%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG213-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:07:10 AM UTC 2026
% Result : Unsatisfiable 90.25s 11.62s
% Output : CNFRefutation 95.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 5
% Syntax : Number of clauses : 840 ( 840 unt; 0 nHn; 4 RR)
% Number of literals : 840 ( 839 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 3630 ( 161 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(f(x,y,z),u,w) != f(x,f(y,u,w),f(z,u,w)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_long) ).
cnf(c2,axiom,
f(X,Y,Z) = f(X,Z,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permute2) ).
cnf(c3,plain,
f(X2,X3,X4) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
f(X2,X4,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
f(f(X5,X4,X3),X4,f(X2,X4,X3)) = f(f(X5,X4,X3),X4,f(X2,X3,X4)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
f(X2,Y2,Z2) = f(Z2,X2,Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permute1) ).
cnf(c7,plain,
f(X2,X3,X4) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
f(X4,X2,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
f(X3,X4,f(X5,X2,X4)) = f(X3,X4,f(X2,X4,X5)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
f(f(X2,W,Y2),W,Z2) = f(X2,W,f(Y2,W,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c11,plain,
f(f(X3,X5,X2),X5,X4) = f(X3,X5,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
f(X3,X5,f(X2,X5,X4)) = f(f(X3,X5,X2),X5,X4),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
f(X5,X4,f(X3,X5,X2)) = f(f(X3,X5,X2),X5,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c14,plain,
f(f(X3,X5,X2),X5,X4) = f(X5,X4,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
f(X3,X5,f(X2,X5,X4)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c12,c14]) ).
cnf(c16,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
f(X2,f(X5,X4,X3),X4) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c18,plain,
f(X4,X2,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
f(X2,f(X5,X4,X3),X4) = f(X2,X4,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
f(X4,X2,f(X5,X4,X3)) = f(X2,X4,f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c18,c19]) ).
cnf(c21,plain,
f(X5,X4,f(X3,X4,X2)) = f(X2,X4,f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c16,c20]) ).
cnf(c22,plain,
f(X3,X4,f(X2,X4,X5)) = f(X5,X4,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
f(X3,X4,f(X5,X2,X4)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c9,c22]) ).
cnf(c24,plain,
f(f(X5,X4,X3),X4,f(X2,X3,X4)) = f(X2,X4,f(f(X5,X4,X3),X4,X3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
f(X3,X2,f(X4,X3,X2)) = f(f(X4,X3,X2),X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c26,plain,
f(f(X4,X3,X2),X3,X2) = f(X3,X2,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c28,plain,
f(X4,X3,X2) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
f(X3,X2,f(X4,X3,X2)) = f(X3,X2,f(X3,X2,X4)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
f(X4,X3,f(X4,X3,X2)) = f(X3,X2,f(X4,X3,X4)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c31,plain,
f(X3,X3,X2) = f(X3,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
f(X3,X2,X3) = f(X3,X3,X2),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,axiom,
f(X2,X2,Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',majority) ).
cnf(c34,plain,
f(X3,X3,X2) = X3,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
f(X3,X2,X3) = X3,
inference(transitivity,[status(thm)],[c32,c34]) ).
cnf(c36,plain,
f(X3,X2,f(X4,X3,X4)) = f(X3,X2,X4),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c38,plain,
f(X3,X2,f(X4,X3,X4)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
f(X4,X3,f(X4,X3,X2)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c30,c38]) ).
cnf(c40,plain,
f(X3,X2,f(X3,X2,X4)) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c42,plain,
f(X3,X2,f(X3,X2,X4)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
f(X3,X2,f(X4,X3,X2)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c29,c42]) ).
cnf(c44,plain,
f(f(X4,X3,X2),X3,X2) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c26,c43]) ).
cnf(c45,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X3)) = f(X2,X4,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
f(X2,X4,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
f(f(X5,X4,X3),X4,f(X2,X3,X4)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c24,c47]) ).
cnf(c49,plain,
f(f(X5,X4,X3),X4,f(X2,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c5,c48]) ).
cnf(c50,plain,
f(f(X5,f(X6,X2,X7),f(X3,X2,X7)),f(X6,X2,X7),f(f(f(X5,X4,X3),X2,X7),f(X6,X2,X7),f(X3,X2,X7))) = f(f(f(X5,X4,X3),X2,X7),f(X5,f(X6,X2,X7),f(X3,X2,X7)),f(X6,X2,X7)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
f(f(f(X7,X6,X5),X4,X3),f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3)) = f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(X5,X4,X3))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c53,plain,
f(X4,X3,X2) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
f(X3,X2,X4) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
f(X4,X3,X2) = f(X3,X4,X2),
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
f(f(X5,X4,X3),f(X6,X4,X3),f(X2,X4,X3)) = f(f(X6,X4,X3),f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
f(f(X6,X4,X3),f(X5,X4,X3),f(X2,X4,X3)) = f(f(X5,X4,X3),f(X6,X4,X3),f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
f(X3,X4,X2) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c59,plain,
f(X3,X4,f(X4,X5,X2)) = f(X3,X4,f(X2,X4,X5)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
f(X3,X4,f(X2,X4,X5)) = f(X5,X4,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c61,plain,
f(X3,X4,f(X4,X5,X2)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
f(X5,X4,f(X4,X3,X2)) = f(X3,X4,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
f(X3,X4,f(X5,X4,X2)) = f(X3,X4,f(X5,X2,X4)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
f(X5,X4,f(X4,X3,X2)) = f(X3,X4,f(X5,X2,X4)),
inference(transitivity,[status(thm)],[c62,c64]) ).
cnf(c66,plain,
f(X6,f(X3,X5,X4),f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X2,f(X3,X5,X4))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X2,f(X3,X5,X4))) = f(X6,f(X3,X5,X4),f(f(X3,X5,X4),f(X6,X5,X4),X2)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
f(X5,X3,f(X5,X4,X2)) = f(X3,X5,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c69,plain,
f(X3,X5,f(X5,X4,X2)) = f(X5,X3,f(X5,X4,X2)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
f(X5,f(X5,X4,X2),X3) = f(X5,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,f(X5,X4,X2),X3),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
f(X4,X3,X2) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c73,plain,
f(X5,f(X5,X4,X3),X2) = f(X5,f(X3,X5,X4),X2),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
f(f(X4,X5,X3),X2,X5) = f(X5,f(X4,X5,X3),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c75,plain,
f(X5,f(X4,X5,X3),X2) = f(f(X4,X5,X3),X2,X5),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
f(X2,X5,f(X4,X5,X3)) = f(f(X4,X5,X3),X2,X5),
inference(substitution,[status(thm)],[c6]) ).
cnf(c77,plain,
f(f(X4,X5,X3),X2,X5) = f(X2,X5,f(X4,X5,X3)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
f(X2,X5,f(X4,X5,X3)) = f(X5,X3,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c79,plain,
f(f(X4,X5,X3),X2,X5) = f(X5,X3,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X3,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c75,c79]) ).
cnf(c81,plain,
f(X5,f(X3,X5,X4),X2) = f(X5,X4,f(X2,X5,X3)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
f(X2,X4,X3) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c83,plain,
f(X5,X4,f(X2,X5,X3)) = f(X5,X4,f(X5,X2,X3)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
f(X5,f(X3,X5,X4),X2) = f(X5,X4,f(X5,X2,X3)),
inference(transitivity,[status(thm)],[c81,c83]) ).
cnf(c85,plain,
f(X5,f(X5,X4,X3),X2) = f(X5,X4,f(X5,X2,X3)),
inference(transitivity,[status(thm)],[c73,c84]) ).
cnf(c86,plain,
f(X5,f(X5,X4,X2),X3) = f(X5,X4,f(X5,X3,X2)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c71,c86]) ).
cnf(c88,plain,
f(X5,X4,f(X5,X3,X2)) = f(X5,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
f(X3,X5,f(X5,X4,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c69,c89]) ).
cnf(c91,plain,
f(X6,f(X3,X5,X4),f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(f(X3,X5,X4),f(X6,X5,X4),f(f(X3,X5,X4),X6,X2)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
f(X2,X4,X3) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
f(X2,X3,X4) = f(X2,X4,X3),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
f(X3,X5,f(X2,X4,X5)) = f(X3,X5,f(X2,X5,X4)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
f(X3,X5,f(X2,X4,X5)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c94,c15]) ).
cnf(c96,plain,
f(X5,X4,f(X3,X2,X4)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
f(X4,X2,f(X5,X4,X3)) = f(X4,f(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c98,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,X2,f(X4,X5,X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c99,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,f(X4,X5,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,f(X4,X5,X3),X2),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
f(X5,f(X4,X5,X3),X2) = f(X4,X5,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,X4,f(X3,X5,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c103,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
f(X4,f(X5,X4,X3),X2) = f(X4,X5,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
f(X4,X2,f(X5,X4,X3)) = f(X4,X5,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c97,c104]) ).
cnf(c106,plain,
f(X5,X4,f(X3,X2,X4)) = f(X4,X5,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c96,c105]) ).
cnf(c107,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c108,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,X2,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
f(X4,X2,X3) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c110,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
f(X5,X2,f(X5,X4,X3)) = f(X5,X2,f(X5,X3,X4)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
f(X5,f(X5,X2,X4),X3) = f(X5,X2,f(X5,X3,X4)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c113,plain,
f(X5,X2,f(X5,X3,X4)) = f(X5,f(X5,X2,X4),X3),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
f(X2,X4,X3) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c115,plain,
f(X4,X2,X3) = f(X2,X4,X3),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
f(X5,f(X5,X2,X4),X3) = f(X5,f(X2,X5,X4),X3),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
f(X5,f(X2,X5,X4),X3) = f(X5,X4,f(X3,X5,X2)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c118,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c55]) ).
cnf(c119,plain,
f(X5,X4,f(X3,X5,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
f(X5,f(X2,X5,X4),X3) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c117,c119]) ).
cnf(c121,plain,
f(X5,f(X5,X2,X4),X3) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c116,c120]) ).
cnf(c122,plain,
f(X5,X2,f(X5,X3,X4)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c113,c121]) ).
cnf(c123,plain,
f(X5,X2,f(X5,X4,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c111,c122]) ).
cnf(c124,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c108,c123]) ).
cnf(c125,plain,
f(X4,X5,f(X3,X4,X2)) = f(X4,X3,f(X4,X2,X5)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
f(X5,X4,f(X3,X2,X4)) = f(X4,X3,f(X4,X2,X5)),
inference(transitivity,[status(thm)],[c106,c125]) ).
cnf(c127,plain,
f(X2,f(X3,X5,X4),f(f(X6,X5,X4),X6,f(X3,X5,X4))) = f(f(X3,X5,X4),f(X6,X5,X4),f(f(X3,X5,X4),X6,X2)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
f(f(X3,X5,X4),f(X6,X5,X4),f(f(X3,X5,X4),X6,X2)) = f(X2,f(X3,X5,X4),f(f(X6,X5,X4),X6,f(X3,X5,X4))),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(f(X5,X4,X3),X5,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c130,plain,
f(f(X5,X4,X3),X5,f(X2,X4,X3)) = f(f(X5,X4,X3),f(X2,X4,X3),X5),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(f(X5,X4,X3),f(X2,X4,X3),X5),
inference(substitution,[status(thm)],[c55]) ).
cnf(c132,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
f(X2,X5,f(X5,X3,X4)) = f(X3,X5,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c134,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c135,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c136,plain,
f(X4,X2,f(X5,X4,X3)) = f(X4,X2,f(X5,X3,X4)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,X2,f(X5,X3,X4)),
inference(transitivity,[status(thm)],[c134,c136]) ).
cnf(c138,plain,
f(X3,X5,f(X2,X5,X4)) = f(X5,X4,f(X3,X2,X5)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
f(X2,X5,f(X5,X3,X4)) = f(X5,X4,f(X3,X2,X5)),
inference(transitivity,[status(thm)],[c133,c138]) ).
cnf(c140,plain,
f(f(X5,X4,X3),X5,f(X5,X2,X4)) = f(X5,X4,f(X2,f(X5,X4,X3),X5)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X4)) = f(X5,X4,f(X2,f(X5,X4,X3),X5)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c142,plain,
f(X5,X4,f(X2,f(X5,X4,X3),X5)) = f(X2,X5,f(f(X5,X4,X3),X5,X4)),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
f(X4,X3,f(X4,X3,X2)) = f(f(X4,X3,X2),X4,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c144,plain,
f(f(X4,X3,X2),X4,X3) = f(X4,X3,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
f(f(X4,X3,X2),X4,X3) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c144,c39]) ).
cnf(c146,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X4)) = f(X2,X5,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
f(X2,X5,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c2]) ).
cnf(c148,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c146,c147]) ).
cnf(c149,plain,
f(X5,X4,f(X2,f(X5,X4,X3),X5)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c142,c148]) ).
cnf(c150,plain,
f(f(X5,X4,X3),X5,f(X5,X2,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c140,c149]) ).
cnf(c151,plain,
f(f(X5,X4,X3),X5,f(X5,f(X2,X4,X3),X4)) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(f(X5,X4,X3),X5,f(X5,f(X2,X4,X3),X4)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
f(f(X5,X4,X2),X4,X3) = f(X3,f(X5,X4,X2),X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c154,plain,
f(X3,f(X5,X4,X2),X4) = f(f(X5,X4,X2),X4,X3),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
f(X4,X3,f(X5,X4,X2)) = f(f(X5,X4,X2),X4,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c156,plain,
f(f(X5,X4,X2),X4,X3) = f(X4,X3,f(X5,X4,X2)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
f(X5,X4,f(X2,X4,X3)) = f(X4,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c158,plain,
f(X4,X3,f(X5,X4,X2)) = f(X5,X4,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
f(X2,X4,X3) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c160,plain,
f(X5,X4,f(X2,X4,X3)) = f(X5,X4,f(X4,X2,X3)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
f(X4,X2,X3) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c162,plain,
f(X5,X4,f(X4,X2,X3)) = f(X5,X4,f(X3,X4,X2)),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
f(X5,X4,f(X2,X4,X3)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c160,c162]) ).
cnf(c164,plain,
f(X4,X3,f(X5,X4,X2)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c158,c163]) ).
cnf(c165,plain,
f(f(X5,X4,X2),X4,X3) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c156,c164]) ).
cnf(c166,plain,
f(X3,f(X5,X4,X2),X4) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c154,c165]) ).
cnf(c167,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X4) = f(X2,X4,f(f(X5,X4,X3),X4,X3)),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X3)) = f(X2,X4,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c169,plain,
f(X2,X4,f(X5,X4,X3)) = f(f(X5,X4,X3),X2,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c170,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X3)) = f(f(X5,X4,X3),X2,X4),
inference(transitivity,[status(thm)],[c168,c169]) ).
cnf(c171,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X4) = f(f(X5,X4,X3),X2,X4),
inference(transitivity,[status(thm)],[c167,c170]) ).
cnf(c172,plain,
f(f(X5,X3,X2),f(X4,X3,X2),X3) = f(f(X5,X3,X2),X4,X3),
inference(substitution,[status(thm)],[c171]) ).
cnf(c173,plain,
f(X4,X3,f(X5,X3,X2)) = f(f(X5,X3,X2),X4,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c174,plain,
f(f(X5,X3,X2),X4,X3) = f(X4,X3,f(X5,X3,X2)),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
f(X5,f(X4,X3,X2),X3) = f(X4,X3,f(X5,X3,X2)),
inference(substitution,[status(thm)],[c166]) ).
cnf(c176,plain,
f(X4,X3,f(X5,X3,X2)) = f(X5,f(X4,X3,X2),X3),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
f(f(X5,X3,X2),X4,X3) = f(X5,f(X4,X3,X2),X3),
inference(transitivity,[status(thm)],[c174,c176]) ).
cnf(c178,plain,
f(f(X5,X3,X2),f(X4,X3,X2),X3) = f(X5,f(X4,X3,X2),X3),
inference(transitivity,[status(thm)],[c172,c177]) ).
cnf(c179,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X4) = f(X5,f(X2,X4,X3),X4),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
f(X5,f(X2,X4,X3),X4) = f(f(X5,X4,X3),f(X2,X4,X3),X4),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
f(f(X5,X4,X3),X5,f(X5,f(X2,X4,X3),X4)) = f(f(X5,X4,X3),X5,f(f(X5,X4,X3),f(X2,X4,X3),X4)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
f(f(X5,X4,X3),f(f(X5,X4,X3),X5,X4),X2) = f(f(X5,X4,X3),X5,f(f(X5,X4,X3),X2,X4)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c183,plain,
f(f(X5,X4,X3),X5,f(f(X5,X4,X3),X2,X4)) = f(f(X5,X4,X3),f(f(X5,X4,X3),X5,X4),X2),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
f(f(X5,X4,X3),f(f(X5,X4,X3),X5,X4),X2) = f(f(X5,X4,X3),f(X5,X4,X3),X2),
inference(congruence,[status(thm)],[c145]) ).
cnf(c185,plain,
f(f(X5,X4,X3),f(X5,X4,X3),X2) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c33]) ).
cnf(c186,plain,
f(f(X5,X4,X3),f(f(X5,X4,X3),X5,X4),X2) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c184,c185]) ).
cnf(c187,plain,
f(f(X5,X4,X3),X5,f(f(X5,X4,X3),X2,X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c183,c186]) ).
cnf(c188,plain,
f(f(X5,X4,X3),X5,f(f(X5,X4,X3),f(X2,X4,X3),X4)) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
f(f(X5,X4,X3),X5,f(X5,f(X2,X4,X3),X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c181,c188]) ).
cnf(c190,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c152,c189]) ).
cnf(c191,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c132,c190]) ).
cnf(c192,plain,
f(f(X5,X4,X3),X5,f(X2,X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c130,c191]) ).
cnf(c193,plain,
f(X2,f(X3,X5,X4),f(f(X6,X5,X4),X6,f(X3,X5,X4))) = f(X2,f(X3,X5,X4),f(X6,X5,X4)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
f(X2,f(X3,X5,X4),f(X6,X5,X4)) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c195,plain,
f(X2,f(X3,X5,X4),f(f(X6,X5,X4),X6,f(X3,X5,X4))) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
f(f(X3,X5,X4),f(X6,X5,X4),f(f(X3,X5,X4),X6,X2)) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c128,c195]) ).
cnf(c197,plain,
f(X6,f(X3,X5,X4),f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c91,c196]) ).
cnf(c198,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X2,f(X3,X5,X4))) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c67,c197]) ).
cnf(c199,plain,
f(f(X6,X4,X3),f(X2,X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(f(X5,X4,X3),f(X6,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
f(f(X5,X4,X3),f(X6,X4,X3),f(X2,X4,X3)) = f(f(X6,X4,X3),f(X2,X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3))),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
f(f(X2,X5,X4),X6,X3) = f(X6,f(X2,X5,X4),X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c202,plain,
f(X6,f(X2,X5,X4),X3) = f(f(X2,X5,X4),X6,X3),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
f(f(X6,X5,X4),X3,f(X6,f(X2,X5,X4),X3)) = f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X6,X3)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
f(f(X2,X5,X4),X3,f(X3,f(X6,X5,X4),X6)) = f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X6,X3)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c205,plain,
f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X6,X3)) = f(f(X2,X5,X4),X3,f(X3,f(X6,X5,X4),X6)),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
f(X4,X5,f(X4,X3,X2)) = f(X4,X3,f(X4,X2,X5)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c207,plain,
f(X4,X3,f(X4,X2,X5)) = f(X4,X5,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
f(X4,X5,f(X4,X3,X2)) = f(X5,X4,f(X4,X3,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c209,plain,
f(X4,X3,f(X4,X2,X5)) = f(X5,X4,f(X4,X3,X2)),
inference(transitivity,[status(thm)],[c207,c208]) ).
cnf(c210,plain,
f(X3,f(X6,X5,X4),f(X3,X6,f(X2,X5,X4))) = f(f(X2,X5,X4),X3,f(X3,f(X6,X5,X4),X6)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
f(f(X2,X5,X4),X3,f(X3,f(X6,X5,X4),X6)) = f(X3,f(X6,X5,X4),f(X3,X6,f(X2,X5,X4))),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
f(X5,f(X2,X4,X3),X6) = f(X6,X5,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c213,plain,
f(X6,X5,f(X2,X4,X3)) = f(X5,f(X2,X4,X3),X6),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
f(X6,f(X5,X4,X3),f(X6,X5,f(X2,X4,X3))) = f(X6,f(X5,X4,X3),f(X5,f(X2,X4,X3),X6)),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
f(f(X2,X4,X3),X5,X6) = f(X5,f(X2,X4,X3),X6),
inference(substitution,[status(thm)],[c55]) ).
cnf(c216,plain,
f(X5,f(X2,X4,X3),X6) = f(f(X2,X4,X3),X5,X6),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
f(X6,f(X5,X4,X3),f(X5,f(X2,X4,X3),X6)) = f(X6,f(X5,X4,X3),f(f(X2,X4,X3),X5,X6)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
f(X5,f(X4,X2,X5),X3) = f(X5,X3,f(X4,X2,X5)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c219,plain,
f(X5,X3,f(X4,X2,X5)) = f(X5,f(X4,X2,X5),X3),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
f(X2,X4,X3) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c221,plain,
f(X3,X2,X4) = f(X2,X4,X3),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
f(X5,f(X4,X3,X5),X2) = f(X5,f(X3,X5,X4),X2),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
f(X5,f(X3,X5,X4),X2) = f(X5,X4,f(X2,X5,X3)),
inference(substitution,[status(thm)],[c80]) ).
cnf(c224,plain,
f(X2,X4,X3) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c225,plain,
f(X5,X4,f(X2,X5,X3)) = f(X5,X4,f(X5,X2,X3)),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
f(X5,f(X3,X5,X4),X2) = f(X5,X4,f(X5,X2,X3)),
inference(transitivity,[status(thm)],[c223,c225]) ).
cnf(c227,plain,
f(X5,f(X4,X3,X5),X2) = f(X5,X4,f(X5,X2,X3)),
inference(transitivity,[status(thm)],[c222,c226]) ).
cnf(c228,plain,
f(X5,f(X4,X2,X5),X3) = f(X5,X4,f(X5,X3,X2)),
inference(substitution,[status(thm)],[c227]) ).
cnf(c229,plain,
f(X5,X3,f(X4,X2,X5)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c219,c228]) ).
cnf(c230,plain,
f(X5,X4,f(X3,X2,X5)) = f(X5,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
f(X5,X2,f(X5,X3,X4)) = f(X5,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c232,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,X2,f(X5,X3,X4)),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
f(X5,X4,f(X3,X2,X5)) = f(X5,X2,f(X5,X3,X4)),
inference(transitivity,[status(thm)],[c230,c232]) ).
cnf(c234,plain,
f(X6,f(X5,X4,X3),f(f(X2,X4,X3),X5,X6)) = f(X6,X5,f(X6,f(X2,X4,X3),f(X5,X4,X3))),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
f(X5,X4,f(X5,X3,X2)) = f(X5,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c236,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,X3,f(X4,X5,X2)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c237,plain,
f(X5,X4,f(X5,X3,X2)) = f(X5,X3,f(X4,X5,X2)),
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
f(X6,X5,f(X6,f(X2,X4,X3),f(X5,X4,X3))) = f(X6,f(X2,X4,X3),f(X5,X6,f(X5,X4,X3))),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
f(X5,X4,X3) = f(f(X5,X4,X3),X5,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c240,plain,
f(X5,X6,f(X5,X4,X3)) = f(X5,X6,f(f(X5,X4,X3),X5,f(X2,X4,X3))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
f(X6,f(X2,X4,X3),f(X5,X6,f(X5,X4,X3))) = f(X6,f(X2,X4,X3),f(X5,X6,f(f(X5,X4,X3),X5,f(X2,X4,X3)))),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
f(X3,f(X5,X3,X2),X4) = f(X3,X5,f(X2,X3,X4)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c243,plain,
f(X3,X5,f(X2,X3,X4)) = f(X3,f(X5,X3,X2),X4),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
f(X5,X4,f(X3,X5,f(X2,X3,X4))) = f(X5,X4,f(X3,f(X5,X3,X2),X4)),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
f(f(X5,X3,X2),X3,X4) = f(X3,f(X5,X3,X2),X4),
inference(substitution,[status(thm)],[c55]) ).
cnf(c246,plain,
f(X3,f(X5,X3,X2),X4) = f(f(X5,X3,X2),X3,X4),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
f(X5,X4,f(X3,f(X5,X3,X2),X4)) = f(X5,X4,f(f(X5,X3,X2),X3,X4)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
f(f(X5,X3,X2),X4,f(X4,X5,X3)) = f(X5,X4,f(f(X5,X3,X2),X3,X4)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c249,plain,
f(X5,X4,f(f(X5,X3,X2),X3,X4)) = f(f(X5,X3,X2),X4,f(X4,X5,X3)),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
f(X4,X5,f(X4,X3,f(X5,X3,X2))) = f(f(X5,X3,X2),X4,f(X4,X5,X3)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c251,plain,
f(f(X5,X3,X2),X4,f(X4,X5,X3)) = f(X4,X5,f(X4,X3,f(X5,X3,X2))),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
f(X5,X4,f(X3,X2,X4)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c253,plain,
f(X2,f(X5,X4,X3),X4) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c254,plain,
f(X4,X2,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
f(X2,f(X5,X4,X3),X4) = f(X2,X4,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c256,plain,
f(X4,X2,f(X5,X4,X3)) = f(X2,X4,f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c254,c255]) ).
cnf(c257,plain,
f(X5,X4,f(X3,X2,X4)) = f(X2,X4,f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c252,c256]) ).
cnf(c258,plain,
f(X4,X3,f(X2,X5,X3)) = f(X5,X3,f(X4,X3,X2)),
inference(substitution,[status(thm)],[c257]) ).
cnf(c259,plain,
f(X5,X3,f(X4,X3,X2)) = f(X4,X3,f(X2,X5,X3)),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
f(X5,X4,f(X5,X3,f(X4,X3,X2))) = f(X5,X4,f(X4,X3,f(X2,X5,X3))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
f(X4,X3,f(X4,X2,X3)) = f(X3,X2,f(X4,X3,X4)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c262,plain,
f(X3,X2,f(X4,X3,X4)) = f(X3,X2,X4),
inference(congruence,[status(thm)],[c35]) ).
cnf(c263,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c264,plain,
f(X3,X2,f(X4,X3,X4)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c262,c263]) ).
cnf(c265,plain,
f(X4,X3,f(X4,X2,X3)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c261,c264]) ).
cnf(c266,plain,
f(X5,X4,f(X5,f(X4,X3,f(X2,X5,X3)),X4)) = f(X5,X4,f(X4,X3,f(X2,X5,X3))),
inference(substitution,[status(thm)],[c265]) ).
cnf(c267,plain,
f(X5,X4,f(X4,X3,f(X2,X5,X3))) = f(X5,X4,f(X5,f(X4,X3,f(X2,X5,X3)),X4)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
f(X5,X4,f(X4,X5,f(X4,X3,f(X2,X5,X3)))) = f(X5,X4,f(X5,f(X4,X3,f(X2,X5,X3)),X4)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c269,plain,
f(X5,X4,f(X5,f(X4,X3,f(X2,X5,X3)),X4)) = f(X5,X4,f(X4,X5,f(X4,X3,f(X2,X5,X3)))),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
f(X4,X5,f(X4,X3,f(X2,X5,X3))) = f(X4,X3,f(X5,X4,f(X2,X5,X3))),
inference(substitution,[status(thm)],[c237]) ).
cnf(c271,plain,
f(X5,X4,f(X4,X5,f(X4,X3,f(X2,X5,X3)))) = f(X5,X4,f(X4,X3,f(X5,X4,f(X2,X5,X3)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
f(X5,X2,f(X5,X4,X3)) = f(X5,X4,f(X2,X5,X3)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c273,plain,
f(X5,X4,f(X2,X5,X3)) = f(X5,X2,f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
f(X4,X3,f(X5,X4,f(X2,X5,X3))) = f(X4,X3,f(X5,X2,f(X5,X4,X3))),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
f(X5,X4,f(X4,X3,f(X5,X4,f(X2,X5,X3)))) = f(X5,X4,f(X4,X3,f(X5,X2,f(X5,X4,X3)))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
f(X3,f(X5,X2,f(X5,X4,X3)),X4) = f(X4,X3,f(X5,X2,f(X5,X4,X3))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c277,plain,
f(X4,X3,f(X5,X2,f(X5,X4,X3))) = f(X3,f(X5,X2,f(X5,X4,X3)),X4),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
f(X5,X4,f(X4,X3,f(X5,X2,f(X5,X4,X3)))) = f(X5,X4,f(X3,f(X5,X2,f(X5,X4,X3)),X4)),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
f(X5,X4,f(X3,f(X5,X2,f(X5,X4,X3)),X4)) = f(X4,X5,f(X3,X4,f(X5,X2,f(X5,X4,X3)))),
inference(substitution,[status(thm)],[c106]) ).
cnf(c280,plain,
f(X4,f(X5,X4,X3),f(X5,X2,f(X5,X4,X3))) = f(X4,X5,f(X3,X4,f(X5,X2,f(X5,X4,X3)))),
inference(substitution,[status(thm)],[c103]) ).
cnf(c281,plain,
f(X4,X5,f(X3,X4,f(X5,X2,f(X5,X4,X3)))) = f(X4,f(X5,X4,X3),f(X5,X2,f(X5,X4,X3))),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
f(X4,f(X5,X4,X3),f(X5,X2,f(X5,X4,X3))) = f(f(X5,X4,X3),X5,f(f(X5,X4,X3),X2,X4)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c283,plain,
f(f(X5,X4,X3),f(X5,X4,f(X5,X4,X3)),X2) = f(f(X5,X4,X3),X5,f(f(X5,X4,X3),X2,X4)),
inference(substitution,[status(thm)],[c227]) ).
cnf(c284,plain,
f(f(X5,X4,X3),X5,f(f(X5,X4,X3),X2,X4)) = f(f(X5,X4,X3),f(X5,X4,f(X5,X4,X3)),X2),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
f(f(X5,X4,X3),f(X5,X4,f(X5,X4,X3)),X2) = f(f(X5,X4,X3),f(X5,X4,X3),X2),
inference(congruence,[status(thm)],[c39]) ).
cnf(c286,plain,
f(f(X5,X4,X3),f(X5,X4,X3),X2) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c33]) ).
cnf(c287,plain,
f(f(X5,X4,X3),f(X5,X4,f(X5,X4,X3)),X2) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c285,c286]) ).
cnf(c288,plain,
f(f(X5,X4,X3),X5,f(f(X5,X4,X3),X2,X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c284,c287]) ).
cnf(c289,plain,
f(X4,f(X5,X4,X3),f(X5,X2,f(X5,X4,X3))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c282,c288]) ).
cnf(c290,plain,
f(X4,X5,f(X3,X4,f(X5,X2,f(X5,X4,X3)))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c281,c289]) ).
cnf(c291,plain,
f(X5,X4,f(X3,f(X5,X2,f(X5,X4,X3)),X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c279,c290]) ).
cnf(c292,plain,
f(X5,X4,f(X4,X3,f(X5,X2,f(X5,X4,X3)))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c278,c291]) ).
cnf(c293,plain,
f(X5,X4,f(X4,X3,f(X5,X4,f(X2,X5,X3)))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c275,c292]) ).
cnf(c294,plain,
f(X5,X4,f(X4,X5,f(X4,X3,f(X2,X5,X3)))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c271,c293]) ).
cnf(c295,plain,
f(X5,X4,f(X5,f(X4,X3,f(X2,X5,X3)),X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c269,c294]) ).
cnf(c296,plain,
f(X5,X4,f(X4,X3,f(X2,X5,X3))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c267,c295]) ).
cnf(c297,plain,
f(X5,X4,f(X5,X3,f(X4,X3,X2))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c260,c296]) ).
cnf(c298,plain,
f(X4,X5,f(X4,X3,f(X5,X3,X2))) = f(X4,X5,X3),
inference(substitution,[status(thm)],[c297]) ).
cnf(c299,plain,
f(f(X5,X3,X2),X4,f(X4,X5,X3)) = f(X4,X5,X3),
inference(transitivity,[status(thm)],[c251,c298]) ).
cnf(c300,plain,
f(X5,X4,f(f(X5,X3,X2),X3,X4)) = f(X4,X5,X3),
inference(transitivity,[status(thm)],[c249,c299]) ).
cnf(c301,plain,
f(X5,X4,f(X3,f(X5,X3,X2),X4)) = f(X4,X5,X3),
inference(transitivity,[status(thm)],[c247,c300]) ).
cnf(c302,plain,
f(X5,X4,f(X3,X5,f(X2,X3,X4))) = f(X4,X5,X3),
inference(transitivity,[status(thm)],[c244,c301]) ).
cnf(c303,plain,
f(X6,f(X2,X4,X3),f(X5,X6,f(f(X5,X4,X3),X5,f(X2,X4,X3)))) = f(f(X2,X4,X3),X6,X5),
inference(substitution,[status(thm)],[c302]) ).
cnf(c304,plain,
f(f(X2,X4,X3),X6,X5) = f(X5,f(X2,X4,X3),X6),
inference(substitution,[status(thm)],[c6]) ).
cnf(c305,plain,
f(X5,f(X2,X4,X3),X6) = f(X6,X5,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c306,plain,
f(f(X2,X4,X3),X6,X5) = f(X6,X5,f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c304,c305]) ).
cnf(c307,plain,
f(X6,f(X2,X4,X3),f(X5,X6,f(f(X5,X4,X3),X5,f(X2,X4,X3)))) = f(X6,X5,f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c303,c306]) ).
cnf(c308,plain,
f(X6,f(X2,X4,X3),f(X5,X6,f(X5,X4,X3))) = f(X6,X5,f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c241,c307]) ).
cnf(c309,plain,
f(X6,X5,f(X6,f(X2,X4,X3),f(X5,X4,X3))) = f(X6,X5,f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c238,c308]) ).
cnf(c310,plain,
f(X6,f(X5,X4,X3),f(f(X2,X4,X3),X5,X6)) = f(X6,X5,f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c234,c309]) ).
cnf(c311,plain,
f(X6,f(X5,X4,X3),f(X5,f(X2,X4,X3),X6)) = f(X6,X5,f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c217,c310]) ).
cnf(c312,plain,
f(X6,f(X5,X4,X3),f(X6,X5,f(X2,X4,X3))) = f(X6,X5,f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c214,c311]) ).
cnf(c313,plain,
f(X3,f(X6,X5,X4),f(X3,X6,f(X2,X5,X4))) = f(X3,X6,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c312]) ).
cnf(c314,plain,
f(f(X2,X5,X4),X3,f(X3,f(X6,X5,X4),X6)) = f(X3,X6,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c211,c313]) ).
cnf(c315,plain,
f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X6,X3)) = f(X3,X6,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c205,c314]) ).
cnf(c316,plain,
f(f(X6,X5,X4),X3,f(X6,f(X2,X5,X4),X3)) = f(X3,X6,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c203,c315]) ).
cnf(c317,plain,
f(f(X6,X4,X3),f(X2,X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(f(X2,X4,X3),X6,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c316]) ).
cnf(c318,plain,
f(f(X2,X4,X3),X6,f(X5,X4,X3)) = f(X6,f(X2,X4,X3),f(X5,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c319,plain,
f(X6,f(X2,X4,X3),f(X5,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c320,plain,
f(f(X2,X4,X3),X6,f(X5,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c318,c319]) ).
cnf(c321,plain,
f(f(X6,X4,X3),f(X2,X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c317,c320]) ).
cnf(c322,plain,
f(f(X5,X4,X3),f(X6,X4,X3),f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c200,c321]) ).
cnf(c323,plain,
f(f(X6,X4,X3),f(X5,X4,X3),f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c57,c322]) ).
cnf(c324,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(X5,X4,X3)) = f(f(X7,X6,X5),f(X2,X4,X3),f(X5,X4,X3)),
inference(substitution,[status(thm)],[c323]) ).
cnf(c325,plain,
f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(X5,X4,X3))) = f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3),f(f(X7,X6,X5),f(X2,X4,X3),f(X5,X4,X3))),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3),f(f(X7,X6,X5),f(X2,X4,X3),f(X5,X4,X3))) = f(f(X7,X6,X5),f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c327,plain,
f(f(X7,X6,X5),f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3)) = f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X7,X6,X5),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c328,plain,
f(f(X7,X2,X3),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X2,X3),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c329,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X2,X3),f(X6,X5,X4)) = f(f(X7,X2,X3),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)),
inference(symmetry,[status(thm)],[c328]) ).
cnf(c330,plain,
f(X2,X4,X3) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c331,plain,
f(X2,X3,X4) = f(X2,X4,X3),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
f(f(X5,X4,X3),X4,f(X2,X4,X5)) = f(f(X5,X4,X3),X4,f(X2,X5,X4)),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
f(f(X5,X4,X3),X4,f(X2,X5,X4)) = f(X2,X4,f(f(X5,X4,X3),X4,X5)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c334,plain,
f(X3,X4,f(X4,X3,X2)) = f(f(X4,X3,X2),X3,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c335,plain,
f(f(X4,X3,X2),X3,X4) = f(X3,X4,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c337,plain,
f(X4,X3,X2) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
f(X3,X4,f(X4,X3,X2)) = f(X3,X4,f(X3,X2,X4)),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
f(X3,X4,f(X3,X2,X4)) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c265]) ).
cnf(c340,plain,
f(X3,X4,X2) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c341,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c342,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c340,c341]) ).
cnf(c343,plain,
f(X3,X4,f(X3,X2,X4)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c339,c342]) ).
cnf(c344,plain,
f(X3,X4,f(X4,X3,X2)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c338,c343]) ).
cnf(c345,plain,
f(f(X4,X3,X2),X3,X4) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c335,c344]) ).
cnf(c346,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X5)) = f(X2,X4,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
f(X2,X4,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c348,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X5)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c346,c347]) ).
cnf(c349,plain,
f(f(X5,X4,X3),X4,f(X2,X5,X4)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c333,c348]) ).
cnf(c350,plain,
f(f(X5,X4,X3),X4,f(X2,X4,X5)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c332,c349]) ).
cnf(c351,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,X2,X3),f(X6,X5,X4),X7)) = f(f(X7,X2,X3),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c350]) ).
cnf(c352,plain,
f(f(X7,X2,X3),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,X2,X3),f(X6,X5,X4),X7)),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
f(X2,X3,X4) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c354,plain,
f(X2,X4,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c353]) ).
cnf(c355,plain,
f(f(X5,X4,X3),X5,f(X2,X5,X3)) = f(f(X5,X4,X3),X5,f(X2,X3,X5)),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
f(f(X5,X4,X3),X5,f(X2,X3,X5)) = f(X2,X5,f(f(X5,X4,X3),X5,X3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c357,plain,
f(X4,X2,f(X4,X3,X2)) = f(f(X4,X3,X2),X4,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c358,plain,
f(f(X4,X3,X2),X4,X2) = f(X4,X2,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
f(X4,X2,f(X4,X3,X2)) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c265]) ).
cnf(c360,plain,
f(X4,X2,X3) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c361,plain,
f(X4,X2,f(X4,X3,X2)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c359,c360]) ).
cnf(c362,plain,
f(f(X4,X3,X2),X4,X2) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c358,c361]) ).
cnf(c363,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X3)) = f(X2,X5,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
f(X2,X5,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c2]) ).
cnf(c365,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X3)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c363,c364]) ).
cnf(c366,plain,
f(f(X5,X4,X3),X5,f(X2,X3,X5)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c356,c365]) ).
cnf(c367,plain,
f(f(X5,X4,X3),X5,f(X2,X5,X3)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c355,c366]) ).
cnf(c368,plain,
f(f(X7,X6,X5),X7,f(f(X7,f(X4,X3,X2),f(X5,X3,X2)),X7,X5)) = f(f(X7,f(X4,X3,X2),f(X5,X3,X2)),f(X7,X6,X5),X7),
inference(substitution,[status(thm)],[c367]) ).
cnf(c369,plain,
f(f(X7,f(X4,X3,X2),f(X5,X3,X2)),f(X7,X6,X5),X7) = f(f(X7,X6,X5),X7,f(f(X7,f(X4,X3,X2),f(X5,X3,X2)),X7,X5)),
inference(symmetry,[status(thm)],[c368]) ).
cnf(c370,plain,
f(X3,f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2) = f(f(X3,f(X6,X5,X4),f(X2,X5,X4)),X3,X2),
inference(substitution,[status(thm)],[c55]) ).
cnf(c371,plain,
f(f(X3,f(X6,X5,X4),f(X2,X5,X4)),X3,X2) = f(X3,f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c372,plain,
f(f(X6,X5,X4),X3,f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3,f(f(X6,X5,X4),X2,X3)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c373,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3,f(f(X6,X5,X4),X2,X3)) = f(f(X6,X5,X4),X3,f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)),
inference(symmetry,[status(thm)],[c372]) ).
cnf(c374,plain,
f(f(X6,X5,X4),X3,f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)) = f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,f(X6,X5,X4),X2)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c375,plain,
f(X2,X3,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X3)) = f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,f(X6,X5,X4),X2)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c376,plain,
f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,f(X6,X5,X4),X2)) = f(X2,X3,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X3)),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X5,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c378,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),X2) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c377]) ).
cnf(c379,plain,
f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c380,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X5,X4,X3)) = f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c379]) ).
cnf(c381,plain,
f(X4,X2,X3) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c382,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
f(f(X5,X4,X3),X4,f(X4,X3,X2)) = f(f(X5,X4,X3),X4,f(X4,X2,X3)),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
f(f(X5,X4,X3),X4,f(X4,X2,X3)) = f(X4,X3,f(X2,f(X5,X4,X3),X4)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c385,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X3)) = f(X4,X3,f(X2,f(X5,X4,X3),X4)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c386,plain,
f(X4,X3,f(X2,f(X5,X4,X3),X4)) = f(X2,X4,f(f(X5,X4,X3),X4,X3)),
inference(symmetry,[status(thm)],[c385]) ).
cnf(c387,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X3)) = f(X2,X4,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c388,plain,
f(X2,X4,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c389,plain,
f(X2,X4,f(f(X5,X4,X3),X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c387,c388]) ).
cnf(c390,plain,
f(X4,X3,f(X2,f(X5,X4,X3),X4)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c386,c389]) ).
cnf(c391,plain,
f(f(X5,X4,X3),X4,f(X4,X2,X3)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c384,c390]) ).
cnf(c392,plain,
f(f(X5,X4,X3),X4,f(X4,X3,X2)) = f(X2,f(X5,X4,X3),X4),
inference(transitivity,[status(thm)],[c383,c391]) ).
cnf(c393,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)) = f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)),
inference(substitution,[status(thm)],[c392]) ).
cnf(c394,plain,
f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
f(X2,X3,X4) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c396,plain,
f(X2,X4,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c395]) ).
cnf(c397,plain,
f(f(X5,X4,X3),X5,f(X2,X5,X4)) = f(f(X5,X4,X3),X5,f(X2,X4,X5)),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
f(f(X5,X4,X3),X5,f(X2,X4,X5)) = f(X2,X5,f(f(X5,X4,X3),X5,X4)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c399,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X4)) = f(X2,X5,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c400,plain,
f(X2,X5,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c2]) ).
cnf(c401,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c399,c400]) ).
cnf(c402,plain,
f(f(X5,X4,X3),X5,f(X2,X4,X5)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c398,c401]) ).
cnf(c403,plain,
f(f(X5,X4,X3),X5,f(X2,X5,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c397,c402]) ).
cnf(c404,plain,
f(f(X2,X4,X3),X2,f(f(X5,X4,X3),X2,X4)) = f(f(X5,X4,X3),f(X2,X4,X3),X2),
inference(substitution,[status(thm)],[c403]) ).
cnf(c405,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X2) = f(f(X2,X4,X3),X2,f(f(X5,X4,X3),X2,X4)),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c406,plain,
f(f(X5,X4,X3),X2,X4) = f(f(X5,X4,X3),f(X2,X4,X3),X4),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c407,plain,
f(f(X2,X4,X3),X2,f(f(X5,X4,X3),X2,X4)) = f(f(X2,X4,X3),X2,f(f(X5,X4,X3),f(X2,X4,X3),X4)),
inference(congruence,[status(thm)],[c406]) ).
cnf(c408,plain,
f(f(X2,X4,X3),f(X5,X4,X3),f(f(X2,X4,X3),X2,X4)) = f(f(X2,X4,X3),X2,f(f(X5,X4,X3),f(X2,X4,X3),X4)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c409,plain,
f(f(X2,X4,X3),X2,f(f(X5,X4,X3),f(X2,X4,X3),X4)) = f(f(X2,X4,X3),f(X5,X4,X3),f(f(X2,X4,X3),X2,X4)),
inference(symmetry,[status(thm)],[c408]) ).
cnf(c410,plain,
f(f(X2,X4,X3),f(X5,X4,X3),f(f(X2,X4,X3),X2,X4)) = f(f(X5,X4,X3),f(X2,X4,X3),f(f(X2,X4,X3),X2,X4)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c411,plain,
f(f(X2,X4,X3),X2,X4) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c145]) ).
cnf(c412,plain,
f(f(X5,X4,X3),f(X2,X4,X3),f(f(X2,X4,X3),X2,X4)) = f(f(X5,X4,X3),f(X2,X4,X3),f(X2,X4,X3)),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
f(X2,X2,X3) = f(X3,X2,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c414,plain,
f(X3,X2,X2) = f(X2,X2,X3),
inference(symmetry,[status(thm)],[c413]) ).
cnf(c415,plain,
f(X2,X2,X3) = X2,
inference(substitution,[status(thm)],[c33]) ).
cnf(c416,plain,
f(X3,X2,X2) = X2,
inference(transitivity,[status(thm)],[c414,c415]) ).
cnf(c417,plain,
f(f(X5,X4,X3),f(X2,X4,X3),f(X2,X4,X3)) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c416]) ).
cnf(c418,plain,
f(f(X5,X4,X3),f(X2,X4,X3),f(f(X2,X4,X3),X2,X4)) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c412,c417]) ).
cnf(c419,plain,
f(f(X2,X4,X3),f(X5,X4,X3),f(f(X2,X4,X3),X2,X4)) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c410,c418]) ).
cnf(c420,plain,
f(f(X2,X4,X3),X2,f(f(X5,X4,X3),f(X2,X4,X3),X4)) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c409,c419]) ).
cnf(c421,plain,
f(f(X2,X4,X3),X2,f(f(X5,X4,X3),X2,X4)) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c407,c420]) ).
cnf(c422,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X2) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c405,c421]) ).
cnf(c423,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(X2,X4,X3)),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c425,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c423,c424]) ).
cnf(c426,plain,
f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c394,c425]) ).
cnf(c427,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X5,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c380,c426]) ).
cnf(c428,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),X2) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c378,c427]) ).
cnf(c429,plain,
f(X2,X3,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X3)) = f(X2,X3,f(X7,f(X6,X5,X4),f(X3,X5,X4))),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
f(X2,X3,f(X7,f(X6,X5,X4),f(X3,X5,X4))) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c431,plain,
f(X2,X3,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X3)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3),
inference(transitivity,[status(thm)],[c429,c430]) ).
cnf(c432,plain,
f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,f(X6,X5,X4),X2)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3),
inference(transitivity,[status(thm)],[c376,c431]) ).
cnf(c433,plain,
f(f(X6,X5,X4),X3,f(X3,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3),
inference(transitivity,[status(thm)],[c374,c432]) ).
cnf(c434,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3,f(f(X6,X5,X4),X2,X3)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X3),
inference(transitivity,[status(thm)],[c373,c433]) ).
cnf(c435,plain,
f(f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)) = f(X3,f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2),
inference(substitution,[status(thm)],[c434]) ).
cnf(c436,plain,
f(X3,f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2) = f(f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)),
inference(symmetry,[status(thm)],[c435]) ).
cnf(c437,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c438,plain,
f(f(X5,X4,X3),X2,f(X4,X5,X2)) = f(f(X5,X4,X3),X2,f(X5,X4,X2)),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
f(X5,X2,f(X2,f(X5,X4,X3),X4)) = f(f(X5,X4,X3),X2,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c440,plain,
f(f(X5,X4,X3),X2,f(X5,X4,X2)) = f(X5,X2,f(X2,f(X5,X4,X3),X4)),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
f(X2,f(X5,X4,X3),f(X2,X4,X5)) = f(X5,X2,f(X2,f(X5,X4,X3),X4)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c442,plain,
f(X5,X2,f(X2,f(X5,X4,X3),X4)) = f(X2,f(X5,X4,X3),f(X2,X4,X5)),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
f(X2,X3,X4) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c444,plain,
f(X4,X2,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c443]) ).
cnf(c445,plain,
f(X5,f(X4,X3,X2),f(X5,X3,X4)) = f(X5,f(X4,X3,X2),f(X3,X4,X5)),
inference(congruence,[status(thm)],[c444]) ).
cnf(c446,plain,
f(X3,X2,X4) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c55]) ).
cnf(c447,plain,
f(X2,X3,X4) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c446]) ).
cnf(c448,plain,
f(X5,f(X4,X3,X2),f(X3,X4,X5)) = f(X5,f(X4,X3,X2),f(X4,X3,X5)),
inference(congruence,[status(thm)],[c447]) ).
cnf(c449,plain,
f(X5,f(X4,X3,X2),f(X4,X3,X5)) = f(X5,X3,f(X5,X4,f(X4,X3,X2))),
inference(substitution,[status(thm)],[c233]) ).
cnf(c450,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c451,plain,
f(X4,X3,X2) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c450]) ).
cnf(c452,plain,
f(X5,X4,f(X4,X3,X2)) = f(X5,X4,f(X3,X2,X4)),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
f(X5,X3,f(X5,X4,f(X4,X3,X2))) = f(X5,X3,f(X5,X4,f(X3,X2,X4))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c455,plain,
f(X4,X2,X3) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c454]) ).
cnf(c456,plain,
f(X5,X3,f(X4,X2,X3)) = f(X5,X3,f(X4,X3,X2)),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
f(X5,X4,f(X5,X3,f(X4,X2,X3))) = f(X5,X4,f(X5,X3,f(X4,X3,X2))),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
f(X5,X4,f(X5,X3,f(X4,X2,X3))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c457,c297]) ).
cnf(c459,plain,
f(X5,X3,f(X5,X4,f(X3,X2,X4))) = f(X5,X3,X4),
inference(substitution,[status(thm)],[c458]) ).
cnf(c460,plain,
f(X5,X3,f(X5,X4,f(X4,X3,X2))) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c453,c459]) ).
cnf(c461,plain,
f(X5,f(X4,X3,X2),f(X4,X3,X5)) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c449,c460]) ).
cnf(c462,plain,
f(X5,f(X4,X3,X2),f(X3,X4,X5)) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c448,c461]) ).
cnf(c463,plain,
f(X5,f(X4,X3,X2),f(X5,X3,X4)) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c445,c462]) ).
cnf(c464,plain,
f(X2,f(X5,X4,X3),f(X2,X4,X5)) = f(X2,X4,X5),
inference(substitution,[status(thm)],[c463]) ).
cnf(c465,plain,
f(X5,X2,f(X2,f(X5,X4,X3),X4)) = f(X2,X4,X5),
inference(transitivity,[status(thm)],[c442,c464]) ).
cnf(c466,plain,
f(f(X5,X4,X3),X2,f(X5,X4,X2)) = f(X2,X4,X5),
inference(transitivity,[status(thm)],[c440,c465]) ).
cnf(c467,plain,
f(f(X5,X4,X3),X2,f(X4,X5,X2)) = f(X2,X4,X5),
inference(transitivity,[status(thm)],[c438,c466]) ).
cnf(c468,plain,
f(f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)) = f(X2,f(X6,X5,X4),X3),
inference(substitution,[status(thm)],[c467]) ).
cnf(c469,plain,
f(X2,f(X6,X5,X4),X3) = f(f(X6,X5,X4),X2,X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c470,plain,
f(f(X6,X5,X4),X2,X3) = f(f(X6,X5,X4),X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c471,plain,
f(X2,f(X6,X5,X4),X3) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c469,c470]) ).
cnf(c472,plain,
f(f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c468,c471]) ).
cnf(c473,plain,
f(X3,f(X3,f(X6,X5,X4),f(X2,X5,X4)),X2) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c436,c472]) ).
cnf(c474,plain,
f(f(X3,f(X6,X5,X4),f(X2,X5,X4)),X3,X2) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c371,c473]) ).
cnf(c475,plain,
f(f(X6,f(X4,X3,X2),f(X5,X3,X2)),X6,X5) = f(f(X4,X3,X2),X6,X5),
inference(substitution,[status(thm)],[c474]) ).
cnf(c476,plain,
f(f(X7,X6,X5),X7,f(f(X7,f(X4,X3,X2),f(X5,X3,X2)),X7,X5)) = f(f(X7,X6,X5),X7,f(f(X4,X3,X2),X7,X5)),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
f(f(X7,X6,X5),X7,f(f(X4,X3,X2),X7,X5)) = f(f(X4,X3,X2),f(X7,X6,X5),X7),
inference(substitution,[status(thm)],[c367]) ).
cnf(c478,plain,
f(f(X4,X3,X2),f(X7,X6,X5),X7) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(substitution,[status(thm)],[c55]) ).
cnf(c479,plain,
f(f(X7,X6,X5),X7,f(f(X4,X3,X2),X7,X5)) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(transitivity,[status(thm)],[c477,c478]) ).
cnf(c480,plain,
f(f(X7,X6,X5),X7,f(f(X7,f(X4,X3,X2),f(X5,X3,X2)),X7,X5)) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(transitivity,[status(thm)],[c476,c479]) ).
cnf(c481,plain,
f(f(X7,f(X4,X3,X2),f(X5,X3,X2)),f(X7,X6,X5),X7) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(transitivity,[status(thm)],[c369,c480]) ).
cnf(c482,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X2,X3),X7) = f(f(X7,X2,X3),f(X6,X5,X4),X7),
inference(substitution,[status(thm)],[c481]) ).
cnf(c483,plain,
f(f(X7,X2,X3),f(X6,X5,X4),X7) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X2,X3),X7),
inference(symmetry,[status(thm)],[c482]) ).
cnf(c484,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,X2,X3),f(X6,X5,X4),X7)) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X2,X3),X7)),
inference(congruence,[status(thm)],[c483]) ).
cnf(c485,plain,
f(f(X5,X4,X3),f(f(X5,X4,X3),X4,X5),X2) = f(f(X5,X4,X3),X4,f(f(X5,X4,X3),X2,X5)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c486,plain,
f(f(X5,X4,X3),X4,f(f(X5,X4,X3),X2,X5)) = f(f(X5,X4,X3),f(f(X5,X4,X3),X4,X5),X2),
inference(symmetry,[status(thm)],[c485]) ).
cnf(c487,plain,
f(f(X5,X4,X3),f(f(X5,X4,X3),X4,X5),X2) = f(f(X5,X4,X3),f(X5,X4,X3),X2),
inference(congruence,[status(thm)],[c345]) ).
cnf(c488,plain,
f(f(X5,X4,X3),f(X5,X4,X3),X2) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c33]) ).
cnf(c489,plain,
f(f(X5,X4,X3),f(f(X5,X4,X3),X4,X5),X2) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c487,c488]) ).
cnf(c490,plain,
f(f(X5,X4,X3),X4,f(f(X5,X4,X3),X2,X5)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c486,c489]) ).
cnf(c491,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X2,X3),X7)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c490]) ).
cnf(c492,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,X2,X3),f(X6,X5,X4),X7)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c484,c491]) ).
cnf(c493,plain,
f(f(X7,X2,X3),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c352,c492]) ).
cnf(c494,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X2,X3),f(X6,X5,X4)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c329,c493]) ).
cnf(c495,plain,
f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X7,X6,X5),f(X2,X4,X3)) = f(X7,f(X2,X4,X3),f(X5,X4,X3)),
inference(substitution,[status(thm)],[c494]) ).
cnf(c496,plain,
f(f(X7,X6,X5),f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3)) = f(X7,f(X2,X4,X3),f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c327,c495]) ).
cnf(c497,plain,
f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3),f(f(X7,X6,X5),f(X2,X4,X3),f(X5,X4,X3))) = f(X7,f(X2,X4,X3),f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c326,c496]) ).
cnf(c498,plain,
f(f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(X5,X4,X3))) = f(X7,f(X2,X4,X3),f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c325,c497]) ).
cnf(c499,plain,
f(f(f(X7,X6,X5),X4,X3),f(X7,f(X2,X4,X3),f(X5,X4,X3)),f(X2,X4,X3)) = f(X7,f(X2,X4,X3),f(X5,X4,X3)),
inference(transitivity,[status(thm)],[c51,c498]) ).
cnf(c500,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c499]) ).
cnf(c501,plain,
f(X6,f(X5,X4,X3),f(X2,X4,X3)) = f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c500]) ).
cnf(c502,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X3,X6,X5)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c503,plain,
f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5)) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X3,X6,X5)),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X5,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c2]) ).
cnf(c505,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),X5) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c504]) ).
cnf(c506,plain,
f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c507,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X5,X4,X3)) = f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c506]) ).
cnf(c508,plain,
f(f(X3,X5,X4),X5,X2) = f(X2,f(X3,X5,X4),X5),
inference(substitution,[status(thm)],[c6]) ).
cnf(c509,plain,
f(X2,f(X3,X5,X4),X5) = f(f(X3,X5,X4),X5,X2),
inference(symmetry,[status(thm)],[c508]) ).
cnf(c510,plain,
f(X5,X2,f(X3,X5,X4)) = f(f(X3,X5,X4),X5,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c511,plain,
f(f(X3,X5,X4),X5,X2) = f(X5,X2,f(X3,X5,X4)),
inference(symmetry,[status(thm)],[c510]) ).
cnf(c512,plain,
f(X4,X3,X2) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c513,plain,
f(X2,X4,X3) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c512]) ).
cnf(c514,plain,
f(X5,X2,f(X3,X5,X4)) = f(X5,X2,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
f(X5,X3,f(X5,X2,X4)) = f(X5,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c516,plain,
f(X5,X2,f(X5,X4,X3)) = f(X5,X3,f(X5,X2,X4)),
inference(symmetry,[status(thm)],[c515]) ).
cnf(c517,plain,
f(X5,X4,f(X5,X3,X2)) = f(X5,X3,f(X5,X2,X4)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c518,plain,
f(X5,X3,f(X5,X2,X4)) = f(X5,X4,f(X5,X3,X2)),
inference(symmetry,[status(thm)],[c517]) ).
cnf(c519,plain,
f(X5,X2,f(X5,X4,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c516,c518]) ).
cnf(c520,plain,
f(X5,X2,f(X3,X5,X4)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c514,c519]) ).
cnf(c521,plain,
f(f(X3,X5,X4),X5,X2) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c511,c520]) ).
cnf(c522,plain,
f(X2,f(X3,X5,X4),X5) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c509,c521]) ).
cnf(c523,plain,
f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(f(X5,X4,X3),f(X2,X4,X3),f(f(X5,X4,X3),X6,X5)),
inference(substitution,[status(thm)],[c522]) ).
cnf(c524,plain,
f(f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X6),X2) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X2,X6)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c525,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X2,X6)) = f(f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X6),X2),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c526,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(f(X5,X4,X3),f(X2,X4,X3),X5),
inference(substitution,[status(thm)],[c55]) ).
cnf(c527,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(symmetry,[status(thm)],[c526]) ).
cnf(c528,plain,
f(f(X5,X4,X3),X5,f(f(X2,X4,X3),X5,X4)) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c403]) ).
cnf(c529,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(f(X5,X4,X3),X5,f(f(X2,X4,X3),X5,X4)),
inference(symmetry,[status(thm)],[c528]) ).
cnf(c530,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X4) = f(f(X2,X4,X3),X5,X4),
inference(substitution,[status(thm)],[c171]) ).
cnf(c531,plain,
f(X5,f(X2,X4,X3),X4) = f(f(X2,X4,X3),X5,X4),
inference(substitution,[status(thm)],[c55]) ).
cnf(c532,plain,
f(f(X2,X4,X3),X5,X4) = f(X5,f(X2,X4,X3),X4),
inference(symmetry,[status(thm)],[c531]) ).
cnf(c533,plain,
f(X5,f(X2,X4,X3),X4) = f(X2,X4,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c166]) ).
cnf(c534,plain,
f(X2,X4,f(X5,X4,X3)) = f(f(X5,X4,X3),X2,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c535,plain,
f(X5,f(X2,X4,X3),X4) = f(f(X5,X4,X3),X2,X4),
inference(transitivity,[status(thm)],[c533,c534]) ).
cnf(c536,plain,
f(f(X2,X4,X3),X5,X4) = f(f(X5,X4,X3),X2,X4),
inference(transitivity,[status(thm)],[c532,c535]) ).
cnf(c537,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X4) = f(f(X5,X4,X3),X2,X4),
inference(transitivity,[status(thm)],[c530,c536]) ).
cnf(c538,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X4) = f(f(X2,X4,X3),X5,X4),
inference(substitution,[status(thm)],[c537]) ).
cnf(c539,plain,
f(f(X2,X4,X3),X5,X4) = f(f(X5,X4,X3),f(X2,X4,X3),X4),
inference(symmetry,[status(thm)],[c538]) ).
cnf(c540,plain,
f(f(X5,X4,X3),X5,f(f(X2,X4,X3),X5,X4)) = f(f(X5,X4,X3),X5,f(f(X5,X4,X3),f(X2,X4,X3),X4)),
inference(congruence,[status(thm)],[c539]) ).
cnf(c541,plain,
f(f(X5,X4,X3),X5,f(f(X5,X4,X3),f(X2,X4,X3),X4)) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c187]) ).
cnf(c542,plain,
f(f(X5,X4,X3),X5,f(f(X2,X4,X3),X5,X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c540,c541]) ).
cnf(c543,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c529,c542]) ).
cnf(c544,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c527,c543]) ).
cnf(c545,plain,
f(f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X6),X2) = f(f(X6,X5,X4),f(X6,X5,X4),X2),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
f(f(X5,X4,X3),f(X5,X4,X3),X2) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c33]) ).
cnf(c547,plain,
f(f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X6),X2) = f(X6,X5,X4),
inference(transitivity,[status(thm)],[c545,c546]) ).
cnf(c548,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X2,X6)) = f(X6,X5,X4),
inference(transitivity,[status(thm)],[c525,c547]) ).
cnf(c549,plain,
f(f(X5,X4,X3),f(X2,X4,X3),f(f(X5,X4,X3),X6,X5)) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c548]) ).
cnf(c550,plain,
f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c523,c549]) ).
cnf(c551,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X5,X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c507,c550]) ).
cnf(c552,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c505,c551]) ).
cnf(c553,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5),X3) = f(X3,X6,X5),
inference(substitution,[status(thm)],[c552]) ).
cnf(c554,plain,
f(X3,X6,X5) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5),X3),
inference(symmetry,[status(thm)],[c553]) ).
cnf(c555,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X3,X6,X5)) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5),X3)),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
f(X5,X2,f(X2,X4,X3)) = f(X5,f(X2,X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c557,plain,
f(X5,f(X2,X4,X3),X2) = f(X5,X2,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c556]) ).
cnf(c558,plain,
f(X6,f(X5,X4,X3),f(X6,f(X2,X4,X3),X2)) = f(X6,f(X5,X4,X3),f(X6,X2,f(X2,X4,X3))),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
f(X2,X4,X3) = f(f(X5,X4,X3),f(X2,X4,X3),X2),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c560,plain,
f(X6,X2,f(X2,X4,X3)) = f(X6,X2,f(f(X5,X4,X3),f(X2,X4,X3),X2)),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
f(X6,f(X5,X4,X3),f(X6,X2,f(X2,X4,X3))) = f(X6,f(X5,X4,X3),f(X6,X2,f(f(X5,X4,X3),f(X2,X4,X3),X2))),
inference(congruence,[status(thm)],[c560]) ).
cnf(c562,plain,
f(X6,f(X5,X4,X3),f(X6,X2,f(f(X5,X4,X3),f(X2,X4,X3),X2))) = f(X6,f(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c458]) ).
cnf(c563,plain,
f(X6,f(X5,X4,X3),f(X6,X2,f(X2,X4,X3))) = f(X6,f(X5,X4,X3),X2),
inference(transitivity,[status(thm)],[c561,c562]) ).
cnf(c564,plain,
f(X6,f(X5,X4,X3),f(X6,f(X2,X4,X3),X2)) = f(X6,f(X5,X4,X3),X2),
inference(transitivity,[status(thm)],[c558,c563]) ).
cnf(c565,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5),X3)) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),X3),
inference(substitution,[status(thm)],[c564]) ).
cnf(c566,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),X3) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c567,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5),X3)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X3),
inference(transitivity,[status(thm)],[c565,c566]) ).
cnf(c568,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X3,X6,X5)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X3),
inference(transitivity,[status(thm)],[c555,c567]) ).
cnf(c569,plain,
f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X3,X6,X5)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X3),
inference(transitivity,[status(thm)],[c503,c568]) ).
cnf(c570,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5),
inference(substitution,[status(thm)],[c569]) ).
cnf(c571,plain,
f(f(f(X6,X5,X2),X4,X3),X5,f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5),
inference(substitution,[status(thm)],[c2]) ).
cnf(c572,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5) = f(f(f(X6,X5,X2),X4,X3),X5,f(X6,f(X5,X4,X3),f(X2,X4,X3))),
inference(symmetry,[status(thm)],[c571]) ).
cnf(c573,plain,
f(X2,X3,X4) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c574,plain,
f(X2,X4,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
f(f(X5,X4,X3),X3,f(X2,X4,X3)) = f(f(X5,X4,X3),X3,f(X2,X3,X4)),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
f(X2,X3,f(f(X5,X4,X3),X4,X3)) = f(f(X5,X4,X3),X3,f(X2,X3,X4)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c577,plain,
f(f(X5,X4,X3),X3,f(X2,X3,X4)) = f(X2,X3,f(f(X5,X4,X3),X4,X3)),
inference(symmetry,[status(thm)],[c576]) ).
cnf(c578,plain,
f(X2,X3,f(f(X5,X4,X3),X4,X3)) = f(X2,X3,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c579,plain,
f(X2,X3,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c580,plain,
f(X2,X3,f(f(X5,X4,X3),X4,X3)) = f(X2,f(X5,X4,X3),X3),
inference(transitivity,[status(thm)],[c578,c579]) ).
cnf(c581,plain,
f(f(X5,X4,X3),X3,f(X2,X3,X4)) = f(X2,f(X5,X4,X3),X3),
inference(transitivity,[status(thm)],[c577,c580]) ).
cnf(c582,plain,
f(f(X5,X4,X3),X3,f(X2,X4,X3)) = f(X2,f(X5,X4,X3),X3),
inference(transitivity,[status(thm)],[c575,c581]) ).
cnf(c583,plain,
f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X6,X4,X3),f(X2,X4,X3))) = f(f(f(X7,X6,X5),X4,X3),f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c582]) ).
cnf(c584,plain,
f(f(f(X7,X6,X5),X4,X3),f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X6,X4,X3),f(X2,X4,X3))),
inference(symmetry,[status(thm)],[c583]) ).
cnf(c585,plain,
f(f(f(X7,X6,X5),X4,X3),f(X6,X4,X3),f(X2,X4,X3)) = f(f(X7,X6,X5),f(X6,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c323]) ).
cnf(c586,plain,
f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X6,X4,X3),f(X2,X4,X3))) = f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X7,X6,X5),f(X6,X4,X3),f(X2,X4,X3))),
inference(congruence,[status(thm)],[c585]) ).
cnf(c587,plain,
f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X7,X6,X5),f(X6,X4,X3),f(X2,X4,X3))) = f(f(X7,X6,X5),f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c582]) ).
cnf(c588,plain,
f(f(X7,X6,X5),f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X7,X6,X5),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c589,plain,
f(f(X7,X6,X2),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4)) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c590,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),f(X3,X5,X4)) = f(f(X7,X6,X2),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4)),
inference(symmetry,[status(thm)],[c589]) ).
cnf(c591,plain,
f(f(X2,X5,X4),X4,X3) = f(X3,f(X2,X5,X4),X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c592,plain,
f(X3,f(X2,X5,X4),X4) = f(f(X2,X5,X4),X4,X3),
inference(symmetry,[status(thm)],[c591]) ).
cnf(c593,plain,
f(X4,X3,f(X2,X5,X4)) = f(f(X2,X5,X4),X4,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c594,plain,
f(f(X2,X5,X4),X4,X3) = f(X4,X3,f(X2,X5,X4)),
inference(symmetry,[status(thm)],[c593]) ).
cnf(c595,plain,
f(X4,X3,X2) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c596,plain,
f(X2,X4,X3) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c595]) ).
cnf(c597,plain,
f(X4,X3,f(X2,X5,X4)) = f(X4,X3,f(X5,X4,X2)),
inference(congruence,[status(thm)],[c596]) ).
cnf(c598,plain,
f(X5,X4,f(X2,X4,X3)) = f(X4,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c599,plain,
f(X4,X3,f(X5,X4,X2)) = f(X5,X4,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c598]) ).
cnf(c600,plain,
f(X2,X4,X3) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c601,plain,
f(X5,X4,f(X2,X4,X3)) = f(X5,X4,f(X4,X2,X3)),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
f(X4,X2,X3) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c603,plain,
f(X5,X4,f(X4,X2,X3)) = f(X5,X4,f(X3,X4,X2)),
inference(congruence,[status(thm)],[c602]) ).
cnf(c604,plain,
f(X5,X4,f(X2,X4,X3)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c601,c603]) ).
cnf(c605,plain,
f(X4,X3,f(X5,X4,X2)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c599,c604]) ).
cnf(c606,plain,
f(X4,X3,f(X2,X5,X4)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c597,c605]) ).
cnf(c607,plain,
f(f(X2,X5,X4),X4,X3) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c594,c606]) ).
cnf(c608,plain,
f(X3,f(X2,X5,X4),X4) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c592,c607]) ).
cnf(c609,plain,
f(f(X7,X6,X2),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X7,X6,X2),f(X3,X5,X4),X7)),
inference(substitution,[status(thm)],[c608]) ).
cnf(c610,plain,
f(f(X7,X6,X5),X7,f(f(X7,f(X6,X3,X2),f(X4,X3,X2)),X7,X6)) = f(f(X7,f(X6,X3,X2),f(X4,X3,X2)),f(X7,X6,X5),X7),
inference(substitution,[status(thm)],[c403]) ).
cnf(c611,plain,
f(f(X7,f(X6,X3,X2),f(X4,X3,X2)),f(X7,X6,X5),X7) = f(f(X7,X6,X5),X7,f(f(X7,f(X6,X3,X2),f(X4,X3,X2)),X7,X6)),
inference(symmetry,[status(thm)],[c610]) ).
cnf(c612,plain,
f(X3,f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2) = f(f(X3,f(X2,X5,X4),f(X6,X5,X4)),X3,X2),
inference(substitution,[status(thm)],[c55]) ).
cnf(c613,plain,
f(f(X3,f(X2,X5,X4),f(X6,X5,X4)),X3,X2) = f(X3,f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2),
inference(symmetry,[status(thm)],[c612]) ).
cnf(c614,plain,
f(f(X3,X5,X4),X6,f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6,f(f(X3,X5,X4),X2,X6)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c615,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6,f(f(X3,X5,X4),X2,X6)) = f(f(X3,X5,X4),X6,f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)),
inference(symmetry,[status(thm)],[c614]) ).
cnf(c616,plain,
f(f(X3,X5,X4),X6,f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)) = f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,f(X3,X5,X4),X2)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c617,plain,
f(X2,X6,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4),X6)) = f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,f(X3,X5,X4),X2)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c618,plain,
f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,f(X3,X5,X4),X2)) = f(X2,X6,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4),X6)),
inference(symmetry,[status(thm)],[c617]) ).
cnf(c619,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X2,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),X5),
inference(substitution,[status(thm)],[c2]) ).
cnf(c620,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),X5) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c619]) ).
cnf(c621,plain,
f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c622,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X2,X4,X3)) = f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c621]) ).
cnf(c623,plain,
f(f(X5,X4,X3),X3,f(X4,X3,X2)) = f(X3,X2,f(f(X5,X4,X3),X4,X3)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c624,plain,
f(X3,X2,f(f(X5,X4,X3),X4,X3)) = f(X3,X2,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c625,plain,
f(X3,X2,f(X5,X4,X3)) = f(f(X5,X4,X3),X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c626,plain,
f(f(X5,X4,X3),X3,X2) = f(X2,f(X5,X4,X3),X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c627,plain,
f(X3,X2,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X3),
inference(transitivity,[status(thm)],[c625,c626]) ).
cnf(c628,plain,
f(X3,X2,f(f(X5,X4,X3),X4,X3)) = f(X2,f(X5,X4,X3),X3),
inference(transitivity,[status(thm)],[c624,c627]) ).
cnf(c629,plain,
f(f(X5,X4,X3),X3,f(X4,X3,X2)) = f(X2,f(X5,X4,X3),X3),
inference(transitivity,[status(thm)],[c623,c628]) ).
cnf(c630,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X5)) = f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c629]) ).
cnf(c631,plain,
f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X5)),
inference(symmetry,[status(thm)],[c630]) ).
cnf(c632,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X5)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(X5,X4,X3)),
inference(congruence,[status(thm)],[c544]) ).
cnf(c633,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(X5,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c634,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c635,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(X5,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c633,c634]) ).
cnf(c636,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X5)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c632,c635]) ).
cnf(c637,plain,
f(X5,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c631,c636]) ).
cnf(c638,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5,f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c622,c637]) ).
cnf(c639,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),X5) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c620,c638]) ).
cnf(c640,plain,
f(X2,X6,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4),X6)) = f(X2,X6,f(X7,f(X6,X5,X4),f(X3,X5,X4))),
inference(congruence,[status(thm)],[c639]) ).
cnf(c641,plain,
f(X2,X6,f(X7,f(X6,X5,X4),f(X3,X5,X4))) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6),
inference(substitution,[status(thm)],[c2]) ).
cnf(c642,plain,
f(X2,X6,f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4),X6)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6),
inference(transitivity,[status(thm)],[c640,c641]) ).
cnf(c643,plain,
f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,f(X3,X5,X4),X2)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6),
inference(transitivity,[status(thm)],[c618,c642]) ).
cnf(c644,plain,
f(f(X3,X5,X4),X6,f(X6,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X2)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6),
inference(transitivity,[status(thm)],[c616,c643]) ).
cnf(c645,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6,f(f(X3,X5,X4),X2,X6)) = f(X2,f(X7,f(X6,X5,X4),f(X3,X5,X4)),X6),
inference(transitivity,[status(thm)],[c615,c644]) ).
cnf(c646,plain,
f(f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)) = f(X3,f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2),
inference(substitution,[status(thm)],[c645]) ).
cnf(c647,plain,
f(X3,f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2) = f(f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)),
inference(symmetry,[status(thm)],[c646]) ).
cnf(c648,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c649,plain,
f(f(X5,X4,X3),X2,f(X3,X5,X2)) = f(f(X5,X4,X3),X2,f(X5,X3,X2)),
inference(congruence,[status(thm)],[c648]) ).
cnf(c650,plain,
f(X5,X2,f(X2,f(X5,X4,X3),X3)) = f(f(X5,X4,X3),X2,f(X5,X3,X2)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c651,plain,
f(f(X5,X4,X3),X2,f(X5,X3,X2)) = f(X5,X2,f(X2,f(X5,X4,X3),X3)),
inference(symmetry,[status(thm)],[c650]) ).
cnf(c652,plain,
f(X2,f(X5,X4,X3),f(X2,X3,X5)) = f(X5,X2,f(X2,f(X5,X4,X3),X3)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c653,plain,
f(X5,X2,f(X2,f(X5,X4,X3),X3)) = f(X2,f(X5,X4,X3),f(X2,X3,X5)),
inference(symmetry,[status(thm)],[c652]) ).
cnf(c654,plain,
f(X2,X3,X4) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c655,plain,
f(X4,X2,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c654]) ).
cnf(c656,plain,
f(X5,f(X4,X3,X2),f(X5,X2,X4)) = f(X5,f(X4,X3,X2),f(X2,X4,X5)),
inference(congruence,[status(thm)],[c655]) ).
cnf(c657,plain,
f(X3,X2,X4) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c55]) ).
cnf(c658,plain,
f(X2,X3,X4) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c657]) ).
cnf(c659,plain,
f(X5,f(X4,X3,X2),f(X2,X4,X5)) = f(X5,f(X4,X3,X2),f(X4,X2,X5)),
inference(congruence,[status(thm)],[c658]) ).
cnf(c660,plain,
f(X5,f(X4,X3,X2),f(X4,X2,X5)) = f(X5,X2,f(X5,X4,f(X4,X3,X2))),
inference(substitution,[status(thm)],[c233]) ).
cnf(c661,plain,
f(X5,X2,f(X5,X4,f(X4,X3,X2))) = f(X5,X4,f(X2,X5,f(X4,X3,X2))),
inference(substitution,[status(thm)],[c237]) ).
cnf(c662,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c663,plain,
f(X4,X3,X2) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c662]) ).
cnf(c664,plain,
f(X2,X5,f(X4,X3,X2)) = f(X2,X5,f(X3,X2,X4)),
inference(congruence,[status(thm)],[c663]) ).
cnf(c665,plain,
f(X5,X4,f(X2,X5,f(X4,X3,X2))) = f(X5,X4,f(X2,X5,f(X3,X2,X4))),
inference(congruence,[status(thm)],[c664]) ).
cnf(c666,plain,
f(X5,X4,f(X2,X5,f(X3,X2,X4))) = f(X4,X5,X2),
inference(substitution,[status(thm)],[c302]) ).
cnf(c667,plain,
f(X3,X4,X2) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c668,plain,
f(X2,X3,X4) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c669,plain,
f(X3,X4,X2) = f(X4,X2,X3),
inference(transitivity,[status(thm)],[c667,c668]) ).
cnf(c670,plain,
f(X5,X4,f(X2,X5,f(X3,X2,X4))) = f(X5,X2,X4),
inference(transitivity,[status(thm)],[c666,c669]) ).
cnf(c671,plain,
f(X5,X4,f(X2,X5,f(X4,X3,X2))) = f(X5,X2,X4),
inference(transitivity,[status(thm)],[c665,c670]) ).
cnf(c672,plain,
f(X5,X2,f(X5,X4,f(X4,X3,X2))) = f(X5,X2,X4),
inference(transitivity,[status(thm)],[c661,c671]) ).
cnf(c673,plain,
f(X5,f(X4,X3,X2),f(X4,X2,X5)) = f(X5,X2,X4),
inference(transitivity,[status(thm)],[c660,c672]) ).
cnf(c674,plain,
f(X5,f(X4,X3,X2),f(X2,X4,X5)) = f(X5,X2,X4),
inference(transitivity,[status(thm)],[c659,c673]) ).
cnf(c675,plain,
f(X5,f(X4,X3,X2),f(X5,X2,X4)) = f(X5,X2,X4),
inference(transitivity,[status(thm)],[c656,c674]) ).
cnf(c676,plain,
f(X2,f(X5,X4,X3),f(X2,X3,X5)) = f(X2,X3,X5),
inference(substitution,[status(thm)],[c675]) ).
cnf(c677,plain,
f(X5,X2,f(X2,f(X5,X4,X3),X3)) = f(X2,X3,X5),
inference(transitivity,[status(thm)],[c653,c676]) ).
cnf(c678,plain,
f(f(X5,X4,X3),X2,f(X5,X3,X2)) = f(X2,X3,X5),
inference(transitivity,[status(thm)],[c651,c677]) ).
cnf(c679,plain,
f(f(X5,X4,X3),X2,f(X3,X5,X2)) = f(X2,X3,X5),
inference(transitivity,[status(thm)],[c649,c678]) ).
cnf(c680,plain,
f(f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)) = f(X2,f(X6,X5,X4),X3),
inference(substitution,[status(thm)],[c679]) ).
cnf(c681,plain,
f(X2,f(X6,X5,X4),X3) = f(f(X6,X5,X4),X2,X3),
inference(substitution,[status(thm)],[c55]) ).
cnf(c682,plain,
f(f(X6,X5,X4),X2,X3) = f(f(X6,X5,X4),X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c683,plain,
f(X2,f(X6,X5,X4),X3) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c681,c682]) ).
cnf(c684,plain,
f(f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2,f(f(X6,X5,X4),X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c680,c683]) ).
cnf(c685,plain,
f(X3,f(X3,f(X2,X5,X4),f(X6,X5,X4)),X2) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c647,c684]) ).
cnf(c686,plain,
f(f(X3,f(X2,X5,X4),f(X6,X5,X4)),X3,X2) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c613,c685]) ).
cnf(c687,plain,
f(f(X6,f(X5,X3,X2),f(X4,X3,X2)),X6,X5) = f(f(X4,X3,X2),X6,X5),
inference(substitution,[status(thm)],[c686]) ).
cnf(c688,plain,
f(f(X7,X6,X5),X7,f(f(X7,f(X6,X3,X2),f(X4,X3,X2)),X7,X6)) = f(f(X7,X6,X5),X7,f(f(X4,X3,X2),X7,X6)),
inference(congruence,[status(thm)],[c687]) ).
cnf(c689,plain,
f(f(X7,X6,X5),X7,f(f(X4,X3,X2),X7,X6)) = f(f(X4,X3,X2),f(X7,X6,X5),X7),
inference(substitution,[status(thm)],[c403]) ).
cnf(c690,plain,
f(f(X4,X3,X2),f(X7,X6,X5),X7) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(substitution,[status(thm)],[c55]) ).
cnf(c691,plain,
f(f(X7,X6,X5),X7,f(f(X4,X3,X2),X7,X6)) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(transitivity,[status(thm)],[c689,c690]) ).
cnf(c692,plain,
f(f(X7,X6,X5),X7,f(f(X7,f(X6,X3,X2),f(X4,X3,X2)),X7,X6)) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(transitivity,[status(thm)],[c688,c691]) ).
cnf(c693,plain,
f(f(X7,f(X6,X3,X2),f(X4,X3,X2)),f(X7,X6,X5),X7) = f(f(X7,X6,X5),f(X4,X3,X2),X7),
inference(transitivity,[status(thm)],[c611,c692]) ).
cnf(c694,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),X7) = f(f(X7,X6,X2),f(X3,X5,X4),X7),
inference(substitution,[status(thm)],[c693]) ).
cnf(c695,plain,
f(f(X7,X6,X2),f(X3,X5,X4),X7) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),X7),
inference(symmetry,[status(thm)],[c694]) ).
cnf(c696,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X7,X6,X2),f(X3,X5,X4),X7)) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),X7)),
inference(congruence,[status(thm)],[c695]) ).
cnf(c697,plain,
f(X2,X3,X4) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c698,plain,
f(X4,X2,X3) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c697]) ).
cnf(c699,plain,
f(f(X3,X6,X5),X6,f(X4,X2,X3)) = f(f(X3,X6,X5),X6,f(X2,X3,X4)),
inference(congruence,[status(thm)],[c698]) ).
cnf(c700,plain,
f(f(X3,X6,X5),f(X2,X3,X4),X6) = f(f(X3,X6,X5),X6,f(X2,X3,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c701,plain,
f(f(X3,X6,X5),X6,f(X2,X3,X4)) = f(f(X3,X6,X5),f(X2,X3,X4),X6),
inference(symmetry,[status(thm)],[c700]) ).
cnf(c702,plain,
f(f(X2,X3,X4),f(X3,X6,X5),X6) = f(f(X3,X6,X5),f(X2,X3,X4),X6),
inference(substitution,[status(thm)],[c55]) ).
cnf(c703,plain,
f(f(X3,X6,X5),f(X2,X3,X4),X6) = f(f(X2,X3,X4),f(X3,X6,X5),X6),
inference(symmetry,[status(thm)],[c702]) ).
cnf(c704,plain,
f(f(X2,X3,X4),f(X3,X6,X5),X6) = f(X6,X5,f(X6,X3,f(X2,X3,X4))),
inference(substitution,[status(thm)],[c522]) ).
cnf(c705,plain,
f(X4,X2,X3) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c706,plain,
f(X4,X2,f(X5,X3,X4)) = f(X4,X2,f(X4,X5,X3)),
inference(congruence,[status(thm)],[c705]) ).
cnf(c707,plain,
f(X4,X2,f(X4,X5,X3)) = f(f(X4,X5,X3),X4,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c708,plain,
f(f(X4,X5,X3),X4,X2) = f(X2,f(X4,X5,X3),X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c709,plain,
f(X4,X2,f(X4,X5,X3)) = f(X2,f(X4,X5,X3),X4),
inference(transitivity,[status(thm)],[c707,c708]) ).
cnf(c710,plain,
f(X4,X2,f(X5,X3,X4)) = f(X2,f(X4,X5,X3),X4),
inference(transitivity,[status(thm)],[c706,c709]) ).
cnf(c711,plain,
f(X5,X4,f(X3,X4,X2)) = f(X2,f(X4,X5,X3),X4),
inference(transitivity,[status(thm)],[c137,c710]) ).
cnf(c712,plain,
f(X5,X3,f(X2,X3,X4)) = f(X4,f(X3,X5,X2),X3),
inference(substitution,[status(thm)],[c711]) ).
cnf(c713,plain,
f(X6,X5,f(X6,X3,f(X2,X3,X4))) = f(X6,X5,f(X4,f(X3,X6,X2),X3)),
inference(congruence,[status(thm)],[c712]) ).
cnf(c714,plain,
f(f(X2,X3,X4),f(X3,X6,X5),X6) = f(X6,X5,f(X4,f(X3,X6,X2),X3)),
inference(transitivity,[status(thm)],[c704,c713]) ).
cnf(c715,plain,
f(f(X3,X6,X5),f(X2,X3,X4),X6) = f(X6,X5,f(X4,f(X3,X6,X2),X3)),
inference(transitivity,[status(thm)],[c703,c714]) ).
cnf(c716,plain,
f(f(X3,X6,X5),X6,f(X2,X3,X4)) = f(X6,X5,f(X4,f(X3,X6,X2),X3)),
inference(transitivity,[status(thm)],[c701,c715]) ).
cnf(c717,plain,
f(f(X3,X6,X5),X6,f(X4,X2,X3)) = f(X6,X5,f(X4,f(X3,X6,X2),X3)),
inference(transitivity,[status(thm)],[c699,c716]) ).
cnf(c718,plain,
f(f(X4,X6,X5),X6,f(X2,X3,X4)) = f(X6,X5,f(X2,f(X4,X6,X3),X4)),
inference(substitution,[status(thm)],[c717]) ).
cnf(c719,plain,
f(X2,f(X4,X5,X3),X4) = f(f(X4,X5,X3),X2,X4),
inference(substitution,[status(thm)],[c55]) ).
cnf(c720,plain,
f(X6,X5,f(X2,f(X4,X6,X3),X4)) = f(X6,X5,f(f(X4,X6,X3),X2,X4)),
inference(congruence,[status(thm)],[c719]) ).
cnf(c721,plain,
f(f(X4,X6,X5),X6,f(X2,X3,X4)) = f(X6,X5,f(f(X4,X6,X3),X2,X4)),
inference(transitivity,[status(thm)],[c718,c720]) ).
cnf(c722,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,X6,X2),f(X3,X5,X4),X7)) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),X7)),
inference(substitution,[status(thm)],[c721]) ).
cnf(c723,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),X7)) = f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,X6,X2),f(X3,X5,X4),X7)),
inference(symmetry,[status(thm)],[c722]) ).
cnf(c724,plain,
f(X3,X4,X2) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c725,plain,
f(X2,X3,X4) = f(X3,X4,X2),
inference(symmetry,[status(thm)],[c724]) ).
cnf(c726,plain,
f(f(X5,X4,X3),X4,f(X2,X3,X5)) = f(f(X5,X4,X3),X4,f(X3,X5,X2)),
inference(congruence,[status(thm)],[c725]) ).
cnf(c727,plain,
f(f(X5,X4,X3),f(X3,X5,X2),X4) = f(f(X5,X4,X3),X4,f(X3,X5,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c728,plain,
f(f(X5,X4,X3),X4,f(X3,X5,X2)) = f(f(X5,X4,X3),f(X3,X5,X2),X4),
inference(symmetry,[status(thm)],[c727]) ).
cnf(c729,plain,
f(f(X3,X5,X2),f(X5,X4,X3),X4) = f(f(X5,X4,X3),f(X3,X5,X2),X4),
inference(substitution,[status(thm)],[c55]) ).
cnf(c730,plain,
f(f(X5,X4,X3),f(X3,X5,X2),X4) = f(f(X3,X5,X2),f(X5,X4,X3),X4),
inference(symmetry,[status(thm)],[c729]) ).
cnf(c731,plain,
f(f(X3,X5,X2),f(X5,X4,X3),X4) = f(X4,X3,f(X4,X5,f(X3,X5,X2))),
inference(substitution,[status(thm)],[c522]) ).
cnf(c732,plain,
f(X4,X3,f(X4,X5,f(X3,X5,X2))) = f(X4,X3,X5),
inference(substitution,[status(thm)],[c297]) ).
cnf(c733,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c734,plain,
f(X4,X3,f(X4,X5,f(X3,X5,X2))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c732,c733]) ).
cnf(c735,plain,
f(f(X3,X5,X2),f(X5,X4,X3),X4) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c731,c734]) ).
cnf(c736,plain,
f(f(X5,X4,X3),f(X3,X5,X2),X4) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c730,c735]) ).
cnf(c737,plain,
f(f(X5,X4,X3),X4,f(X3,X5,X2)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c728,c736]) ).
cnf(c738,plain,
f(f(X5,X4,X3),X4,f(X2,X3,X5)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c726,c737]) ).
cnf(c739,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),f(f(X7,X6,X2),f(X3,X5,X4),X7)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c738]) ).
cnf(c740,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),X7)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c723,c739]) ).
cnf(c741,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X7,X6,X2),f(X3,X5,X4),X7)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c696,c740]) ).
cnf(c742,plain,
f(f(X7,X6,X2),f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X3,X5,X4)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c609,c741]) ).
cnf(c743,plain,
f(f(X7,f(X6,X5,X4),f(X3,X5,X4)),f(X7,X6,X2),f(X3,X5,X4)) = f(X7,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c590,c742]) ).
cnf(c744,plain,
f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X7,X6,X5),f(X2,X4,X3)) = f(X7,f(X6,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c743]) ).
cnf(c745,plain,
f(f(X7,X6,X5),f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(X7,f(X6,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c588,c744]) ).
cnf(c746,plain,
f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X7,X6,X5),f(X6,X4,X3),f(X2,X4,X3))) = f(X7,f(X6,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c587,c745]) ).
cnf(c747,plain,
f(f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X6,X4,X3),f(X2,X4,X3))) = f(X7,f(X6,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c586,c746]) ).
cnf(c748,plain,
f(f(f(X7,X6,X5),X4,X3),f(X7,f(X6,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(X7,f(X6,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c584,c747]) ).
cnf(c749,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c748]) ).
cnf(c750,plain,
f(X6,f(X5,X4,X3),f(X2,X4,X3)) = f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c749]) ).
cnf(c751,plain,
f(f(f(X6,X5,X2),X4,X3),X5,f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(f(f(X6,X5,X2),X4,X3),X5,f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3))),
inference(congruence,[status(thm)],[c750]) ).
cnf(c752,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X2,X6,X5)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c753,plain,
f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5)) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X2,X6,X5)),
inference(symmetry,[status(thm)],[c752]) ).
cnf(c754,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X2,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c755,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),X2) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c754]) ).
cnf(c756,plain,
f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c757,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X2,X4,X3)) = f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c756]) ).
cnf(c758,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)) = f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c629]) ).
cnf(c759,plain,
f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)),
inference(symmetry,[status(thm)],[c758]) ).
cnf(c760,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(X2,X4,X3)),
inference(congruence,[status(thm)],[c422]) ).
cnf(c761,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(X2,X4,X3)) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c416]) ).
cnf(c762,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c760,c761]) ).
cnf(c763,plain,
f(X2,f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c759,c762]) ).
cnf(c764,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2,f(X2,X4,X3)) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c757,c763]) ).
cnf(c765,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),X2) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c755,c764]) ).
cnf(c766,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5),X2) = f(X2,X6,X5),
inference(substitution,[status(thm)],[c765]) ).
cnf(c767,plain,
f(X2,X6,X5) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5),X2),
inference(symmetry,[status(thm)],[c766]) ).
cnf(c768,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X2,X6,X5)) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5),X2)),
inference(congruence,[status(thm)],[c767]) ).
cnf(c769,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5),X2)) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),X2),
inference(substitution,[status(thm)],[c564]) ).
cnf(c770,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),X2) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X2),
inference(substitution,[status(thm)],[c55]) ).
cnf(c771,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5),X2)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X2),
inference(transitivity,[status(thm)],[c769,c770]) ).
cnf(c772,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X7,X6,X5),f(X2,X6,X5)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X2),
inference(transitivity,[status(thm)],[c768,c771]) ).
cnf(c773,plain,
f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(X2,X6,X5)) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X2),
inference(transitivity,[status(thm)],[c753,c772]) ).
cnf(c774,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3)) = f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2),
inference(substitution,[status(thm)],[c773]) ).
cnf(c775,plain,
f(f(f(X6,X5,X2),X4,X3),X5,f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3))) = f(f(f(X6,X5,X2),X4,X3),X5,f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2)),
inference(congruence,[status(thm)],[c774]) ).
cnf(c776,plain,
f(f(f(X6,X5,X2),X4,X3),X5,f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2)) = f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(f(f(X6,X5,X2),X4,X3),X5,X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c777,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c778,plain,
f(X4,X3,X2) = f(X3,X2,X4),
inference(symmetry,[status(thm)],[c777]) ).
cnf(c779,plain,
f(X5,f(X4,X3,X2),f(X5,X3,X2)) = f(X5,f(X4,X3,X2),f(X3,X2,X5)),
inference(congruence,[status(thm)],[c778]) ).
cnf(c780,plain,
f(X2,X3,X4) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c55]) ).
cnf(c781,plain,
f(X3,X2,X4) = f(X2,X3,X4),
inference(symmetry,[status(thm)],[c780]) ).
cnf(c782,plain,
f(X5,f(X4,X3,X2),f(X3,X2,X5)) = f(X5,f(X4,X3,X2),f(X2,X3,X5)),
inference(congruence,[status(thm)],[c781]) ).
cnf(c783,plain,
f(X5,f(X4,X3,X2),f(X2,X3,X5)) = f(X5,X3,f(X5,X2,f(X4,X3,X2))),
inference(substitution,[status(thm)],[c233]) ).
cnf(c784,plain,
f(X5,X3,f(X5,X2,f(X4,X3,X2))) = f(X5,X2,f(X3,X5,f(X4,X3,X2))),
inference(substitution,[status(thm)],[c237]) ).
cnf(c785,plain,
f(X5,X2,f(X3,X5,f(X4,X3,X2))) = f(X2,X5,X3),
inference(substitution,[status(thm)],[c302]) ).
cnf(c786,plain,
f(X2,X4,X3) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c6]) ).
cnf(c787,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c788,plain,
f(X2,X4,X3) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c786,c787]) ).
cnf(c789,plain,
f(X5,X2,f(X3,X5,f(X4,X3,X2))) = f(X5,X3,X2),
inference(transitivity,[status(thm)],[c785,c788]) ).
cnf(c790,plain,
f(X5,X3,f(X5,X2,f(X4,X3,X2))) = f(X5,X3,X2),
inference(transitivity,[status(thm)],[c784,c789]) ).
cnf(c791,plain,
f(X5,f(X4,X3,X2),f(X2,X3,X5)) = f(X5,X3,X2),
inference(transitivity,[status(thm)],[c783,c790]) ).
cnf(c792,plain,
f(X5,f(X4,X3,X2),f(X3,X2,X5)) = f(X5,X3,X2),
inference(transitivity,[status(thm)],[c782,c791]) ).
cnf(c793,plain,
f(X5,f(X4,X3,X2),f(X5,X3,X2)) = f(X5,X3,X2),
inference(transitivity,[status(thm)],[c779,c792]) ).
cnf(c794,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X5,X4),f(f(f(X6,X5,X4),X3,X2),X5,X4)) = f(f(f(X6,X5,X4),X3,X2),X5,X4),
inference(substitution,[status(thm)],[c793]) ).
cnf(c795,plain,
f(f(f(X6,X5,X4),X3,X2),X5,X4) = f(f(f(X6,X5,X4),X3,X2),f(X6,X5,X4),f(f(f(X6,X5,X4),X3,X2),X5,X4)),
inference(symmetry,[status(thm)],[c794]) ).
cnf(c796,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,f(X9,X4,X3),f(X8,X4,X3)),f(f(f(X7,X6,X5),X4,X3),X6,X5)) = f(f(f(X7,X6,X5),X4,X3),f(X2,f(X9,X4,X3),f(X8,X4,X3)),f(f(f(X7,X6,X5),X4,X3),f(X7,X6,X5),f(f(f(X7,X6,X5),X4,X3),X6,X5))),
inference(congruence,[status(thm)],[c795]) ).
cnf(c797,plain,
f(X5,X2,f(X5,X4,X3)) = f(X5,f(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c798,plain,
f(X5,f(X5,X4,X3),X2) = f(X5,X2,f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c797]) ).
cnf(c799,plain,
f(X5,f(X5,X4,X3),X2) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c798,c123]) ).
cnf(c800,plain,
f(f(X8,X7,X6),f(f(X8,X7,X6),f(X5,f(X4,X7,X6),f(X3,X7,X6)),X8),X2) = f(f(X8,X7,X6),f(X5,f(X4,X7,X6),f(X3,X7,X6)),f(f(X8,X7,X6),X8,X2)),
inference(substitution,[status(thm)],[c799]) ).
cnf(c801,plain,
f(f(X8,X7,X6),f(X5,f(X4,X7,X6),f(X3,X7,X6)),f(f(X8,X7,X6),X8,X2)) = f(f(X8,X7,X6),f(f(X8,X7,X6),f(X5,f(X4,X7,X6),f(X3,X7,X6)),X8),X2),
inference(symmetry,[status(thm)],[c800]) ).
cnf(c802,plain,
f(f(X7,X6,X5),X7,f(X4,f(X3,X6,X5),f(X2,X6,X5))) = f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X7),
inference(substitution,[status(thm)],[c2]) ).
cnf(c803,plain,
f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X7) = f(f(X7,X6,X5),X7,f(X4,f(X3,X6,X5),f(X2,X6,X5))),
inference(symmetry,[status(thm)],[c802]) ).
cnf(c804,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3),
inference(substitution,[status(thm)],[c793]) ).
cnf(c805,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3)),
inference(symmetry,[status(thm)],[c804]) ).
cnf(c806,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3),
inference(substitution,[status(thm)],[c793]) ).
cnf(c807,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3)),
inference(symmetry,[status(thm)],[c806]) ).
cnf(c808,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3)) = f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3))),
inference(congruence,[status(thm)],[c807]) ).
cnf(c809,plain,
f(f(X5,X4,X3),X4,f(f(X5,X4,X3),X3,X2)) = f(f(X5,X4,X3),X3,f(f(X5,X4,X3),X2,X4)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c810,plain,
f(f(X5,X4,X3),X3,f(f(X5,X4,X3),X2,X4)) = f(f(X5,X4,X3),X2,f(f(X5,X4,X3),X4,X3)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c811,plain,
f(f(X5,X4,X3),X2,f(f(X5,X4,X3),X4,X3)) = f(f(X5,X4,X3),X2,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c812,plain,
f(f(X5,X4,X3),X2,f(X5,X4,X3)) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c35]) ).
cnf(c813,plain,
f(f(X5,X4,X3),X2,f(f(X5,X4,X3),X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c811,c812]) ).
cnf(c814,plain,
f(f(X5,X4,X3),X3,f(f(X5,X4,X3),X2,X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c810,c813]) ).
cnf(c815,plain,
f(f(X5,X4,X3),X4,f(f(X5,X4,X3),X3,X2)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c809,c814]) ).
cnf(c816,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3))) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(substitution,[status(thm)],[c815]) ).
cnf(c817,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3),f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3)) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c808,c816]) ).
cnf(c818,plain,
f(f(X6,f(X5,X4,X3),f(X2,X4,X3)),X4,X3) = f(X6,f(X5,X4,X3),f(X2,X4,X3)),
inference(transitivity,[status(thm)],[c805,c817]) ).
cnf(c819,plain,
f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),X6,X5) = f(X4,f(X3,X6,X5),f(X2,X6,X5)),
inference(substitution,[status(thm)],[c818]) ).
cnf(c820,plain,
f(X4,f(X3,X6,X5),f(X2,X6,X5)) = f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),X6,X5),
inference(symmetry,[status(thm)],[c819]) ).
cnf(c821,plain,
f(f(X7,X6,X5),X7,f(X4,f(X3,X6,X5),f(X2,X6,X5))) = f(f(X7,X6,X5),X7,f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),X6,X5)),
inference(congruence,[status(thm)],[c820]) ).
cnf(c822,plain,
f(f(X7,X6,X5),X7,f(f(X4,f(X3,X6,X5),f(X2,X6,X5)),X6,X5)) = f(X7,X6,X5),
inference(substitution,[status(thm)],[c192]) ).
cnf(c823,plain,
f(f(X7,X6,X5),X7,f(X4,f(X3,X6,X5),f(X2,X6,X5))) = f(X7,X6,X5),
inference(transitivity,[status(thm)],[c821,c822]) ).
cnf(c824,plain,
f(f(X7,X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),X7) = f(X7,X6,X5),
inference(transitivity,[status(thm)],[c803,c823]) ).
cnf(c825,plain,
f(f(X8,X7,X6),f(f(X8,X7,X6),f(X5,f(X4,X7,X6),f(X3,X7,X6)),X8),X2) = f(f(X8,X7,X6),f(X8,X7,X6),X2),
inference(congruence,[status(thm)],[c824]) ).
cnf(c826,plain,
f(f(X5,X4,X3),f(X5,X4,X3),X2) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c33]) ).
cnf(c827,plain,
f(f(X8,X7,X6),f(f(X8,X7,X6),f(X5,f(X4,X7,X6),f(X3,X7,X6)),X8),X2) = f(X8,X7,X6),
inference(transitivity,[status(thm)],[c825,c826]) ).
cnf(c828,plain,
f(f(X8,X7,X6),f(X5,f(X4,X7,X6),f(X3,X7,X6)),f(f(X8,X7,X6),X8,X2)) = f(X8,X7,X6),
inference(transitivity,[status(thm)],[c801,c827]) ).
cnf(c829,plain,
f(f(f(X9,X8,X7),X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(f(f(X9,X8,X7),X6,X5),f(X9,X8,X7),f(f(f(X9,X8,X7),X6,X5),X8,X7))) = f(f(X9,X8,X7),X6,X5),
inference(substitution,[status(thm)],[c828]) ).
cnf(c830,plain,
f(f(f(X9,X8,X7),X6,X5),f(X4,f(X3,X6,X5),f(X2,X6,X5)),f(f(f(X9,X8,X7),X6,X5),X8,X7)) = f(f(X9,X8,X7),X6,X5),
inference(transitivity,[status(thm)],[c796,c829]) ).
cnf(c831,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(f(f(X6,X5,X2),X4,X3),X5,X2)) = f(f(X6,X5,X2),X4,X3),
inference(substitution,[status(thm)],[c830]) ).
cnf(c832,plain,
f(f(f(X6,X5,X2),X4,X3),X5,f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X2)) = f(f(X6,X5,X2),X4,X3),
inference(transitivity,[status(thm)],[c776,c831]) ).
cnf(c833,plain,
f(f(f(X6,X5,X2),X4,X3),X5,f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X2,X4,X3))) = f(f(X6,X5,X2),X4,X3),
inference(transitivity,[status(thm)],[c775,c832]) ).
cnf(c834,plain,
f(f(f(X6,X5,X2),X4,X3),X5,f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(f(X6,X5,X2),X4,X3),
inference(transitivity,[status(thm)],[c751,c833]) ).
cnf(c835,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),X5) = f(f(X6,X5,X2),X4,X3),
inference(transitivity,[status(thm)],[c572,c834]) ).
cnf(c836,plain,
f(f(f(X6,X5,X2),X4,X3),f(X6,f(X5,X4,X3),f(X2,X4,X3)),f(X5,X4,X3)) = f(f(X6,X5,X2),X4,X3),
inference(transitivity,[status(thm)],[c570,c835]) ).
cnf(c837,plain,
f(X6,f(X5,X4,X3),f(X2,X4,X3)) = f(f(X6,X5,X2),X4,X3),
inference(transitivity,[status(thm)],[c501,c836]) ).
cnf(c838,plain,
f(x,f(y,u,w),f(z,u,w)) = f(f(x,y,z),u,w),
inference(substitution,[status(thm)],[c837]) ).
cnf(c839,plain,
f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)),
inference(symmetry,[status(thm)],[c838]) ).
cnf(c840,plain,
$false,
inference(resolution,[status(thm)],[c1,c839]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG213-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 19:43:40 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 90.25/11.62 Command-line arguments: --flatten --complete-subsets
% 90.25/11.62
% 90.25/11.62 % SZS status Unsatisfiable
% 90.25/11.62
% 91.06/11.71 % SZS output start CNFRefutation
% See solution above
% 95.51/12.28
% 95.51/12.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------