%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL050-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:54 AM UTC 2026
% Result : Unsatisfiable 99.63s 13.18s
% Output : CNFRefutation 101.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 86
% Number of leaves : 6
% Syntax : Number of clauses : 424 ( 424 unt; 0 nHn; 3 RR)
% Number of literals : 424 ( 423 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 1205 ( 156 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_21) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),true) = is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
is_a_theorem(implies(X3,implies(implies(X3,X2),X2))) = ifeq(true,true,is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))),true) = is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))) = ifeq(true,true,is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))),true) = is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))) = ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))),true),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))),true) = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))),true),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))),true) = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))),true),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))),true) = is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))) = ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))),true),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
cnf(c22,plain,
is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
true = is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
is_a_theorem(implies(implies(not(X2),X2),X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c29,plain,
true = is_a_theorem(implies(implies(not(X2),X2),X2)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
ifeq(is_a_theorem(implies(X2,Y2)),true,ifeq(is_a_theorem(X2),true,is_a_theorem(Y2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(c33,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c27,c34]) ).
cnf(c36,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c24,c36]) ).
cnf(c38,plain,
is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))) = true,
inference(transitivity,[status(thm)],[c20,c37]) ).
cnf(c39,plain,
is_a_theorem(implies(implies(X2,X2),implies(implies(not(X2),X2),X2))) = true,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
true = is_a_theorem(implies(implies(X2,X2),implies(implies(not(X2),X2),X2))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))),true) = ifeq(is_a_theorem(implies(implies(X2,X2),implies(implies(not(X2),X2),X2))),true,is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))),true),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true),true) = ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,plain,
ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true),true),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true) = is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true) = is_a_theorem(implies(X3,implies(X2,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
is_a_theorem(implies(X3,implies(X2,X2))) = ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X4,X4)),X3),X2),implies(X5,X2))),true) = is_a_theorem(implies(implies(implies(not(implies(X4,X4)),X3),X2),implies(X5,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))) = ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))) = ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = is_a_theorem(implies(not(implies(X3,X3)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
is_a_theorem(implies(not(implies(X3,X3)),X2)) = ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
ifeq(true,true,is_a_theorem(implies(X2,X2)),true) = is_a_theorem(implies(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c57,plain,
is_a_theorem(implies(X2,X2)) = ifeq(true,true,is_a_theorem(implies(X2,X2)),true),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c61,plain,
true = is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,axiom,
is_a_theorem(implies(X2,implies(not(X2),Y2))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
cnf(c67,plain,
is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
true = is_a_theorem(implies(X3,implies(not(X3),X2))),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c72,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c65,c72]) ).
cnf(c74,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = true,
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c62,c74]) ).
cnf(c76,plain,
is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))) = true,
inference(transitivity,[status(thm)],[c59,c75]) ).
cnf(c77,plain,
is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))) = true,
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
true = is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
ifeq(true,true,is_a_theorem(implies(X2,X2)),true) = ifeq(is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))),true,is_a_theorem(implies(X2,X2)),true),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))),true,is_a_theorem(implies(X2,X2)),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c81,plain,
ifeq(true,true,is_a_theorem(implies(X2,X2)),true) = true,
inference(transitivity,[status(thm)],[c79,c80]) ).
cnf(c82,plain,
is_a_theorem(implies(X2,X2)) = true,
inference(transitivity,[status(thm)],[c57,c81]) ).
cnf(c83,plain,
true = is_a_theorem(implies(X2,X2)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c86,plain,
ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c88,plain,
true = is_a_theorem(implies(X3,implies(not(X3),X2))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c91,plain,
ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true) = true,
inference(transitivity,[status(thm)],[c86,c91]) ).
cnf(c93,plain,
ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = true,
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = true,
inference(transitivity,[status(thm)],[c84,c93]) ).
cnf(c95,plain,
is_a_theorem(implies(not(implies(X3,X3)),X2)) = true,
inference(transitivity,[status(thm)],[c55,c94]) ).
cnf(c96,plain,
is_a_theorem(implies(not(implies(X2,X2)),X3)) = true,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
true = is_a_theorem(implies(not(implies(X2,X2)),X3)),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = ifeq(is_a_theorem(implies(not(implies(X2,X2)),X4)),true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c102,plain,
true = is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c105,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c100,c105]) ).
cnf(c107,plain,
ifeq(is_a_theorem(implies(not(implies(X2,X2)),X4)),true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = true,
inference(transitivity,[status(thm)],[c98,c107]) ).
cnf(c109,plain,
is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))) = true,
inference(transitivity,[status(thm)],[c53,c108]) ).
cnf(c110,plain,
is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))) = true,
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
true = is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))),true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
true = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c116,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c118,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c116,c117]) ).
cnf(c119,plain,
ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = true,
inference(transitivity,[status(thm)],[c114,c118]) ).
cnf(c120,plain,
ifeq(is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))),true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = true,
inference(transitivity,[status(thm)],[c112,c120]) ).
cnf(c122,plain,
is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))) = true,
inference(transitivity,[status(thm)],[c51,c121]) ).
cnf(c123,plain,
is_a_theorem(implies(X2,implies(not(implies(X4,X4)),X3))) = true,
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
true = is_a_theorem(implies(X2,implies(not(implies(X4,X4)),X3))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true) = ifeq(is_a_theorem(implies(X2,implies(not(implies(X5,X5)),X4))),true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
ifeq(is_a_theorem(implies(X2,implies(not(implies(X5,X5)),X4))),true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c127,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))) = true,
inference(transitivity,[status(thm)],[c49,c127]) ).
cnf(c129,plain,
is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))) = true,
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
true = is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))),true,is_a_theorem(implies(X3,implies(X2,X2))),true),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
ifeq(is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))),true,is_a_theorem(implies(X3,implies(X2,X2))),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c133,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true) = true,
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
is_a_theorem(implies(X3,implies(X2,X2))) = true,
inference(transitivity,[status(thm)],[c47,c133]) ).
cnf(c135,plain,
is_a_theorem(implies(X2,implies(X3,X3))) = true,
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
true = is_a_theorem(implies(X2,implies(X3,X3))),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true) = ifeq(is_a_theorem(implies(X2,implies(X4,X4))),true,is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
ifeq(is_a_theorem(implies(X2,implies(X4,X4))),true,is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c139,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c137,c138]) ).
cnf(c140,plain,
is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))) = true,
inference(transitivity,[status(thm)],[c45,c139]) ).
cnf(c141,plain,
true = is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true),true) = ifeq(is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true,ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true),true),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
ifeq(is_a_theorem(implies(implies(implies(X4,X4),X3),implies(X2,X3))),true,ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c144,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true),true) = true,
inference(transitivity,[status(thm)],[c142,c143]) ).
cnf(c145,plain,
ifeq(is_a_theorem(implies(implies(X4,X4),X3)),true,is_a_theorem(implies(X2,X3)),true) = true,
inference(transitivity,[status(thm)],[c43,c144]) ).
cnf(c146,plain,
ifeq(is_a_theorem(implies(implies(X2,X2),implies(implies(not(X2),X2),X2))),true,is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))),true) = true,
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))),true) = true,
inference(transitivity,[status(thm)],[c41,c146]) ).
cnf(c148,plain,
is_a_theorem(implies(X3,implies(implies(not(X2),X2),X2))) = true,
inference(transitivity,[status(thm)],[c18,c147]) ).
cnf(c149,plain,
is_a_theorem(implies(X2,implies(implies(not(X3),X3),X3))) = true,
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
true = is_a_theorem(implies(X2,implies(implies(not(X3),X3),X3))),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))),true) = ifeq(is_a_theorem(implies(X2,implies(implies(not(X4),X4),X4))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))),true),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
ifeq(is_a_theorem(implies(X2,implies(implies(not(X4),X4),X4))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c153,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c151,c152]) ).
cnf(c154,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X4),X3),implies(X2,X3))) = true,
inference(transitivity,[status(thm)],[c16,c153]) ).
cnf(c155,plain,
is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(X2,implies(X4,X3)))) = true,
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
true = is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(X2,implies(X4,X3)))),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(X2,implies(X4,X3)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))),true),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c159,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c161,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
is_a_theorem(implies(implies(X2,X4),implies(implies(X4,X3),implies(X2,X3)))) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c163,plain,
true = is_a_theorem(implies(implies(X2,X4),implies(implies(X4,X3),implies(X2,X3)))),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = ifeq(is_a_theorem(implies(implies(X3,X5),implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
ifeq(is_a_theorem(implies(implies(X3,X5),implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c166,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = true,
inference(transitivity,[status(thm)],[c164,c165]) ).
cnf(c167,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))) = true,
inference(transitivity,[status(thm)],[c161,c166]) ).
cnf(c168,plain,
true = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c171,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c169,c170]) ).
cnf(c172,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true) = true,
inference(transitivity,[status(thm)],[c159,c171]) ).
cnf(c173,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X3),implies(X4,X3)),implies(X2,implies(X4,X3)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))),true) = true,
inference(transitivity,[status(thm)],[c157,c173]) ).
cnf(c175,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(X2,implies(X4,X3)))) = true,
inference(transitivity,[status(thm)],[c14,c174]) ).
cnf(c176,plain,
is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(X2,implies(implies(X3,X4),X4)))) = true,
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
true = is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(X2,implies(implies(X3,X4),X4)))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))),true) = ifeq(is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(X2,implies(implies(X3,X4),X4)))),true,is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))),true),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
ifeq(is_a_theorem(implies(implies(implies(X3,X4),implies(not(X4),X4)),implies(X2,implies(implies(X3,X4),X4)))),true,is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c180,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))),true) = true,
inference(transitivity,[status(thm)],[c178,c179]) ).
cnf(c181,plain,
is_a_theorem(implies(implies(not(X4),X3),implies(X2,implies(implies(X3,X4),X4)))) = true,
inference(transitivity,[status(thm)],[c12,c180]) ).
cnf(c182,plain,
is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(X3),X2),implies(implies(X2,X3),X3)))) = true,
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
true = is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(X3),X2),implies(implies(X2,X3),X3)))),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))),true) = ifeq(is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(X3),X2),implies(implies(X2,X3),X3)))),true,is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))),true),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true),true) = ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c186,plain,
ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true),true),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true) = is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c188,plain,
is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)),true) = is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c190,plain,
is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)) = ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)),true),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))),true) = is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c192,plain,
is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))) = ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))),true),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true) = is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c194,plain,
is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c196,plain,
is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))) = ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c198,plain,
is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c200,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c202,plain,
is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))) = ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))) = true,
inference(substitution,[status(thm)],[c38]) ).
cnf(c204,plain,
true = is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))),true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
ifeq(is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))),true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c207,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = true,
inference(transitivity,[status(thm)],[c205,c206]) ).
cnf(c208,plain,
is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))) = true,
inference(transitivity,[status(thm)],[c202,c207]) ).
cnf(c209,plain,
true = is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(X4,implies(implies(not(not(X4)),not(X4)),X3))),true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
ifeq(is_a_theorem(implies(X4,implies(implies(not(not(X4)),not(X4)),X3))),true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c212,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c210,c211]) ).
cnf(c213,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))) = true,
inference(transitivity,[status(thm)],[c200,c212]) ).
cnf(c214,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c213]) ).
cnf(c215,plain,
true = is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c218,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c216,c217]) ).
cnf(c219,plain,
is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c198,c218]) ).
cnf(c220,plain,
is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))) = true,
inference(substitution,[status(thm)],[c219]) ).
cnf(c221,plain,
true = is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = ifeq(is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c224,plain,
ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c226,plain,
is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c228,plain,
is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c230,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c232,plain,
is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c234,plain,
true = is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = ifeq(is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))),true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
ifeq(is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))),true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c237,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = true,
inference(transitivity,[status(thm)],[c235,c236]) ).
cnf(c238,plain,
is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))) = true,
inference(transitivity,[status(thm)],[c232,c237]) ).
cnf(c239,plain,
is_a_theorem(implies(X2,implies(implies(X4,X3),implies(not(X2),X3)))) = true,
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
true = is_a_theorem(implies(X2,implies(implies(X4,X3),implies(not(X2),X3)))),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(X3,implies(implies(X5,X4),implies(not(X3),X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
ifeq(is_a_theorem(implies(X3,implies(implies(X5,X4),implies(not(X3),X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c243,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c241,c242]) ).
cnf(c244,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))) = true,
inference(transitivity,[status(thm)],[c230,c243]) ).
cnf(c245,plain,
is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))) = true,
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
true = is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))),true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c249,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
true = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c252,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(X5,X3))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(X5,X3))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(X5,X3))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c255,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c253,c254]) ).
cnf(c256,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c250,c255]) ).
cnf(c257,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))),true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = true,
inference(substitution,[status(thm)],[c256]) ).
cnf(c258,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = true,
inference(transitivity,[status(thm)],[c247,c257]) ).
cnf(c259,plain,
is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))) = true,
inference(transitivity,[status(thm)],[c228,c258]) ).
cnf(c260,plain,
is_a_theorem(implies(X3,implies(X4,implies(not(X3),X2)))) = true,
inference(substitution,[status(thm)],[c259]) ).
cnf(c261,plain,
true = is_a_theorem(implies(X3,implies(X4,implies(not(X3),X2)))),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(X4,implies(X5,implies(not(X4),X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
ifeq(is_a_theorem(implies(X4,implies(X5,implies(not(X4),X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c264,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c262,c263]) ).
cnf(c265,plain,
is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))) = true,
inference(transitivity,[status(thm)],[c226,c264]) ).
cnf(c266,plain,
true = is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c269,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c267,c268]) ).
cnf(c270,plain,
ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true) = true,
inference(transitivity,[status(thm)],[c224,c269]) ).
cnf(c271,plain,
ifeq(is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = true,
inference(substitution,[status(thm)],[c270]) ).
cnf(c272,plain,
ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = true,
inference(transitivity,[status(thm)],[c222,c271]) ).
cnf(c273,plain,
is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))) = true,
inference(transitivity,[status(thm)],[c196,c272]) ).
cnf(c274,plain,
true = is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true) = ifeq(is_a_theorem(implies(not(X5),implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
ifeq(is_a_theorem(implies(not(X5),implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c277,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true) = true,
inference(transitivity,[status(thm)],[c275,c276]) ).
cnf(c278,plain,
is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))) = true,
inference(transitivity,[status(thm)],[c194,c277]) ).
cnf(c279,plain,
is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),implies(not(X4),X4))) = true,
inference(substitution,[status(thm)],[c278]) ).
cnf(c280,plain,
true = is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),implies(not(X4),X4))),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c281,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))),true) = ifeq(is_a_theorem(implies(implies(implies(X5,implies(X3,X2)),X5),implies(not(X5),X5))),true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))),true),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c283,plain,
ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c285,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c287,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
true = is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c289,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(not(X4),X4),X3))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(not(X4),X4),X3))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c291,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c289,c290]) ).
cnf(c292,plain,
is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))) = true,
inference(transitivity,[status(thm)],[c287,c291]) ).
cnf(c293,plain,
is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c292]) ).
cnf(c294,plain,
true = is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c297,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c295,c296]) ).
cnf(c298,plain,
is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c285,c297]) ).
cnf(c299,plain,
true = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c302,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
inference(transitivity,[status(thm)],[c300,c301]) ).
cnf(c303,plain,
ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c283,c302]) ).
cnf(c304,plain,
ifeq(is_a_theorem(implies(implies(implies(X5,implies(X3,X2)),X5),implies(not(X5),X5))),true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))),true) = true,
inference(substitution,[status(thm)],[c303]) ).
cnf(c305,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))),true) = true,
inference(transitivity,[status(thm)],[c281,c304]) ).
cnf(c306,plain,
is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X5,implies(X3,X2)),X5),X4))) = true,
inference(transitivity,[status(thm)],[c192,c305]) ).
cnf(c307,plain,
is_a_theorem(implies(implies(X4,X4),implies(implies(implies(X4,implies(X3,X2)),X4),X4))) = true,
inference(substitution,[status(thm)],[c306]) ).
cnf(c308,plain,
true = is_a_theorem(implies(implies(X4,X4),implies(implies(implies(X4,implies(X3,X2)),X4),X4))),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)),true) = ifeq(is_a_theorem(implies(implies(X4,X4),implies(implies(implies(X4,implies(X3,X2)),X4),X4))),true,is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)),true),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c311,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c310]) ).
cnf(c312,plain,
ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
true = is_a_theorem(implies(X2,X2)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c314,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c317,plain,
ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c315,c316]) ).
cnf(c318,plain,
ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c312,c317]) ).
cnf(c319,plain,
ifeq(is_a_theorem(implies(implies(X4,X4),implies(implies(implies(X4,implies(X3,X2)),X4),X4))),true,is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)),true) = true,
inference(substitution,[status(thm)],[c318]) ).
cnf(c320,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)),true) = true,
inference(transitivity,[status(thm)],[c309,c319]) ).
cnf(c321,plain,
is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X4),X4)) = true,
inference(transitivity,[status(thm)],[c190,c320]) ).
cnf(c322,plain,
is_a_theorem(implies(implies(implies(implies(X4,implies(X3,X2)),implies(X3,X2)),implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))) = true,
inference(substitution,[status(thm)],[c321]) ).
cnf(c323,plain,
true = is_a_theorem(implies(implies(implies(implies(X4,implies(X3,X2)),implies(X3,X2)),implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),
inference(symmetry,[status(thm)],[c322]) ).
cnf(c324,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X4,implies(X3,X2)),implies(X3,X2)),implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X4,implies(X3,X2)),implies(X3,X2)),implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c326,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true) = true,
inference(transitivity,[status(thm)],[c324,c325]) ).
cnf(c327,plain,
is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))) = true,
inference(transitivity,[status(thm)],[c188,c326]) ).
cnf(c328,plain,
true = is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true),true),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(X4,implies(X3,X2))),implies(X4,implies(X3,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c331,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true),true) = true,
inference(transitivity,[status(thm)],[c329,c330]) ).
cnf(c332,plain,
ifeq(is_a_theorem(implies(X4,implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(X4,implies(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c186,c331]) ).
cnf(c333,plain,
ifeq(is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(X3),X2),implies(implies(X2,X3),X3)))),true,is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))),true) = true,
inference(substitution,[status(thm)],[c332]) ).
cnf(c334,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))),true) = true,
inference(transitivity,[status(thm)],[c184,c333]) ).
cnf(c335,plain,
is_a_theorem(implies(implies(not(X3),X2),implies(implies(X2,X3),X3))) = true,
inference(transitivity,[status(thm)],[c10,c334]) ).
cnf(c336,plain,
is_a_theorem(implies(implies(not(X2),X3),implies(implies(X3,X2),X2))) = true,
inference(substitution,[status(thm)],[c335]) ).
cnf(c337,plain,
true = is_a_theorem(implies(implies(not(X2),X3),implies(implies(X3,X2),X2))),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X2),X3),implies(implies(X3,X2),X2))),true,is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),true),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true),true) = ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c340,plain,
ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true),true),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true) = is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c342,plain,
is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c344,plain,
is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c346,plain,
is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true),
inference(symmetry,[status(thm)],[c345]) ).
cnf(c347,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c348,plain,
is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))) = ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c350,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c352,plain,
is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))) = true,
inference(substitution,[status(thm)],[c298]) ).
cnf(c354,plain,
true = is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))),
inference(symmetry,[status(thm)],[c353]) ).
cnf(c355,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = ifeq(is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))),true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
ifeq(is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))),true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = true,
inference(substitution,[status(thm)],[c270]) ).
cnf(c357,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c355,c356]) ).
cnf(c358,plain,
is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))) = true,
inference(transitivity,[status(thm)],[c352,c357]) ).
cnf(c359,plain,
true = is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),
inference(symmetry,[status(thm)],[c358]) ).
cnf(c360,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = ifeq(is_a_theorem(implies(X5,implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
ifeq(is_a_theorem(implies(X5,implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c362,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = true,
inference(transitivity,[status(thm)],[c360,c361]) ).
cnf(c363,plain,
is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))) = true,
inference(transitivity,[status(thm)],[c350,c362]) ).
cnf(c364,plain,
is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))) = true,
inference(substitution,[status(thm)],[c363]) ).
cnf(c365,plain,
true = is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))),true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))),true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c368,plain,
ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = true,
inference(transitivity,[status(thm)],[c366,c367]) ).
cnf(c369,plain,
is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))) = true,
inference(transitivity,[status(thm)],[c348,c368]) ).
cnf(c370,plain,
is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))) = true,
inference(substitution,[status(thm)],[c369]) ).
cnf(c371,plain,
true = is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c372,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = ifeq(is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))),true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c374,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c373]) ).
cnf(c375,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
true = is_a_theorem(implies(X3,implies(X2,X2))),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c377,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X4,implies(X3,X3))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(X3,X3))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(X3,X3))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c380,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c378,c379]) ).
cnf(c381,plain,
ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c375,c380]) ).
cnf(c382,plain,
ifeq(is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))),true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = true,
inference(substitution,[status(thm)],[c381]) ).
cnf(c383,plain,
ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = true,
inference(transitivity,[status(thm)],[c372,c382]) ).
cnf(c384,plain,
is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))) = true,
inference(transitivity,[status(thm)],[c346,c383]) ).
cnf(c385,plain,
is_a_theorem(implies(X2,implies(X4,implies(X3,X2)))) = true,
inference(substitution,[status(thm)],[c384]) ).
cnf(c386,plain,
true = is_a_theorem(implies(X2,implies(X4,implies(X3,X2)))),
inference(symmetry,[status(thm)],[c385]) ).
cnf(c387,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(X3,implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
ifeq(is_a_theorem(implies(X3,implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c389,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c387,c388]) ).
cnf(c390,plain,
is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))) = true,
inference(transitivity,[status(thm)],[c344,c389]) ).
cnf(c391,plain,
is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(X3,X2))) = true,
inference(substitution,[status(thm)],[c390]) ).
cnf(c392,plain,
true = is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(X3,X2))),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(X3,X2))),true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c395,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true),
inference(symmetry,[status(thm)],[c394]) ).
cnf(c396,plain,
true = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),
inference(symmetry,[status(thm)],[c292]) ).
cnf(c397,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true),
inference(congruence,[status(thm)],[c396]) ).
cnf(c398,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c399,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c397,c398]) ).
cnf(c400,plain,
ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true) = true,
inference(transitivity,[status(thm)],[c395,c399]) ).
cnf(c401,plain,
ifeq(is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(X3,X2))),true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true) = true,
inference(substitution,[status(thm)],[c400]) ).
cnf(c402,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c393,c401]) ).
cnf(c403,plain,
is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))) = true,
inference(transitivity,[status(thm)],[c342,c402]) ).
cnf(c404,plain,
true = is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),
inference(symmetry,[status(thm)],[c403]) ).
cnf(c405,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true,ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true),true),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
ifeq(is_a_theorem(implies(implies(implies(X4,X3),X2),implies(X3,X2))),true,ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c407,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c405,c406]) ).
cnf(c408,plain,
ifeq(is_a_theorem(implies(implies(X4,X3),X2)),true,is_a_theorem(implies(X3,X2)),true) = true,
inference(transitivity,[status(thm)],[c340,c407]) ).
cnf(c409,plain,
ifeq(is_a_theorem(implies(implies(not(X2),X3),implies(implies(X3,X2),X2))),true,is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),true) = true,
inference(substitution,[status(thm)],[c408]) ).
cnf(c410,plain,
ifeq(true,true,is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),true) = true,
inference(transitivity,[status(thm)],[c338,c409]) ).
cnf(c411,plain,
is_a_theorem(implies(X3,implies(implies(X3,X2),X2))) = true,
inference(transitivity,[status(thm)],[c8,c410]) ).
cnf(c412,plain,
true = is_a_theorem(implies(X3,implies(implies(X3,X2),X2))),
inference(symmetry,[status(thm)],[c411]) ).
cnf(c413,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(X4,implies(implies(X4,X3),X3))),true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))),true),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
ifeq(is_a_theorem(implies(X4,implies(implies(X4,X3),X3))),true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c415,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c413,c414]) ).
cnf(c416,plain,
is_a_theorem(implies(implies(implies(implies(X4,X3),X3),X2),implies(X4,X2))) = true,
inference(transitivity,[status(thm)],[c6,c415]) ).
cnf(c417,plain,
is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))) = true,
inference(substitution,[status(thm)],[c416]) ).
cnf(c418,plain,
true = is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),
inference(symmetry,[status(thm)],[c417]) ).
cnf(c419,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X3,X2),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c421,plain,
ifeq(true,true,is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))),true) = true,
inference(transitivity,[status(thm)],[c419,c420]) ).
cnf(c422,plain,
is_a_theorem(implies(implies(X4,implies(X3,X2)),implies(X3,implies(X4,X2)))) = true,
inference(transitivity,[status(thm)],[c4,c421]) ).
cnf(c423,plain,
is_a_theorem(implies(implies(a,implies(b,c)),implies(b,implies(a,c)))) = true,
inference(substitution,[status(thm)],[c422]) ).
cnf(c424,plain,
$false,
inference(resolution,[status(thm)],[c1,c423]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL050-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 15:18:51 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 99.63/13.18 Command-line arguments: --no-flatten-goal
% 99.63/13.18
% 99.63/13.18 % SZS status Unsatisfiable
% 99.63/13.18
% 99.63/13.19 % SZS output start CNFRefutation
% See solution above
% 101.27/13.38
% 101.27/13.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------