%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL024-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 11:48:51 AM UTC 2026
% Result : Unsatisfiable 86.29s 12.91s
% Output : CNFRefutation 88.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 4
% Syntax : Number of clauses : 211 ( 211 unt; 0 nHn; 3 RR)
% Number of literals : 211 ( 210 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 650 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_pyo) ).
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(X3,X2)),X2),equivalent(X3,X4))),true) = is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))),true) = is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))),true),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(equivalent(X6,equivalent(X5,X2)),equivalent(X5,X6)))),true) = is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(equivalent(X6,equivalent(X5,X2)),equivalent(X5,X6)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))),true) = is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))) = ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))),true),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))),true) = is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))) = ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))),true),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true) = is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))),true) = is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))),true),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq(true,true,is_a_theorem(equivalent(X2,X2)),true) = is_a_theorem(equivalent(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
is_a_theorem(equivalent(X2,X2)) = ifeq(true,true,is_a_theorem(equivalent(X2,X2)),true),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true) = is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,X)),equivalent(Z,Y)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xgk) ).
cnf(c24,plain,
is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))) = true,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
true = is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true) = ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(true,true,ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true),true) = ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c28,plain,
ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true) = ifeq(true,true,ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true),true),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))) = true,
inference(substitution,[status(thm)],[c23]) ).
cnf(c30,plain,
true = is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(true,true,ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true),true) = ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true,ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true),true),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,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(c33,plain,
ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true,ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
ifeq(true,true,ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true),true) = true,
inference(transitivity,[status(thm)],[c31,c33]) ).
cnf(c35,plain,
ifeq(is_a_theorem(X4),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c28,c34]) ).
cnf(c36,plain,
ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true) = true,
inference(transitivity,[status(thm)],[c26,c36]) ).
cnf(c38,plain,
is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))) = true,
inference(transitivity,[status(thm)],[c22,c37]) ).
cnf(c39,plain,
is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),equivalent(X3,equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5))))),equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2))) = true,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
true = is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),equivalent(X3,equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5))))),equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true) = ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),equivalent(X3,equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5))))),equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4))),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))) = true,
inference(substitution,[status(thm)],[c23]) ).
cnf(c46,plain,
true = is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4)))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4))),X2)),true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4)))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4))),X2)),true,ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4)))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c50,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(X4,equivalent(X3,X5)),equivalent(X3,X4))),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c44,c50]) ).
cnf(c52,plain,
ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),equivalent(X3,equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5))))),equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true) = true,
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true) = true,
inference(transitivity,[status(thm)],[c41,c52]) ).
cnf(c54,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)) = true,
inference(transitivity,[status(thm)],[c20,c53]) ).
cnf(c55,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X3)))),equivalent(X2,equivalent(X3,X3)))) = true,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X3)))),equivalent(X2,equivalent(X3,X3)))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,X3)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X3)))),equivalent(X2,equivalent(X3,X3)))),true,is_a_theorem(equivalent(X3,X3)),true),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true),true),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c61,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2)),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c63,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(X4,X3)),equivalent(X4,X5)),equivalent(X3,X2))),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c59,c63]) ).
cnf(c65,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,equivalent(X3,X3)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X3)))),equivalent(X2,equivalent(X3,X3)))),true,is_a_theorem(equivalent(X3,X3)),true) = true,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
ifeq(true,true,is_a_theorem(equivalent(X2,X2)),true) = true,
inference(transitivity,[status(thm)],[c57,c65]) ).
cnf(c67,plain,
is_a_theorem(equivalent(X2,X2)) = true,
inference(transitivity,[status(thm)],[c18,c66]) ).
cnf(c68,plain,
true = is_a_theorem(equivalent(X2,X2)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))),true) = ifeq(is_a_theorem(equivalent(X2,X2)),true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))),true),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
ifeq(is_a_theorem(equivalent(X2,X2)),true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c71,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))),true) = true,
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X2,X2))),equivalent(X3,X4))) = true,
inference(transitivity,[status(thm)],[c16,c71]) ).
cnf(c73,plain,
is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X3,X2)),equivalent(X3,X3))),equivalent(equivalent(X3,equivalent(X3,X2)),X2))) = true,
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
true = is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X3,X2)),equivalent(X3,X3))),equivalent(equivalent(X3,equivalent(X3,X2)),X2))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true) = ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X3,X2)),equivalent(X3,X3))),equivalent(equivalent(X3,equivalent(X3,X2)),X2))),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X3,X2)),equivalent(X3,X3))),equivalent(equivalent(X3,equivalent(X3,X2)),X2))),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true) = true,
inference(substitution,[status(thm)],[c51]) ).
cnf(c77,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true) = true,
inference(transitivity,[status(thm)],[c75,c76]) ).
cnf(c78,plain,
is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)) = true,
inference(transitivity,[status(thm)],[c14,c77]) ).
cnf(c79,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))) = true,
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
true = is_a_theorem(equivalent(equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))),true),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true),true) = ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c83,plain,
ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true),true),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
true = is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c85,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true,ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true),true),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
ifeq(is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3))))),equivalent(X5,X6))),true,ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c87,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true),true) = true,
inference(transitivity,[status(thm)],[c85,c86]) ).
cnf(c88,plain,
ifeq(is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X5,X6)),true) = true,
inference(transitivity,[status(thm)],[c83,c87]) ).
cnf(c89,plain,
ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))),true) = true,
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))),true) = true,
inference(transitivity,[status(thm)],[c81,c89]) ).
cnf(c91,plain,
is_a_theorem(equivalent(X6,equivalent(X5,equivalent(X5,equivalent(X6,equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))))) = true,
inference(transitivity,[status(thm)],[c12,c90]) ).
cnf(c92,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X5,equivalent(X5,equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X2,equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)))))))) = true,
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X5,equivalent(X5,equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X2,equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)))))))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X5,equivalent(X5,equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X2,equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)))))))),true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))),true),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X5,equivalent(X5,equivalent(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)),equivalent(X2,equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)))))))),true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))),true) = true,
inference(substitution,[status(thm)],[c88]) ).
cnf(c96,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))),true) = true,
inference(transitivity,[status(thm)],[c94,c95]) ).
cnf(c97,plain,
is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),equivalent(X3,X4)),equivalent(X2,X5)))) = true,
inference(transitivity,[status(thm)],[c10,c96]) ).
cnf(c98,plain,
is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))) = true,
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true) = true,
inference(substitution,[status(thm)],[c88]) ).
cnf(c102,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(X5,X4)),equivalent(X5,X6)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))) = true,
inference(transitivity,[status(thm)],[c8,c102]) ).
cnf(c104,plain,
is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2)),equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3))))) = true,
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2)),equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3))))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2)),equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3))))),true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))),true),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c108,plain,
ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true),true),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true) = is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c110,plain,
is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))),true) = is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))),true),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true) = is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))) = ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X2)))))) = true,
inference(substitution,[status(thm)],[c103]) ).
cnf(c116,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X2)))))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X2)))))),true,is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c119,plain,
ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true),true),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
true = is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c121,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true,ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
ifeq(is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),true,ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c123,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c121,c122]) ).
cnf(c124,plain,
ifeq(is_a_theorem(equivalent(X3,equivalent(X3,X2))),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c119,c123]) ).
cnf(c125,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(X3,X2)),equivalent(X3,equivalent(X2,equivalent(X3,X2)))))),true,is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true) = true,
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true) = true,
inference(transitivity,[status(thm)],[c117,c125]) ).
cnf(c127,plain,
is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))) = true,
inference(transitivity,[status(thm)],[c114,c126]) ).
cnf(c128,plain,
true = is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))),true) = ifeq(is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))),true),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
ifeq(is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c131,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))),true) = true,
inference(transitivity,[status(thm)],[c129,c130]) ).
cnf(c132,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(X4,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X4,X5))) = true,
inference(transitivity,[status(thm)],[c112,c131]) ).
cnf(c133,plain,
is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,equivalent(X3,equivalent(X2,X3))))),equivalent(equivalent(X3,equivalent(X2,X3)),X2))) = true,
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
true = is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,equivalent(X3,equivalent(X2,X3))))),equivalent(equivalent(X3,equivalent(X2,X3)),X2))),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true) = ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,equivalent(X3,equivalent(X2,X3))))),equivalent(equivalent(X3,equivalent(X2,X3)),X2))),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c137,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X4,X3))),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X4,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
true = is_a_theorem(equivalent(X3,equivalent(X2,equivalent(X3,X2)))),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c140,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(X4,X3)))),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X4,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X4,X3))),X2)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(X4,X3)))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X4,X3))),X2)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(X4,X3)))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c143,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X4,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(X4,X3))),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c138,c143]) ).
cnf(c145,plain,
ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,equivalent(X3,equivalent(X2,X3))))),equivalent(equivalent(X3,equivalent(X2,X3)),X2))),true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true) = true,
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true) = true,
inference(transitivity,[status(thm)],[c135,c145]) ).
cnf(c147,plain,
is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)) = true,
inference(transitivity,[status(thm)],[c110,c146]) ).
cnf(c148,plain,
true = is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true,ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
ifeq(is_a_theorem(equivalent(equivalent(X3,equivalent(X2,X3)),X2)),true,ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c151,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
ifeq(is_a_theorem(equivalent(X3,equivalent(X2,X3))),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c108,c151]) ).
cnf(c153,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3)),equivalent(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2)),equivalent(equivalent(X3,equivalent(X4,X2)),equivalent(X4,X3))))),true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))),true) = true,
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))),true) = true,
inference(transitivity,[status(thm)],[c106,c153]) ).
cnf(c155,plain,
is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(X3,equivalent(X4,X2)),X2))) = true,
inference(transitivity,[status(thm)],[c6,c154]) ).
cnf(c156,plain,
is_a_theorem(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,equivalent(X3,X2)),X2))) = true,
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
true = is_a_theorem(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,equivalent(X3,X2)),X2))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))),true) = ifeq(is_a_theorem(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,equivalent(X3,X2)),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))),true),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true),true) = ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c160,plain,
ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true),true),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true) = is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c162,plain,
is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true) = is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c164,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
ifeq(true,true,is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))),true) = is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c166,plain,
is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))) = ifeq(true,true,is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))),true),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))),true) = is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c168,plain,
is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))) = ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))),true),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))),equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))))))) = true,
inference(substitution,[status(thm)],[c132]) ).
cnf(c170,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))),equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))))))),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))),equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))))))),true,is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))),true),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c173,plain,
is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,X3)),X3),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,X3)),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
true = is_a_theorem(equivalent(equivalent(X3,equivalent(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c176,plain,
ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X4,X3)),X3)),true,is_a_theorem(X2),true),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,X3)),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,X3)),X3),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X4,X3)),X3)),true,is_a_theorem(X2),true),true),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,X3)),X3),X2)),true,ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X4,X3)),X3)),true,is_a_theorem(X2),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c179,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,X3)),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,X3)),X3),X2)),true,is_a_theorem(X2),true) = true,
inference(transitivity,[status(thm)],[c174,c179]) ).
cnf(c181,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))),equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))),equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2))))))))),true,is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))),true) = true,
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))),true) = true,
inference(transitivity,[status(thm)],[c171,c181]) ).
cnf(c183,plain,
is_a_theorem(equivalent(X5,equivalent(X4,equivalent(X4,equivalent(X5,equivalent(X3,equivalent(X2,equivalent(X3,X2)))))))) = true,
inference(transitivity,[status(thm)],[c168,c182]) ).
cnf(c184,plain,
is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X4,equivalent(X4,equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X2,equivalent(X3,equivalent(X2,X3)))))))) = true,
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X4,equivalent(X4,equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X2,equivalent(X3,equivalent(X2,X3)))))))),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
ifeq(true,true,is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X4,equivalent(X4,equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X2,equivalent(X3,equivalent(X2,X3)))))))),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))),true),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X4,equivalent(X4,equivalent(equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)),equivalent(X2,equivalent(X3,equivalent(X2,X3)))))))),true,is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))),true) = true,
inference(substitution,[status(thm)],[c88]) ).
cnf(c188,plain,
ifeq(true,true,is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))),true) = true,
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
is_a_theorem(equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X3)),equivalent(X2,X4)))) = true,
inference(transitivity,[status(thm)],[c166,c188]) ).
cnf(c190,plain,
is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))) = true,
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
true = is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)),equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(X4,equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))))),true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true) = true,
inference(substitution,[status(thm)],[c88]) ).
cnf(c194,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))),true) = true,
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
is_a_theorem(equivalent(equivalent(X5,equivalent(X4,X5)),equivalent(equivalent(X3,equivalent(X2,X4)),equivalent(X2,X3)))) = true,
inference(transitivity,[status(thm)],[c164,c194]) ).
cnf(c196,plain,
is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(equivalent(equivalent(X3,X2),equivalent(X2,X3)),equivalent(X2,equivalent(X3,X2))))) = true,
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
true = is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(equivalent(equivalent(X3,X2),equivalent(X2,X3)),equivalent(X2,equivalent(X3,X2))))),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true) = ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(equivalent(equivalent(X3,X2),equivalent(X2,X3)),equivalent(X2,equivalent(X3,X2))))),true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
ifeq(is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X2)),equivalent(equivalent(equivalent(X3,X2),equivalent(X2,X3)),equivalent(X2,equivalent(X3,X2))))),true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true) = true,
inference(substitution,[status(thm)],[c152]) ).
cnf(c200,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true) = true,
inference(transitivity,[status(thm)],[c198,c199]) ).
cnf(c201,plain,
is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))) = true,
inference(transitivity,[status(thm)],[c162,c200]) ).
cnf(c202,plain,
true = is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true,ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true),true),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
ifeq(is_a_theorem(equivalent(equivalent(X3,X2),equivalent(X2,X3))),true,ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true),true) = true,
inference(substitution,[status(thm)],[c32]) ).
cnf(c205,plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true),true) = true,
inference(transitivity,[status(thm)],[c203,c204]) ).
cnf(c206,plain,
ifeq(is_a_theorem(equivalent(X3,X2)),true,is_a_theorem(equivalent(X2,X3)),true) = true,
inference(transitivity,[status(thm)],[c160,c205]) ).
cnf(c207,plain,
ifeq(is_a_theorem(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,equivalent(X3,X2)),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))),true) = true,
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))),true) = true,
inference(transitivity,[status(thm)],[c158,c207]) ).
cnf(c209,plain,
is_a_theorem(equivalent(equivalent(equivalent(X4,equivalent(X3,X2)),X2),equivalent(X3,X4))) = true,
inference(transitivity,[status(thm)],[c4,c208]) ).
cnf(c210,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),c),equivalent(b,a))) = true,
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
$false,
inference(resolution,[status(thm)],[c1,c210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL024-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n010.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 15:18:01 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 86.29/12.91 Command-line arguments: --no-flatten-goal
% 86.29/12.91
% 86.29/12.91 % SZS status Unsatisfiable
% 86.29/12.91
% 86.29/12.95 % SZS output start CNFRefutation
% See solution above
% 88.70/13.24
% 88.70/13.24 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------