%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 11:49:01 AM UTC 2026
% Result : Unsatisfiable 17.23s 2.76s
% Output : CNFRefutation 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 6
% Syntax : Number of clauses : 269 ( 269 unt; 0 nHn; 3 RR)
% Number of literals : 269 ( 268 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 : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 920 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_1) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)),true) = is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),X2),equivalent(X3,equivalent(equivalent(X4,equivalent(X5,X5)),X2)))),true) = is_a_theorem(equivalent(equivalent(equivalent(X4,X3),X2),equivalent(X3,equivalent(equivalent(X4,equivalent(X5,X5)),X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3)))),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true) = is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))) = ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true) = is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true) = is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_2) ).
cnf(c14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(X5,X4)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))) = true,
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(X5,X4)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(X5,X4)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true),true),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),true),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2,Y2),equivalent(X2,Z2)),U2),equivalent(equivalent(Y2,Z2),U2)),V),V)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_3) ).
cnf(c22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)))) = true,
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,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(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3))),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X4,equivalent(X3,X2)))),true) = is_a_theorem(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X4,equivalent(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
is_a_theorem(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X4,equivalent(X3,X2)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X4,equivalent(X3,X2)))),true),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true) = is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,Y2),Z2),U2),equivalent(equivalent(equivalent(X2,V2),Z2),equivalent(equivalent(Y2,V2),U2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_4) ).
cnf(c33,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),equivalent(X5,X3)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3))))) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),equivalent(X5,X3)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3))))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),equivalent(X5,X3)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3))))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true),true),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2),X2)) = true,
inference(substitution,[status(thm)],[c13]) ).
cnf(c39,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2),X2)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,axiom,
ifeq(is_a_theorem(equivalent(X2,Y2)),true,ifeq(is_a_theorem(X2),true,is_a_theorem(Y2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(c42,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c37,c43]) ).
cnf(c45,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),equivalent(X5,X3)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3))))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true) = true,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c35,c45]) ).
cnf(c47,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))) = true,
inference(transitivity,[status(thm)],[c31,c46]) ).
cnf(c48,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))) = true,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3)))),true),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true),true),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c54,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true),true),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(equivalent(X2,X4),equivalent(X2,X3)))),true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c56,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true),true) = true,
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X3))),true,is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c52,c56]) ).
cnf(c58,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(equivalent(X4,X2),equivalent(X4,X3)))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3)))),true) = true,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X4,equivalent(X3,X2)))),true) = true,
inference(transitivity,[status(thm)],[c50,c58]) ).
cnf(c60,plain,
is_a_theorem(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X4,equivalent(X3,X2)))) = true,
inference(transitivity,[status(thm)],[c29,c59]) ).
cnf(c61,plain,
true = is_a_theorem(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X4,equivalent(X3,X2)))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3)))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3))),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3)))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3))),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3)))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c65,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X5,equivalent(X4,X3))),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c27,c65]) ).
cnf(c67,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c24,c67]) ).
cnf(c69,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))) = true,
inference(transitivity,[status(thm)],[c20,c68]) ).
cnf(c70,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true),true),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2),equivalent(equivalent(X4,X3),X2))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c73,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),X2)),true,is_a_theorem(equivalent(equivalent(X4,X3),X2)),true) = true,
inference(transitivity,[status(thm)],[c18,c73]) ).
cnf(c75,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(X5,X4)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3)),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true) = true,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))),true) = true,
inference(transitivity,[status(thm)],[c16,c75]) ).
cnf(c77,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),X3))) = true,
inference(transitivity,[status(thm)],[c12,c76]) ).
cnf(c78,plain,
is_a_theorem(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))) = true,
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,X5),equivalent(X2,X4)),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true) = true,
inference(substitution,[status(thm)],[c74]) ).
cnf(c82,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))),true) = true,
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X5)),equivalent(X2,X4)))) = true,
inference(transitivity,[status(thm)],[c10,c82]) ).
cnf(c84,plain,
is_a_theorem(equivalent(equivalent(equivalent(X2,X2),X5),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))) = true,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X2,X2),X5),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,X2),X5),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c88,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true),true),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c90,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))),true) = is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c92,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))),true),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))),true) = is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))),true),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),X3),equivalent(equivalent(X5,X2),X3)),equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3))))) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c96,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),X3),equivalent(equivalent(X5,X2),X3)),equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3))))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),X3),equivalent(equivalent(X5,X2),X3)),equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3))))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))),true),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c99,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X3,X2))),true) = is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c102,plain,
is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X3,X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X3,X2))),true),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))),true) = is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c104,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))),true),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)))) = true,
inference(substitution,[status(thm)],[c60]) ).
cnf(c106,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))),true),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))),true) = true,
inference(substitution,[status(thm)],[c44]) ).
cnf(c109,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c107,c108]) ).
cnf(c110,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X2)),equivalent(X3,X2))) = true,
inference(transitivity,[status(thm)],[c104,c109]) ).
cnf(c111,plain,
is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X4,X3)),equivalent(X2,equivalent(X4,X3))),equivalent(equivalent(X4,X3),equivalent(X4,X3)))) = true,
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X4,X3)),equivalent(X2,equivalent(X4,X3))),equivalent(equivalent(X4,X3),equivalent(X4,X3)))),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X4,X3)),equivalent(X2,equivalent(X4,X3))),equivalent(equivalent(X4,X3),equivalent(X4,X3)))),true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X4,X3)),equivalent(X2,equivalent(X4,X3))),equivalent(equivalent(X4,X3),equivalent(X4,X3)))),true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true) = true,
inference(substitution,[status(thm)],[c66]) ).
cnf(c115,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X3,X2))) = true,
inference(transitivity,[status(thm)],[c102,c115]) ).
cnf(c117,plain,
true = is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X3,X2))),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c121,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c119,c120]) ).
cnf(c122,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c100,c121]) ).
cnf(c123,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,X2),X3),equivalent(equivalent(X5,X2),X3)),equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3))))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))),true) = true,
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))),true) = true,
inference(transitivity,[status(thm)],[c97,c123]) ).
cnf(c125,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(equivalent(X2,X4),equivalent(equivalent(X5,X2),X3)))) = true,
inference(transitivity,[status(thm)],[c94,c124]) ).
cnf(c126,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3))))) = true,
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3))))),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3))))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))),true),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X2),equivalent(X4,X3)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3))))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))),true) = true,
inference(substitution,[status(thm)],[c44]) ).
cnf(c130,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X2),X5),equivalent(X2,X3)))) = true,
inference(transitivity,[status(thm)],[c92,c130]) ).
cnf(c132,plain,
is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X4,X4),X2)),equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2)))) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
true = is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X4,X4),X2)),equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2)))),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true) = ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X4,X4),X2)),equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c136,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),true) = is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c139,plain,
is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))) = ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),true),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
ifeq(true,true,is_a_theorem(equivalent(X2,X2)),true) = is_a_theorem(equivalent(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c141,plain,
is_a_theorem(equivalent(X2,X2)) = ifeq(true,true,is_a_theorem(equivalent(X2,X2)),true),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
is_a_theorem(equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),equivalent(X3,X3))) = true,
inference(substitution,[status(thm)],[c110]) ).
cnf(c143,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),equivalent(X3,X3))),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,X3)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),equivalent(X3,X3))),true,is_a_theorem(equivalent(X3,X3)),true),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,X3),equivalent(X2,X3)),equivalent(X3,X3))),true,is_a_theorem(equivalent(X3,X3)),true) = true,
inference(substitution,[status(thm)],[c122]) ).
cnf(c146,plain,
ifeq(true,true,is_a_theorem(equivalent(X2,X2)),true) = true,
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
is_a_theorem(equivalent(X2,X2)) = true,
inference(transitivity,[status(thm)],[c141,c146]) ).
cnf(c148,plain,
true = is_a_theorem(equivalent(X2,X2)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),true) = ifeq(is_a_theorem(equivalent(X3,X3)),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),true),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true),true) = ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c151,plain,
ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true),true),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))),true) = is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c153,plain,
is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))),true),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X3),X5),X4),equivalent(equivalent(equivalent(X2,X3),X5),equivalent(equivalent(X3,X3),X4)))) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c155,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X4),X2),X5),equivalent(equivalent(equivalent(X3,X4),X2),equivalent(equivalent(X4,X4),X5)))),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X6,X5),equivalent(X6,equivalent(equivalent(X4,X4),X5)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X4),X2),X5),equivalent(equivalent(equivalent(X3,X4),X2),equivalent(equivalent(X4,X4),X5)))),true,is_a_theorem(equivalent(equivalent(X6,X5),equivalent(X6,equivalent(equivalent(X4,X4),X5)))),true),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X4),X2),X5),equivalent(equivalent(equivalent(X3,X4),X2),equivalent(equivalent(X4,X4),X5)))),true,is_a_theorem(equivalent(equivalent(X6,X5),equivalent(X6,equivalent(equivalent(X4,X4),X5)))),true) = true,
inference(substitution,[status(thm)],[c57]) ).
cnf(c158,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))),true) = true,
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))) = true,
inference(transitivity,[status(thm)],[c153,c158]) ).
cnf(c160,plain,
true = is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))),true,ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true),true),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(equivalent(X2,X2),X3)))),true,ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c163,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true),true) = true,
inference(transitivity,[status(thm)],[c161,c162]) ).
cnf(c164,plain,
ifeq(is_a_theorem(equivalent(X4,X3)),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X2,X2),X3))),true) = true,
inference(transitivity,[status(thm)],[c151,c163]) ).
cnf(c165,plain,
ifeq(is_a_theorem(equivalent(X3,X3)),true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),true) = true,
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),true) = true,
inference(transitivity,[status(thm)],[c149,c165]) ).
cnf(c167,plain,
is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))) = true,
inference(transitivity,[status(thm)],[c139,c166]) ).
cnf(c168,plain,
true = is_a_theorem(equivalent(X3,equivalent(equivalent(X2,X2),X3))),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X4))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X4))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X4))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c172,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c137,c172]) ).
cnf(c174,plain,
ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X4,X4),X2)),equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true) = true,
inference(substitution,[status(thm)],[c173]) ).
cnf(c175,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true) = true,
inference(transitivity,[status(thm)],[c134,c174]) ).
cnf(c176,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))) = true,
inference(transitivity,[status(thm)],[c90,c175]) ).
cnf(c177,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true),true),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X4),X3),X2),equivalent(X3,X2))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c180,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c178,c179]) ).
cnf(c181,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X4),X3),X2)),true,is_a_theorem(equivalent(X3,X2)),true) = true,
inference(transitivity,[status(thm)],[c88,c180]) ).
cnf(c182,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,X2),X5),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true) = true,
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))),true) = true,
inference(transitivity,[status(thm)],[c86,c182]) ).
cnf(c184,plain,
is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,X3),equivalent(X4,equivalent(X2,X2))),equivalent(X3,X5)))) = true,
inference(transitivity,[status(thm)],[c8,c183]) ).
cnf(c185,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X2,X2)),X3),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,equivalent(X2,X2))),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3))))) = true,
inference(substitution,[status(thm)],[c184]) ).
cnf(c186,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X2,X2)),X3),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,equivalent(X2,X2))),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3))))),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X2,X2)),X3),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,equivalent(X2,X2))),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3))))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3)))),true),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c189,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true),true),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true) = is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c191,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c193,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))),true),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X2),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2)))) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c195,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X2),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2)))),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X2),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))),true),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c198,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2),X2)) = true,
inference(substitution,[status(thm)],[c13]) ).
cnf(c201,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X3)),equivalent(X4,X3)),X2),X2)),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3)),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3)),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3)),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c205,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c203,c204]) ).
cnf(c206,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X3),X3),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c199,c205]) ).
cnf(c207,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),equivalent(X5,X4)),X2),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))),true) = true,
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))),true) = true,
inference(transitivity,[status(thm)],[c196,c207]) ).
cnf(c209,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X4)),X3),X2),equivalent(equivalent(equivalent(X5,X4),X3),X2))) = true,
inference(transitivity,[status(thm)],[c193,c208]) ).
cnf(c210,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X5),equivalent(X3,X4)),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)))) = true,
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X5),equivalent(X3,X4)),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)))),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X5),equivalent(X3,X4)),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X5),equivalent(X3,X4)),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true) = true,
inference(substitution,[status(thm)],[c44]) ).
cnf(c214,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true) = true,
inference(transitivity,[status(thm)],[c212,c213]) ).
cnf(c215,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))) = true,
inference(transitivity,[status(thm)],[c191,c214]) ).
cnf(c216,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true),true),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2)),equivalent(equivalent(X3,X4),X2))),true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c219,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true),true) = true,
inference(transitivity,[status(thm)],[c217,c218]) ).
cnf(c220,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,X4),equivalent(equivalent(X3,X5),X2))),true,is_a_theorem(equivalent(equivalent(X3,X4),X2)),true) = true,
inference(transitivity,[status(thm)],[c189,c219]) ).
cnf(c221,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X2,X2)),X3),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,equivalent(X2,X2))),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3))))),true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3)))),true) = true,
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3)))),true) = true,
inference(transitivity,[status(thm)],[c187,c221]) ).
cnf(c223,plain,
is_a_theorem(equivalent(equivalent(equivalent(X5,X4),X3),equivalent(X4,equivalent(equivalent(X5,equivalent(X2,X2)),X3)))) = true,
inference(transitivity,[status(thm)],[c6,c222]) ).
cnf(c224,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),equivalent(equivalent(equivalent(X3,X3),X4),equivalent(equivalent(X4,equivalent(X3,X3)),X2)))) = true,
inference(substitution,[status(thm)],[c223]) ).
cnf(c225,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),equivalent(equivalent(equivalent(X3,X3),X4),equivalent(equivalent(X4,equivalent(X3,X3)),X2)))),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),equivalent(equivalent(equivalent(X3,X3),X4),equivalent(equivalent(X4,equivalent(X3,X3)),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)),true),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true),true) = ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c228,plain,
ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true),true),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true) = is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c230,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)),true) = is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c232,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)),true),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(X3,X3),X2))) = true,
inference(substitution,[status(thm)],[c215]) ).
cnf(c234,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(X3,X3),X2))),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)),true),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true),true) = ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c237,plain,
ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true),true),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))),true) = is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c239,plain,
is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))),true),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(equivalent(X4,X4),X3)),equivalent(equivalent(X4,X2),X3))) = true,
inference(substitution,[status(thm)],[c215]) ).
cnf(c241,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(equivalent(X4,X4),X3)),equivalent(equivalent(X4,X2),X3))),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X4),X3)),equivalent(X5,X3))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(equivalent(X4,X4),X3)),equivalent(equivalent(X4,X2),X3))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X4),X3)),equivalent(X5,X3))),true),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X2),equivalent(equivalent(X4,X4),X3)),equivalent(equivalent(X4,X2),X3))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X4),X3)),equivalent(X5,X3))),true) = true,
inference(substitution,[status(thm)],[c57]) ).
cnf(c244,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))),true) = true,
inference(transitivity,[status(thm)],[c242,c243]) ).
cnf(c245,plain,
is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))) = true,
inference(transitivity,[status(thm)],[c239,c244]) ).
cnf(c246,plain,
true = is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))),true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true),true),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X2)),equivalent(X4,X2))),true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c249,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c247,c248]) ).
cnf(c250,plain,
ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(X4,X2)),true) = true,
inference(transitivity,[status(thm)],[c237,c249]) ).
cnf(c251,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),equivalent(equivalent(X3,X3),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)),true) = true,
inference(substitution,[status(thm)],[c250]) ).
cnf(c252,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)),true) = true,
inference(transitivity,[status(thm)],[c235,c251]) ).
cnf(c253,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)),X2)) = true,
inference(transitivity,[status(thm)],[c232,c252]) ).
cnf(c254,plain,
is_a_theorem(equivalent(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(equivalent(X3,X4),X2))) = true,
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(equivalent(X3,X4),X2))),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(equivalent(X3,X4),X2))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(equivalent(X3,X4),X2))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true) = true,
inference(substitution,[status(thm)],[c57]) ).
cnf(c258,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true) = true,
inference(transitivity,[status(thm)],[c256,c257]) ).
cnf(c259,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))) = true,
inference(transitivity,[status(thm)],[c230,c258]) ).
cnf(c260,plain,
true = is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true),true),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2))),equivalent(X5,X2))),true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c263,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c261,c262]) ).
cnf(c264,plain,
ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,X3),equivalent(equivalent(X3,X4),X2)))),true,is_a_theorem(equivalent(X5,X2)),true) = true,
inference(transitivity,[status(thm)],[c228,c263]) ).
cnf(c265,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),equivalent(equivalent(equivalent(X3,X3),X4),equivalent(equivalent(X4,equivalent(X3,X3)),X2)))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)),true) = true,
inference(substitution,[status(thm)],[c264]) ).
cnf(c266,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)),true) = true,
inference(transitivity,[status(thm)],[c226,c265]) ).
cnf(c267,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(equivalent(X3,X3),X4)),X2),X2)) = true,
inference(transitivity,[status(thm)],[c4,c266]) ).
cnf(c268,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) = true,
inference(substitution,[status(thm)],[c267]) ).
cnf(c269,plain,
$false,
inference(resolution,[status(thm)],[c1,c268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n026.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 27 15:24:26 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.23/2.76 Command-line arguments: --no-flatten-goal
% 17.23/2.76
% 17.23/2.76 % SZS status Unsatisfiable
% 17.23/2.76
% 17.23/2.80 % SZS output start CNFRefutation
% See solution above
% 20.22/3.20
% 20.22/3.20 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------