%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG212+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 : Theorem 143.62s 18.30s
% Output : CNFRefutation 145.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 5
% Syntax : Number of formulae : 584 ( 584 unt; 0 def)
% Number of atoms : 584 ( 583 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 2525 ( 58 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
f(f(X,Y,Z),U,W) = f(f(X,U,W),f(Y,U,W),f(Z,U,W)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_long) ).
fof(c2,negated_conjecture,
~ ! [X2,Y2,Z2,W2,U2] : f(f(X2,Y2,Z2),U2,W2) = f(f(X2,U2,W2),f(Y2,U2,W2),f(Z2,U2,W2)),
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
f(f(x,y,z),u,w) != f(f(x,u,w),f(y,u,w),f(z,u,w)),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
f(X2,Y2,Z2) = f(Z2,X2,Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permute1) ).
cnf(c5,plain,
f(X4,X2,X3) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
f(X3,X4,X2) = f(X4,X2,X3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
f(X2,Y2,Z2) = f(X2,Z2,Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permute2) ).
cnf(c8,plain,
f(X4,X2,X3) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
f(f(f(X4,X3,X2),f(X6,X3,X2),f(X7,X3,X2)),X5,X6) = f(X5,f(f(X4,X3,X2),f(X6,X3,X2),f(X7,X3,X2)),X6),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(f(f(X7,X6,X5),f(X3,X6,X5),f(X4,X6,X5)),X2,X3)) = f(f(X7,X6,X5),f(X4,X6,X5),f(X2,f(f(X7,X6,X5),f(X3,X6,X5),f(X4,X6,X5)),X3)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
f(X3,X2,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5))) = f(X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c13,plain,
f(X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),X2) = f(X3,X2,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),X2)) = f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X2,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),X3,f(X6,X5,X4)) = f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c16,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),X3) = f(f(f(X6,X5,X4),f(X3,X5,X4),X2),X3,f(X6,X5,X4)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),X3,f(X6,X5,X4)) = f(X3,f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c18,plain,
f(X4,X3,X2) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c19,plain,
f(X3,X5,f(X5,X4,X2)) = f(X3,X5,f(X2,X5,X4)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
f(f(X2,W2,Y2),W2,Z2) = f(X2,W2,f(Y2,W2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c21,plain,
f(f(X3,X5,X2),X5,X4) = f(X3,X5,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
f(X3,X5,f(X2,X5,X4)) = f(f(X3,X5,X2),X5,X4),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
f(X5,X4,f(X3,X5,X2)) = f(f(X3,X5,X2),X5,X4),
inference(substitution,[status(thm)],[c4]) ).
cnf(c24,plain,
f(f(X3,X5,X2),X5,X4) = f(X5,X4,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
f(X3,X5,f(X2,X5,X4)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
f(X3,X5,f(X5,X4,X2)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c19,c25]) ).
cnf(c27,plain,
f(X5,X4,f(X4,X3,X2)) = f(X4,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c29,plain,
f(X4,X3,f(X5,X4,X2)) = f(X4,X3,f(X5,X2,X4)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
f(X5,X4,f(X4,X3,X2)) = f(X4,X3,f(X5,X2,X4)),
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
f(X4,X3,f(X5,X2,X4)) = f(X4,f(X5,X2,X4),X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c32,plain,
f(X3,X4,X2) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c7]) ).
cnf(c33,plain,
f(X3,X2,X4) = f(X3,X4,X2),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
f(X5,f(X4,X3,X5),X2) = f(X5,f(X4,X5,X3),X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c36,plain,
f(X4,X2,f(X5,X4,X3)) = f(X4,f(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c37,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,f(X5,X4,X3),X2),
inference(transitivity,[status(thm)],[c35,c36]) ).
cnf(c38,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,f(X4,X5,X3),X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
f(X5,f(X4,X5,X3),X2) = f(X4,X5,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
f(X5,X4,f(X3,X5,X2)) = f(X4,X5,f(X3,X5,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c41,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,X4,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
f(X4,X3,X2) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c44,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
f(X5,X4,f(X3,X5,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c42,c45]) ).
cnf(c47,plain,
f(X5,f(X4,X3,X5),X2) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c34,c46]) ).
cnf(c48,plain,
f(X4,f(X5,X2,X4),X3) = f(X4,X5,f(X4,X2,X3)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
f(X4,X3,f(X5,X2,X4)) = f(X4,X5,f(X4,X2,X3)),
inference(transitivity,[status(thm)],[c31,c48]) ).
cnf(c50,plain,
f(X5,X4,f(X4,X3,X2)) = f(X4,X5,f(X4,X2,X3)),
inference(transitivity,[status(thm)],[c30,c49]) ).
cnf(c51,plain,
f(f(X5,X4,X3),X5,f(X5,X4,X2)) = f(X5,f(X5,X4,X3),f(X5,X2,X4)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c53,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c54,plain,
f(X4,X2,f(X5,X4,X3)) = f(X4,X2,f(X5,X3,X4)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,X2,f(X5,X3,X4)),
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,X2,f(X4,X3,X5)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
f(X5,X2,f(X4,X3,X5)) = f(X4,X5,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
f(X5,X4,f(X3,X5,X2)) = f(X4,X5,f(X3,X5,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c59,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,X4,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
f(X5,X2,f(X4,X3,X5)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c57,c59]) ).
cnf(c61,plain,
f(X5,X4,f(X3,X2,X5)) = f(X5,X3,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
f(X4,X5,f(X5,X3,X2)) = f(X5,X3,f(X4,X5,X2)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c63,plain,
f(X5,X3,f(X4,X5,X2)) = f(X4,X5,f(X5,X3,X2)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
f(X5,X4,f(X5,X3,X2)) = f(X4,X5,f(X5,X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c65,plain,
f(X4,X5,f(X5,X3,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
f(X5,X3,f(X4,X5,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
f(X5,X3,f(X2,X5,X4)) = f(X5,X2,f(X5,X3,X4)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
f(X5,X4,f(X3,X2,X5)) = f(X5,X2,f(X5,X3,X4)),
inference(transitivity,[status(thm)],[c61,c67]) ).
cnf(c69,plain,
f(X5,X4,f(X2,f(X5,X4,X3),X5)) = f(X5,f(X5,X4,X3),f(X5,X2,X4)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
f(X5,f(X5,X4,X3),f(X5,X2,X4)) = f(X5,X4,f(X2,f(X5,X4,X3),X5)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,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)],[c55]) ).
cnf(c72,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)],[c71]) ).
cnf(c73,plain,
f(X4,X3,f(X4,X3,X2)) = f(f(X4,X3,X2),X4,X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c74,plain,
f(f(X4,X3,X2),X4,X3) = f(X4,X3,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
f(X4,X3,f(X4,X3,X2)) = f(X3,X2,f(X4,X3,X4)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c76,plain,
f(X3,X3,X2) = f(X3,X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c77,plain,
f(X3,X2,X3) = f(X3,X3,X2),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,axiom,
f(X2,X2,Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',majority) ).
cnf(c79,plain,
f(X3,X3,X2) = X3,
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
f(X3,X2,X3) = X3,
inference(transitivity,[status(thm)],[c77,c79]) ).
cnf(c81,plain,
f(X3,X2,f(X4,X3,X4)) = f(X3,X2,X4),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c83,plain,
f(X3,X2,f(X4,X3,X4)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
f(X4,X3,f(X4,X3,X2)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c75,c83]) ).
cnf(c85,plain,
f(f(X4,X3,X2),X4,X3) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c74,c84]) ).
cnf(c86,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X4)) = f(X2,X5,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
f(X2,X5,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c7]) ).
cnf(c88,plain,
f(X2,X5,f(f(X5,X4,X3),X5,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c86,c87]) ).
cnf(c89,plain,
f(X5,X4,f(X2,f(X5,X4,X3),X5)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c72,c88]) ).
cnf(c90,plain,
f(X5,f(X5,X4,X3),f(X5,X2,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c70,c89]) ).
cnf(c91,plain,
f(f(X5,X4,X3),X5,f(X5,X4,X2)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c51,c90]) ).
cnf(c92,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X3)) = f(X3,f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
f(X3,f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4)) = f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X3)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
f(f(X2,X4,X3),X2,f(X5,X4,X3)) = f(f(X5,X4,X3),f(X2,X4,X3),X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c95,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X2) = f(f(X2,X4,X3),X2,f(X5,X4,X3)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,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)],[c7]) ).
cnf(c97,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)],[c96]) ).
cnf(c98,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c9]) ).
cnf(c99,plain,
f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c91]) ).
cnf(c100,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
f(f(X5,X4,X2),X4,X3) = f(X3,f(X5,X4,X2),X4),
inference(substitution,[status(thm)],[c4]) ).
cnf(c102,plain,
f(X3,f(X5,X4,X2),X4) = f(f(X5,X4,X2),X4,X3),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
f(X4,X3,f(X5,X4,X2)) = f(f(X5,X4,X2),X4,X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c104,plain,
f(f(X5,X4,X2),X4,X3) = f(X4,X3,f(X5,X4,X2)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
f(X5,X4,f(X2,X4,X3)) = f(X4,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c106,plain,
f(X4,X3,f(X5,X4,X2)) = f(X5,X4,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
f(X4,X2,X3) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c108,plain,
f(X2,X4,X3) = f(X4,X2,X3),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
f(X5,X4,f(X2,X4,X3)) = f(X5,X4,f(X4,X2,X3)),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
f(X4,X2,X3) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c111,plain,
f(X5,X4,f(X4,X2,X3)) = f(X5,X4,f(X3,X4,X2)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
f(X5,X4,f(X2,X4,X3)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c109,c111]) ).
cnf(c113,plain,
f(X4,X3,f(X5,X4,X2)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c106,c112]) ).
cnf(c114,plain,
f(f(X5,X4,X2),X4,X3) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c104,c113]) ).
cnf(c115,plain,
f(X3,f(X5,X4,X2),X4) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c102,c114]) ).
cnf(c116,plain,
f(X2,f(X5,X4,X3),X4) = f(X5,X4,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
f(X5,X4,f(X2,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))) = f(f(X5,X4,X3),X5,f(X2,f(X5,X4,X3),X4)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
f(X2,f(X5,X4,X3),f(f(X5,X4,X3),X5,X4)) = f(f(X5,X4,X3),X5,f(X2,f(X5,X4,X3),X4)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c120,plain,
f(f(X5,X4,X3),X5,f(X2,f(X5,X4,X3),X4)) = f(X2,f(X5,X4,X3),f(f(X5,X4,X3),X5,X4)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
f(X2,f(X5,X4,X3),f(f(X5,X4,X3),X5,X4)) = f(X2,f(X5,X4,X3),f(X5,X4,X3)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c122,plain,
f(X2,X2,X3) = f(X3,X2,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c123,plain,
f(X3,X2,X2) = f(X2,X2,X3),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
f(X2,X2,X3) = X2,
inference(substitution,[status(thm)],[c78]) ).
cnf(c125,plain,
f(X3,X2,X2) = X2,
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
f(X2,f(X5,X4,X3),f(X5,X4,X3)) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
f(X2,f(X5,X4,X3),f(f(X5,X4,X3),X5,X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c121,c126]) ).
cnf(c128,plain,
f(f(X5,X4,X3),X5,f(X2,f(X5,X4,X3),X4)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c120,c127]) ).
cnf(c129,plain,
f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c118,c128]) ).
cnf(c130,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c100,c129]) ).
cnf(c131,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c98,c130]) ).
cnf(c132,plain,
f(f(X5,X4,X3),X5,f(X2,X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c97,c131]) ).
cnf(c133,plain,
f(f(X2,X4,X3),X2,f(X5,X4,X3)) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X2) = f(X2,X4,X3),
inference(transitivity,[status(thm)],[c95,c133]) ).
cnf(c135,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X3)) = f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),f(X3,X5,X4)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),f(X3,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c137,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X3)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c135,c136]) ).
cnf(c138,plain,
f(X3,f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c93,c137]) ).
cnf(c139,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),X3,f(X6,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c17,c138]) ).
cnf(c140,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),X2),f(X6,X5,X4),X3) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c16,c139]) ).
cnf(c141,plain,
f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X2) = f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)) = f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X2),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),X2,f(X6,X5,X4)) = f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c144,plain,
f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X2) = f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),X2,f(X6,X5,X4)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),X2,f(X6,X5,X4)) = f(X2,f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c146,plain,
f(X3,X5,f(X5,X4,X2)) = f(X3,f(X5,X4,X2),X5),
inference(substitution,[status(thm)],[c7]) ).
cnf(c147,plain,
f(X3,f(X5,X4,X2),X5) = f(X3,X5,f(X5,X4,X2)),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
f(X3,f(X5,X4,X2),X5) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c147,c26]) ).
cnf(c149,plain,
f(X2,f(X5,X4,X3),X5) = f(X5,X4,f(X2,X5,X3)),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,X2,f(X4,X5,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c151,plain,
f(X5,X2,f(X4,X5,X3)) = f(X4,X5,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
f(X5,X4,f(X3,X5,X2)) = f(X4,X5,f(X3,X5,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c153,plain,
f(X4,X5,f(X3,X5,X2)) = f(X5,X4,f(X3,X5,X2)),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c151,c153]) ).
cnf(c155,plain,
f(X5,X3,f(X4,X5,X2)) = f(X5,X4,f(X2,X5,X3)),
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
f(X5,X4,f(X2,X5,X3)) = f(X5,X3,f(X4,X5,X2)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
f(X5,X4,f(X2,X5,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c156,c66]) ).
cnf(c158,plain,
f(X2,f(X5,X4,X3),X5) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c149,c157]) ).
cnf(c159,plain,
f(X2,f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)) = f(f(X6,X5,X4),f(X2,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X2)),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
f(X4,X3,X2) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c161,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,X3,f(X4,X5,X2)),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c161,c66]) ).
cnf(c163,plain,
f(X5,X4,f(X5,X3,X2)) = f(X5,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c162]) ).
cnf(c164,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c165,plain,
f(X5,X3,f(X5,X4,X2)) = f(X5,X3,f(X5,X2,X4)),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
f(X5,X4,f(X5,X3,X2)) = f(X5,X3,f(X5,X2,X4)),
inference(transitivity,[status(thm)],[c163,c165]) ).
cnf(c167,plain,
f(X6,f(X5,X4,X3),f(X6,f(X2,X4,X3),X5)) = f(X6,f(X2,X4,X3),f(X6,X5,f(X5,X4,X3))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
f(f(X5,X4,X3),X5,f(X2,X4,X3)) = f(f(X5,X4,X3),f(X2,X4,X3),X5),
inference(substitution,[status(thm)],[c7]) ).
cnf(c169,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(f(X5,X4,X3),X5,f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c169,c132]) ).
cnf(c171,plain,
f(X5,X4,X3) = f(f(X5,X4,X3),f(X2,X4,X3),X5),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,plain,
f(X6,X5,f(X5,X4,X3)) = f(X6,X5,f(f(X5,X4,X3),f(X2,X4,X3),X5)),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
f(X6,f(X2,X4,X3),f(X6,X5,f(X5,X4,X3))) = f(X6,f(X2,X4,X3),f(X6,X5,f(f(X5,X4,X3),f(X2,X4,X3),X5))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
f(X4,X3,X2) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c175,plain,
f(X5,f(X5,X4,X3),X2) = f(X5,f(X4,X5,X3),X2),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
f(X4,X3,X2) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c177,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
f(X5,X4,f(X3,X5,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c42,c178]) ).
cnf(c180,plain,
f(X5,f(X5,X4,X3),X2) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c175,c179]) ).
cnf(c181,plain,
f(X5,f(X5,X4,X3),f(X2,X4,X3)) = f(X5,X4,f(X5,X3,f(X2,X4,X3))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
f(X5,X4,f(X5,X3,f(X2,X4,X3))) = f(X5,f(X5,X4,X3),f(X2,X4,X3)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
f(X5,f(X5,X4,X3),f(X2,X4,X3)) = f(f(X5,X4,X3),X5,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c184,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)],[c7]) ).
cnf(c185,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)],[c184]) ).
cnf(c186,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c9]) ).
cnf(c187,plain,
f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))) = f(f(X2,X4,X3),f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c91]) ).
cnf(c188,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
f(X2,f(X5,X4,X3),X4) = f(X5,X4,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c190,plain,
f(X5,X4,f(X2,X4,X3)) = f(X2,f(X5,X4,X3),X4),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))) = f(f(X5,X4,X3),X5,f(X2,f(X5,X4,X3),X4)),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
f(f(X5,X4,X3),X5,f(X5,X4,f(X2,X4,X3))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c191,c128]) ).
cnf(c193,plain,
f(f(X2,X4,X3),f(X5,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c188,c192]) ).
cnf(c194,plain,
f(f(X5,X4,X3),f(X2,X4,X3),X5) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c186,c193]) ).
cnf(c195,plain,
f(f(X5,X4,X3),X5,f(X2,X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c185,c194]) ).
cnf(c196,plain,
f(X5,f(X5,X4,X3),f(X2,X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c183,c195]) ).
cnf(c197,plain,
f(X5,X4,f(X5,X3,f(X2,X4,X3))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c182,c196]) ).
cnf(c198,plain,
f(X6,f(X2,X4,X3),f(X6,X5,f(f(X5,X4,X3),f(X2,X4,X3),X5))) = f(X6,f(X2,X4,X3),X5),
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,plain,
f(X6,f(X2,X4,X3),f(X6,X5,f(X5,X4,X3))) = f(X6,f(X2,X4,X3),X5),
inference(transitivity,[status(thm)],[c173,c198]) ).
cnf(c200,plain,
f(X6,f(X5,X4,X3),f(X6,f(X2,X4,X3),X5)) = f(X6,f(X2,X4,X3),X5),
inference(transitivity,[status(thm)],[c167,c199]) ).
cnf(c201,plain,
f(f(X6,X5,X4),f(X2,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X2)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(substitution,[status(thm)],[c200]) ).
cnf(c202,plain,
f(X2,f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c159,c201]) ).
cnf(c203,plain,
f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),X2,f(X6,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c145,c202]) ).
cnf(c204,plain,
f(f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),f(X6,X5,X4),X2) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c144,c203]) ).
cnf(c205,plain,
f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c142,c204]) ).
cnf(c206,plain,
f(X3,X2,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5))) = f(X3,X2,f(f(X7,X6,X5),f(X4,X6,X5),X2)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X2,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)))) = f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X2,f(f(X7,X6,X5),f(X4,X6,X5),X2))),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
f(X3,f(X5,X4,X2),X2) = f(X3,X2,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c209,plain,
f(X3,X2,f(X5,X4,X2)) = f(X3,f(X5,X4,X2),X2),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
f(X5,X4,f(X3,X2,f(X5,X4,X2))) = f(X5,X4,f(X3,f(X5,X4,X2),X2)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
f(X3,X4,f(X5,X2,X4)) = f(X3,f(X5,X2,X4),X4),
inference(substitution,[status(thm)],[c7]) ).
cnf(c212,plain,
f(X3,f(X5,X2,X4),X4) = f(X3,X4,f(X5,X2,X4)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
f(X2,X4,X3) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c4]) ).
cnf(c214,plain,
f(X3,X2,X4) = f(X2,X4,X3),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
f(X3,X5,f(X4,X2,X5)) = f(X3,X5,f(X2,X5,X4)),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
f(X3,X5,f(X4,X2,X5)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c215,c25]) ).
cnf(c217,plain,
f(X3,X4,f(X5,X2,X4)) = f(X4,X5,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c216]) ).
cnf(c218,plain,
f(X5,X4,f(X3,X4,X2)) = f(X4,X5,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c219,plain,
f(X4,X5,f(X3,X4,X2)) = f(X5,X4,f(X3,X4,X2)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
f(X3,X4,X2) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c7]) ).
cnf(c221,plain,
f(X5,X4,f(X3,X4,X2)) = f(X5,X4,f(X3,X2,X4)),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
f(X4,X5,f(X3,X4,X2)) = f(X5,X4,f(X3,X2,X4)),
inference(transitivity,[status(thm)],[c219,c221]) ).
cnf(c223,plain,
f(X3,X4,f(X5,X2,X4)) = f(X5,X4,f(X3,X2,X4)),
inference(transitivity,[status(thm)],[c217,c222]) ).
cnf(c224,plain,
f(X3,f(X5,X2,X4),X4) = f(X5,X4,f(X3,X2,X4)),
inference(transitivity,[status(thm)],[c212,c223]) ).
cnf(c225,plain,
f(X3,f(X5,X4,X2),X2) = f(X5,X2,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
f(X5,X4,f(X3,f(X5,X4,X2),X2)) = f(X5,X4,f(X5,X2,f(X3,X4,X2))),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
f(X5,X4,f(X5,X2,f(X3,X4,X2))) = f(X5,X4,X2),
inference(substitution,[status(thm)],[c197]) ).
cnf(c228,plain,
f(X5,X4,f(X3,f(X5,X4,X2),X2)) = f(X5,X4,X2),
inference(transitivity,[status(thm)],[c226,c227]) ).
cnf(c229,plain,
f(X5,X4,f(X3,X2,f(X5,X4,X2))) = f(X5,X4,X2),
inference(transitivity,[status(thm)],[c210,c228]) ).
cnf(c230,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X2,f(f(X7,X6,X5),f(X4,X6,X5),X2))) = f(f(X7,X6,X5),f(X4,X6,X5),X2),
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
f(f(X6,X5,X4),f(X3,X5,X4),X2) = f(f(X6,X5,X4),f(X2,X5,X4),f(X3,X5,X4)),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c232,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X2,f(f(X7,X6,X5),f(X4,X6,X5),X2))) = f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),
inference(transitivity,[status(thm)],[c230,c231]) ).
cnf(c233,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X2,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)))) = f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),
inference(transitivity,[status(thm)],[c207,c232]) ).
cnf(c234,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),X2)) = f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),
inference(transitivity,[status(thm)],[c14,c233]) ).
cnf(c235,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(X2,f(f(X7,X6,X5),f(X3,X6,X5),f(X4,X6,X5)),X3)) = f(f(X7,X6,X5),f(X3,X6,X5),f(X4,X6,X5)),
inference(substitution,[status(thm)],[c234]) ).
cnf(c236,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(f(f(X7,X6,X5),f(X3,X6,X5),f(X4,X6,X5)),X2,X3)) = f(f(X7,X6,X5),f(X3,X6,X5),f(X4,X6,X5)),
inference(transitivity,[status(thm)],[c11,c235]) ).
cnf(c237,plain,
f(f(X6,X3,X2),f(X4,X3,X2),f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),X5)) = f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)) = f(f(X6,X3,X2),f(X4,X3,X2),f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),X5)),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
f(f(f(X7,X6,X5),f(X3,X6,X5),f(X2,X6,X5)),f(X4,X3,X2),X3) = f(X4,X3,f(f(f(X7,X6,X5),f(X3,X6,X5),f(X2,X6,X5)),X3,X2)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c240,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X2,X3) = f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c241,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X3,X2) = f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X2,X3),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X2,X3) = f(X2,f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c243,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4,X2) = f(X2,f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4),
inference(substitution,[status(thm)],[c4]) ).
cnf(c244,plain,
f(X2,f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4) = f(f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4,X2),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
f(X4,X2,f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5))) = f(f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c246,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4,X2) = f(X4,X2,f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5))),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)) = f(f(X6,X5,X4),f(X2,X5,X4),X3),
inference(substitution,[status(thm)],[c205]) ).
cnf(c248,plain,
f(X4,X2,f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5))) = f(X4,X2,f(f(X7,X6,X5),f(X3,X6,X5),X4)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
f(f(X7,X6,X5),X4,f(X4,X2,f(X3,X6,X5))) = f(X4,X2,f(f(X7,X6,X5),f(X3,X6,X5),X4)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c250,plain,
f(X4,X2,f(f(X7,X6,X5),f(X3,X6,X5),X4)) = f(f(X7,X6,X5),X4,f(X4,X2,f(X3,X6,X5))),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
f(X4,X2,f(X3,X6,X5)) = f(f(X3,X6,X5),X4,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c252,plain,
f(f(X7,X6,X5),X4,f(X4,X2,f(X3,X6,X5))) = f(f(X7,X6,X5),X4,f(f(X3,X6,X5),X4,X2)),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
f(X4,X2,f(f(X7,X6,X5),f(X3,X6,X5),X4)) = f(f(X7,X6,X5),X4,f(f(X3,X6,X5),X4,X2)),
inference(transitivity,[status(thm)],[c250,c252]) ).
cnf(c254,plain,
f(X4,X2,f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5))) = f(f(X7,X6,X5),X4,f(f(X3,X6,X5),X4,X2)),
inference(transitivity,[status(thm)],[c248,c253]) ).
cnf(c255,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4,X2) = f(f(X7,X6,X5),X4,f(f(X3,X6,X5),X4,X2)),
inference(transitivity,[status(thm)],[c246,c254]) ).
cnf(c256,plain,
f(X2,f(f(X7,X6,X5),f(X4,X6,X5),f(X3,X6,X5)),X4) = f(f(X7,X6,X5),X4,f(f(X3,X6,X5),X4,X2)),
inference(transitivity,[status(thm)],[c244,c255]) ).
cnf(c257,plain,
f(X2,f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X3) = f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X3,X2)),
inference(substitution,[status(thm)],[c256]) ).
cnf(c258,plain,
f(f(X2,X5,X4),X3,X2) = f(X3,f(X2,X5,X4),X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c259,plain,
f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X3,X2)) = f(f(X6,X5,X4),X3,f(X3,f(X2,X5,X4),X2)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
f(f(X6,X5,X4),X3,f(X3,f(X2,X5,X4),X2)) = f(X3,f(X6,X5,X4),f(X3,f(X2,X5,X4),X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c261,plain,
f(X6,f(X5,X4,X3),f(X6,f(X2,X4,X3),X2)) = f(X6,f(X2,X4,X3),f(X6,X2,f(X5,X4,X3))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c262,plain,
f(X6,f(X2,X4,X3),f(X6,X2,f(X5,X4,X3))) = f(X6,X2,f(X6,f(X5,X4,X3),f(X2,X4,X3))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c263,plain,
f(X2,X4,X3) = f(f(X5,X4,X3),f(X2,X4,X3),X2),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c264,plain,
f(X6,f(X5,X4,X3),f(X2,X4,X3)) = f(X6,f(X5,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2)),
inference(congruence,[status(thm)],[c263]) ).
cnf(c265,plain,
f(X6,X2,f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(X6,X2,f(X6,f(X5,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
f(X5,f(X3,X2,X4),X3) = f(X5,X3,f(X3,X2,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c267,plain,
f(X5,X3,f(X3,X2,X4)) = f(X5,f(X3,X2,X4),X3),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
f(X5,X4,f(X5,X3,f(X3,X2,X4))) = f(X5,X4,f(X5,f(X3,X2,X4),X3)),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
f(X5,X4,f(X5,f(X3,X2,X4),X3)) = f(X5,f(X3,X2,X4),f(X5,X3,X4)),
inference(substitution,[status(thm)],[c166]) ).
cnf(c270,plain,
f(X5,f(X3,X2,X4),f(X5,X3,X4)) = f(X5,X3,f(X5,X4,f(X3,X2,X4))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c271,plain,
f(X4,X2,f(X4,X3,X2)) = f(f(X4,X3,X2),X4,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c272,plain,
f(f(X4,X3,X2),X4,X2) = f(X4,X2,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
f(X2,X4,X3) = f(X2,X3,X4),
inference(substitution,[status(thm)],[c7]) ).
cnf(c274,plain,
f(X2,X3,X4) = f(X2,X4,X3),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
f(X3,X5,f(X2,X4,X5)) = f(X3,X5,f(X2,X5,X4)),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
f(X3,X5,f(X2,X4,X5)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c275,c25]) ).
cnf(c277,plain,
f(X4,X3,f(X4,X2,X3)) = f(X3,X2,f(X4,X3,X4)),
inference(substitution,[status(thm)],[c276]) ).
cnf(c278,plain,
f(X3,X2,f(X4,X3,X4)) = f(X3,X2,X4),
inference(congruence,[status(thm)],[c80]) ).
cnf(c279,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c280,plain,
f(X3,X2,f(X4,X3,X4)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c278,c279]) ).
cnf(c281,plain,
f(X4,X3,f(X4,X2,X3)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c277,c280]) ).
cnf(c282,plain,
f(X4,X2,f(X4,X3,X2)) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
f(X4,X2,X3) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c284,plain,
f(X4,X2,f(X4,X3,X2)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c282,c283]) ).
cnf(c285,plain,
f(f(X4,X3,X2),X4,X2) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c272,c284]) ).
cnf(c286,plain,
f(f(X3,X2,X4),X3,X4) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
f(X3,X2,X4) = f(f(X3,X2,X4),X3,X4),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
f(X5,X4,f(X3,X2,X4)) = f(X5,X4,f(f(X3,X2,X4),X3,X4)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
f(X5,X3,f(X5,X4,f(X3,X2,X4))) = f(X5,X3,f(X5,X4,f(f(X3,X2,X4),X3,X4))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
f(X5,X3,f(X5,X4,f(f(X3,X2,X4),X3,X4))) = f(X5,X3,X4),
inference(substitution,[status(thm)],[c197]) ).
cnf(c291,plain,
f(X5,X3,f(X5,X4,f(X3,X2,X4))) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c289,c290]) ).
cnf(c292,plain,
f(X5,f(X3,X2,X4),f(X5,X3,X4)) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c270,c291]) ).
cnf(c293,plain,
f(X5,X4,f(X5,f(X3,X2,X4),X3)) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c269,c292]) ).
cnf(c294,plain,
f(X5,X4,f(X5,X3,f(X3,X2,X4))) = f(X5,X3,X4),
inference(transitivity,[status(thm)],[c268,c293]) ).
cnf(c295,plain,
f(X6,X2,f(X6,f(X5,X4,X3),f(f(X5,X4,X3),f(X2,X4,X3),X2))) = f(X6,f(X5,X4,X3),X2),
inference(substitution,[status(thm)],[c294]) ).
cnf(c296,plain,
f(X6,X2,f(X6,f(X5,X4,X3),f(X2,X4,X3))) = f(X6,f(X5,X4,X3),X2),
inference(transitivity,[status(thm)],[c265,c295]) ).
cnf(c297,plain,
f(X6,f(X2,X4,X3),f(X6,X2,f(X5,X4,X3))) = f(X6,f(X5,X4,X3),X2),
inference(transitivity,[status(thm)],[c262,c296]) ).
cnf(c298,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)],[c261,c297]) ).
cnf(c299,plain,
f(X3,f(X6,X5,X4),f(X3,f(X2,X5,X4),X2)) = f(X3,f(X6,X5,X4),X2),
inference(substitution,[status(thm)],[c298]) ).
cnf(c300,plain,
f(f(X6,X5,X4),X3,f(X3,f(X2,X5,X4),X2)) = f(X3,f(X6,X5,X4),X2),
inference(transitivity,[status(thm)],[c260,c299]) ).
cnf(c301,plain,
f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X3,X2)) = f(X3,f(X6,X5,X4),X2),
inference(transitivity,[status(thm)],[c259,c300]) ).
cnf(c302,plain,
f(f(X6,X5,X4),X3,X2) = f(X3,f(X6,X5,X4),X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c303,plain,
f(X3,f(X6,X5,X4),X2) = f(f(X6,X5,X4),X3,X2),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c301,c303]) ).
cnf(c305,plain,
f(X2,f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X3) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c257,c304]) ).
cnf(c306,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X2,X3) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c242,c305]) ).
cnf(c307,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),X3,X2) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c241,c306]) ).
cnf(c308,plain,
f(X4,X3,f(f(f(X7,X6,X5),f(X3,X6,X5),f(X2,X6,X5)),X3,X2)) = f(X4,X3,f(f(X7,X6,X5),X3,X2)),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
f(f(X7,X6,X5),f(X4,X3,X2),X3) = f(X4,X3,f(f(X7,X6,X5),X3,X2)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c310,plain,
f(X4,X3,f(f(X7,X6,X5),X3,X2)) = f(f(X7,X6,X5),f(X4,X3,X2),X3),
inference(symmetry,[status(thm)],[c309]) ).
cnf(c311,plain,
f(X4,X3,f(f(f(X7,X6,X5),f(X3,X6,X5),f(X2,X6,X5)),X3,X2)) = f(f(X7,X6,X5),f(X4,X3,X2),X3),
inference(transitivity,[status(thm)],[c308,c310]) ).
cnf(c312,plain,
f(f(f(X7,X6,X5),f(X3,X6,X5),f(X2,X6,X5)),f(X4,X3,X2),X3) = f(f(X7,X6,X5),f(X4,X3,X2),X3),
inference(transitivity,[status(thm)],[c239,c311]) ).
cnf(c313,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),X5) = f(f(X6,X3,X2),f(X6,X5,X4),X5),
inference(substitution,[status(thm)],[c312]) ).
cnf(c314,plain,
f(f(X6,X3,X2),f(X4,X3,X2),f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),X5)) = f(f(X6,X3,X2),f(X4,X3,X2),f(f(X6,X3,X2),f(X6,X5,X4),X5)),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
f(f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5),X3) = f(X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c316,plain,
f(X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5)) = f(f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5),X3),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
f(f(X7,X6,X5),X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5))) = f(f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5),X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c318,plain,
f(f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5),X3) = f(f(X7,X6,X5),X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5))),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
f(f(X7,X6,X5),X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5))) = f(f(X7,X6,X5),X3,f(f(X7,X6,X5),f(X4,X6,X5),X2)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c320,plain,
f(f(X7,X6,X5),f(X4,X6,X5),f(f(X7,X6,X5),X3,X2)) = f(f(X7,X6,X5),X3,f(f(X7,X6,X5),f(X4,X6,X5),X2)),
inference(substitution,[status(thm)],[c162]) ).
cnf(c321,plain,
f(f(X7,X6,X5),X3,f(f(X7,X6,X5),f(X4,X6,X5),X2)) = f(f(X7,X6,X5),f(X4,X6,X5),f(f(X7,X6,X5),X3,X2)),
inference(symmetry,[status(thm)],[c320]) ).
cnf(c322,plain,
f(f(X7,X6,X5),X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5))) = f(f(X7,X6,X5),f(X4,X6,X5),f(f(X7,X6,X5),X3,X2)),
inference(transitivity,[status(thm)],[c319,c321]) ).
cnf(c323,plain,
f(f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5),X3) = f(f(X7,X6,X5),f(X4,X6,X5),f(f(X7,X6,X5),X3,X2)),
inference(transitivity,[status(thm)],[c318,c322]) ).
cnf(c324,plain,
f(X3,f(f(X7,X6,X5),f(X2,X6,X5),f(X4,X6,X5)),f(X7,X6,X5)) = f(f(X7,X6,X5),f(X4,X6,X5),f(f(X7,X6,X5),X3,X2)),
inference(transitivity,[status(thm)],[c316,c323]) ).
cnf(c325,plain,
f(f(X6,X5,X4),f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2)) = f(f(X6,X3,X2),f(X4,X3,X2),f(f(X6,X3,X2),f(X6,X5,X4),X5)),
inference(substitution,[status(thm)],[c324]) ).
cnf(c326,plain,
f(f(X6,X3,X2),f(X4,X3,X2),f(f(X6,X3,X2),f(X6,X5,X4),X5)) = f(f(X6,X5,X4),f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2)),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),f(X6,X3,X2)) = f(f(X6,X5,X4),f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c328,plain,
f(f(X6,X5,X4),f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2)) = f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),f(X6,X3,X2)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),f(X6,X3,X2)) = f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c330,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(f(X7,X4,X2),X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(f(X7,X4,X2),X6,X5),f(X7,X6,X5)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c331,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(f(X7,X4,X2),X6,X5),f(X7,X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(f(X7,X4,X2),X6,X5)),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X3,X2)) = f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c333,plain,
f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X3,X2)),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X3,X2)) = f(f(X3,X5,X4),f(X6,X5,X4),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c335,plain,
f(X3,X4,f(X4,X2,X5)) = f(X4,X2,f(X3,X4,X5)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c336,plain,
f(f(X4,X5,X3),X2,X5) = f(X5,f(X4,X5,X3),X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c337,plain,
f(X5,f(X4,X5,X3),X2) = f(f(X4,X5,X3),X2,X5),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
f(X2,X5,f(X4,X5,X3)) = f(f(X4,X5,X3),X2,X5),
inference(substitution,[status(thm)],[c4]) ).
cnf(c339,plain,
f(f(X4,X5,X3),X2,X5) = f(X2,X5,f(X4,X5,X3)),
inference(symmetry,[status(thm)],[c338]) ).
cnf(c340,plain,
f(X2,X5,f(X4,X5,X3)) = f(X5,X3,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c341,plain,
f(f(X4,X5,X3),X2,X5) = f(X5,X3,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c339,c340]) ).
cnf(c342,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X3,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c337,c341]) ).
cnf(c343,plain,
f(X4,f(X5,X4,X2),X3) = f(X4,X2,f(X3,X4,X5)),
inference(substitution,[status(thm)],[c342]) ).
cnf(c344,plain,
f(X4,X2,f(X3,X4,X5)) = f(X4,f(X5,X4,X2),X3),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
f(X4,f(X5,X4,X2),X3) = f(X3,X4,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c346,plain,
f(X5,f(X3,X4,X2),X4) = f(X3,X4,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c347,plain,
f(X3,X4,f(X5,X4,X2)) = f(X5,f(X3,X4,X2),X4),
inference(symmetry,[status(thm)],[c346]) ).
cnf(c348,plain,
f(X5,f(X3,X4,X2),X4) = f(X5,X4,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c349,plain,
f(X3,X4,f(X5,X4,X2)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c347,c348]) ).
cnf(c350,plain,
f(X4,f(X5,X4,X2),X3) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c345,c349]) ).
cnf(c351,plain,
f(X4,X2,f(X3,X4,X5)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c344,c350]) ).
cnf(c352,plain,
f(X3,X4,f(X4,X2,X5)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c335,c351]) ).
cnf(c353,plain,
f(X5,X4,f(X4,X3,X2)) = f(X2,X4,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c352]) ).
cnf(c354,plain,
f(X4,X3,X2) = f(X4,X2,X3),
inference(substitution,[status(thm)],[c7]) ).
cnf(c355,plain,
f(X2,X4,f(X5,X4,X3)) = f(X2,X4,f(X5,X3,X4)),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
f(X5,X4,f(X4,X3,X2)) = f(X2,X4,f(X5,X3,X4)),
inference(transitivity,[status(thm)],[c353,c355]) ).
cnf(c357,plain,
f(f(X2,X5,X4),X3,f(X3,X6,f(X6,X5,X4))) = f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X6,X3)),
inference(substitution,[status(thm)],[c356]) ).
cnf(c358,plain,
f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X6,X3)) = f(f(X2,X5,X4),X3,f(X3,X6,f(X6,X5,X4))),
inference(symmetry,[status(thm)],[c357]) ).
cnf(c359,plain,
f(X5,X4,f(X4,X3,X2)) = f(X4,X3,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c360,plain,
f(X4,f(X5,X4,X2),X3) = f(X4,X5,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c361,plain,
f(X4,X5,f(X2,X4,X3)) = f(X4,f(X5,X4,X2),X3),
inference(symmetry,[status(thm)],[c360]) ).
cnf(c362,plain,
f(f(X5,X4,X2),X3,X4) = f(X4,f(X5,X4,X2),X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c363,plain,
f(X4,f(X5,X4,X2),X3) = f(f(X5,X4,X2),X3,X4),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
f(X3,X4,f(X5,X4,X2)) = f(f(X5,X4,X2),X3,X4),
inference(substitution,[status(thm)],[c4]) ).
cnf(c365,plain,
f(f(X5,X4,X2),X3,X4) = f(X3,X4,f(X5,X4,X2)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
f(X5,f(X3,X4,X2),X4) = f(X3,X4,f(X5,X4,X2)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c367,plain,
f(X3,X4,f(X5,X4,X2)) = f(X5,f(X3,X4,X2),X4),
inference(symmetry,[status(thm)],[c366]) ).
cnf(c368,plain,
f(X5,f(X3,X4,X2),X4) = f(X5,X4,f(X3,X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c369,plain,
f(X3,X4,f(X5,X4,X2)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c367,c368]) ).
cnf(c370,plain,
f(f(X5,X4,X2),X3,X4) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c365,c369]) ).
cnf(c371,plain,
f(X4,f(X5,X4,X2),X3) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c363,c370]) ).
cnf(c372,plain,
f(X4,X5,f(X2,X4,X3)) = f(X5,X4,f(X3,X4,X2)),
inference(transitivity,[status(thm)],[c361,c371]) ).
cnf(c373,plain,
f(X4,X3,f(X5,X4,X2)) = f(X3,X4,f(X2,X4,X5)),
inference(substitution,[status(thm)],[c372]) ).
cnf(c374,plain,
f(X5,X4,f(X4,X3,X2)) = f(X3,X4,f(X2,X4,X5)),
inference(transitivity,[status(thm)],[c359,c373]) ).
cnf(c375,plain,
f(f(X2,X5,X4),X3,f(X3,X6,f(X6,X5,X4))) = f(X6,X3,f(f(X6,X5,X4),X3,f(X2,X5,X4))),
inference(substitution,[status(thm)],[c374]) ).
cnf(c376,plain,
f(X2,f(X4,X5,X3),X5) = f(X2,X5,f(X4,X5,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c377,plain,
f(X2,X5,f(X4,X5,X3)) = f(X2,f(X4,X5,X3),X5),
inference(symmetry,[status(thm)],[c376]) ).
cnf(c378,plain,
f(f(X4,X5,X3),X5,X2) = f(X2,f(X4,X5,X3),X5),
inference(substitution,[status(thm)],[c4]) ).
cnf(c379,plain,
f(X2,f(X4,X5,X3),X5) = f(f(X4,X5,X3),X5,X2),
inference(symmetry,[status(thm)],[c378]) ).
cnf(c380,plain,
f(X5,X2,f(X4,X5,X3)) = f(f(X4,X5,X3),X5,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c381,plain,
f(f(X4,X5,X3),X5,X2) = f(X5,X2,f(X4,X5,X3)),
inference(symmetry,[status(thm)],[c380]) ).
cnf(c382,plain,
f(X3,X2,f(X4,X3,X2)) = f(f(X4,X3,X2),X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c383,plain,
f(f(X4,X3,X2),X3,X2) = f(X3,X2,f(X4,X3,X2)),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
f(X2,X4,f(X3,X4,X3)) = f(X4,X3,f(X2,X4,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c385,plain,
f(X4,X3,f(X2,X4,X3)) = f(X2,X4,f(X3,X4,X3)),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
f(X2,X3,X2) = X2,
inference(substitution,[status(thm)],[c80]) ).
cnf(c387,plain,
f(X2,X4,f(X3,X4,X3)) = f(X2,X4,X3),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
f(X4,X2,X3) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c389,plain,
f(X2,X4,X3) = f(X4,X2,X3),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
f(X4,X2,X3) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c391,plain,
f(X2,X4,X3) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c389,c390]) ).
cnf(c392,plain,
f(X2,X4,f(X3,X4,X3)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c387,c391]) ).
cnf(c393,plain,
f(X4,X3,f(X2,X4,X3)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c385,c392]) ).
cnf(c394,plain,
f(X3,X2,f(X4,X3,X2)) = f(X3,X2,X4),
inference(substitution,[status(thm)],[c393]) ).
cnf(c395,plain,
f(X3,X2,X4) = f(X4,X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c396,plain,
f(X3,X2,f(X4,X3,X2)) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c394,c395]) ).
cnf(c397,plain,
f(f(X4,X3,X2),X3,X2) = f(X4,X3,X2),
inference(transitivity,[status(thm)],[c383,c396]) ).
cnf(c398,plain,
f(f(X3,X4,X2),X4,X2) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c397]) ).
cnf(c399,plain,
f(X3,X4,X2) = f(f(X3,X4,X2),X4,X2),
inference(symmetry,[status(thm)],[c398]) ).
cnf(c400,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,X2,f(f(X4,X5,X3),X5,X3)),
inference(congruence,[status(thm)],[c399]) ).
cnf(c401,plain,
f(f(X4,X5,X3),X5,f(X5,X2,X3)) = f(X5,X2,f(f(X4,X5,X3),X5,X3)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c402,plain,
f(X5,X2,f(f(X4,X5,X3),X5,X3)) = f(f(X4,X5,X3),X5,f(X5,X2,X3)),
inference(symmetry,[status(thm)],[c401]) ).
cnf(c403,plain,
f(f(X4,X5,X3),X5,f(X5,X2,X3)) = f(X5,f(X4,X5,X3),f(X5,X3,X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c404,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,f(X4,X5,X3),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c405,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X2,f(X4,X5,X3)),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c406,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,X4,f(X5,X2,X3)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c407,plain,
f(X5,f(X4,X5,X3),X2) = f(X5,X4,f(X5,X2,X3)),
inference(transitivity,[status(thm)],[c405,c406]) ).
cnf(c408,plain,
f(X5,f(X4,X5,X3),f(X5,X3,X2)) = f(X5,X4,f(X5,f(X5,X3,X2),X3)),
inference(substitution,[status(thm)],[c407]) ).
cnf(c409,plain,
f(X4,f(X4,X3,X2),X3) = f(X4,X3,f(X4,X2,X3)),
inference(substitution,[status(thm)],[c180]) ).
cnf(c410,plain,
f(X5,X4,f(X5,f(X5,X3,X2),X3)) = f(X5,X4,f(X5,X3,f(X5,X2,X3))),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
f(X5,X4,f(X5,X3,f(X5,X2,X3))) = f(X5,X4,f(X5,X3,X2)),
inference(congruence,[status(thm)],[c281]) ).
cnf(c412,plain,
f(X5,X4,f(X5,f(X5,X3,X2),X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c410,c411]) ).
cnf(c413,plain,
f(X5,f(X4,X5,X3),f(X5,X3,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c408,c412]) ).
cnf(c414,plain,
f(f(X4,X5,X3),X5,f(X5,X2,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c403,c413]) ).
cnf(c415,plain,
f(X5,X2,f(f(X4,X5,X3),X5,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c402,c414]) ).
cnf(c416,plain,
f(X5,X2,f(X4,X5,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c400,c415]) ).
cnf(c417,plain,
f(f(X4,X5,X3),X5,X2) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c381,c416]) ).
cnf(c418,plain,
f(X2,f(X4,X5,X3),X5) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c379,c417]) ).
cnf(c419,plain,
f(X2,X5,f(X4,X5,X3)) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c377,c418]) ).
cnf(c420,plain,
f(X6,X3,f(f(X6,X5,X4),X3,f(X2,X5,X4))) = f(X3,f(X6,X5,X4),f(X3,f(X2,X5,X4),X6)),
inference(substitution,[status(thm)],[c419]) ).
cnf(c421,plain,
f(X3,f(X6,X5,X4),f(X3,f(X2,X5,X4),X6)) = f(X3,f(X2,X5,X4),X6),
inference(substitution,[status(thm)],[c200]) ).
cnf(c422,plain,
f(X6,X3,f(f(X6,X5,X4),X3,f(X2,X5,X4))) = f(X3,f(X2,X5,X4),X6),
inference(transitivity,[status(thm)],[c420,c421]) ).
cnf(c423,plain,
f(f(X2,X5,X4),X3,f(X3,X6,f(X6,X5,X4))) = f(X3,f(X2,X5,X4),X6),
inference(transitivity,[status(thm)],[c375,c422]) ).
cnf(c424,plain,
f(f(X6,X5,X4),X3,f(f(X2,X5,X4),X6,X3)) = f(X3,f(X2,X5,X4),X6),
inference(transitivity,[status(thm)],[c358,c423]) ).
cnf(c425,plain,
f(f(f(X6,X3,X2),X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4))) = f(f(X3,X5,X4),f(X6,X5,X4),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c424]) ).
cnf(c426,plain,
f(f(X3,X5,X4),f(X6,X5,X4),f(X6,X3,X2)) = f(f(f(X6,X3,X2),X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4))),
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
f(X2,X6,f(X3,X5,X4)) = f(X6,X2,f(X3,X5,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c428,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X6,f(X3,X5,X4))) = f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X2,f(X3,X5,X4))),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
f(X6,f(X3,X5,X4),f(f(X3,X5,X4),X2,f(X6,X5,X4))) = f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X2,f(X3,X5,X4))),
inference(substitution,[status(thm)],[c356]) ).
cnf(c430,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),X2,f(X6,X5,X4))),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
f(X4,X2,X3) = f(X2,X4,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c432,plain,
f(X3,X5,f(X5,X2,X4)) = f(X3,X5,f(X2,X5,X4)),
inference(congruence,[status(thm)],[c431]) ).
cnf(c433,plain,
f(X3,X5,f(X5,X2,X4)) = f(X5,X4,f(X3,X5,X2)),
inference(transitivity,[status(thm)],[c432,c25]) ).
cnf(c434,plain,
f(X5,X4,f(X4,X3,X2)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c433]) ).
cnf(c435,plain,
f(X4,X3,f(X2,X5,X4)) = f(X4,X2,f(X5,X4,X3)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c436,plain,
f(X4,X2,f(X5,X4,X3)) = f(X4,X3,f(X2,X5,X4)),
inference(symmetry,[status(thm)],[c435]) ).
cnf(c437,plain,
f(X5,X4,f(X4,X3,X2)) = f(X4,X3,f(X2,X5,X4)),
inference(transitivity,[status(thm)],[c434,c436]) ).
cnf(c438,plain,
f(X6,f(X3,X5,X4),f(f(X3,X5,X4),X2,f(X6,X5,X4))) = f(f(X3,X5,X4),X2,f(f(X6,X5,X4),X6,f(X3,X5,X4))),
inference(substitution,[status(thm)],[c437]) ).
cnf(c439,plain,
f(f(X3,X5,X4),X2,f(f(X6,X5,X4),X6,f(X3,X5,X4))) = f(f(X3,X5,X4),X2,f(X6,X5,X4)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c440,plain,
f(f(X3,X5,X4),X2,f(X6,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c441,plain,
f(f(X6,X5,X4),f(X3,X5,X4),X2) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c442,plain,
f(f(X3,X5,X4),X2,f(X6,X5,X4)) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c440,c441]) ).
cnf(c443,plain,
f(f(X3,X5,X4),X2,f(f(X6,X5,X4),X6,f(X3,X5,X4))) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c439,c442]) ).
cnf(c444,plain,
f(X6,f(X3,X5,X4),f(f(X3,X5,X4),X2,f(X6,X5,X4))) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c438,c443]) ).
cnf(c445,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)],[c430,c444]) ).
cnf(c446,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X6,f(X3,X5,X4))) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c428,c445]) ).
cnf(c447,plain,
f(f(f(X6,X3,X2),X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4))) = f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c446]) ).
cnf(c448,plain,
f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X3,X5,X4)) = f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c449,plain,
f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X3,X5,X4)) = f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X3,X5,X4)),
inference(symmetry,[status(thm)],[c448]) ).
cnf(c450,plain,
f(X2,X4,X3) = f(f(X5,X4,X3),f(X2,X4,X3),X2),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c451,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X2,X5,X4),X2)),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X2,X5,X4),X2)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(substitution,[status(thm)],[c298]) ).
cnf(c453,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),X2),
inference(transitivity,[status(thm)],[c451,c452]) ).
cnf(c454,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(X5,X3,X2)) = f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X5),
inference(substitution,[status(thm)],[c453]) ).
cnf(c455,plain,
f(f(f(X6,X5,X4),X3,X2),X5,f(X6,X3,X2)) = f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X5),
inference(substitution,[status(thm)],[c7]) ).
cnf(c456,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X5) = f(f(f(X6,X5,X4),X3,X2),X5,f(X6,X3,X2)),
inference(symmetry,[status(thm)],[c455]) ).
cnf(c457,plain,
f(f(f(X6,X5,X4),X3,X2),X5,f(X6,X3,X2)) = f(X5,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c458,plain,
f(f(X6,X5,X4),X3,f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X3,X2)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c459,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X3,X2)) = f(f(X6,X5,X4),X3,f(f(X3,X5,X4),f(X6,X5,X4),X2)),
inference(symmetry,[status(thm)],[c458]) ).
cnf(c460,plain,
f(X5,X4,f(X3,X5,X2)) = f(X5,X3,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c154]) ).
cnf(c461,plain,
f(X2,X5,f(X5,X3,X4)) = f(X5,X3,f(X2,X5,X4)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c462,plain,
f(X5,X3,f(X2,X5,X4)) = f(X2,X5,f(X5,X3,X4)),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
f(X5,X4,f(X3,X5,X2)) = f(X2,X5,f(X5,X3,X4)),
inference(transitivity,[status(thm)],[c460,c462]) ).
cnf(c464,plain,
f(f(X6,X5,X4),X3,f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(X2,f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X3)),
inference(substitution,[status(thm)],[c463]) ).
cnf(c465,plain,
f(X2,f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X3)) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c466,plain,
f(f(X6,X5,X4),X3,f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c464,c465]) ).
cnf(c467,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X3,X2)) = f(X2,f(X6,X5,X4),f(X3,X5,X4)),
inference(transitivity,[status(thm)],[c459,c466]) ).
cnf(c468,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(f(f(X6,X5,X4),X3,X2),X6,X5)) = f(X5,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c467]) ).
cnf(c469,plain,
f(X5,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)) = f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(f(f(X6,X5,X4),X3,X2),X6,X5)),
inference(symmetry,[status(thm)],[c468]) ).
cnf(c470,plain,
f(X5,f(X4,X3,X2),f(X5,X4,X3)) = f(X5,X4,f(X5,X3,f(X4,X3,X2))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c471,plain,
f(X4,X3,X2) = f(f(X4,X3,X2),X4,X3),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c472,plain,
f(X5,X3,f(X4,X3,X2)) = f(X5,X3,f(f(X4,X3,X2),X4,X3)),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
f(X5,X4,f(X5,X3,f(X4,X3,X2))) = f(X5,X4,f(X5,X3,f(f(X4,X3,X2),X4,X3))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
f(X5,X4,f(X5,X3,f(f(X4,X3,X2),X4,X3))) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c197]) ).
cnf(c475,plain,
f(X5,X4,f(X5,X3,f(X4,X3,X2))) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c473,c474]) ).
cnf(c476,plain,
f(X5,f(X4,X3,X2),f(X5,X4,X3)) = f(X5,X4,X3),
inference(transitivity,[status(thm)],[c470,c475]) ).
cnf(c477,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X5,X4),f(f(f(X6,X5,X4),X3,X2),X6,X5)) = f(f(f(X6,X5,X4),X3,X2),X6,X5),
inference(substitution,[status(thm)],[c476]) ).
cnf(c478,plain,
f(f(f(X6,X5,X4),X3,X2),X6,X5) = f(f(f(X6,X5,X4),X3,X2),f(X6,X5,X4),f(f(f(X6,X5,X4),X3,X2),X6,X5)),
inference(symmetry,[status(thm)],[c477]) ).
cnf(c479,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),X7,X6)) = f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X7,X6,X5),f(f(f(X7,X6,X5),X4,X3),X7,X6))),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,plain,
f(f(X6,X5,X4),X6,f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X6,X2)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c481,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X6,X2)) = f(f(X6,X5,X4),X6,f(f(X3,X5,X4),f(X6,X5,X4),X2)),
inference(symmetry,[status(thm)],[c480]) ).
cnf(c482,plain,
f(f(X6,X5,X4),X6,f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(X2,f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X6)),
inference(substitution,[status(thm)],[c463]) ).
cnf(c483,plain,
f(X2,f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X6)) = f(X2,f(X6,X5,X4),f(X6,X5,X4)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c484,plain,
f(X2,f(X5,X4,X3),f(X5,X4,X3)) = f(X5,X4,X3),
inference(substitution,[status(thm)],[c125]) ).
cnf(c485,plain,
f(X2,f(X6,X5,X4),f(f(X6,X5,X4),f(X3,X5,X4),X6)) = f(X6,X5,X4),
inference(transitivity,[status(thm)],[c483,c484]) ).
cnf(c486,plain,
f(f(X6,X5,X4),X6,f(f(X3,X5,X4),f(X6,X5,X4),X2)) = f(X6,X5,X4),
inference(transitivity,[status(thm)],[c482,c485]) ).
cnf(c487,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),X6,X2)) = f(X6,X5,X4),
inference(transitivity,[status(thm)],[c481,c486]) ).
cnf(c488,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X7,X6,X5),f(f(f(X7,X6,X5),X4,X3),X7,X6))) = f(f(X7,X6,X5),X4,X3),
inference(substitution,[status(thm)],[c487]) ).
cnf(c489,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),X7,X6)) = f(f(X7,X6,X5),X4,X3),
inference(transitivity,[status(thm)],[c479,c488]) ).
cnf(c490,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(f(f(X6,X5,X4),X3,X2),X6,X5)) = f(f(X6,X5,X4),X3,X2),
inference(substitution,[status(thm)],[c489]) ).
cnf(c491,plain,
f(X5,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c469,c490]) ).
cnf(c492,plain,
f(f(f(X6,X5,X4),X3,X2),X5,f(X6,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c457,c491]) ).
cnf(c493,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X5) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c456,c492]) ).
cnf(c494,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(X5,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c454,c493]) ).
cnf(c495,plain,
f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X3,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(substitution,[status(thm)],[c494]) ).
cnf(c496,plain,
f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X3,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c449,c495]) ).
cnf(c497,plain,
f(f(f(X6,X3,X2),X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4))) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c447,c496]) ).
cnf(c498,plain,
f(f(X3,X5,X4),f(X6,X5,X4),f(X6,X3,X2)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c426,c497]) ).
cnf(c499,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(X6,X3,X2)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c334,c498]) ).
cnf(c500,plain,
f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c333,c499]) ).
cnf(c501,plain,
f(f(X6,X3,X2),X5,X4) = f(f(X6,X5,X4),f(X6,X3,X2),f(X3,X5,X4)),
inference(symmetry,[status(thm)],[c500]) ).
cnf(c502,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(f(X7,X4,X2),X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(f(X7,X6,X5),f(X7,X4,X2),f(X4,X6,X5))),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
f(f(X5,X4,X3),X5,f(X5,X2,X4)) = f(X5,X2,f(f(X5,X4,X3),X5,X4)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c504,plain,
f(X5,X2,f(f(X5,X4,X3),X5,X4)) = f(X5,X2,f(X5,X4,X3)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c505,plain,
f(X5,X2,f(X5,X4,X3)) = f(f(X5,X4,X3),X5,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c506,plain,
f(f(X5,X4,X3),X5,X2) = f(X2,f(X5,X4,X3),X5),
inference(substitution,[status(thm)],[c4]) ).
cnf(c507,plain,
f(X5,X2,f(X5,X4,X3)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c505,c506]) ).
cnf(c508,plain,
f(X5,X2,f(f(X5,X4,X3),X5,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c504,c507]) ).
cnf(c509,plain,
f(f(X5,X4,X3),X5,f(X5,X2,X4)) = f(X2,f(X5,X4,X3),X5),
inference(transitivity,[status(thm)],[c503,c508]) ).
cnf(c510,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(f(X7,X6,X5),f(X7,X4,X2),f(X4,X6,X5))) = f(f(X7,X4,X2),f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5)),
inference(substitution,[status(thm)],[c509]) ).
cnf(c511,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X4,X2),f(X7,X6,X5)) = f(f(X7,X4,X2),f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c512,plain,
f(f(X7,X4,X2),f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X4,X2),f(X7,X6,X5)),
inference(symmetry,[status(thm)],[c511]) ).
cnf(c513,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X4,X2),f(X7,X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(X7,X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c514,plain,
f(f(X7,X4,X2),f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(X7,X4,X2)),
inference(transitivity,[status(thm)],[c512,c513]) ).
cnf(c515,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(f(X7,X6,X5),f(X7,X4,X2),f(X4,X6,X5))) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(X7,X4,X2)),
inference(transitivity,[status(thm)],[c510,c514]) ).
cnf(c516,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(f(X7,X4,X2),X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(X7,X4,X2)),
inference(transitivity,[status(thm)],[c502,c515]) ).
cnf(c517,plain,
f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(f(X7,X4,X2),X6,X5),f(X7,X6,X5)) = f(f(f(X7,X6,X5),f(X4,X6,X5),X3),f(X7,X6,X5),f(X7,X4,X2)),
inference(transitivity,[status(thm)],[c331,c516]) ).
cnf(c518,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)) = f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c517]) ).
cnf(c519,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2),f(X6,X5,X4)) = f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)),
inference(symmetry,[status(thm)],[c518]) ).
cnf(c520,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(f(X6,X3,X2),X5,X4),f(X6,X5,X4)) = f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X5,X4),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c517]) ).
cnf(c521,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X3,X2),f(X6,X5,X4)) = f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X5,X4),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c522,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X5,X4),f(X6,X3,X2)) = f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X3,X2),f(X6,X5,X4)),
inference(symmetry,[status(thm)],[c521]) ).
cnf(c523,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X3,X2),f(X6,X5,X4)) = f(f(X6,X3,X2),f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X5,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c524,plain,
f(X4,X3,X2) = f(X3,X4,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c525,plain,
f(X3,X4,X2) = f(X4,X3,X2),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c526,plain,
f(X5,X4,f(X3,X5,X2)) = f(X5,X4,f(X5,X3,X2)),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
f(X3,f(X5,X4,X2),X5) = f(X5,X4,f(X5,X3,X2)),
inference(transitivity,[status(thm)],[c148,c526]) ).
cnf(c528,plain,
f(f(X6,X3,X2),f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X5,X4)) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4))),
inference(substitution,[status(thm)],[c527]) ).
cnf(c529,plain,
f(f(X6,X5,X4),f(X2,X5,X4),f(X6,X3,X2)) = f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c530,plain,
f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4)) = f(f(X6,X5,X4),f(X2,X5,X4),f(X6,X3,X2)),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
f(f(X6,X5,X4),f(X2,X5,X4),f(X6,X3,X2)) = f(f(X2,X5,X4),f(X6,X5,X4),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c532,plain,
f(f(f(X6,X3,X2),X5,X4),f(X2,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4))) = f(f(X2,X5,X4),f(X6,X5,X4),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c424]) ).
cnf(c533,plain,
f(f(X2,X5,X4),f(X6,X5,X4),f(X6,X3,X2)) = f(f(f(X6,X3,X2),X5,X4),f(X2,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4))),
inference(symmetry,[status(thm)],[c532]) ).
cnf(c534,plain,
f(f(f(X6,X3,X2),X5,X4),f(X2,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4))) = f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X2,X5,X4)),
inference(substitution,[status(thm)],[c446]) ).
cnf(c535,plain,
f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X2,X5,X4)) = f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X2,X5,X4)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c536,plain,
f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X2,X5,X4)) = f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X2,X5,X4)),
inference(symmetry,[status(thm)],[c535]) ).
cnf(c537,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(X4,X3,X2)) = f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X4),
inference(substitution,[status(thm)],[c453]) ).
cnf(c538,plain,
f(f(f(X6,X5,X4),X3,X2),X4,f(X6,X3,X2)) = f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X4),
inference(substitution,[status(thm)],[c7]) ).
cnf(c539,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X4) = f(f(f(X6,X5,X4),X3,X2),X4,f(X6,X3,X2)),
inference(symmetry,[status(thm)],[c538]) ).
cnf(c540,plain,
f(f(f(X6,X5,X4),X3,X2),X4,f(X6,X3,X2)) = f(X4,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c541,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(f(f(X6,X5,X4),X3,X2),X6,X4)) = f(X4,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)),
inference(substitution,[status(thm)],[c467]) ).
cnf(c542,plain,
f(X4,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)) = f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(f(f(X6,X5,X4),X3,X2),X6,X4)),
inference(symmetry,[status(thm)],[c541]) ).
cnf(c543,plain,
f(X5,f(X4,X3,X2),f(X5,X4,X2)) = f(X5,X4,f(X5,X2,f(X4,X3,X2))),
inference(substitution,[status(thm)],[c166]) ).
cnf(c544,plain,
f(X4,X3,X2) = f(f(X4,X3,X2),X4,X2),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c545,plain,
f(X5,X2,f(X4,X3,X2)) = f(X5,X2,f(f(X4,X3,X2),X4,X2)),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
f(X5,X4,f(X5,X2,f(X4,X3,X2))) = f(X5,X4,f(X5,X2,f(f(X4,X3,X2),X4,X2))),
inference(congruence,[status(thm)],[c545]) ).
cnf(c547,plain,
f(X5,X4,f(X5,X2,f(f(X4,X3,X2),X4,X2))) = f(X5,X4,X2),
inference(substitution,[status(thm)],[c197]) ).
cnf(c548,plain,
f(X5,X4,f(X5,X2,f(X4,X3,X2))) = f(X5,X4,X2),
inference(transitivity,[status(thm)],[c546,c547]) ).
cnf(c549,plain,
f(X5,f(X4,X3,X2),f(X5,X4,X2)) = f(X5,X4,X2),
inference(transitivity,[status(thm)],[c543,c548]) ).
cnf(c550,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X5,X4),f(f(f(X6,X5,X4),X3,X2),X6,X4)) = f(f(f(X6,X5,X4),X3,X2),X6,X4),
inference(substitution,[status(thm)],[c549]) ).
cnf(c551,plain,
f(f(f(X6,X5,X4),X3,X2),X6,X4) = f(f(f(X6,X5,X4),X3,X2),f(X6,X5,X4),f(f(f(X6,X5,X4),X3,X2),X6,X4)),
inference(symmetry,[status(thm)],[c550]) ).
cnf(c552,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),X7,X5)) = f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X7,X6,X5),f(f(f(X7,X6,X5),X4,X3),X7,X5))),
inference(congruence,[status(thm)],[c551]) ).
cnf(c553,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),f(X7,X6,X5),f(f(f(X7,X6,X5),X4,X3),X7,X5))) = f(f(X7,X6,X5),X4,X3),
inference(substitution,[status(thm)],[c487]) ).
cnf(c554,plain,
f(f(f(X7,X6,X5),X4,X3),f(X2,X4,X3),f(f(f(X7,X6,X5),X4,X3),X7,X5)) = f(f(X7,X6,X5),X4,X3),
inference(transitivity,[status(thm)],[c552,c553]) ).
cnf(c555,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(f(f(X6,X5,X4),X3,X2),X6,X4)) = f(f(X6,X5,X4),X3,X2),
inference(substitution,[status(thm)],[c554]) ).
cnf(c556,plain,
f(X4,f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c542,c555]) ).
cnf(c557,plain,
f(f(f(X6,X5,X4),X3,X2),X4,f(X6,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c540,c556]) ).
cnf(c558,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),X4) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c539,c557]) ).
cnf(c559,plain,
f(f(f(X6,X5,X4),X3,X2),f(X6,X3,X2),f(X4,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c537,c558]) ).
cnf(c560,plain,
f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X2,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(substitution,[status(thm)],[c559]) ).
cnf(c561,plain,
f(f(X6,X5,X4),f(f(X6,X3,X2),X5,X4),f(X2,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c536,c560]) ).
cnf(c562,plain,
f(f(f(X6,X3,X2),X5,X4),f(X2,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4))) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c534,c561]) ).
cnf(c563,plain,
f(f(X2,X5,X4),f(X6,X5,X4),f(X6,X3,X2)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c533,c562]) ).
cnf(c564,plain,
f(f(X6,X5,X4),f(X2,X5,X4),f(X6,X3,X2)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c531,c563]) ).
cnf(c565,plain,
f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c530,c564]) ).
cnf(c566,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4))) = f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X3,X2),X5,X4)),
inference(congruence,[status(thm)],[c565]) ).
cnf(c567,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X3,X2),X5,X4)) = f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X3,X5,X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c568,plain,
f(f(f(X6,X3,X2),X5,X4),f(X6,X5,X4),f(X3,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(substitution,[status(thm)],[c494]) ).
cnf(c569,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X3,X2),X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c567,c568]) ).
cnf(c570,plain,
f(f(X6,X5,X4),f(X3,X5,X4),f(f(X6,X5,X4),f(X6,X3,X2),f(X2,X5,X4))) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c566,c569]) ).
cnf(c571,plain,
f(f(X6,X3,X2),f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c528,c570]) ).
cnf(c572,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X3,X2),f(X6,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c523,c571]) ).
cnf(c573,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(X6,X5,X4),f(X6,X3,X2)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c522,c572]) ).
cnf(c574,plain,
f(f(f(X6,X5,X4),f(X3,X5,X4),f(X2,X5,X4)),f(f(X6,X3,X2),X5,X4),f(X6,X5,X4)) = f(f(X6,X3,X2),X5,X4),
inference(transitivity,[status(thm)],[c520,c573]) ).
cnf(c575,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(f(X6,X5,X4),X3,X2),f(X6,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(substitution,[status(thm)],[c574]) ).
cnf(c576,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2),f(X6,X5,X4)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c519,c575]) ).
cnf(c577,plain,
f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),f(X6,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c329,c576]) ).
cnf(c578,plain,
f(f(X6,X5,X4),f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c328,c577]) ).
cnf(c579,plain,
f(f(X6,X3,X2),f(X4,X3,X2),f(f(X6,X3,X2),f(X6,X5,X4),X5)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c326,c578]) ).
cnf(c580,plain,
f(f(X6,X3,X2),f(X4,X3,X2),f(f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)),f(X6,X5,X4),X5)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c314,c579]) ).
cnf(c581,plain,
f(f(X6,X3,X2),f(X5,X3,X2),f(X4,X3,X2)) = f(f(X6,X5,X4),X3,X2),
inference(transitivity,[status(thm)],[c238,c580]) ).
cnf(c582,plain,
f(f(x,u,w),f(y,u,w),f(z,u,w)) = f(f(x,y,z),u,w),
inference(substitution,[status(thm)],[c581]) ).
cnf(c583,plain,
f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)),
inference(symmetry,[status(thm)],[c582]) ).
cnf(c584,plain,
$false,
inference(resolution,[status(thm)],[c3,c583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG212+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n020.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 19:44:30 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 143.62/18.30 Command-line arguments: --flatten-regeneralise
% 143.62/18.30
% 143.62/18.30 % SZS status Theorem
% 143.62/18.30
% 143.62/18.34 % SZS output start CNFRefutation
% See solution above
% 145.23/18.55
% 145.23/18.55 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------