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c724,plain,
f(X6,f(f(X4,X5),f(X3,X5))) = f(f(f(X4,X5),f(X3,X5)),f(f(X6,f(f(X4,X5),f(X3,X5))),f(f(f(f(f(f(f(X2,f(f(X4,X5),f(X3,X5))),f(X2,f(f(X4,X5),f(X3,X5)))),f(X6,f(f(X4,X5),f(X3,X5)))),X),X),f(X6,f(f(X4,X5),f(X3,X5)))),f(X2,f(f(X4,X5),f(X3,X5)))))),
inference(symmetry,[status(thm)],[c723]) ).
cnf(c725,plain,
f(f(X6,f(f(X4,X5),f(X3,X5))),f(X5,f(f(f(f(f(f(X4,X4),X5),X3),X3),X5),X4))) = f(f(f(f(X4,X5),f(X3,X5)),f(f(X6,f(f(X4,X5),f(X3,X5))),f(f(f(f(f(f(f(X2,f(f(X4,X5),f(X3,X5))),f(X2,f(f(X4,X5),f(X3,X5)))),f(X6,f(f(X4,X5),f(X3,X5)))),X),X),f(X6,f(f(X4,X5),f(X3,X5)))),f(X2,f(f(X4,X5),f(X3,X5)))))),f(X5,f(f(f(f(f(f(X4,X4),X5),X3),X3),X5),X4))),
inference(congruence,[status(thm)],[c724]) ).
cnf(c726,plain,
f(f(f(f(X4,X5),f(X3,X5)),f(f(X6,f(f(X4,X5),f(X3,X5))),f(f(f(f(f(f(f(X2,f(f(X4,X5),f(X3,X5))),f(X2,f(f(X4,X5),f(X3,X5)))),f(X6,f(f(X4,X5),f(X3,X5)))),X),X),f(X6,f(f(X4,X5),f(X3,X5)))),f(X2,f(f(X4,X5),f(X3,X5)))))),f(X5,f(f(f(f(f(f(X4,X4),X5),X3),X3),X5),X4))) = X5,
inference(substitution,[status(thm)],[c2]) ).
cnf(c727,plain,
f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(f(f(f(f(f(X2,X2),X3),X),X),X3),X2))) = X3,
inference(transitivity,[status(thm)],[c725,c726]) ).
cnf(c728,plain,
f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(f(f(f(f(X2,X2),X3),X),X),X3)))) = X3,
inference(transitivity,[status(thm)],[c722,c727]) ).
cnf(c729,plain,
f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(X3,f(f(f(f(X2,X2),X3),X),X))))) = X3,
inference(transitivity,[status(thm)],[c719,c728]) ).
cnf(c730,plain,
f(f(X4,f(f(X2,X3),f(X,X3))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = X3,
inference(transitivity,[status(thm)],[c715,c729]) ).
cnf(c731,plain,
f(f(X4,f(f(X3,X2),f(X,X3))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = X3,
inference(transitivity,[status(thm)],[c710,c730]) ).
cnf(c732,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(f(f(X2,X2),X3),X)))))) = X3,
inference(transitivity,[status(thm)],[c706,c731]) ).
cnf(c733,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(X,f(f(X2,X2),X3))))))) = X3,
inference(transitivity,[status(thm)],[c702,c732]) ).
cnf(c734,plain,
f(f(X4,f(f(X3,X2),f(X3,X))),f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2)))))))) = X3,
inference(transitivity,[status(thm)],[c696,c733]) ).
cnf(c735,plain,
f(f(X3,f(f(f(X5,X4),f(X5,f(X,f(X,f(X5,X4))))),f(f(X5,X4),X2))),f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(f(X5,X4),f(X2,f(X2,f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(X5,f(X,f(X,f(X5,X4)))))))))))) = f(X5,X4),
inference(substitution,[status(thm)],[c734]) ).
cnf(c736,plain,
f(f(X3,f(X5,f(f(X5,X4),X2))),f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(f(X5,X4),f(X2,f(X2,f(f(X5,X4),f(f(X5,f(X,f(X,f(X5,X4)))),f(X5,f(X,f(X,f(X5,X4)))))))))))) = f(X5,X4),
inference(transitivity,[status(thm)],[c689,c735]) ).
cnf(c737,plain,
f(f(X2,f(X4,f(f(X4,X3),X))),f(f(X4,X3),f(X4,X3))) = f(X4,X3),
inference(transitivity,[status(thm)],[c685,c736]) ).
cnf(c738,plain,
f(f(f(X4,X3),f(X4,X3)),f(X2,f(X4,f(f(X4,X3),X)))) = f(X4,X3),
inference(transitivity,[status(thm)],[c682,c737]) ).
cnf(c739,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)],[c681,c738]) ).
cnf(c740,plain,
f(f(f(X3,X2),f(X3,X2)),f(X4,f(X3,f(X,f(X3,X2))))) = f(X3,X2),
inference(substitution,[status(thm)],[c739]) ).
cnf(c741,plain,
f(X3,X2) = f(f(f(X3,X2),f(X3,X2)),f(X4,f(X3,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c740]) ).
cnf(c742,plain,
f(X4,f(X3,X2)) = f(X4,f(f(f(X3,X2),f(X3,X2)),f(X4,f(X3,f(X,f(X3,X2)))))),
inference(congruence,[status(thm)],[c741]) ).
cnf(c743,plain,
f(f(X4,f(X4,f(X3,f(X,f(X3,X2))))),f(X4,f(X3,X2))) = f(f(X4,f(X4,f(X3,f(X,f(X3,X2))))),f(X4,f(f(f(X3,X2),f(X3,X2)),f(X4,f(X3,f(X,f(X3,X2))))))),
inference(congruence,[status(thm)],[c742]) ).
cnf(c744,plain,
f(X,f(X3,X2)) = f(f(X3,X2),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c745,plain,
f(X3,f(X,f(X3,X2))) = f(X3,f(f(X3,X2),X)),
inference(congruence,[status(thm)],[c744]) ).
cnf(c746,plain,
f(f(X3,f(X3,X2)),f(X3,f(X,f(X3,X2)))) = f(f(X3,f(X3,X2)),f(X3,f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c745]) ).
cnf(c747,plain,
f(X2,f(X2,X)) = f(f(X2,X),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c748,plain,
f(f(X3,f(X3,X2)),f(X3,f(f(X3,X2),X))) = f(f(f(X3,X2),X3),f(X3,f(f(X3,X2),X))),
inference(congruence,[status(thm)],[c747]) ).
cnf(c749,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c750,plain,
f(X4,f(f(X4,X3),X2)) = f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2)),
inference(congruence,[status(thm)],[c749]) ).
cnf(c751,plain,
f(f(f(X4,X3),X4),f(X4,f(f(X4,X3),X2))) = f(f(f(X4,X3),X4),f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2))),
inference(congruence,[status(thm)],[c750]) ).
cnf(c752,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c753,plain,
f(f(X3,X2),X3) = f(f(X3,X2),f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))),
inference(congruence,[status(thm)],[c752]) ).
cnf(c754,plain,
f(f(f(X4,X3),X4),f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2))) = f(f(f(X4,X3),f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3)))))),f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2))),
inference(congruence,[status(thm)],[c753]) ).
cnf(c755,plain,
f(X2,f(X2,X)) = f(f(X2,X),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c756,plain,
f(f(X3,f(X3,X2)),f(f(X3,X2),f(X3,X))) = f(f(f(X3,X2),X3),f(f(X3,X2),f(X3,X))),
inference(congruence,[status(thm)],[c755]) ).
cnf(c757,plain,
f(f(f(X3,X2),X3),f(f(X3,X2),f(X3,X))) = f(f(f(X3,X2),f(X3,X)),f(f(X3,X2),X3)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c758,plain,
f(f(X4,X4),f(X3,f(f(X4,X2),f(X4,X)))) = f(f(X3,f(f(X4,X2),f(X4,X))),f(X4,X4)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c759,plain,
f(X3,X3) = f(X3,f(X2,f(X3,f(X,f(X,f(X3,f(X2,X2))))))),
inference(symmetry,[status(thm)],[c653]) ).
cnf(c760,plain,
f(f(X3,f(f(X4,X2),f(X4,X))),f(X4,X4)) = f(f(X3,f(f(X4,X2),f(X4,X))),f(X4,f(X2,f(X4,f(X,f(X,f(X4,f(X2,X2)))))))),
inference(congruence,[status(thm)],[c759]) ).
cnf(c761,plain,
f(f(X3,f(f(X4,X2),f(X4,X))),f(X4,f(X2,f(X4,f(X,f(X,f(X4,f(X2,X2)))))))) = X4,
inference(substitution,[status(thm)],[c734]) ).
cnf(c762,plain,
f(f(X3,f(f(X4,X2),f(X4,X))),f(X4,X4)) = X4,
inference(transitivity,[status(thm)],[c760,c761]) ).
cnf(c763,plain,
f(f(X4,X4),f(X3,f(f(X4,X2),f(X4,X)))) = X4,
inference(transitivity,[status(thm)],[c758,c762]) ).
cnf(c764,plain,
f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X)))) = X3,
inference(substitution,[status(thm)],[c763]) ).
cnf(c765,plain,
X3 = f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X)))),
inference(symmetry,[status(thm)],[c764]) ).
cnf(c766,plain,
f(f(X3,X2),X3) = f(f(X3,X2),f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X))))),
inference(congruence,[status(thm)],[c765]) ).
cnf(c767,plain,
f(f(f(X3,X2),f(X3,X)),f(f(X3,X2),X3)) = f(f(f(X3,X2),f(X3,X)),f(f(X3,X2),f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X)))))),
inference(congruence,[status(thm)],[c766]) ).
cnf(c768,plain,
f(f(f(X3,X2),f(X3,X)),f(f(X3,X2),f(f(X3,X3),f(f(X3,X3),f(f(X3,X2),f(X3,X)))))) = f(X3,X2),
inference(substitution,[status(thm)],[c658]) ).
cnf(c769,plain,
f(f(f(X3,X2),f(X3,X)),f(f(X3,X2),X3)) = f(X3,X2),
inference(transitivity,[status(thm)],[c767,c768]) ).
cnf(c770,plain,
f(f(f(X3,X2),X3),f(f(X3,X2),f(X3,X))) = f(X3,X2),
inference(transitivity,[status(thm)],[c757,c769]) ).
cnf(c771,plain,
f(f(X3,f(X3,X2)),f(f(X3,X2),f(X3,X))) = f(X3,X2),
inference(transitivity,[status(thm)],[c756,c770]) ).
cnf(c772,plain,
f(f(f(X4,X3),f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3)))))),f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2))) = f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),
inference(substitution,[status(thm)],[c771]) ).
cnf(c773,plain,
f(f(f(X4,X3),f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3)))))),f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2))) = X4,
inference(transitivity,[status(thm)],[c772,c658]) ).
cnf(c774,plain,
f(f(f(X4,X3),X4),f(f(f(X4,X3),f(X4,f(X,f(X,f(X4,X3))))),f(f(X4,X3),X2))) = X4,
inference(transitivity,[status(thm)],[c754,c773]) ).
cnf(c775,plain,
f(f(f(X3,X2),X3),f(X3,f(f(X3,X2),X))) = X3,
inference(transitivity,[status(thm)],[c751,c774]) ).
cnf(c776,plain,
f(f(X3,f(X3,X2)),f(X3,f(f(X3,X2),X))) = X3,
inference(transitivity,[status(thm)],[c748,c775]) ).
cnf(c777,plain,
f(f(X3,f(X3,X2)),f(X3,f(X,f(X3,X2)))) = X3,
inference(transitivity,[status(thm)],[c746,c776]) ).
cnf(c778,plain,
f(f(X4,f(X4,f(X3,f(X,f(X3,X2))))),f(X4,f(f(f(X3,X2),f(X3,X2)),f(X4,f(X3,f(X,f(X3,X2))))))) = X4,
inference(substitution,[status(thm)],[c777]) ).
cnf(c779,plain,
f(f(X4,f(X4,f(X3,f(X,f(X3,X2))))),f(X4,f(X3,X2))) = X4,
inference(transitivity,[status(thm)],[c743,c778]) ).
cnf(c780,plain,
f(f(X4,f(X3,X2)),f(X4,f(X4,f(X3,f(X,f(X3,X2)))))) = X4,
inference(transitivity,[status(thm)],[c677,c779]) ).
cnf(c781,plain,
f(f(X3,f(X2,X)),f(X3,f(X3,f(X2,f(X3,f(X2,X)))))) = X3,
inference(substitution,[status(thm)],[c780]) ).
cnf(c782,plain,
X3 = f(f(X3,f(X2,X)),f(X3,f(X3,f(X2,f(X3,f(X2,X)))))),
inference(symmetry,[status(thm)],[c781]) ).
cnf(c783,plain,
f(f(X2,f(X3,f(X2,X))),X3) = f(f(X2,f(X3,f(X2,X))),f(f(X3,f(X2,X)),f(X3,f(X3,f(X2,f(X3,f(X2,X))))))),
inference(congruence,[status(thm)],[c782]) ).
cnf(c784,plain,
f(X,f(X4,f(X3,X2))) = f(f(X4,f(X3,X2)),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c785,plain,
f(X,f(X,f(X4,f(X3,X2)))) = f(X,f(f(X4,f(X3,X2)),X)),
inference(congruence,[status(thm)],[c784]) ).
cnf(c786,plain,
f(f(X3,X2),f(X,f(X,f(X4,f(X3,X2))))) = f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X))),
inference(congruence,[status(thm)],[c785]) ).
cnf(c787,plain,
f(f(X4,f(X3,X2)),f(f(X3,X2),f(X,f(X,f(X4,f(X3,X2)))))) = f(f(X4,f(X3,X2)),f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X)))),
inference(congruence,[status(thm)],[c786]) ).
cnf(c788,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c789,plain,
f(X3,f(X2,X)) = f(X3,f(X,X2)),
inference(congruence,[status(thm)],[c788]) ).
cnf(c790,plain,
f(f(X4,f(X3,X2)),f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X)))) = f(f(X4,f(X2,X3)),f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X)))),
inference(congruence,[status(thm)],[c789]) ).
cnf(c791,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c792,plain,
f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X))) = f(f(X2,X3),f(X,f(f(X4,f(X3,X2)),X))),
inference(congruence,[status(thm)],[c791]) ).
cnf(c793,plain,
f(f(X4,f(X2,X3)),f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X)))) = f(f(X4,f(X2,X3)),f(f(X2,X3),f(X,f(f(X4,f(X3,X2)),X)))),
inference(congruence,[status(thm)],[c792]) ).
cnf(c794,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c795,plain,
f(X3,f(X2,X)) = f(X3,f(X,X2)),
inference(congruence,[status(thm)],[c794]) ).
cnf(c796,plain,
f(f(X4,f(X3,X2)),X) = f(f(X4,f(X2,X3)),X),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
f(X,f(f(X4,f(X3,X2)),X)) = f(X,f(f(X4,f(X2,X3)),X)),
inference(congruence,[status(thm)],[c796]) ).
cnf(c798,plain,
f(f(X2,X3),f(X,f(f(X4,f(X3,X2)),X))) = f(f(X2,X3),f(X,f(f(X4,f(X2,X3)),X))),
inference(congruence,[status(thm)],[c797]) ).
cnf(c799,plain,
f(f(X4,f(X2,X3)),f(f(X2,X3),f(X,f(f(X4,f(X3,X2)),X)))) = f(f(X4,f(X2,X3)),f(f(X2,X3),f(X,f(f(X4,f(X2,X3)),X)))),
inference(congruence,[status(thm)],[c798]) ).
cnf(c800,plain,
f(X3,f(X2,X)) = f(f(X2,X),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c801,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X3,f(X2,X2)))) = f(f(f(X2,X),X3),f(f(X2,X),f(X3,f(X2,X2)))),
inference(congruence,[status(thm)],[c800]) ).
cnf(c802,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c803,plain,
f(X3,X3) = f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))),
inference(congruence,[status(thm)],[c802]) ).
cnf(c804,plain,
f(X4,f(X3,X3)) = f(X4,f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))),
inference(congruence,[status(thm)],[c803]) ).
cnf(c805,plain,
f(f(X3,X2),f(X4,f(X3,X3))) = f(f(X3,X2),f(X4,f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))))),
inference(congruence,[status(thm)],[c804]) ).
cnf(c806,plain,
f(f(f(X3,X2),X4),f(f(X3,X2),f(X4,f(X3,X3)))) = f(f(f(X3,X2),X4),f(f(X3,X2),f(X4,f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))))),
inference(congruence,[status(thm)],[c805]) ).
cnf(c807,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c808,plain,
f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))) = f(f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))),
inference(congruence,[status(thm)],[c807]) ).
cnf(c809,plain,
f(X4,f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))) = f(X4,f(f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))),
inference(congruence,[status(thm)],[c808]) ).
cnf(c810,plain,
f(f(X3,X2),f(X4,f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))))) = f(f(X3,X2),f(X4,f(f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))))),
inference(congruence,[status(thm)],[c809]) ).
cnf(c811,plain,
f(f(f(X3,X2),X4),f(f(X3,X2),f(X4,f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))))) = f(f(f(X3,X2),X4),f(f(X3,X2),f(X4,f(f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))))),
inference(congruence,[status(thm)],[c810]) ).
cnf(c812,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c813,plain,
f(f(X3,X2),f(X3,f(X2,f(f(X3,X),f(X3,X))))) = f(f(X2,X3),f(X3,f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c812]) ).
cnf(c814,plain,
f(X3,f(X2,f(f(X3,X),f(X3,X)))) = f(f(X2,f(f(X3,X),f(X3,X))),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c815,plain,
f(f(X2,X3),f(X3,f(X2,f(f(X3,X),f(X3,X))))) = f(f(X2,X3),f(f(X2,f(f(X3,X),f(X3,X))),X3)),
inference(congruence,[status(thm)],[c814]) ).
cnf(c816,plain,
X3 = f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c817,plain,
f(f(X2,f(f(X3,X),f(X3,X))),X3) = f(f(X2,f(f(X3,X),f(X3,X))),f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c816]) ).
cnf(c818,plain,
f(f(X2,X3),f(f(X2,f(f(X3,X),f(X3,X))),X3)) = f(f(X2,X3),f(f(X2,f(f(X3,X),f(X3,X))),f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c817]) ).
cnf(c819,plain,
X3 = f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c820,plain,
f(X2,X3) = f(X2,f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X))))),
inference(congruence,[status(thm)],[c819]) ).
cnf(c821,plain,
f(f(X2,X3),f(f(X2,f(f(X3,X),f(X3,X))),f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X2,f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X))))),f(f(X2,f(f(X3,X),f(X3,X))),f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))))),
inference(congruence,[status(thm)],[c820]) ).
cnf(c822,plain,
f(X2,f(X3,X)) = f(f(X3,X),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c823,plain,
f(X3,f(X2,f(X3,X))) = f(X3,f(f(X3,X),X2)),
inference(congruence,[status(thm)],[c822]) ).
cnf(c824,plain,
f(f(X3,f(X2,f(X3,X))),f(f(X3,X),f(X2,f(X3,X)))) = f(f(X3,f(f(X3,X),X2)),f(f(X3,X),f(X2,f(X3,X)))),
inference(congruence,[status(thm)],[c823]) ).
cnf(c825,plain,
f(X2,f(X3,X)) = f(f(X3,X),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c826,plain,
f(f(X3,X),f(X2,f(X3,X))) = f(f(X3,X),f(f(X3,X),X2)),
inference(congruence,[status(thm)],[c825]) ).
cnf(c827,plain,
f(f(X3,f(f(X3,X),X2)),f(f(X3,X),f(X2,f(X3,X)))) = f(f(X3,f(f(X3,X),X2)),f(f(X3,X),f(f(X3,X),X2))),
inference(congruence,[status(thm)],[c826]) ).
cnf(c828,plain,
f(X3,f(f(X3,X),X2)) = f(f(f(X3,X),X2),X3),
inference(substitution,[status(thm)],[c333]) ).
cnf(c829,plain,
f(f(X3,f(f(X3,X),X2)),f(f(X3,X),f(f(X3,X),X2))) = f(f(f(f(X3,X),X2),X3),f(f(X3,X),f(f(X3,X),X2))),
inference(congruence,[status(thm)],[c828]) ).
cnf(c830,plain,
f(f(f(f(X3,X),X2),X3),f(f(X3,X),f(f(X3,X),X2))) = f(f(f(X3,X),f(f(X3,X),X2)),f(f(f(X3,X),X2),X3)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c831,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c832,plain,
f(f(f(X4,X2),X3),X4) = f(f(f(X4,X2),X3),f(f(X4,X2),f(X4,f(X,f(X,f(X4,X2)))))),
inference(congruence,[status(thm)],[c831]) ).
cnf(c833,plain,
f(f(f(X4,X2),f(f(X4,X2),X3)),f(f(f(X4,X2),X3),X4)) = f(f(f(X4,X2),f(f(X4,X2),X3)),f(f(f(X4,X2),X3),f(f(X4,X2),f(X4,f(X,f(X,f(X4,X2))))))),
inference(congruence,[status(thm)],[c832]) ).
cnf(c834,plain,
f(f(f(X4,X2),f(f(X4,X2),X3)),f(f(f(X4,X2),X3),f(f(X4,X2),f(X4,f(X,f(X,f(X4,X2))))))) = f(f(X4,X2),X3),
inference(substitution,[status(thm)],[c771]) ).
cnf(c835,plain,
f(X2,f(X3,X)) = f(f(X3,X),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c836,plain,
f(f(X3,X),X2) = f(X2,f(X3,X)),
inference(symmetry,[status(thm)],[c835]) ).
cnf(c837,plain,
f(f(f(X4,X2),f(f(X4,X2),X3)),f(f(f(X4,X2),X3),f(f(X4,X2),f(X4,f(X,f(X,f(X4,X2))))))) = f(X3,f(X4,X2)),
inference(transitivity,[status(thm)],[c834,c836]) ).
cnf(c838,plain,
f(f(f(X3,X),f(f(X3,X),X2)),f(f(f(X3,X),X2),X3)) = f(X2,f(X3,X)),
inference(transitivity,[status(thm)],[c833,c837]) ).
cnf(c839,plain,
f(f(f(f(X3,X),X2),X3),f(f(X3,X),f(f(X3,X),X2))) = f(X2,f(X3,X)),
inference(transitivity,[status(thm)],[c830,c838]) ).
cnf(c840,plain,
f(f(X3,f(f(X3,X),X2)),f(f(X3,X),f(f(X3,X),X2))) = f(X2,f(X3,X)),
inference(transitivity,[status(thm)],[c829,c839]) ).
cnf(c841,plain,
f(f(X3,f(f(X3,X),X2)),f(f(X3,X),f(X2,f(X3,X)))) = f(X2,f(X3,X)),
inference(transitivity,[status(thm)],[c827,c840]) ).
cnf(c842,plain,
f(f(X3,f(X2,f(X3,X))),f(f(X3,X),f(X2,f(X3,X)))) = f(X2,f(X3,X)),
inference(transitivity,[status(thm)],[c824,c841]) ).
cnf(c843,plain,
f(f(X2,f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X))))),f(f(X2,f(f(X3,X),f(X3,X))),f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))))) = f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))),
inference(substitution,[status(thm)],[c842]) ).
cnf(c844,plain,
f(f(X2,f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X))))),f(f(X2,f(f(X3,X),f(X3,X))),f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))))) = X3,
inference(transitivity,[status(thm)],[c843,c529]) ).
cnf(c845,plain,
f(f(X2,X3),f(f(X2,f(f(X3,X),f(X3,X))),f(f(X3,X3),f(X2,f(f(X3,X),f(X3,X)))))) = X3,
inference(transitivity,[status(thm)],[c821,c844]) ).
cnf(c846,plain,
f(f(X2,X3),f(f(X2,f(f(X3,X),f(X3,X))),X3)) = X3,
inference(transitivity,[status(thm)],[c818,c845]) ).
cnf(c847,plain,
f(f(X2,X3),f(X3,f(X2,f(f(X3,X),f(X3,X))))) = X3,
inference(transitivity,[status(thm)],[c815,c846]) ).
cnf(c848,plain,
f(f(X3,X2),f(X3,f(X2,f(f(X3,X),f(X3,X))))) = X3,
inference(transitivity,[status(thm)],[c813,c847]) ).
cnf(c849,plain,
f(f(f(X3,X2),X4),f(f(X3,X2),f(X4,f(f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))))) = f(X3,X2),
inference(substitution,[status(thm)],[c848]) ).
cnf(c850,plain,
f(f(f(X3,X2),X4),f(f(X3,X2),f(X4,f(X3,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))))) = f(X3,X2),
inference(transitivity,[status(thm)],[c811,c849]) ).
cnf(c851,plain,
f(f(f(X2,X),X3),f(f(X2,X),f(X3,f(X2,X2)))) = f(X2,X),
inference(transitivity,[status(thm)],[c806,c850]) ).
cnf(c852,plain,
f(f(X3,f(X2,X)),f(f(X2,X),f(X3,f(X2,X2)))) = f(X2,X),
inference(transitivity,[status(thm)],[c801,c851]) ).
cnf(c853,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(X3,f(X,X)))) = f(X,X2),
inference(substitution,[status(thm)],[c852]) ).
cnf(c854,plain,
f(X,X2) = f(f(X3,f(X,X2)),f(f(X,X2),f(X3,f(X,X)))),
inference(symmetry,[status(thm)],[c853]) ).
cnf(c855,plain,
f(f(X2,X3),f(X,f(f(X4,f(X2,X3)),X))) = f(f(f(X4,f(X2,X3)),f(f(X2,X3),f(X4,f(X2,X2)))),f(X,f(f(X4,f(X2,X3)),X))),
inference(congruence,[status(thm)],[c854]) ).
cnf(c856,plain,
f(f(X4,f(X2,X3)),f(f(X2,X3),f(X,f(f(X4,f(X2,X3)),X)))) = f(f(X4,f(X2,X3)),f(f(f(X4,f(X2,X3)),f(f(X2,X3),f(X4,f(X2,X2)))),f(X,f(f(X4,f(X2,X3)),X)))),
inference(congruence,[status(thm)],[c855]) ).
cnf(c857,plain,
f(f(X4,f(X2,X3)),f(f(f(X4,f(X2,X3)),f(f(X2,X3),f(X4,f(X2,X2)))),f(X,f(f(X4,f(X2,X3)),X)))) = f(f(X4,f(X2,X3)),f(f(X2,X3),f(X4,f(X2,X2)))),
inference(substitution,[status(thm)],[c669]) ).
cnf(c858,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(X3,f(X,X)))) = f(X,X2),
inference(substitution,[status(thm)],[c852]) ).
cnf(c859,plain,
f(X2,X) = f(X,X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c860,plain,
f(X,X2) = f(X2,X),
inference(symmetry,[status(thm)],[c859]) ).
cnf(c861,plain,
f(f(X3,f(X,X2)),f(f(X,X2),f(X3,f(X,X)))) = f(X2,X),
inference(transitivity,[status(thm)],[c858,c860]) ).
cnf(c862,plain,
f(f(X4,f(X2,X3)),f(f(f(X4,f(X2,X3)),f(f(X2,X3),f(X4,f(X2,X2)))),f(X,f(f(X4,f(X2,X3)),X)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c857,c861]) ).
cnf(c863,plain,
f(f(X4,f(X2,X3)),f(f(X2,X3),f(X,f(f(X4,f(X2,X3)),X)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c856,c862]) ).
cnf(c864,plain,
f(f(X4,f(X2,X3)),f(f(X2,X3),f(X,f(f(X4,f(X3,X2)),X)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c799,c863]) ).
cnf(c865,plain,
f(f(X4,f(X2,X3)),f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c793,c864]) ).
cnf(c866,plain,
f(f(X4,f(X3,X2)),f(f(X3,X2),f(X,f(f(X4,f(X3,X2)),X)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c790,c865]) ).
cnf(c867,plain,
f(f(X4,f(X3,X2)),f(f(X3,X2),f(X,f(X,f(X4,f(X3,X2)))))) = f(X3,X2),
inference(transitivity,[status(thm)],[c787,c866]) ).
cnf(c868,plain,
f(f(X2,f(X3,f(X2,X))),f(f(X3,f(X2,X)),f(X3,f(X3,f(X2,f(X3,f(X2,X))))))) = f(X3,f(X2,X)),
inference(substitution,[status(thm)],[c867]) ).
cnf(c869,plain,
f(f(X2,f(X3,f(X2,X))),X3) = f(X3,f(X2,X)),
inference(transitivity,[status(thm)],[c783,c868]) ).
cnf(c870,plain,
f(X3,f(X2,f(X3,f(X2,X)))) = f(X3,f(X2,X)),
inference(transitivity,[status(thm)],[c676,c869]) ).
cnf(c871,plain,
f(X3,f(X2,f(X3,f(X2,f(X,f(X,f(X2,f(X3,X3)))))))) = f(X3,f(X2,f(X,f(X,f(X2,f(X3,X3)))))),
inference(substitution,[status(thm)],[c870]) ).
cnf(c872,plain,
f(X3,f(X2,f(X,f(X,f(X2,f(X3,X3)))))) = f(X3,f(X2,f(X3,f(X2,f(X,f(X,f(X2,f(X3,X3)))))))),
inference(symmetry,[status(thm)],[c871]) ).
cnf(c873,plain,
f(X2,f(X3,f(X2,f(X,f(X,f(X2,f(X3,X3))))))) = f(X2,X2),
inference(substitution,[status(thm)],[c653]) ).
cnf(c874,plain,
f(X3,f(X2,f(X3,f(X2,f(X,f(X,f(X2,f(X3,X3)))))))) = f(X3,f(X2,X2)),
inference(congruence,[status(thm)],[c873]) ).
cnf(c875,plain,
f(X3,f(X2,f(X,f(X,f(X2,f(X3,X3)))))) = f(X3,f(X2,X2)),
inference(transitivity,[status(thm)],[c872,c874]) ).
cnf(c876,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,f(X,f(f(X,X3),f(f(f(X3,X2),f(X3,X2)),f(f(X3,X2),f(X3,X2)))))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,X3))),
inference(substitution,[status(thm)],[c875]) ).
cnf(c877,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,X3))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,f(X,f(f(X,X3),f(f(f(X3,X2),f(X3,X2)),f(f(X3,X2),f(X3,X2)))))))),
inference(symmetry,[status(thm)],[c876]) ).
cnf(c878,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(f(f(X3,X),f(X3,X)),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c879,plain,
f(f(X3,f(X3,X3)),f(X2,f(f(X4,X),f(X4,X)))) = f(f(X3,f(X3,X3)),f(f(f(X4,X),f(X4,X)),X2)),
inference(congruence,[status(thm)],[c878]) ).
cnf(c880,plain,
f(X4,f(f(X3,f(X3,X3)),f(X2,f(f(X4,X),f(X4,X))))) = f(X4,f(f(X3,f(X3,X3)),f(f(f(X4,X),f(X4,X)),X2))),
inference(congruence,[status(thm)],[c879]) ).
cnf(c881,plain,
f(f(X2,f(X2,X2)),X) = f(X,f(X2,f(X2,X2))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c882,plain,
f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c532]) ).
cnf(c883,plain,
f(X,f(X,X)) = f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2)))),
inference(symmetry,[status(thm)],[c882]) ).
cnf(c884,plain,
f(X2,f(X,f(X,X))) = f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))),
inference(congruence,[status(thm)],[c883]) ).
cnf(c885,plain,
f(X2,f(f(X,X),f(f(X,f(X2,X2)),f(X,f(X2,X2))))) = f(X2,X2),
inference(substitution,[status(thm)],[c548]) ).
cnf(c886,plain,
f(X2,f(X,f(X,X))) = f(X2,X2),
inference(transitivity,[status(thm)],[c884,c885]) ).
cnf(c887,plain,
f(X,f(X2,f(X2,X2))) = f(X,X),
inference(substitution,[status(thm)],[c886]) ).
cnf(c888,plain,
f(f(X2,f(X2,X2)),X) = f(X,X),
inference(transitivity,[status(thm)],[c881,c887]) ).
cnf(c889,plain,
f(f(X3,f(X3,X3)),f(f(f(X4,X),f(X4,X)),X2)) = f(f(f(f(X4,X),f(X4,X)),X2),f(f(f(X4,X),f(X4,X)),X2)),
inference(substitution,[status(thm)],[c888]) ).
cnf(c890,plain,
f(X4,f(f(X3,f(X3,X3)),f(f(f(X4,X),f(X4,X)),X2))) = f(X4,f(f(f(f(X4,X),f(X4,X)),X2),f(f(f(X4,X),f(X4,X)),X2))),
inference(congruence,[status(thm)],[c889]) ).
cnf(c891,plain,
f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))) = X2,
inference(substitution,[status(thm)],[c529]) ).
cnf(c892,plain,
X2 = f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c891]) ).
cnf(c893,plain,
f(X3,f(f(f(f(X3,X),f(X3,X)),X2),f(f(f(X3,X),f(X3,X)),X2))) = f(f(f(X3,X3),f(f(f(X3,X),f(X3,X)),f(f(X3,X),f(X3,X)))),f(f(f(f(X3,X),f(X3,X)),X2),f(f(f(X3,X),f(X3,X)),X2))),
inference(congruence,[status(thm)],[c892]) ).
cnf(c894,plain,
f(f(X3,f(X2,X2)),f(f(X2,X),f(X2,X))) = f(f(f(X2,X),f(X2,X)),f(X3,f(X2,X2))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c895,plain,
f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))) = f(X2,X2),
inference(substitution,[status(thm)],[c294]) ).
cnf(c896,plain,
f(X2,X2) = f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))),
inference(symmetry,[status(thm)],[c895]) ).
cnf(c897,plain,
f(X3,f(X2,X2)) = f(X3,f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))))),
inference(congruence,[status(thm)],[c896]) ).
cnf(c898,plain,
f(f(f(X2,X),f(X2,X)),f(X3,f(X2,X2))) = f(f(f(X2,X),f(X2,X)),f(X3,f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))))),
inference(congruence,[status(thm)],[c897]) ).
cnf(c899,plain,
f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))) = X2,
inference(substitution,[status(thm)],[c529]) ).
cnf(c900,plain,
X2 = f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))),
inference(symmetry,[status(thm)],[c899]) ).
cnf(c901,plain,
f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))) = f(f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))),f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))),
inference(congruence,[status(thm)],[c900]) ).
cnf(c902,plain,
f(X3,f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))))) = f(X3,f(f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))),f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))))),
inference(congruence,[status(thm)],[c901]) ).
cnf(c903,plain,
f(f(f(X2,X),f(X2,X)),f(X3,f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))))) = f(f(f(X2,X),f(X2,X)),f(X3,f(f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))),f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))))),
inference(congruence,[status(thm)],[c902]) ).
cnf(c904,plain,
f(f(f(X2,X),f(X2,X)),f(X3,f(f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))),f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))))) = f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))),
inference(substitution,[status(thm)],[c548]) ).
cnf(c905,plain,
f(f(f(X2,X),f(X2,X)),f(X3,f(f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X)))),f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))))) = f(X2,X),
inference(transitivity,[status(thm)],[c904,c63]) ).
cnf(c906,plain,
f(f(f(X2,X),f(X2,X)),f(X3,f(X2,f(f(X2,X2),f(f(f(X2,X),f(X2,X)),f(f(X2,X),f(X2,X))))))) = f(X2,X),
inference(transitivity,[status(thm)],[c903,c905]) ).
cnf(c907,plain,
f(f(f(X2,X),f(X2,X)),f(X3,f(X2,X2))) = f(X2,X),
inference(transitivity,[status(thm)],[c898,c906]) ).
cnf(c908,plain,
f(f(X3,f(X2,X2)),f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c894,c907]) ).
cnf(c909,plain,
f(f(f(X3,X3),f(f(f(X3,X),f(X3,X)),f(f(X3,X),f(X3,X)))),f(f(f(f(X3,X),f(X3,X)),X2),f(f(f(X3,X),f(X3,X)),X2))) = f(f(f(X3,X),f(X3,X)),X2),
inference(substitution,[status(thm)],[c908]) ).
cnf(c910,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(f(f(X3,X),f(X3,X)),X2),
inference(substitution,[status(thm)],[c333]) ).
cnf(c911,plain,
f(f(f(X3,X),f(X3,X)),X2) = f(X2,f(f(X3,X),f(X3,X))),
inference(symmetry,[status(thm)],[c910]) ).
cnf(c912,plain,
f(f(f(X3,X3),f(f(f(X3,X),f(X3,X)),f(f(X3,X),f(X3,X)))),f(f(f(f(X3,X),f(X3,X)),X2),f(f(f(X3,X),f(X3,X)),X2))) = f(X2,f(f(X3,X),f(X3,X))),
inference(transitivity,[status(thm)],[c909,c911]) ).
cnf(c913,plain,
f(X3,f(f(f(f(X3,X),f(X3,X)),X2),f(f(f(X3,X),f(X3,X)),X2))) = f(X2,f(f(X3,X),f(X3,X))),
inference(transitivity,[status(thm)],[c893,c912]) ).
cnf(c914,plain,
f(X4,f(f(X3,f(X3,X3)),f(f(f(X4,X),f(X4,X)),X2))) = f(X2,f(f(X4,X),f(X4,X))),
inference(transitivity,[status(thm)],[c890,c913]) ).
cnf(c915,plain,
f(X4,f(f(X3,f(X3,X3)),f(X2,f(f(X4,X),f(X4,X))))) = f(X2,f(f(X4,X),f(X4,X))),
inference(transitivity,[status(thm)],[c880,c914]) ).
cnf(c916,plain,
f(X4,f(f(X,f(X,X)),f(X3,f(f(X4,X2),f(X4,X2))))) = f(X3,f(f(X4,X2),f(X4,X2))),
inference(substitution,[status(thm)],[c915]) ).
cnf(c917,plain,
f(X3,f(f(X4,X2),f(X4,X2))) = f(X4,f(f(X,f(X,X)),f(X3,f(f(X4,X2),f(X4,X2))))),
inference(symmetry,[status(thm)],[c916]) ).
cnf(c918,plain,
f(f(X5,X4),f(X3,f(f(X4,X2),f(X4,X2)))) = f(f(X5,X4),f(X4,f(f(X,f(X,X)),f(X3,f(f(X4,X2),f(X4,X2)))))),
inference(congruence,[status(thm)],[c917]) ).
cnf(c919,plain,
f(X5,f(f(X5,X4),f(X3,f(f(X4,X2),f(X4,X2))))) = f(X5,f(f(X5,X4),f(X4,f(f(X,f(X,X)),f(X3,f(f(X4,X2),f(X4,X2))))))),
inference(congruence,[status(thm)],[c918]) ).
cnf(c920,plain,
f(f(X3,X2),f(X2,X)) = f(f(X2,X),f(X3,X2)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c921,plain,
f(X3,f(f(X3,X2),f(X2,X))) = f(X3,f(f(X2,X),f(X3,X2))),
inference(congruence,[status(thm)],[c920]) ).
cnf(c922,plain,
X3 = f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))),
inference(symmetry,[status(thm)],[c658]) ).
cnf(c923,plain,
f(X4,X3) = f(X4,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))),
inference(congruence,[status(thm)],[c922]) ).
cnf(c924,plain,
f(f(X3,X2),f(X4,X3)) = f(f(X3,X2),f(X4,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2))))))),
inference(congruence,[status(thm)],[c923]) ).
cnf(c925,plain,
f(X4,f(f(X3,X2),f(X4,X3))) = f(X4,f(f(X3,X2),f(X4,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))))),
inference(congruence,[status(thm)],[c924]) ).
cnf(c926,plain,
f(X4,f(f(X3,X2),f(X4,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))))) = f(X4,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))),
inference(substitution,[status(thm)],[c870]) ).
cnf(c927,plain,
f(X4,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))) = f(X4,X3),
inference(congruence,[status(thm)],[c658]) ).
cnf(c928,plain,
f(X4,f(f(X3,X2),f(X4,f(f(X3,X2),f(X3,f(X,f(X,f(X3,X2)))))))) = f(X4,X3),
inference(transitivity,[status(thm)],[c926,c927]) ).
cnf(c929,plain,
f(X3,f(f(X2,X),f(X3,X2))) = f(X3,X2),
inference(transitivity,[status(thm)],[c925,c928]) ).
cnf(c930,plain,
f(X3,f(f(X3,X2),f(X2,X))) = f(X3,X2),
inference(transitivity,[status(thm)],[c921,c929]) ).
cnf(c931,plain,
f(X5,f(f(X5,X4),f(X4,f(f(X,f(X,X)),f(X3,f(f(X4,X2),f(X4,X2))))))) = f(X5,X4),
inference(substitution,[status(thm)],[c930]) ).
cnf(c932,plain,
f(X4,f(f(X4,X3),f(X2,f(f(X3,X),f(X3,X))))) = f(X4,X3),
inference(transitivity,[status(thm)],[c919,c931]) ).
cnf(c933,plain,
f(X,f(f(X,X3),f(f(f(X3,X2),f(X3,X2)),f(f(X3,X2),f(X3,X2))))) = f(X,X3),
inference(substitution,[status(thm)],[c932]) ).
cnf(c934,plain,
f(X,f(X,f(f(X,X3),f(f(f(X3,X2),f(X3,X2)),f(f(X3,X2),f(X3,X2)))))) = f(X,f(X,X3)),
inference(congruence,[status(thm)],[c933]) ).
cnf(c935,plain,
f(f(X,X3),f(X,f(X,f(f(X,X3),f(f(f(X3,X2),f(X3,X2)),f(f(X3,X2),f(X3,X2))))))) = f(f(X,X3),f(X,f(X,X3))),
inference(congruence,[status(thm)],[c934]) ).
cnf(c936,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,f(X,f(f(X,X3),f(f(f(X3,X2),f(X3,X2)),f(f(X3,X2),f(X3,X2)))))))) = f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,f(X,X3)))),
inference(congruence,[status(thm)],[c935]) ).
cnf(c937,plain,
f(X2,X) = f(f(X2,f(X2,X)),X2),
inference(symmetry,[status(thm)],[c464]) ).
cnf(c938,plain,
f(f(X2,X),f(X2,f(X2,X))) = f(f(f(X2,f(X2,X)),X2),f(X2,f(X2,X))),
inference(congruence,[status(thm)],[c937]) ).
cnf(c939,plain,
f(X2,X) = f(f(f(X2,X),f(X2,X)),X2),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c940,plain,
f(f(f(X2,X),X2),f(X2,X)) = f(f(f(X2,X),X2),f(f(f(X2,X),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c939]) ).
cnf(c941,plain,
f(X2,X) = f(f(f(X2,X),f(X2,X)),X2),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c942,plain,
f(f(X2,X),X2) = f(f(f(f(X2,X),f(X2,X)),X2),X2),
inference(congruence,[status(thm)],[c941]) ).
cnf(c943,plain,
f(f(f(X2,X),X2),f(f(f(X2,X),f(X2,X)),X2)) = f(f(f(f(f(X2,X),f(X2,X)),X2),X2),f(f(f(X2,X),f(X2,X)),X2)),
inference(congruence,[status(thm)],[c942]) ).
cnf(c944,plain,
f(f(f(f(f(X2,X),f(X2,X)),X2),X2),f(f(f(X2,X),f(X2,X)),X2)) = X2,
inference(substitution,[status(thm)],[c454]) ).
cnf(c945,plain,
f(f(f(X2,X),X2),f(f(f(X2,X),f(X2,X)),X2)) = X2,
inference(transitivity,[status(thm)],[c943,c944]) ).
cnf(c946,plain,
f(f(f(X2,X),X2),f(X2,X)) = X2,
inference(transitivity,[status(thm)],[c940,c945]) ).
cnf(c947,plain,
f(f(f(X2,f(X2,X)),X2),f(X2,f(X2,X))) = X2,
inference(substitution,[status(thm)],[c946]) ).
cnf(c948,plain,
f(f(X2,X),f(X2,f(X2,X))) = X2,
inference(transitivity,[status(thm)],[c938,c947]) ).
cnf(c949,plain,
f(f(X,X2),f(X,f(X,X2))) = X,
inference(substitution,[status(thm)],[c948]) ).
cnf(c950,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,f(X,X3)))) = f(f(f(X3,X2),f(X3,X2)),X),
inference(congruence,[status(thm)],[c949]) ).
cnf(c951,plain,
f(X,f(f(X3,X2),f(X3,X2))) = f(f(f(X3,X2),f(X3,X2)),X),
inference(substitution,[status(thm)],[c333]) ).
cnf(c952,plain,
f(f(f(X3,X2),f(X3,X2)),X) = f(X,f(f(X3,X2),f(X3,X2))),
inference(symmetry,[status(thm)],[c951]) ).
cnf(c953,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,f(X,X3)))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c950,c952]) ).
cnf(c954,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,f(X,f(f(X,X3),f(f(f(X3,X2),f(X3,X2)),f(f(X3,X2),f(X3,X2)))))))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c936,c953]) ).
cnf(c955,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X,X3),f(X,X3))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c877,c954]) ).
cnf(c956,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,X),f(X,X3))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c675,c955]) ).
cnf(c957,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,X),f(X3,X))) = f(X,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c674,c956]) ).
cnf(c958,plain,
f(f(f(X,X3),f(X,X3)),f(f(X,X2),f(X,X2))) = f(X2,f(f(X,X3),f(X,X3))),
inference(substitution,[status(thm)],[c957]) ).
cnf(c959,plain,
f(X2,f(f(X,X3),f(X,X3))) = f(f(f(X,X3),f(X,X3)),f(f(X,X2),f(X,X2))),
inference(symmetry,[status(thm)],[c958]) ).
cnf(c960,plain,
f(f(X3,f(f(X2,X4),f(X2,X4))),f(X,f(f(f(X2,X4),f(X2,X4)),X))) = f(f(f(f(X2,X4),f(X2,X4)),f(f(X2,X3),f(X2,X3))),f(X,f(f(f(X2,X4),f(X2,X4)),X))),
inference(congruence,[status(thm)],[c959]) ).
cnf(c961,plain,
f(f(f(X2,X4),f(X2,X4)),f(f(X3,f(f(X2,X4),f(X2,X4))),f(X,f(f(f(X2,X4),f(X2,X4)),X)))) = f(f(f(X2,X4),f(X2,X4)),f(f(f(f(X2,X4),f(X2,X4)),f(f(X2,X3),f(X2,X3))),f(X,f(f(f(X2,X4),f(X2,X4)),X)))),
inference(congruence,[status(thm)],[c960]) ).
cnf(c962,plain,
f(f(f(X2,X4),f(X2,X4)),f(f(f(f(X2,X4),f(X2,X4)),f(f(X2,X3),f(X2,X3))),f(X,f(f(f(X2,X4),f(X2,X4)),X)))) = f(f(f(X2,X4),f(X2,X4)),f(f(X2,X3),f(X2,X3))),
inference(substitution,[status(thm)],[c669]) ).
cnf(c963,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,X),f(X3,X))) = f(f(f(X3,X),f(X3,X)),f(f(X3,X2),f(X3,X2))),
inference(substitution,[status(thm)],[c333]) ).
cnf(c964,plain,
f(f(f(X3,X),f(X3,X)),f(f(X3,X2),f(X3,X2))) = f(X2,f(f(X3,X),f(X3,X))),
inference(substitution,[status(thm)],[c957]) ).
cnf(c965,plain,
f(f(f(X3,X2),f(X3,X2)),f(f(X3,X),f(X3,X))) = f(X2,f(f(X3,X),f(X3,X))),
inference(transitivity,[status(thm)],[c963,c964]) ).
cnf(c966,plain,
f(f(f(X,X3),f(X,X3)),f(f(X,X2),f(X,X2))) = f(X3,f(f(X,X2),f(X,X2))),
inference(substitution,[status(thm)],[c965]) ).
cnf(c967,plain,
f(f(X,X2),f(X,X2)) = f(f(X2,X),f(X,X2)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c968,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(X3,f(f(X2,X),f(X,X2))),
inference(congruence,[status(thm)],[c967]) ).
cnf(c969,plain,
f(X3,f(f(X2,X),f(X,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c281]) ).
cnf(c970,plain,
f(X3,f(f(X,X2),f(X,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c968,c969]) ).
cnf(c971,plain,
f(f(f(X,X3),f(X,X3)),f(f(X,X2),f(X,X2))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c966,c970]) ).
cnf(c972,plain,
f(f(f(X2,X4),f(X2,X4)),f(f(f(f(X2,X4),f(X2,X4)),f(f(X2,X3),f(X2,X3))),f(X,f(f(f(X2,X4),f(X2,X4)),X)))) = f(X4,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c962,c971]) ).
cnf(c973,plain,
f(f(f(X2,X4),f(X2,X4)),f(f(X3,f(f(X2,X4),f(X2,X4))),f(X,f(f(f(X2,X4),f(X2,X4)),X)))) = f(X4,f(f(X3,X2),f(X3,X2))),
inference(transitivity,[status(thm)],[c961,c972]) ).
cnf(c974,plain,
f(f(f(X,X3),f(X,X3)),X2) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c672,c973]) ).
cnf(c975,plain,
f(X2,f(f(X,X3),f(X,X3))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c344,c974]) ).
cnf(c976,plain,
f(X2,f(f(X3,X),f(X,X3))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c343,c975]) ).
cnf(c977,plain,
f(X2,f(f(X3,X),f(X3,X))) = f(X3,f(f(X2,X),f(X2,X))),
inference(transitivity,[status(thm)],[c342,c976]) ).
cnf(c978,plain,
f(a,f(f(c,b),f(c,b))) = f(c,f(f(a,b),f(a,b))),
inference(substitution,[status(thm)],[c977]) ).
cnf(c979,plain,
f(a,b) = f(b,a),
inference(substitution,[status(thm)],[c333]) ).
cnf(c980,plain,
f(f(a,b),f(a,b)) = f(f(b,a),f(a,b)),
inference(congruence,[status(thm)],[c979]) ).
cnf(c981,plain,
f(c,f(f(a,b),f(a,b))) = f(c,f(f(b,a),f(a,b))),
inference(congruence,[status(thm)],[c980]) ).
cnf(c982,plain,
f(a,b) = f(b,a),
inference(substitution,[status(thm)],[c333]) ).
cnf(c983,plain,
f(f(b,a),f(a,b)) = f(f(b,a),f(b,a)),
inference(congruence,[status(thm)],[c982]) ).
cnf(c984,plain,
f(c,f(f(b,a),f(a,b))) = f(c,f(f(b,a),f(b,a))),
inference(congruence,[status(thm)],[c983]) ).
cnf(c985,plain,
f(c,f(f(a,b),f(a,b))) = f(c,f(f(b,a),f(b,a))),
inference(transitivity,[status(thm)],[c981,c984]) ).
cnf(c986,plain,
f(a,f(f(c,b),f(c,b))) = f(c,f(f(b,a),f(b,a))),
inference(transitivity,[status(thm)],[c978,c985]) ).
cnf(c987,plain,
f(a,f(f(c,b),f(b,c))) = f(c,f(f(b,a),f(b,a))),
inference(transitivity,[status(thm)],[c340,c986]) ).
cnf(c988,plain,
f(a,f(f(b,c),f(c,b))) = f(c,f(f(b,a),f(b,a))),
inference(transitivity,[status(thm)],[c336,c987]) ).
cnf(c989,plain,
f(a,f(f(b,c),f(b,c))) = f(c,f(f(b,a),f(b,a))),
inference(transitivity,[status(thm)],[c284,c988]) ).
cnf(c990,plain,
$false,
inference(resolution,[status(thm)],[c1,c989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT076-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 13:59:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 253.60/32.49 Command-line arguments: --no-flatten-goal
% 253.60/32.49
% 253.60/32.49 % SZS status Unsatisfiable
% 253.60/32.49
% 224.10/32.77 % SZS output start CNFRefutation
% See solution above
% 233.54/34.11
% 233.54/34.11 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------