%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% 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 11:45:45 AM UTC 2026
% Result : Unsatisfiable 3.10s 0.87s
% Output : CNFRefutation 7.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 104
% Number of leaves : 4
% Syntax : Number of clauses : 627 ( 627 unt; 0 nHn; 4 RR)
% Number of literals : 627 ( 626 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 1184 ( 121 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
neg(A) = f(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_003) ).
cnf(c3,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
f(neg(X),X) = f(f(X,X),X),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
f(X2,f(neg(X),X)) = f(X2,f(f(X,X),X)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
f(f(X,f(neg(X2),X2)),X3) = f(f(X,f(f(X2,X2),X2)),X3),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
f(X2,f(f(X2,f(neg(X3),X3)),X)) = f(X2,f(f(X2,f(f(X3,X3),X3)),X)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
f(f(f(f(X3,X2),f(X2,X)),X4),f(X2,f(f(X2,f(neg(X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X4),f(X2,f(f(X2,f(f(X3,X3),X3)),X))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
f(f(f(f(A2,B),f(B,C)),D),f(B,f(f(B,f(f(A2,A2),A2)),C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos) ).
cnf(c10,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(f(X4,X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
f(f(f(f(X4,X3),f(X3,X2)),X),f(X3,f(f(X3,f(neg(X4),X4)),X2))) = X3,
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))) = X3,
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
X3 = f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
f(f(f(X4,X3),f(X3,X2)),X3) = f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2)))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),X3)) = f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
neg(f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,axiom,
and(A2,B2) = f(f(A2,B2),f(A2,B2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_002) ).
cnf(c18,plain,
and(X2,X) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
f(f(X2,X),f(X2,X)) = and(X2,X),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
neg(f(X2,X)) = and(X2,X),
inference(transitivity,[status(thm)],[c16,c19]) ).
cnf(c21,plain,
neg(f(X,X2)) = and(X,X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
and(X,X2) = neg(f(X,X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
f(and(X,X2),f(X,X2)) = f(neg(f(X,X2)),f(X,X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
f(f(X3,X2),f(and(X,X3),f(X,X3))) = f(f(X3,X2),f(neg(f(X,X3)),f(X,X3))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X) = f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X)) = f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X))) = f(X4,f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))) = X4,
inference(substitution,[status(thm)],[c11]) ).
cnf(c29,plain,
X4 = f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))) = f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))),f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
f(f(f(f(f(X2,X4),f(X4,X3)),f(f(X4,X3),X)),f(X4,f(f(X4,f(neg(X2),X2)),X3))),f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))) = f(X4,X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c32,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(neg(f(X2,X4)),f(X2,X4))),X))) = f(X4,X3),
inference(transitivity,[status(thm)],[c30,c31]) ).
cnf(c33,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),X))) = f(X4,X3),
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X3,X2)),f(f(f(f(X4,X3),f(X3,X2)),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),f(X3,f(f(X3,f(neg(X4),X4)),X2))))) = f(f(X4,X3),f(X3,X2)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2)) = f(f(X3,X2),f(X2,X)),
inference(transitivity,[status(thm)],[c15,c34]) ).
cnf(c36,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c39,plain,
f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2) = f(X2,X2),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c42,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)),
inference(transitivity,[status(thm)],[c40,c43]) ).
cnf(c45,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)),
inference(transitivity,[status(thm)],[c37,c44]) ).
cnf(c46,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)) = f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),f(X2,f(f(X2,f(neg(X3),X3)),X))) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c48,plain,
f(f(f(f(X3,X2),f(X2,X)),X2),neg(X2)) = X2,
inference(transitivity,[status(thm)],[c46,c47]) ).
cnf(c49,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),neg(f(X3,f(X3,X3)))) = f(X3,f(X3,X3)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
f(X3,f(X3,X3)) = f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),neg(f(X3,f(X3,X3)))),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),neg(f(X3,f(X3,X3)))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c52,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),neg(f(X3,f(X3,X3)))) = f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c54,plain,
neg(and(X2,X)) = neg(neg(f(X2,X))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
neg(neg(X)) = f(neg(X),neg(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c56,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c57,plain,
f(neg(X),neg(X)) = f(f(X,X),neg(X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))) = X3,
inference(substitution,[status(thm)],[c11]) ).
cnf(c59,plain,
X3 = f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
f(X3,X3) = f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),X3),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
f(f(X3,X3),neg(X3)) = f(f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),X3),neg(X3)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
f(f(f(f(f(f(X2,X3),f(X3,X)),X3),f(X3,f(f(X3,f(neg(X2),X2)),X))),X3),neg(X3)) = X3,
inference(substitution,[status(thm)],[c48]) ).
cnf(c63,plain,
f(f(X,X),neg(X)) = X,
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
f(neg(X),neg(X)) = X,
inference(transitivity,[status(thm)],[c57,c63]) ).
cnf(c65,plain,
neg(neg(X)) = X,
inference(transitivity,[status(thm)],[c55,c64]) ).
cnf(c66,plain,
neg(neg(f(X2,X))) = f(X2,X),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
neg(and(X2,X)) = f(X2,X),
inference(transitivity,[status(thm)],[c54,c66]) ).
cnf(c68,plain,
neg(and(f(X2,f(X2,X2)),f(X,f(X,X)))) = f(f(X2,f(X2,X2)),f(X,f(X,X))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
f(f(X2,f(X2,X2)),f(X,f(X,X))) = neg(and(f(X2,f(X2,X2)),f(X,f(X,X)))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c71,plain,
neg(and(X2,X)) = neg(neg(f(X2,X))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
and(f(X2,X),neg(and(X2,X))) = and(f(X2,X),neg(neg(f(X2,X)))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
neg(f(X,neg(neg(X)))) = and(X,neg(neg(X))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c74,plain,
and(X,neg(neg(X))) = neg(f(X,neg(neg(X)))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
neg(neg(X)) = f(neg(X),neg(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c76,plain,
f(X,neg(neg(X))) = f(X,f(neg(X),neg(X))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
neg(neg(neg(X))) = f(neg(neg(X)),neg(neg(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
f(neg(neg(neg(X))),f(X,f(f(X,f(neg(X),X)),X))) = f(f(neg(neg(X)),neg(neg(X))),f(X,f(f(X,f(neg(X),X)),X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
neg(f(X,X)) = and(X,X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c80,plain,
and(X,X) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c82,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
neg(f(X,X)) = neg(neg(X)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
and(X,X) = neg(neg(X)),
inference(transitivity,[status(thm)],[c80,c83]) ).
cnf(c85,plain,
neg(neg(X)) = and(X,X),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
f(neg(neg(X2)),X) = f(and(X2,X2),X),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(and(X2,X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
neg(f(X,X)) = and(X,X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c89,plain,
and(X,X) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
f(and(X2,X2),X) = f(neg(f(X2,X2)),X),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
f(f(and(X2,X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
f(neg(f(X2,X2)),X) = f(f(f(X2,X2),f(X2,X2)),X),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(f(f(X2,X2),f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
f(f(f(f(X2,X2),f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c96,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c94,c95]) ).
cnf(c97,plain,
f(f(and(X2,X2),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c91,c96]) ).
cnf(c98,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c87,c97]) ).
cnf(c99,plain,
f(f(neg(neg(X)),neg(neg(X))),f(X,f(f(X,f(neg(X),X)),X))) = X,
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
f(neg(neg(neg(X))),f(X,f(f(X,f(neg(X),X)),X))) = X,
inference(transitivity,[status(thm)],[c78,c99]) ).
cnf(c101,plain,
X = f(neg(neg(neg(X))),f(X,f(f(X,f(neg(X),X)),X))),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))) = f(f(neg(neg(neg(X))),f(X,f(f(X,f(neg(X),X)),X))),f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
f(f(neg(neg(neg(X))),f(X,f(f(X,f(neg(X),X)),X))),f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))) = neg(X),
inference(substitution,[status(thm)],[c98]) ).
cnf(c104,plain,
f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))) = neg(X),
inference(transitivity,[status(thm)],[c102,c103]) ).
cnf(c105,plain,
neg(X) = f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
f(neg(X),neg(X)) = f(f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))),neg(X)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
f(X,f(neg(X),neg(X))) = f(X,f(f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))),neg(X))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)) = f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c109,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = X,
inference(substitution,[status(thm)],[c98]) ).
cnf(c111,plain,
f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X) = f(X,X),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)) = f(f(neg(neg(X)),X),f(X,X)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
f(f(neg(neg(X)),X),f(X,X)) = f(f(neg(neg(X)),X),neg(X)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
f(f(neg(neg(X)),X),f(f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),X)) = f(f(neg(neg(X)),X),neg(X)),
inference(transitivity,[status(thm)],[c112,c115]) ).
cnf(c117,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = f(f(neg(neg(X)),X),neg(X)),
inference(transitivity,[status(thm)],[c109,c116]) ).
cnf(c118,plain,
f(f(neg(neg(X)),X),neg(X)) = f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
f(f(neg(neg(X)),X),f(X,f(f(X,f(neg(X),X)),X))) = X,
inference(substitution,[status(thm)],[c98]) ).
cnf(c120,plain,
f(f(neg(neg(X)),X),neg(X)) = X,
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
X = f(f(neg(neg(X)),X),neg(X)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
f(X2,f(neg(X2),X)) = f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
f(f(X2,f(neg(X2),X)),neg(X2)) = f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
f(X2,f(f(X2,f(neg(X2),X)),neg(X2))) = f(X2,f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
X = f(f(neg(neg(X)),X),neg(X)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c126,plain,
f(X2,f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(f(f(neg(neg(X2)),X2),neg(X2)),f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
f(f(f(neg(neg(X2)),X2),neg(X2)),f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c128,plain,
f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)) = f(X2,f(neg(X2),X)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c129,plain,
f(f(f(neg(neg(X2)),X2),neg(X2)),f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(X2,f(neg(X2),X)),
inference(transitivity,[status(thm)],[c127,c128]) ).
cnf(c130,plain,
f(X2,f(f(f(f(neg(neg(X2)),X2),neg(X2)),f(neg(X2),X)),neg(X2))) = f(X2,f(neg(X2),X)),
inference(transitivity,[status(thm)],[c126,c129]) ).
cnf(c131,plain,
f(X2,f(f(X2,f(neg(X2),X)),neg(X2))) = f(X2,f(neg(X2),X)),
inference(transitivity,[status(thm)],[c124,c130]) ).
cnf(c132,plain,
f(X,f(f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))),neg(X))) = f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
f(X,f(f(X,f(neg(X),f(f(neg(X),f(neg(neg(X)),neg(X))),neg(X)))),neg(X))) = neg(X),
inference(transitivity,[status(thm)],[c132,c104]) ).
cnf(c134,plain,
f(X,f(neg(X),neg(X))) = neg(X),
inference(transitivity,[status(thm)],[c107,c133]) ).
cnf(c135,plain,
f(X,neg(neg(X))) = neg(X),
inference(transitivity,[status(thm)],[c76,c134]) ).
cnf(c136,plain,
neg(f(X,neg(neg(X)))) = neg(neg(X)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
and(X,neg(neg(X))) = neg(neg(X)),
inference(transitivity,[status(thm)],[c74,c136]) ).
cnf(c138,plain,
and(f(X2,X),neg(neg(f(X2,X)))) = neg(neg(f(X2,X))),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
neg(neg(f(X2,X))) = neg(and(X2,X)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c140,plain,
and(f(X2,X),neg(neg(f(X2,X)))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
and(f(X2,X),neg(and(X2,X))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c72,c140]) ).
cnf(c142,plain,
and(f(f(X2,f(X2,X2)),f(X,f(X,X))),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = neg(and(f(X2,f(X2,X2)),f(X,f(X,X)))),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
neg(and(f(X2,f(X2,X2)),f(X,f(X,X)))) = and(f(f(X2,f(X2,X2)),f(X,f(X,X))),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c145,plain,
f(X2,X) = f(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
f(f(X2,X),neg(X2)) = f(f(neg(neg(X2)),X),neg(X2)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
neg(f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c148,plain,
and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = neg(f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
neg(f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = neg(X2),
inference(congruence,[status(thm)],[c98]) ).
cnf(c150,plain,
and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = neg(X2),
inference(transitivity,[status(thm)],[c148,c149]) ).
cnf(c151,plain,
neg(X2) = and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
f(f(neg(neg(X2)),X),neg(X2)) = f(f(neg(neg(X2)),X),and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c154,plain,
f(X2,and(X2,X)) = f(X2,neg(f(X2,X))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
neg(f(X2,X)) = f(f(X2,X),f(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c156,plain,
f(X2,neg(f(X2,X))) = f(X2,f(f(X2,X),f(X2,X))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c158,plain,
f(f(X2,X),and(X2,X)) = f(f(X2,X),neg(f(X2,X))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
f(X2,f(f(X2,X),and(X2,X))) = f(X2,f(f(X2,X),neg(f(X2,X)))),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
f(f(X2,X),f(X2,f(f(X2,X),and(X2,X)))) = f(f(X2,X),f(X2,f(f(X2,X),neg(f(X2,X))))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c162,plain,
f(X2,X) = f(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
f(f(X2,X),f(X2,f(f(X2,X),neg(f(X2,X))))) = f(f(neg(neg(X2)),X),f(X2,f(f(X2,X),neg(f(X2,X))))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c165,plain,
f(X2,X) = f(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
f(f(X2,X),neg(f(X2,X))) = f(f(neg(neg(X2)),X),neg(f(X2,X))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
f(X2,f(f(X2,X),neg(f(X2,X)))) = f(X2,f(f(neg(neg(X2)),X),neg(f(X2,X)))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(X2,X),neg(f(X2,X))))) = f(f(neg(neg(X2)),X),f(X2,f(f(neg(neg(X2)),X),neg(f(X2,X))))),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c170,plain,
f(X2,X) = f(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
neg(f(X2,X)) = neg(f(neg(neg(X2)),X)),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
f(f(neg(neg(X2)),X),neg(f(X2,X))) = f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
f(X2,f(f(neg(neg(X2)),X),neg(f(X2,X)))) = f(X2,f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X)))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(neg(neg(X2)),X),neg(f(X2,X))))) = f(f(neg(neg(X2)),X),f(X2,f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X))))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
X2 = f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c176,plain,
f(X2,f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X)))) = f(f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X)))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X))))) = f(f(neg(neg(X2)),X),f(f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X))))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c179,plain,
f(X,neg(X)) = f(neg(neg(X)),neg(X)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
f(f(X2,X),f(X2,neg(X2))) = f(f(X2,X),f(neg(neg(X2)),neg(X2))),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
f(X2,f(f(X2,X),f(X2,neg(X2)))) = f(X2,f(f(X2,X),f(neg(neg(X2)),neg(X2)))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
neg(neg(X)) = and(X,X),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c183,plain,
f(neg(neg(X)),neg(X)) = f(and(X,X),neg(X)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
f(f(X2,X),f(neg(neg(X2)),neg(X2))) = f(f(X2,X),f(and(X2,X2),neg(X2))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
f(X2,f(f(X2,X),f(neg(neg(X2)),neg(X2)))) = f(X2,f(f(X2,X),f(and(X2,X2),neg(X2)))),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c187,plain,
f(and(X,X),neg(X)) = f(and(X,X),f(X,X)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
f(f(X2,X),f(and(X2,X2),neg(X2))) = f(f(X2,X),f(and(X2,X2),f(X2,X2))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
f(X2,f(f(X2,X),f(and(X2,X2),neg(X2)))) = f(X2,f(f(X2,X),f(and(X2,X2),f(X2,X2)))),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
f(f(X4,X3),f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),f(f(f(f(X4,X3),f(and(X2,X4),f(X2,X4))),f(and(X,f(X4,X3)),f(X,f(X4,X3)))),X5))) = f(f(X4,X3),f(and(X2,X4),f(X2,X4))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c191,plain,
f(f(X5,X4),f(and(X3,X5),f(X3,X5))) = f(f(X5,X4),f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(and(X2,f(X5,X4)),f(X2,f(X5,X4)))),X))),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
f(X5,f(f(X5,X4),f(and(X3,X5),f(X3,X5)))) = f(X5,f(f(X5,X4),f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(and(X2,f(X5,X4)),f(X2,f(X5,X4)))),X)))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(f(f(f(X5,X4),f(and(X3,X5),f(X3,X5))),f(and(X2,f(X5,X4)),f(X2,f(X5,X4)))),X)))) = f(X5,X4),
inference(substitution,[status(thm)],[c33]) ).
cnf(c194,plain,
f(X3,f(f(X3,X2),f(and(X,X3),f(X,X3)))) = f(X3,X2),
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
f(X2,f(f(X2,X),f(and(X2,X2),f(X2,X2)))) = f(X2,X),
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
f(X2,f(f(X2,X),f(and(X2,X2),neg(X2)))) = f(X2,X),
inference(transitivity,[status(thm)],[c189,c195]) ).
cnf(c197,plain,
f(X2,f(f(X2,X),f(neg(neg(X2)),neg(X2)))) = f(X2,X),
inference(transitivity,[status(thm)],[c185,c196]) ).
cnf(c198,plain,
f(X2,f(f(X2,X),f(X2,neg(X2)))) = f(X2,X),
inference(transitivity,[status(thm)],[c181,c197]) ).
cnf(c199,plain,
f(f(neg(neg(X2)),X),f(f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X))))) = f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
f(f(neg(neg(X2)),X),f(f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X))))) = X2,
inference(transitivity,[status(thm)],[c199,c98]) ).
cnf(c201,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(neg(neg(X2)),X),neg(f(neg(neg(X2)),X))))) = X2,
inference(transitivity,[status(thm)],[c177,c200]) ).
cnf(c202,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(neg(neg(X2)),X),neg(f(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c174,c201]) ).
cnf(c203,plain,
f(f(neg(neg(X2)),X),f(X2,f(f(X2,X),neg(f(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c168,c202]) ).
cnf(c204,plain,
f(f(X2,X),f(X2,f(f(X2,X),neg(f(X2,X))))) = X2,
inference(transitivity,[status(thm)],[c163,c203]) ).
cnf(c205,plain,
f(f(X2,X),f(X2,f(f(X2,X),and(X2,X)))) = X2,
inference(transitivity,[status(thm)],[c160,c204]) ).
cnf(c206,plain,
f(f(f(X3,X2),f(and(X,X3),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),and(f(X3,X2),f(and(X,X3),f(X,X3)))))) = f(X3,X2),
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
f(X3,X2) = f(f(f(X3,X2),f(and(X,X3),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),and(f(X3,X2),f(and(X,X3),f(X,X3)))))),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
f(f(X3,X2),f(X3,X2)) = f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),and(f(X3,X2),f(and(X,X3),f(X,X3))))))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
f(X3,f(f(X3,X2),f(X3,X2))) = f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),and(f(X3,X2),f(and(X,X3),f(X,X3)))))))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),f(f(X3,X2),f(f(f(X3,X2),f(and(X,X3),f(X,X3))),and(f(X3,X2),f(and(X,X3),f(X,X3)))))))) = f(X3,X2),
inference(substitution,[status(thm)],[c33]) ).
cnf(c211,plain,
f(X2,f(f(X2,X),f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
f(X2,neg(f(X2,X))) = f(X2,X),
inference(transitivity,[status(thm)],[c156,c211]) ).
cnf(c213,plain,
f(X2,and(X2,X)) = f(X2,X),
inference(transitivity,[status(thm)],[c154,c212]) ).
cnf(c214,plain,
f(f(neg(neg(X2)),X),and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(substitution,[status(thm)],[c213]) ).
cnf(c215,plain,
f(f(neg(neg(X2)),X),and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = X2,
inference(transitivity,[status(thm)],[c214,c98]) ).
cnf(c216,plain,
f(f(neg(neg(X2)),X),neg(X2)) = X2,
inference(transitivity,[status(thm)],[c152,c215]) ).
cnf(c217,plain,
f(f(X2,X),neg(X2)) = X2,
inference(transitivity,[status(thm)],[c146,c216]) ).
cnf(c218,plain,
f(f(and(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,X)),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = and(f(X2,f(X2,X2)),f(X,f(X,X))),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
and(f(X2,f(X2,X2)),f(X,f(X,X))) = f(f(and(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,X)),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2))))) = f(neg(f(X2,f(X2,X2))),X),
inference(substitution,[status(thm)],[c205]) ).
cnf(c221,plain,
f(neg(f(X2,f(X2,X2))),X) = f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2))))),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c223,plain,
f(f(neg(X2),X),X2) = f(f(neg(X2),X),neg(neg(X2))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
f(f(neg(X2),X),neg(neg(X2))) = neg(X2),
inference(substitution,[status(thm)],[c217]) ).
cnf(c225,plain,
f(f(neg(X2),X),X2) = neg(X2),
inference(transitivity,[status(thm)],[c223,c224]) ).
cnf(c226,plain,
f(f(neg(f(X,f(X,X))),X),f(X,f(X,X))) = neg(f(X,f(X,X))),
inference(substitution,[status(thm)],[c225]) ).
cnf(c227,plain,
neg(f(X,f(X,X))) = f(f(neg(f(X,f(X,X))),X),f(X,f(X,X))),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
f(neg(f(X2,f(X2,X2))),X) = f(f(f(neg(f(X2,f(X2,X2))),X2),f(X2,f(X2,X2))),X),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)) = and(f(f(f(neg(f(X2,f(X2,X2))),X2),f(X2,f(X2,X2))),X),f(X2,X2)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
neg(f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2))) = and(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c231,plain,
and(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2)) = neg(f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2))),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c233,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c232]) ).
cnf(c234,plain,
neg(f(X,X)) = neg(neg(X)),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
neg(neg(X)) = f(neg(X),neg(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c236,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c237,plain,
f(neg(X),neg(X)) = f(f(X,X),neg(X)),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c239,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
f(f(X,X),X) = f(neg(X),X),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
f(X,f(f(X,X),X)) = f(X,f(neg(X),X)),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
f(f(X,f(f(X,X),X)),X) = f(f(X,f(neg(X),X)),X),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
f(X,f(f(X,f(f(X,X),X)),X)) = f(X,f(f(X,f(neg(X),X)),X)),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))) = f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c246,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
neg(f(X,X)) = neg(neg(X)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
f(neg(f(X2,X2)),X) = f(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = f(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c249,c98]) ).
cnf(c251,plain,
f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))) = X2,
inference(transitivity,[status(thm)],[c244,c250]) ).
cnf(c252,plain,
f(f(neg(f(X,X)),X),f(X,f(f(X,f(f(X,X),X)),X))) = X,
inference(substitution,[status(thm)],[c251]) ).
cnf(c253,plain,
X = f(f(neg(f(X,X)),X),f(X,f(f(X,f(f(X,X),X)),X))),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
f(X,X) = f(f(f(neg(f(X,X)),X),f(X,f(f(X,f(f(X,X),X)),X))),X),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
f(f(X,X),neg(X)) = f(f(f(f(neg(f(X,X)),X),f(X,f(f(X,f(f(X,X),X)),X))),X),neg(X)),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
f(f(f(f(neg(f(X,X)),X),f(X,f(f(X,f(f(X,X),X)),X))),X),neg(X)) = X,
inference(substitution,[status(thm)],[c48]) ).
cnf(c257,plain,
f(f(X,X),neg(X)) = X,
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
f(neg(X),neg(X)) = X,
inference(transitivity,[status(thm)],[c237,c257]) ).
cnf(c259,plain,
neg(neg(X)) = X,
inference(transitivity,[status(thm)],[c235,c258]) ).
cnf(c260,plain,
neg(f(X,X)) = X,
inference(transitivity,[status(thm)],[c234,c259]) ).
cnf(c261,plain,
X = neg(f(X,X)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
f(X2,X) = f(neg(f(X2,X2)),X),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
f(f(X2,X),f(X2,X2)) = f(f(neg(f(X2,X2)),X),f(X2,X2)),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
neg(and(X,f(f(X,f(f(X,X),X)),X))) = f(X,f(f(X,f(f(X,X),X)),X)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c265,plain,
f(X,f(f(X,f(f(X,X),X)),X)) = neg(and(X,f(f(X,f(f(X,X),X)),X))),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
neg(f(f(f(f(X2,X),neg(X)),X),neg(X))) = and(f(f(f(X2,X),neg(X)),X),neg(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c267,plain,
and(f(f(f(X2,X),neg(X)),X),neg(X)) = neg(f(f(f(f(X2,X),neg(X)),X),neg(X))),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c269,plain,
f(f(X2,X),neg(X)) = f(f(X2,X),f(X,X)),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
f(f(f(X2,X),neg(X)),X) = f(f(f(X2,X),f(X,X)),X),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
f(f(f(f(X2,X),neg(X)),X),neg(X)) = f(f(f(f(X2,X),f(X,X)),X),neg(X)),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
f(f(f(f(X2,X),f(X,X)),X),neg(X)) = X,
inference(substitution,[status(thm)],[c48]) ).
cnf(c273,plain,
f(f(f(f(X2,X),neg(X)),X),neg(X)) = X,
inference(transitivity,[status(thm)],[c271,c272]) ).
cnf(c274,plain,
neg(f(f(f(f(X2,X),neg(X)),X),neg(X))) = neg(X),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
and(f(f(f(X2,X),neg(X)),X),neg(X)) = neg(X),
inference(transitivity,[status(thm)],[c267,c274]) ).
cnf(c276,plain,
and(f(f(f(X,and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = neg(and(X,f(f(X,f(f(X,X),X)),X))),
inference(substitution,[status(thm)],[c275]) ).
cnf(c277,plain,
neg(and(X,f(f(X,f(f(X,X),X)),X))) = and(f(f(f(X,and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
neg(f(X,f(f(X,f(f(X,X),X)),X))) = and(X,f(f(X,f(f(X,X),X)),X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c279,plain,
and(X,f(f(X,f(f(X,X),X)),X)) = neg(f(X,f(f(X,f(f(X,X),X)),X))),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
f(X,and(X,f(f(X,f(f(X,X),X)),X))) = f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
neg(neg(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))))) = f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c282,plain,
f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))) = neg(neg(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
and(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,neg(f(X,f(f(X,f(f(X,X),X)),X))))) = neg(neg(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))))),
inference(substitution,[status(thm)],[c84]) ).
cnf(c284,plain,
neg(neg(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))))) = and(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,neg(f(X,f(f(X,f(f(X,X),X)),X))))),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
X = neg(f(X,X)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c286,plain,
f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))) = f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
and(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,neg(f(X,f(f(X,f(f(X,X),X)),X))))) = and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,neg(f(X,f(f(X,f(f(X,X),X)),X))))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
f(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))) = X,
inference(substitution,[status(thm)],[c251]) ).
cnf(c289,plain,
X = f(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))) = f(f(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))),neg(f(X,f(f(X,f(f(X,X),X)),X)))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,neg(f(X,f(f(X,f(f(X,X),X)),X))))) = and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(f(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))),neg(f(X,f(f(X,f(f(X,X),X)),X))))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c293,plain,
f(f(X2,neg(X)),X) = f(f(X2,neg(X)),neg(neg(X))),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
f(f(f(X2,neg(X)),X),neg(X)) = f(f(f(X2,neg(X)),neg(neg(X))),neg(X)),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
and(f(X2,neg(X)),f(f(f(X2,neg(X)),X),neg(X))) = and(f(X2,neg(X)),f(f(f(X2,neg(X)),neg(neg(X))),neg(X))),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
neg(f(f(X2,X),f(f(f(X2,X),neg(X)),X))) = and(f(X2,X),f(f(f(X2,X),neg(X)),X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c297,plain,
and(f(X2,X),f(f(f(X2,X),neg(X)),X)) = neg(f(f(X2,X),f(f(f(X2,X),neg(X)),X))),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c299,plain,
f(f(X2,X),neg(X)) = f(f(X2,X),f(X,X)),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
f(f(f(X2,X),neg(X)),X) = f(f(f(X2,X),f(X,X)),X),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
f(f(X2,X),f(f(f(X2,X),neg(X)),X)) = f(f(X2,X),f(f(f(X2,X),f(X,X)),X)),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
f(f(X2,X),f(f(f(X2,X),f(X,X)),X)) = f(f(X2,X),f(X,X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c303,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c304,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c303]) ).
cnf(c305,plain,
f(f(X2,X),f(X,X)) = f(f(X2,X),neg(X)),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
f(f(X2,X),f(f(f(X2,X),f(X,X)),X)) = f(f(X2,X),neg(X)),
inference(transitivity,[status(thm)],[c302,c305]) ).
cnf(c307,plain,
f(f(X2,X),f(f(f(X2,X),neg(X)),X)) = f(f(X2,X),neg(X)),
inference(transitivity,[status(thm)],[c301,c306]) ).
cnf(c308,plain,
neg(f(f(X2,X),f(f(f(X2,X),neg(X)),X))) = neg(f(f(X2,X),neg(X))),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
neg(f(f(X2,X),neg(X))) = and(f(X2,X),neg(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c310,plain,
neg(f(f(X2,X),f(f(f(X2,X),neg(X)),X))) = and(f(X2,X),neg(X)),
inference(transitivity,[status(thm)],[c308,c309]) ).
cnf(c311,plain,
and(f(X2,X),f(f(f(X2,X),neg(X)),X)) = and(f(X2,X),neg(X)),
inference(transitivity,[status(thm)],[c297,c310]) ).
cnf(c312,plain,
and(f(X2,neg(X)),f(f(f(X2,neg(X)),neg(neg(X))),neg(X))) = and(f(X2,neg(X)),neg(neg(X))),
inference(substitution,[status(thm)],[c311]) ).
cnf(c313,plain,
and(f(X2,neg(X)),neg(neg(X))) = and(f(X2,neg(X)),X),
inference(congruence,[status(thm)],[c65]) ).
cnf(c314,plain,
and(f(X2,neg(X)),f(f(f(X2,neg(X)),neg(neg(X))),neg(X))) = and(f(X2,neg(X)),X),
inference(transitivity,[status(thm)],[c312,c313]) ).
cnf(c315,plain,
and(f(X2,neg(X)),f(f(f(X2,neg(X)),X),neg(X))) = and(f(X2,neg(X)),X),
inference(transitivity,[status(thm)],[c295,c314]) ).
cnf(c316,plain,
and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(f(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))),neg(f(X,f(f(X,f(f(X,X),X)),X))))) = and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))),
inference(substitution,[status(thm)],[c315]) ).
cnf(c317,plain,
neg(f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2)))) = and(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c318,plain,
and(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))) = neg(f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2)))),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
neg(f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2)))) = neg(X2),
inference(congruence,[status(thm)],[c251]) ).
cnf(c320,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c321,plain,
neg(f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2)))) = f(X2,X2),
inference(transitivity,[status(thm)],[c319,c320]) ).
cnf(c322,plain,
and(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c318,c321]) ).
cnf(c323,plain,
and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))) = f(X,X),
inference(substitution,[status(thm)],[c322]) ).
cnf(c324,plain,
and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(f(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,f(f(X,f(f(X,X),X)),X))),neg(f(X,f(f(X,f(f(X,X),X)),X))))) = f(X,X),
inference(transitivity,[status(thm)],[c316,c323]) ).
cnf(c325,plain,
and(f(neg(f(X,X)),neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,neg(f(X,f(f(X,f(f(X,X),X)),X))))) = f(X,X),
inference(transitivity,[status(thm)],[c291,c324]) ).
cnf(c326,plain,
and(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))),f(X,neg(f(X,f(f(X,f(f(X,X),X)),X))))) = f(X,X),
inference(transitivity,[status(thm)],[c287,c325]) ).
cnf(c327,plain,
neg(neg(f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))))) = f(X,X),
inference(transitivity,[status(thm)],[c284,c326]) ).
cnf(c328,plain,
f(X,neg(f(X,f(f(X,f(f(X,X),X)),X)))) = f(X,X),
inference(transitivity,[status(thm)],[c282,c327]) ).
cnf(c329,plain,
f(X,and(X,f(f(X,f(f(X,X),X)),X))) = f(X,X),
inference(transitivity,[status(thm)],[c280,c328]) ).
cnf(c330,plain,
f(f(X,and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = f(f(X,X),neg(and(X,f(f(X,f(f(X,X),X)),X)))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
f(f(f(X,and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))) = f(f(f(X,X),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
and(f(f(f(X,and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = and(f(f(f(X,X),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
neg(and(X,f(f(X,f(f(X,X),X)),X))) = f(X,f(f(X,f(f(X,X),X)),X)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c334,plain,
f(f(X,X),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
f(f(f(X,X),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))) = f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
and(f(f(f(X,X),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = and(f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
neg(and(X,f(f(X,f(f(X,X),X)),X))) = f(X,f(f(X,f(f(X,X),X)),X)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c338,plain,
and(f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = and(f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))),f(X,f(f(X,f(f(X,X),X)),X))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = f(f(X2,X2),f(X2,X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c340,plain,
f(f(X2,X2),f(X2,X)) = f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c342,plain,
f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))) = neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c344,plain,
neg(and(X2,X)) = neg(neg(f(X2,X))),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
f(neg(and(X2,X)),f(X2,X)) = f(neg(neg(f(X2,X))),f(X2,X)),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
f(and(X2,X),f(neg(and(X2,X)),f(X2,X))) = f(and(X2,X),f(neg(neg(f(X2,X))),f(X2,X))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
and(X2,X) = neg(f(X2,X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c348,plain,
f(and(X2,X),f(neg(neg(f(X2,X))),f(X2,X))) = f(neg(f(X2,X)),f(neg(neg(f(X2,X))),f(X2,X))),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c350,plain,
f(neg(X),f(neg(neg(X)),X)) = f(f(X,X),f(neg(neg(X)),X)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c352,plain,
neg(neg(X)) = neg(f(X,X)),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
f(neg(neg(X)),X) = f(neg(f(X,X)),X),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
f(f(X,X),f(neg(neg(X)),X)) = f(f(X,X),f(neg(f(X,X)),X)),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c356,plain,
f(neg(f(X,X)),X) = f(f(f(X,X),f(X,X)),X),
inference(congruence,[status(thm)],[c355]) ).
cnf(c357,plain,
f(f(X,X),f(neg(f(X,X)),X)) = f(f(X,X),f(f(f(X,X),f(X,X)),X)),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c359,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c360,plain,
f(f(X,X),f(X,X)) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
neg(f(X,X)) = and(X,X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c362,plain,
neg(f(X,X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c361,c84]) ).
cnf(c363,plain,
f(f(X,X),f(X,X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c360,c362]) ).
cnf(c364,plain,
f(f(X,X),f(f(f(X,X),f(X,X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c358,c363]) ).
cnf(c365,plain,
f(f(X,X),f(neg(f(X,X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c357,c364]) ).
cnf(c366,plain,
f(f(X,X),f(neg(neg(X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c354,c365]) ).
cnf(c367,plain,
f(neg(X),f(neg(neg(X)),X)) = neg(neg(X)),
inference(transitivity,[status(thm)],[c350,c366]) ).
cnf(c368,plain,
f(neg(f(X2,X)),f(neg(neg(f(X2,X))),f(X2,X))) = neg(neg(f(X2,X))),
inference(substitution,[status(thm)],[c367]) ).
cnf(c369,plain,
neg(neg(f(X2,X))) = neg(and(X2,X)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c370,plain,
f(neg(f(X2,X)),f(neg(neg(f(X2,X))),f(X2,X))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c368,c369]) ).
cnf(c371,plain,
f(and(X2,X),f(neg(neg(f(X2,X))),f(X2,X))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c348,c370]) ).
cnf(c372,plain,
f(and(X2,X),f(neg(and(X2,X)),f(X2,X))) = neg(and(X2,X)),
inference(transitivity,[status(thm)],[c346,c371]) ).
cnf(c373,plain,
f(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))) = neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),
inference(substitution,[status(thm)],[c372]) ).
cnf(c374,plain,
neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
neg(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c376,plain,
and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))) = neg(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),
inference(symmetry,[status(thm)],[c375]) ).
cnf(c377,plain,
neg(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c378,plain,
X = neg(f(X,X)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c379,plain,
f(X,f(X,X)) = f(neg(f(X,X)),f(X,X)),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
f(f(X,X),f(X,f(X,X))) = f(f(X,X),f(neg(f(X,X)),f(X,X))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
f(f(f(X,X),f(X,f(X,X))),f(X,X)) = f(f(f(X,X),f(neg(f(X,X)),f(X,X))),f(X,X)),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))) = f(f(X,X),f(f(f(X,X),f(neg(f(X,X)),f(X,X))),f(X,X))),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(f(f(X2,X2),f(X2,f(X2,X2))),f(X2,X2)))) = f(f(f(X2,X2),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c385,plain,
f(X,X) = neg(X),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
f(f(X2,X2),X) = f(neg(X2),X),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))) = f(f(neg(X2),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
X = neg(f(X,X)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c389,plain,
neg(X) = neg(neg(f(X,X))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
f(neg(X2),X) = f(neg(neg(f(X2,X2))),X),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
f(f(neg(X2),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))) = f(f(neg(neg(f(X2,X2))),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
f(f(neg(neg(f(X2,X2))),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))) = f(X2,X2),
inference(substitution,[status(thm)],[c98]) ).
cnf(c393,plain,
f(f(neg(X2),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))) = f(X2,X2),
inference(transitivity,[status(thm)],[c391,c392]) ).
cnf(c394,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(f(f(X2,X2),f(neg(f(X2,X2)),f(X2,X2))),f(X2,X2)))) = f(X2,X2),
inference(transitivity,[status(thm)],[c387,c393]) ).
cnf(c395,plain,
f(f(f(X2,X2),X),f(f(X2,X2),f(f(f(X2,X2),f(X2,f(X2,X2))),f(X2,X2)))) = f(X2,X2),
inference(transitivity,[status(thm)],[c383,c394]) ).
cnf(c396,plain,
f(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(X,X),
inference(substitution,[status(thm)],[c395]) ).
cnf(c397,plain,
neg(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(X,X),
inference(transitivity,[status(thm)],[c377,c396]) ).
cnf(c398,plain,
and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))) = f(X,X),
inference(transitivity,[status(thm)],[c376,c397]) ).
cnf(c399,plain,
f(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))) = f(f(X,X),f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c401,plain,
f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
f(f(X,X),f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))) = f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
f(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = f(X,X),
inference(substitution,[status(thm)],[c395]) ).
cnf(c404,plain,
f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))) = f(f(X,X),f(X,X)),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c406,plain,
f(f(X,X),f(X,X)) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c405]) ).
cnf(c407,plain,
f(f(X,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c406,c260]) ).
cnf(c408,plain,
f(f(X,X),f(f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))) = X,
inference(transitivity,[status(thm)],[c404,c407]) ).
cnf(c409,plain,
f(f(X,X),f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))) = X,
inference(transitivity,[status(thm)],[c402,c408]) ).
cnf(c410,plain,
f(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),f(neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))),f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))))) = X,
inference(transitivity,[status(thm)],[c399,c409]) ).
cnf(c411,plain,
neg(and(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X)))) = X,
inference(transitivity,[status(thm)],[c374,c410]) ).
cnf(c412,plain,
f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))) = X,
inference(transitivity,[status(thm)],[c342,c411]) ).
cnf(c413,plain,
X = f(f(X,X),f(f(f(X,X),f(X,f(X,X))),f(X,X))),
inference(symmetry,[status(thm)],[c412]) ).
cnf(c414,plain,
f(f(f(X2,X2),X),X2) = f(f(f(X2,X2),X),f(f(X2,X2),f(f(f(X2,X2),f(X2,f(X2,X2))),f(X2,X2)))),
inference(congruence,[status(thm)],[c413]) ).
cnf(c415,plain,
f(f(f(X2,X2),X),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c414,c395]) ).
cnf(c416,plain,
f(f(f(X2,X2),f(X2,X)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c415]) ).
cnf(c417,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = f(f(X2,X2),f(X2,X2)),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
neg(f(X,X)) = f(f(X,X),f(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c419,plain,
f(f(X,X),f(X,X)) = neg(f(X,X)),
inference(symmetry,[status(thm)],[c418]) ).
cnf(c420,plain,
f(f(X,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c419,c260]) ).
cnf(c421,plain,
f(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = X2,
inference(transitivity,[status(thm)],[c417,c420]) ).
cnf(c422,plain,
f(f(X2,X2),f(X2,X)) = X2,
inference(transitivity,[status(thm)],[c340,c421]) ).
cnf(c423,plain,
f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))) = X,
inference(substitution,[status(thm)],[c422]) ).
cnf(c424,plain,
f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))) = f(X,and(X,f(f(X,f(f(X,X),X)),X))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
and(f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))),f(X,f(f(X,f(f(X,X),X)),X))) = and(f(X,and(X,f(f(X,f(f(X,X),X)),X))),f(X,f(f(X,f(f(X,X),X)),X))),
inference(congruence,[status(thm)],[c424]) ).
cnf(c426,plain,
and(f(X,and(X,f(f(X,f(f(X,X),X)),X))),f(X,f(f(X,f(f(X,X),X)),X))) = and(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c427,plain,
neg(f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2))) = and(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c428,plain,
and(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2)) = neg(f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2))),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
neg(f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2))) = neg(f(f(X3,X2),f(X2,X))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c430,plain,
neg(f(f(X3,X2),f(X2,X))) = and(f(X3,X2),f(X2,X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c431,plain,
neg(f(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2))) = and(f(X3,X2),f(X2,X)),
inference(transitivity,[status(thm)],[c429,c430]) ).
cnf(c432,plain,
and(f(X3,X2),f(f(f(X3,X2),f(X2,X)),X2)) = and(f(X3,X2),f(X2,X)),
inference(transitivity,[status(thm)],[c428,c431]) ).
cnf(c433,plain,
and(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = and(f(X2,X2),f(X2,X)),
inference(substitution,[status(thm)],[c432]) ).
cnf(c434,plain,
and(f(X2,X2),f(X2,X)) = and(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)),
inference(symmetry,[status(thm)],[c433]) ).
cnf(c435,plain,
f(f(f(X2,X2),f(X2,X)),X2) = f(X2,X2),
inference(substitution,[status(thm)],[c415]) ).
cnf(c436,plain,
and(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = and(f(X2,X2),f(X2,X2)),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
and(f(X,X),f(X,X)) = neg(neg(f(X,X))),
inference(substitution,[status(thm)],[c84]) ).
cnf(c438,plain,
neg(neg(f(X,X))) = f(X,X),
inference(substitution,[status(thm)],[c65]) ).
cnf(c439,plain,
and(f(X,X),f(X,X)) = f(X,X),
inference(transitivity,[status(thm)],[c437,c438]) ).
cnf(c440,plain,
and(f(X2,X2),f(f(f(X2,X2),f(X2,X)),X2)) = f(X2,X2),
inference(transitivity,[status(thm)],[c436,c439]) ).
cnf(c441,plain,
and(f(X2,X2),f(X2,X)) = f(X2,X2),
inference(transitivity,[status(thm)],[c434,c440]) ).
cnf(c442,plain,
and(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))) = f(X,X),
inference(substitution,[status(thm)],[c441]) ).
cnf(c443,plain,
and(f(X,and(X,f(f(X,f(f(X,X),X)),X))),f(X,f(f(X,f(f(X,X),X)),X))) = f(X,X),
inference(transitivity,[status(thm)],[c426,c442]) ).
cnf(c444,plain,
and(f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))),f(X,f(f(X,f(f(X,X),X)),X))) = f(X,X),
inference(transitivity,[status(thm)],[c425,c443]) ).
cnf(c445,plain,
and(f(f(f(X,X),f(X,f(f(X,f(f(X,X),X)),X))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = f(X,X),
inference(transitivity,[status(thm)],[c338,c444]) ).
cnf(c446,plain,
and(f(f(f(X,X),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = f(X,X),
inference(transitivity,[status(thm)],[c336,c445]) ).
cnf(c447,plain,
and(f(f(f(X,and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))),and(X,f(f(X,f(f(X,X),X)),X))),neg(and(X,f(f(X,f(f(X,X),X)),X)))) = f(X,X),
inference(transitivity,[status(thm)],[c332,c446]) ).
cnf(c448,plain,
neg(and(X,f(f(X,f(f(X,X),X)),X))) = f(X,X),
inference(transitivity,[status(thm)],[c277,c447]) ).
cnf(c449,plain,
f(X,f(f(X,f(f(X,X),X)),X)) = f(X,X),
inference(transitivity,[status(thm)],[c265,c448]) ).
cnf(c450,plain,
f(X,X) = f(X,f(f(X,f(f(X,X),X)),X)),
inference(symmetry,[status(thm)],[c449]) ).
cnf(c451,plain,
f(f(neg(f(X2,X2)),X),f(X2,X2)) = f(f(neg(f(X2,X2)),X),f(X2,f(f(X2,f(f(X2,X2),X2)),X2))),
inference(congruence,[status(thm)],[c450]) ).
cnf(c452,plain,
f(f(neg(f(X2,X2)),X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c451,c251]) ).
cnf(c453,plain,
f(f(X2,X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c263,c452]) ).
cnf(c454,plain,
f(f(X,f(neg(X2),X2)),f(X,X)) = X,
inference(substitution,[status(thm)],[c453]) ).
cnf(c455,plain,
X = f(f(X,f(neg(X2),X2)),f(X,X)),
inference(symmetry,[status(thm)],[c454]) ).
cnf(c456,plain,
f(X,X) = f(X,f(f(X,f(neg(X2),X2)),f(X,X))),
inference(congruence,[status(thm)],[c455]) ).
cnf(c457,plain,
f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2)) = f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,f(f(X2,f(neg(X3),X3)),f(X2,X2)))),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,f(f(X2,f(neg(X3),X3)),f(X2,X2)))) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c459,plain,
f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c457,c458]) ).
cnf(c460,plain,
neg(f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2))) = neg(X2),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
neg(X) = f(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c462,plain,
neg(f(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2))) = f(X2,X2),
inference(transitivity,[status(thm)],[c460,c461]) ).
cnf(c463,plain,
and(f(f(f(X3,X2),f(X2,f(X2,X2))),X),f(X2,X2)) = f(X2,X2),
inference(transitivity,[status(thm)],[c231,c462]) ).
cnf(c464,plain,
and(f(f(f(neg(f(X2,f(X2,X2))),X2),f(X2,f(X2,X2))),X),f(X2,X2)) = f(X2,X2),
inference(substitution,[status(thm)],[c463]) ).
cnf(c465,plain,
and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)) = f(X2,X2),
inference(transitivity,[status(thm)],[c229,c464]) ).
cnf(c466,plain,
f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2))) = f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)),
inference(congruence,[status(thm)],[c465]) ).
cnf(c467,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)))) = f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2))))) = f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)))),
inference(congruence,[status(thm)],[c467]) ).
cnf(c469,plain,
f(f(neg(f(X,f(X,X))),X),f(X,f(X,X))) = neg(f(X,f(X,X))),
inference(substitution,[status(thm)],[c225]) ).
cnf(c470,plain,
neg(f(X,f(X,X))) = f(f(neg(f(X,f(X,X))),X),f(X,f(X,X))),
inference(symmetry,[status(thm)],[c469]) ).
cnf(c471,plain,
f(neg(f(X2,f(X2,X2))),X) = f(f(f(neg(f(X2,f(X2,X2))),X2),f(X2,f(X2,X2))),X),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)) = f(f(f(f(neg(f(X2,f(X2,X2))),X2),f(X2,f(X2,X2))),X),f(X2,X2)),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
f(f(f(f(neg(f(X2,f(X2,X2))),X2),f(X2,f(X2,X2))),X),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c459]) ).
cnf(c474,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c472,c473]) ).
cnf(c475,plain,
f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)))) = f(X2,f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)))),
inference(congruence,[status(thm)],[c474]) ).
cnf(c476,plain,
f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)) = f(X2,f(X2,X2)),
inference(congruence,[status(thm)],[c474]) ).
cnf(c477,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2))) = f(f(neg(f(X2,f(X2,X2))),X),f(X2,f(X2,X2))),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
f(X2,f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)))) = f(X2,f(f(neg(f(X2,f(X2,X2))),X),f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(X2,f(X2,X2))) = neg(f(X2,f(X2,X2))),
inference(substitution,[status(thm)],[c225]) ).
cnf(c480,plain,
f(X2,f(f(neg(f(X2,f(X2,X2))),X),f(X2,f(X2,X2)))) = f(X2,neg(f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
neg(f(X,f(X,X))) = f(f(X,f(X,X)),f(X,f(X,X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c482,plain,
f(X,neg(f(X,f(X,X)))) = f(X,f(f(X,f(X,X)),f(X,f(X,X)))),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
f(f(X4,X3),f(f(f(X4,X3),f(X4,f(X4,X4))),f(f(f(f(X4,X3),f(X4,f(X4,X4))),f(and(X2,f(X4,X3)),f(X2,f(X4,X3)))),X))) = f(f(X4,X3),f(X4,f(X4,X4))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c484,plain,
f(f(X4,X3),f(X4,f(X4,X4))) = f(f(X4,X3),f(f(f(X4,X3),f(X4,f(X4,X4))),f(f(f(f(X4,X3),f(X4,f(X4,X4))),f(and(X2,f(X4,X3)),f(X2,f(X4,X3)))),X))),
inference(symmetry,[status(thm)],[c483]) ).
cnf(c485,plain,
f(X4,f(f(X4,X3),f(X4,f(X4,X4)))) = f(X4,f(f(X4,X3),f(f(f(X4,X3),f(X4,f(X4,X4))),f(f(f(f(X4,X3),f(X4,f(X4,X4))),f(and(X2,f(X4,X3)),f(X2,f(X4,X3)))),X)))),
inference(congruence,[status(thm)],[c484]) ).
cnf(c486,plain,
X = neg(f(X,X)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c487,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2) = f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),neg(f(X2,X2))),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),neg(f(X2,X2))) = f(X2,X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c489,plain,
f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2) = f(X2,X2),
inference(transitivity,[status(thm)],[c487,c488]) ).
cnf(c490,plain,
f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3) = f(X3,X3),
inference(substitution,[status(thm)],[c489]) ).
cnf(c491,plain,
f(X3,X3) = f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3),
inference(symmetry,[status(thm)],[c490]) ).
cnf(c492,plain,
f(X3,f(X3,X3)) = f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3)),
inference(congruence,[status(thm)],[c491]) ).
cnf(c493,plain,
f(f(X4,X3),f(X4,f(X4,X4))) = f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),f(X4,X4)),X4))),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
f(f(f(X5,X4),f(X5,f(X5,X5))),X3) = f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
f(f(X5,X4),f(f(f(X5,X4),f(X5,f(X5,X5))),X3)) = f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3)),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(X5,f(X5,X5))),X3))) = f(X5,f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3))),
inference(congruence,[status(thm)],[c495]) ).
cnf(c497,plain,
neg(f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2)) = and(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c498,plain,
and(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2) = neg(f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2)),
inference(symmetry,[status(thm)],[c497]) ).
cnf(c499,plain,
neg(f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2)) = neg(f(X2,X2)),
inference(congruence,[status(thm)],[c489]) ).
cnf(c500,plain,
neg(f(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2)) = X2,
inference(transitivity,[status(thm)],[c499,c260]) ).
cnf(c501,plain,
and(f(f(f(X3,f(X2,X2)),f(f(X2,X2),X)),f(X2,X2)),X2) = X2,
inference(transitivity,[status(thm)],[c498,c500]) ).
cnf(c502,plain,
and(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3) = X3,
inference(substitution,[status(thm)],[c501]) ).
cnf(c503,plain,
X3 = and(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
f(X3,f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3)) = f(and(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3),f(f(f(f(X2,f(X3,X3)),f(f(X3,X3),X)),f(X3,X3)),X3)),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
f(f(X4,X3),f(X4,f(f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),f(X4,X4)),X4))) = f(f(X4,X3),f(and(f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),f(X4,X4)),X4),f(f(f(f(X2,f(X4,X4)),f(f(X4,X4),X)),f(X4,X4)),X4))),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3) = f(f(f(X5,X4),f(and(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5),f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3)) = f(f(X5,X4),f(f(f(X5,X4),f(and(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5),f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3)),
inference(congruence,[status(thm)],[c506]) ).
cnf(c508,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3))) = f(X5,f(f(X5,X4),f(f(f(X5,X4),f(and(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5),f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3))),
inference(congruence,[status(thm)],[c507]) ).
cnf(c509,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(and(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5),f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3))) = f(X5,X4),
inference(substitution,[status(thm)],[c33]) ).
cnf(c510,plain,
f(X5,f(f(X5,X4),f(f(f(X5,X4),f(X5,f(f(f(f(X2,f(X5,X5)),f(f(X5,X5),X)),f(X5,X5)),X5))),X3))) = f(X5,X4),
inference(transitivity,[status(thm)],[c508,c509]) ).
cnf(c511,plain,
f(X3,f(f(X3,X2),f(f(f(X3,X2),f(X3,f(X3,X3))),X))) = f(X3,X2),
inference(transitivity,[status(thm)],[c496,c510]) ).
cnf(c512,plain,
f(X4,f(f(X4,X3),f(f(f(X4,X3),f(X4,f(X4,X4))),f(f(f(f(X4,X3),f(X4,f(X4,X4))),f(and(X2,f(X4,X3)),f(X2,f(X4,X3)))),X)))) = f(X4,X3),
inference(substitution,[status(thm)],[c511]) ).
cnf(c513,plain,
f(X2,f(f(X2,X),f(X2,f(X2,X2)))) = f(X2,X),
inference(transitivity,[status(thm)],[c485,c512]) ).
cnf(c514,plain,
f(X,f(f(X,f(X,X)),f(X,f(X,X)))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c513]) ).
cnf(c515,plain,
f(X,neg(f(X,f(X,X)))) = f(X,f(X,X)),
inference(transitivity,[status(thm)],[c482,c514]) ).
cnf(c516,plain,
f(X2,f(f(neg(f(X2,f(X2,X2))),X),f(X2,f(X2,X2)))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c480,c515]) ).
cnf(c517,plain,
f(X2,f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c478,c516]) ).
cnf(c518,plain,
f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(X2,X2)))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c475,c517]) ).
cnf(c519,plain,
f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X2,X2)),and(f(neg(f(X2,f(X2,X2))),X),f(X2,X2))))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c468,c518]) ).
cnf(c520,plain,
f(neg(f(X2,f(X2,X2))),X) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c221,c519]) ).
cnf(c521,plain,
f(X2,f(X2,X2)) = f(neg(f(X2,f(X2,X2))),X),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c522,plain,
and(f(X2,f(X2,X2)),f(X,f(X,X))) = and(f(neg(f(X2,f(X2,X2))),X),f(X,f(X,X))),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
f(and(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,X)) = f(and(f(neg(f(X2,f(X2,X2))),X),f(X,f(X,X))),f(X,X)),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
neg(f(f(X2,X),f(X,f(X,X)))) = and(f(X2,X),f(X,f(X,X))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c525,plain,
and(f(X2,X),f(X,f(X,X))) = neg(f(f(X2,X),f(X,f(X,X)))),
inference(symmetry,[status(thm)],[c524]) ).
cnf(c526,plain,
f(and(f(X2,X),f(X,f(X,X))),f(X,X)) = f(neg(f(f(X2,X),f(X,f(X,X)))),f(X,X)),
inference(congruence,[status(thm)],[c525]) ).
cnf(c527,plain,
neg(f(f(X2,X),f(X,f(X,X)))) = f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(X,f(X,X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c528,plain,
f(neg(f(f(X2,X),f(X,f(X,X)))),f(X,X)) = f(f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(X,f(X,X)))),f(X,X)),
inference(congruence,[status(thm)],[c527]) ).
cnf(c529,plain,
f(f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(X,f(X,X)))),f(X,X)) = X,
inference(substitution,[status(thm)],[c459]) ).
cnf(c530,plain,
f(neg(f(f(X2,X),f(X,f(X,X)))),f(X,X)) = X,
inference(transitivity,[status(thm)],[c528,c529]) ).
cnf(c531,plain,
f(and(f(X2,X),f(X,f(X,X))),f(X,X)) = X,
inference(transitivity,[status(thm)],[c526,c530]) ).
cnf(c532,plain,
f(and(f(neg(f(X2,f(X2,X2))),X),f(X,f(X,X))),f(X,X)) = X,
inference(substitution,[status(thm)],[c531]) ).
cnf(c533,plain,
f(and(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,X)) = X,
inference(transitivity,[status(thm)],[c523,c532]) ).
cnf(c534,plain,
f(f(and(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,X)),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = f(X,neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
neg(and(f(X2,f(X2,X2)),f(X,f(X,X)))) = f(f(X2,f(X2,X2)),f(X,f(X,X))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c536,plain,
f(X,neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = f(X,f(f(X2,f(X2,X2)),f(X,f(X,X)))),
inference(congruence,[status(thm)],[c535]) ).
cnf(c537,plain,
f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))) = f(X2,X),
inference(substitution,[status(thm)],[c205]) ).
cnf(c538,plain,
f(X2,X) = f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))),
inference(symmetry,[status(thm)],[c537]) ).
cnf(c539,plain,
f(f(X2,X),f(X,X)) = f(f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))),f(X,X)),
inference(congruence,[status(thm)],[c538]) ).
cnf(c540,plain,
f(f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))),f(X,X)) = X,
inference(substitution,[status(thm)],[c459]) ).
cnf(c541,plain,
f(f(X2,X),f(X,X)) = X,
inference(transitivity,[status(thm)],[c539,c540]) ).
cnf(c542,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(X,X)) = X,
inference(substitution,[status(thm)],[c541]) ).
cnf(c543,plain,
X = f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),
inference(symmetry,[status(thm)],[c542]) ).
cnf(c544,plain,
f(X,X) = f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X),
inference(congruence,[status(thm)],[c543]) ).
cnf(c545,plain,
f(f(X2,f(X2,X2)),f(X,X)) = f(f(X2,f(X2,X2)),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
f(X2,f(X2,X2)) = f(neg(f(X2,f(X2,X2))),X),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c547,plain,
f(f(X2,f(X2,X2)),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)),
inference(congruence,[status(thm)],[c546]) ).
cnf(c548,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c549,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(X,X)) = X,
inference(substitution,[status(thm)],[c541]) ).
cnf(c550,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c548,c549]) ).
cnf(c551,plain,
f(f(X2,f(X2,X2)),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = X,
inference(transitivity,[status(thm)],[c547,c550]) ).
cnf(c552,plain,
f(f(X2,f(X2,X2)),f(X,X)) = X,
inference(transitivity,[status(thm)],[c545,c551]) ).
cnf(c553,plain,
f(f(X,f(X,X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c552]) ).
cnf(c554,plain,
X2 = f(f(X,f(X,X)),f(X2,X2)),
inference(symmetry,[status(thm)],[c553]) ).
cnf(c555,plain,
f(X2,f(f(X,f(X,X)),f(X2,f(X2,X2)))) = f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
f(f(X,f(X,X)),f(X2,X2)) = X2,
inference(substitution,[status(thm)],[c552]) ).
cnf(c557,plain,
X2 = f(f(X,f(X,X)),f(X2,X2)),
inference(symmetry,[status(thm)],[c556]) ).
cnf(c558,plain,
f(X2,f(X2,X2)) = f(f(f(X,f(X,X)),f(X2,X2)),f(X2,X2)),
inference(congruence,[status(thm)],[c557]) ).
cnf(c559,plain,
f(f(X,f(X,X)),f(X2,f(X2,X2))) = f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),f(X2,X2))),
inference(congruence,[status(thm)],[c558]) ).
cnf(c560,plain,
f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(X2,f(X2,X2)))) = f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),f(X2,X2)))),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
f(f(neg(f(X2,f(X2,X2))),X),f(X,X)) = X,
inference(substitution,[status(thm)],[c541]) ).
cnf(c562,plain,
X = f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),
inference(symmetry,[status(thm)],[c561]) ).
cnf(c563,plain,
f(X,X) = f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
and(f(X2,f(X2,X2)),f(X,X)) = and(f(X2,f(X2,X2)),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)),
inference(congruence,[status(thm)],[c563]) ).
cnf(c565,plain,
f(X2,f(X2,X2)) = f(neg(f(X2,f(X2,X2))),X),
inference(symmetry,[status(thm)],[c520]) ).
cnf(c566,plain,
and(f(X2,f(X2,X2)),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = and(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)),
inference(congruence,[status(thm)],[c565]) ).
cnf(c567,plain,
and(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = and(f(neg(f(X2,f(X2,X2))),X),f(X,X)),
inference(substitution,[status(thm)],[c432]) ).
cnf(c568,plain,
f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))) = f(X2,X),
inference(substitution,[status(thm)],[c205]) ).
cnf(c569,plain,
f(X2,X) = f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))),
inference(symmetry,[status(thm)],[c568]) ).
cnf(c570,plain,
and(f(X2,X),f(X,X)) = and(f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))),f(X,X)),
inference(congruence,[status(thm)],[c569]) ).
cnf(c571,plain,
and(f(f(f(X2,X),f(X,f(X,X))),f(f(X2,X),f(f(f(X2,X),f(X,f(X,X))),and(f(X2,X),f(X,f(X,X)))))),f(X,X)) = f(X,X),
inference(substitution,[status(thm)],[c463]) ).
cnf(c572,plain,
and(f(X2,X),f(X,X)) = f(X,X),
inference(transitivity,[status(thm)],[c570,c571]) ).
cnf(c573,plain,
and(f(neg(f(X2,f(X2,X2))),X),f(X,X)) = f(X,X),
inference(substitution,[status(thm)],[c572]) ).
cnf(c574,plain,
and(f(neg(f(X2,f(X2,X2))),X),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = f(X,X),
inference(transitivity,[status(thm)],[c567,c573]) ).
cnf(c575,plain,
and(f(X2,f(X2,X2)),f(f(f(neg(f(X2,f(X2,X2))),X),f(X,X)),X)) = f(X,X),
inference(transitivity,[status(thm)],[c566,c574]) ).
cnf(c576,plain,
and(f(X2,f(X2,X2)),f(X,X)) = f(X,X),
inference(transitivity,[status(thm)],[c564,c575]) ).
cnf(c577,plain,
and(f(X,f(X,X)),f(X2,X2)) = f(X2,X2),
inference(substitution,[status(thm)],[c576]) ).
cnf(c578,plain,
f(X2,X2) = and(f(X,f(X,X)),f(X2,X2)),
inference(symmetry,[status(thm)],[c577]) ).
cnf(c579,plain,
f(f(f(X,f(X,X)),f(X2,X2)),f(X2,X2)) = f(f(f(X,f(X,X)),f(X2,X2)),and(f(X,f(X,X)),f(X2,X2))),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),f(X2,X2))) = f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),and(f(X,f(X,X)),f(X2,X2)))),
inference(congruence,[status(thm)],[c579]) ).
cnf(c581,plain,
f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),f(X2,X2)))) = f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),and(f(X,f(X,X)),f(X2,X2))))),
inference(congruence,[status(thm)],[c580]) ).
cnf(c582,plain,
f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),and(f(X,f(X,X)),f(X2,X2))))) = f(X,f(X,X)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c583,plain,
f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(f(f(X,f(X,X)),f(X2,X2)),f(X2,X2)))) = f(X,f(X,X)),
inference(transitivity,[status(thm)],[c581,c582]) ).
cnf(c584,plain,
f(f(f(X,f(X,X)),f(X2,X2)),f(f(X,f(X,X)),f(X2,f(X2,X2)))) = f(X,f(X,X)),
inference(transitivity,[status(thm)],[c560,c583]) ).
cnf(c585,plain,
f(X2,f(f(X,f(X,X)),f(X2,f(X2,X2)))) = f(X,f(X,X)),
inference(transitivity,[status(thm)],[c555,c584]) ).
cnf(c586,plain,
f(X,f(f(X2,f(X2,X2)),f(X,f(X,X)))) = f(X2,f(X2,X2)),
inference(substitution,[status(thm)],[c585]) ).
cnf(c587,plain,
f(X,neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c536,c586]) ).
cnf(c588,plain,
f(f(and(f(X2,f(X2,X2)),f(X,f(X,X))),f(X,X)),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c534,c587]) ).
cnf(c589,plain,
and(f(X2,f(X2,X2)),f(X,f(X,X))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c219,c588]) ).
cnf(c590,plain,
neg(and(f(X2,f(X2,X2)),f(X,f(X,X)))) = neg(f(X2,f(X2,X2))),
inference(congruence,[status(thm)],[c589]) ).
cnf(c591,plain,
and(f(f(X2,f(X2,X2)),f(X,f(X,X))),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = and(f(f(X2,f(X2,X2)),f(X,f(X,X))),neg(f(X2,f(X2,X2)))),
inference(congruence,[status(thm)],[c590]) ).
cnf(c592,plain,
X = neg(neg(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c593,plain,
f(X2,X) = f(neg(neg(X2)),X),
inference(congruence,[status(thm)],[c592]) ).
cnf(c594,plain,
and(f(X2,X),neg(X2)) = and(f(neg(neg(X2)),X),neg(X2)),
inference(congruence,[status(thm)],[c593]) ).
cnf(c595,plain,
neg(X2) = and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c596,plain,
and(f(neg(neg(X2)),X),neg(X2)) = and(f(neg(neg(X2)),X),and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))),
inference(congruence,[status(thm)],[c595]) ).
cnf(c597,plain,
neg(f(X2,and(X2,X))) = and(X2,and(X2,X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c598,plain,
and(X2,and(X2,X)) = neg(f(X2,and(X2,X))),
inference(symmetry,[status(thm)],[c597]) ).
cnf(c599,plain,
neg(f(X2,and(X2,X))) = neg(f(X2,X)),
inference(congruence,[status(thm)],[c213]) ).
cnf(c600,plain,
neg(f(X2,and(X2,X))) = and(X2,X),
inference(transitivity,[status(thm)],[c599,c20]) ).
cnf(c601,plain,
and(X2,and(X2,X)) = and(X2,X),
inference(transitivity,[status(thm)],[c598,c600]) ).
cnf(c602,plain,
and(f(neg(neg(X2)),X),and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2))),
inference(substitution,[status(thm)],[c601]) ).
cnf(c603,plain,
and(f(neg(neg(X2)),X),and(f(neg(neg(X2)),X),f(X2,f(f(X2,f(neg(X2),X2)),X2)))) = neg(X2),
inference(transitivity,[status(thm)],[c602,c150]) ).
cnf(c604,plain,
and(f(neg(neg(X2)),X),neg(X2)) = neg(X2),
inference(transitivity,[status(thm)],[c596,c603]) ).
cnf(c605,plain,
and(f(X2,X),neg(X2)) = neg(X2),
inference(transitivity,[status(thm)],[c594,c604]) ).
cnf(c606,plain,
and(f(f(X2,f(X2,X2)),f(X,f(X,X))),neg(f(X2,f(X2,X2)))) = neg(f(X2,f(X2,X2))),
inference(substitution,[status(thm)],[c605]) ).
cnf(c607,plain,
and(f(f(X2,f(X2,X2)),f(X,f(X,X))),neg(and(f(X2,f(X2,X2)),f(X,f(X,X))))) = neg(f(X2,f(X2,X2))),
inference(transitivity,[status(thm)],[c591,c606]) ).
cnf(c608,plain,
neg(and(f(X2,f(X2,X2)),f(X,f(X,X)))) = neg(f(X2,f(X2,X2))),
inference(transitivity,[status(thm)],[c143,c607]) ).
cnf(c609,plain,
f(f(X2,f(X2,X2)),f(X,f(X,X))) = neg(f(X2,f(X2,X2))),
inference(transitivity,[status(thm)],[c69,c608]) ).
cnf(c610,plain,
f(f(X,f(X,X)),f(X2,f(X2,X2))) = neg(f(X,f(X,X))),
inference(substitution,[status(thm)],[c609]) ).
cnf(c611,plain,
f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)) = f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),X)),
inference(congruence,[status(thm)],[c610]) ).
cnf(c612,plain,
f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))) = f(f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),
inference(congruence,[status(thm)],[c611]) ).
cnf(c613,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(f(f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))),
inference(congruence,[status(thm)],[c612]) ).
cnf(c614,plain,
f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),X)) = f(X2,f(X2,X2)),
inference(substitution,[status(thm)],[c520]) ).
cnf(c615,plain,
f(f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))) = f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),
inference(congruence,[status(thm)],[c614]) ).
cnf(c616,plain,
f(f(f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))),
inference(congruence,[status(thm)],[c615]) ).
cnf(c617,plain,
f(f(X,f(X,X)),f(X2,f(X2,X2))) = neg(f(X,f(X,X))),
inference(substitution,[status(thm)],[c609]) ).
cnf(c618,plain,
f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))),
inference(congruence,[status(thm)],[c617]) ).
cnf(c619,plain,
f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(X2,f(X2,X2)),
inference(substitution,[status(thm)],[c520]) ).
cnf(c620,plain,
f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c618,c619]) ).
cnf(c621,plain,
f(f(f(neg(f(X2,f(X2,X2))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c616,c620]) ).
cnf(c622,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),f(f(f(X3,f(X3,X3)),f(neg(f(X2,f(X2,X2))),f(X2,f(X2,X2)))),X))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c613,c621]) ).
cnf(c623,plain,
f(f(f(f(f(X2,f(X2,X2)),f(X3,f(X3,X3))),f(f(X3,f(X3,X3)),X)),f(X3,f(X3,X3))),neg(f(X3,f(X3,X3)))) = f(X2,f(X2,X2)),
inference(transitivity,[status(thm)],[c52,c622]) ).
cnf(c624,plain,
f(X2,f(X2,X2)) = f(X,f(X,X)),
inference(transitivity,[status(thm)],[c50,c623]) ).
cnf(c625,plain,
f(x1,f(x1,x1)) = f(x0,f(x0,x0)),
inference(substitution,[status(thm)],[c624]) ).
cnf(c626,plain,
f(x0,f(x0,x0)) = f(x1,f(x1,x1)),
inference(symmetry,[status(thm)],[c625]) ).
cnf(c627,plain,
$false,
inference(resolution,[status(thm)],[c1,c626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 27 15:15:04 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.10/0.87 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.10/0.87
% 3.10/0.87 % SZS status Unsatisfiable
% 3.10/0.87
% 3.88/0.96 % SZS output start CNFRefutation
% See solution above
% 7.06/1.38
% 7.06/1.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------