TSTP Solution File: LCL068-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL068-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:49:11 EDT 2022
% Result : Unsatisfiable 57.95s 58.12s
% Output : CNFRefutation 57.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 5
% Syntax : Number of clauses : 286 ( 165 unt; 0 nHn; 101 RR)
% Number of literals : 432 ( 0 equ; 147 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 767 ( 168 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_19,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))) ).
cnf(cn_37,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))) ).
cnf(cn_59,axiom,
is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))) ).
cnf(prove_cn_2,negated_conjecture,
~ is_a_theorem(implies(implies(not(a),a),a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(not(not(X_43508)),X_43508))
| ~ is_a_theorem(not(not(X_43508)))
| is_a_theorem(X_43508) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(not(not(X_43508)))),bind(Y,$fot(X_43508))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507)),implies(not(not(X_43507)),X_43507)))
| ~ is_a_theorem(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507)))
| is_a_theorem(implies(not(not(X_43507)),X_43507)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507)))),bind(Y,$fot(implies(not(not(X_43507)),X_43507)))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X_13399,implies(X_13399,X_13398)))
| ~ is_a_theorem(implies(implies(X_13399,implies(X_13399,X_13398)),implies(X_13399,X_13398)))
| is_a_theorem(implies(X_13399,X_13398)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_13399,implies(X_13399,X_13398)))),bind(Y,$fot(implies(X_13399,X_13398)))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X_6082,X_6083),implies(implies(X_6081,X_6083),X_6084)))
| ~ is_a_theorem(implies(implies(implies(X_6082,X_6083),implies(implies(X_6081,X_6083),X_6084)),implies(X_6083,X_6084)))
| is_a_theorem(implies(X_6083,X_6084)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_6082,X_6083),implies(implies(X_6081,X_6083),X_6084)))),bind(Y,$fot(implies(X_6083,X_6084)))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(X,X_6070),X_6071),implies(X_6070,X_6071))),
inference(subst,[],[cn_19:[bind(Y,$fot(X_6070)),bind(Z,$fot(X_6071))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(X_204,implies(X_202,X_203)))
| ~ is_a_theorem(implies(implies(X_204,implies(X_202,X_203)),implies(implies(implies(X_201,X_202),X_204),implies(X_202,X_203))))
| is_a_theorem(implies(implies(implies(X_201,X_202),X_204),implies(X_202,X_203))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_204,implies(X_202,X_203)))),bind(Y,$fot(implies(implies(implies(X_201,X_202),X_204),implies(X_202,X_203))))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(X,Y),X_38),implies(Y,X_38))),
inference(subst,[],[cn_19:[bind(Z,$fot(X_38))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| ~ is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z)))
| is_a_theorem(implies(not(X),Z)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Z))),bind(Y,$fot(implies(not(X),Z)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| is_a_theorem(implies(not(X),Z)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))) )],[cn_37,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_38),implies(Y,X_38)))
| is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_38))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_38)),bind(Z,$fot(implies(Y,X_38)))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_38))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_38),implies(Y,X_38))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z))))
| ~ is_a_theorem(implies(not(X),Z))
| is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),Z))),bind(Y,$fot(implies(implies(Y,Z),implies(implies(X,Y),Z))))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(not(X),Z))
| is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))) )],[cn_59,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_38)))
| is_a_theorem(implies(implies(X_72,implies(Y,X_38)),implies(implies(implies(X,Y),X_72),implies(Y,X_38)))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_72)),bind(Z,$fot(implies(Y,X_38)))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(X_72,implies(Y,X_38)),implies(implies(implies(X,Y),X_72),implies(Y,X_38)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_38))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(X_204,implies(X_202,X_203)),implies(implies(implies(X_201,X_202),X_204),implies(X_202,X_203)))),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_201)),bind(Y,$fot(X_202)),bind(X_38,$fot(X_203)),bind(X_72,$fot(X_204))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(X_204,implies(X_202,X_203)))
| is_a_theorem(implies(implies(implies(X_201,X_202),X_204),implies(X_202,X_203))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_204,implies(X_202,X_203)),implies(implies(implies(X_201,X_202),X_204),implies(X_202,X_203)))) )],[refute_0_15,refute_0_5]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(implies(X,X_6070),X_6071),implies(X_6070,X_6071)))
| is_a_theorem(implies(implies(implies(X_6069,X_6070),implies(implies(X,X_6070),X_6071)),implies(X_6070,X_6071))) ),
inference(subst,[],[refute_0_16:[bind(X_201,$fot(X_6069)),bind(X_202,$fot(X_6070)),bind(X_203,$fot(X_6071)),bind(X_204,$fot(implies(implies(X,X_6070),X_6071)))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(implies(X_6069,X_6070),implies(implies(X,X_6070),X_6071)),implies(X_6070,X_6071))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,X_6070),X_6071),implies(X_6070,X_6071))) )],[refute_0_4,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(X_6082,X_6083),implies(implies(X_6081,X_6083),X_6084)),implies(X_6083,X_6084))),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_6081)),bind(X_6069,$fot(X_6082)),bind(X_6070,$fot(X_6083)),bind(X_6071,$fot(X_6084))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(X_6082,X_6083),implies(implies(X_6081,X_6083),X_6084)))
| is_a_theorem(implies(X_6083,X_6084)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_6082,X_6083),implies(implies(X_6081,X_6083),X_6084)),implies(X_6083,X_6084))) )],[refute_0_19,refute_0_3]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(X_13397,implies(X_13397,implies(X_13397,X_13396))),implies(implies(X_6081,implies(X_13397,implies(X_13397,X_13396))),implies(X_13397,X_13396))))
| is_a_theorem(implies(implies(X_13397,implies(X_13397,X_13396)),implies(X_13397,X_13396))) ),
inference(subst,[],[refute_0_20:[bind(X_6082,$fot(X_13397)),bind(X_6083,$fot(implies(X_13397,implies(X_13397,X_13396)))),bind(X_6084,$fot(implies(X_13397,X_13396)))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(X_85,implies(X_82,implies(X_84,X_83))))
| ~ is_a_theorem(implies(implies(X_85,implies(X_82,implies(X_84,X_83))),implies(implies(X_84,X_85),implies(X_82,implies(X_84,X_83)))))
| is_a_theorem(implies(implies(X_84,X_85),implies(X_82,implies(X_84,X_83)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_85,implies(X_82,implies(X_84,X_83))))),bind(Y,$fot(implies(implies(X_84,X_85),implies(X_82,implies(X_84,X_83)))))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(X,Y),X_12),implies(Y,X_12))),
inference(subst,[],[cn_19:[bind(Z,$fot(X_12))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| ~ is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z)))
| is_a_theorem(implies(Y,Z)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Z))),bind(Y,$fot(implies(Y,Z)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| is_a_theorem(implies(Y,Z)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))) )],[cn_19,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_12),implies(Y,X_12)))
| is_a_theorem(implies(X_12,implies(Y,X_12))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_12)),bind(Z,$fot(implies(Y,X_12)))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(X_12,implies(Y,X_12))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_12),implies(Y,X_12))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(X_37,X_38),implies(Y,implies(X_37,X_38)))),
inference(subst,[],[refute_0_27:[bind(X_12,$fot(implies(X_37,X_38)))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(X_37,X_38),implies(Y,implies(X_37,X_38))))
| is_a_theorem(implies(not(X_37),implies(Y,implies(X_37,X_38)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(implies(Y,implies(X_37,X_38))))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(not(X_37),implies(Y,implies(X_37,X_38)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_37,X_38),implies(Y,implies(X_37,X_38)))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(not(X_71),implies(Y,implies(X_71,X_38)))),
inference(subst,[],[refute_0_30:[bind(X_37,$fot(X_71))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(not(X_71),implies(Y,implies(X_71,X_38))))
| is_a_theorem(implies(implies(X_72,implies(Y,implies(X_71,X_38))),implies(implies(X_71,X_72),implies(Y,implies(X_71,X_38))))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_71)),bind(Y,$fot(X_72)),bind(Z,$fot(implies(Y,implies(X_71,X_38))))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(X_72,implies(Y,implies(X_71,X_38))),implies(implies(X_71,X_72),implies(Y,implies(X_71,X_38))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_71),implies(Y,implies(X_71,X_38)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(X_85,implies(X_82,implies(X_84,X_83))),implies(implies(X_84,X_85),implies(X_82,implies(X_84,X_83))))),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_82)),bind(X_38,$fot(X_83)),bind(X_71,$fot(X_84)),bind(X_72,$fot(X_85))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(X_85,implies(X_82,implies(X_84,X_83))))
| is_a_theorem(implies(implies(X_84,X_85),implies(X_82,implies(X_84,X_83)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_85,implies(X_82,implies(X_84,X_83))),implies(implies(X_84,X_85),implies(X_82,implies(X_84,X_83))))) )],[refute_0_34,refute_0_22]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(X_13390,implies(X_13390,X_13389)),implies(X_13388,implies(X_13390,X_13389))))
| is_a_theorem(implies(implies(X_13390,implies(X_13390,implies(X_13390,X_13389))),implies(X_13388,implies(X_13390,X_13389)))) ),
inference(subst,[],[refute_0_35:[bind(X_82,$fot(X_13388)),bind(X_83,$fot(X_13389)),bind(X_84,$fot(X_13390)),bind(X_85,$fot(implies(X_13390,implies(X_13390,X_13389))))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(X_13341,X_13340),implies(X_13339,implies(X_13341,X_13340)))),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_13339)),bind(X_12,$fot(implies(X_13341,X_13340)))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(X_13341,X_13340),implies(X_13339,implies(X_13341,X_13340))))
| is_a_theorem(implies(implies(X_13341,implies(X_13341,X_13340)),implies(X_13339,implies(X_13341,X_13340)))) ),
inference(subst,[],[refute_0_35:[bind(X_82,$fot(X_13339)),bind(X_83,$fot(X_13340)),bind(X_84,$fot(X_13341)),bind(X_85,$fot(implies(X_13341,X_13340)))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(X_13341,implies(X_13341,X_13340)),implies(X_13339,implies(X_13341,X_13340)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13341,X_13340),implies(X_13339,implies(X_13341,X_13340)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(X_13390,implies(X_13390,X_13389)),implies(X_13388,implies(X_13390,X_13389)))),
inference(subst,[],[refute_0_39:[bind(X_13339,$fot(X_13388)),bind(X_13340,$fot(X_13389)),bind(X_13341,$fot(X_13390))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(X_13390,implies(X_13390,implies(X_13390,X_13389))),implies(X_13388,implies(X_13390,X_13389)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13390,implies(X_13390,X_13389)),implies(X_13388,implies(X_13390,X_13389)))) )],[refute_0_40,refute_0_36]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(X_13397,implies(X_13397,implies(X_13397,X_13396))),implies(implies(X_6081,implies(X_13397,implies(X_13397,X_13396))),implies(X_13397,X_13396)))),
inference(subst,[],[refute_0_41:[bind(X_13388,$fot(implies(X_6081,implies(X_13397,implies(X_13397,X_13396))))),bind(X_13389,$fot(X_13396)),bind(X_13390,$fot(X_13397))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_13397,implies(X_13397,X_13396)),implies(X_13397,X_13396))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13397,implies(X_13397,implies(X_13397,X_13396))),implies(implies(X_6081,implies(X_13397,implies(X_13397,X_13396))),implies(X_13397,X_13396)))) )],[refute_0_42,refute_0_21]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(X_13399,implies(X_13399,X_13398)),implies(X_13399,X_13398))),
inference(subst,[],[refute_0_43:[bind(X_13396,$fot(X_13398)),bind(X_13397,$fot(X_13399))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(X_13399,implies(X_13399,X_13398)))
| is_a_theorem(implies(X_13399,X_13398)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13399,implies(X_13399,X_13398)),implies(X_13399,X_13398))) )],[refute_0_44,refute_0_2]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(not(not(X_43504)),X_43504))))
| is_a_theorem(implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(not(not(X_43504)),X_43504))) ),
inference(subst,[],[refute_0_45:[bind(X_13398,$fot(implies(not(not(X_43504)),X_43504))),bind(X_13399,$fot(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504))))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(not(not(X_53)),implies(implies(X_54,X_55),implies(implies(X_53,X_54),X_55))))
| ~ is_a_theorem(not(not(X_53)))
| is_a_theorem(implies(implies(X_54,X_55),implies(implies(X_53,X_54),X_55))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(not(not(X_53)))),bind(Y,$fot(implies(implies(X_54,X_55),implies(implies(X_53,X_54),X_55))))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(not(X),X_38),implies(implies(Y,X_38),implies(implies(X,Y),X_38)))),
inference(subst,[],[cn_59:[bind(Z,$fot(X_38))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(implies(not(X),X_38),implies(implies(Y,X_38),implies(implies(X,Y),X_38))))
| is_a_theorem(implies(not(not(X)),implies(implies(Y,X_38),implies(implies(X,Y),X_38)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(not(X))),bind(Y,$fot(X_38)),bind(Z,$fot(implies(implies(Y,X_38),implies(implies(X,Y),X_38))))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(not(not(X)),implies(implies(Y,X_38),implies(implies(X,Y),X_38)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_38),implies(implies(Y,X_38),implies(implies(X,Y),X_38)))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(not(not(X_53)),implies(implies(X_54,X_55),implies(implies(X_53,X_54),X_55)))),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_53)),bind(Y,$fot(X_54)),bind(X_38,$fot(X_55))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(not(not(X_53)))
| is_a_theorem(implies(implies(X_54,X_55),implies(implies(X_53,X_54),X_55))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_53)),implies(implies(X_54,X_55),implies(implies(X_53,X_54),X_55)))) )],[refute_0_51,refute_0_47]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(not(not(implies(not(not(X_43095)),X_43095))))
| is_a_theorem(implies(implies(X_54,X_55),implies(implies(implies(not(not(X_43095)),X_43095),X_54),X_55))) ),
inference(subst,[],[refute_0_52:[bind(X_53,$fot(implies(not(not(X_43095)),X_43095)))]]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(implies(not(X_15236),X_15236),not(not(X_15236))))
| ~ is_a_theorem(implies(not(X_15236),X_15236))
| is_a_theorem(not(not(X_15236))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_15236),X_15236))),bind(Y,$fot(not(not(X_15236))))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(X_880,implies(implies(X_878,X_879),not(X_880))))
| ~ is_a_theorem(implies(implies(X_880,implies(implies(X_878,X_879),not(X_880))),implies(X_879,not(X_880))))
| is_a_theorem(implies(X_879,not(X_880))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_880,implies(implies(X_878,X_879),not(X_880))))),bind(Y,$fot(implies(X_879,not(X_880))))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(implies(X,X_873),not(X_874)),implies(X_873,not(X_874)))),
inference(subst,[],[cn_19:[bind(Y,$fot(X_873)),bind(Z,$fot(not(X_874)))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(X_112,implies(X_110,not(X_111))))
| ~ is_a_theorem(implies(implies(X_112,implies(X_110,not(X_111))),implies(implies(X_111,X_112),implies(X_110,not(X_111)))))
| is_a_theorem(implies(implies(X_111,X_112),implies(X_110,not(X_111)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_112,implies(X_110,not(X_111))))),bind(Y,$fot(implies(implies(X_111,X_112),implies(X_110,not(X_111)))))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(not(X_71),implies(Y,not(X_71)))),
inference(subst,[],[refute_0_27:[bind(X_12,$fot(not(X_71)))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(not(X_71),implies(Y,not(X_71))))
| is_a_theorem(implies(implies(X_72,implies(Y,not(X_71))),implies(implies(X_71,X_72),implies(Y,not(X_71))))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_71)),bind(Y,$fot(X_72)),bind(Z,$fot(implies(Y,not(X_71))))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(X_72,implies(Y,not(X_71))),implies(implies(X_71,X_72),implies(Y,not(X_71))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_71),implies(Y,not(X_71)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(X_112,implies(X_110,not(X_111))),implies(implies(X_111,X_112),implies(X_110,not(X_111))))),
inference(subst,[],[refute_0_60:[bind(Y,$fot(X_110)),bind(X_71,$fot(X_111)),bind(X_72,$fot(X_112))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(X_112,implies(X_110,not(X_111))))
| is_a_theorem(implies(implies(X_111,X_112),implies(X_110,not(X_111)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_112,implies(X_110,not(X_111))),implies(implies(X_111,X_112),implies(X_110,not(X_111))))) )],[refute_0_61,refute_0_57]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(implies(X,X_873),not(X_874)),implies(X_873,not(X_874))))
| is_a_theorem(implies(implies(X_874,implies(implies(X,X_873),not(X_874))),implies(X_873,not(X_874)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(X_873)),bind(X_111,$fot(X_874)),bind(X_112,$fot(implies(implies(X,X_873),not(X_874))))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(X_874,implies(implies(X,X_873),not(X_874))),implies(X_873,not(X_874)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,X_873),not(X_874)),implies(X_873,not(X_874)))) )],[refute_0_56,refute_0_63]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(X_880,implies(implies(X_878,X_879),not(X_880))),implies(X_879,not(X_880)))),
inference(subst,[],[refute_0_64:[bind(X,$fot(X_878)),bind(X_873,$fot(X_879)),bind(X_874,$fot(X_880))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(X_880,implies(implies(X_878,X_879),not(X_880))))
| is_a_theorem(implies(X_879,not(X_880))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_880,implies(implies(X_878,X_879),not(X_880))),implies(X_879,not(X_880)))) )],[refute_0_65,refute_0_55]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(not(X_15234),implies(implies(not(X_15234),implies(not(X_15234),X_15234)),not(not(X_15234)))))
| is_a_theorem(implies(implies(not(X_15234),X_15234),not(not(X_15234)))) ),
inference(subst,[],[refute_0_66:[bind(X_878,$fot(not(X_15234))),bind(X_879,$fot(implies(not(X_15234),X_15234))),bind(X_880,$fot(not(X_15234)))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(X_13960,implies(implies(X_13961,X_13958),X_13959)))
| ~ is_a_theorem(implies(implies(X_13960,implies(implies(X_13961,X_13958),X_13959)),implies(X_13958,implies(X_13960,X_13959))))
| is_a_theorem(implies(X_13958,implies(X_13960,X_13959))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_13960,implies(implies(X_13961,X_13958),X_13959)))),bind(Y,$fot(implies(X_13958,implies(X_13960,X_13959))))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(X_16,implies(X,Y))))
| is_a_theorem(implies(Y,implies(X_16,implies(X,Y)))) ),
inference(subst,[],[refute_0_25:[bind(Z,$fot(implies(X_16,implies(X,Y))))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(X,Y),implies(X_16,implies(X,Y)))),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_16)),bind(X_12,$fot(implies(X,Y)))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(Y,implies(X_16,implies(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(X_16,implies(X,Y)))) )],[refute_0_70,refute_0_69]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(X_6072,implies(X_6070,implies(X,X_6072)))),
inference(subst,[],[refute_0_71:[bind(Y,$fot(X_6072)),bind(X_16,$fot(X_6070))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(X_6072,implies(X_6070,implies(X,X_6072))))
| is_a_theorem(implies(implies(implies(X_6069,X_6070),X_6072),implies(X_6070,implies(X,X_6072)))) ),
inference(subst,[],[refute_0_16:[bind(X_201,$fot(X_6069)),bind(X_202,$fot(X_6070)),bind(X_203,$fot(implies(X,X_6072))),bind(X_204,$fot(X_6072))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(implies(X_6069,X_6070),X_6072),implies(X_6070,implies(X,X_6072)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_6072,implies(X_6070,implies(X,X_6072)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(implies(X_6069,X_13339),X_13340),implies(X_13339,implies(X_13341,X_13340)))),
inference(subst,[],[refute_0_74:[bind(X,$fot(X_13341)),bind(X_6070,$fot(X_13339)),bind(X_6072,$fot(X_13340))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(implies(X_6069,X_13339),X_13340),implies(X_13339,implies(X_13341,X_13340))))
| is_a_theorem(implies(implies(X_13341,implies(implies(X_6069,X_13339),X_13340)),implies(X_13339,implies(X_13341,X_13340)))) ),
inference(subst,[],[refute_0_35:[bind(X_82,$fot(X_13339)),bind(X_83,$fot(X_13340)),bind(X_84,$fot(X_13341)),bind(X_85,$fot(implies(implies(X_6069,X_13339),X_13340)))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(X_13341,implies(implies(X_6069,X_13339),X_13340)),implies(X_13339,implies(X_13341,X_13340)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_6069,X_13339),X_13340),implies(X_13339,implies(X_13341,X_13340)))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(X_13960,implies(implies(X_13961,X_13958),X_13959)),implies(X_13958,implies(X_13960,X_13959)))),
inference(subst,[],[refute_0_77:[bind(X_13339,$fot(X_13958)),bind(X_13340,$fot(X_13959)),bind(X_13341,$fot(X_13960)),bind(X_6069,$fot(X_13961))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(X_13960,implies(implies(X_13961,X_13958),X_13959)))
| is_a_theorem(implies(X_13958,implies(X_13960,X_13959))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13960,implies(implies(X_13961,X_13958),X_13959)),implies(X_13958,implies(X_13960,X_13959)))) )],[refute_0_78,refute_0_68]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(implies(X_15233,implies(X_15233,X_15232)),implies(implies(X_15233,not(X_15232)),not(X_15233))))
| is_a_theorem(implies(not(X_15232),implies(implies(X_15233,implies(X_15233,X_15232)),not(X_15233)))) ),
inference(subst,[],[refute_0_79:[bind(X_13958,$fot(not(X_15232))),bind(X_13959,$fot(not(X_15233))),bind(X_13960,$fot(implies(X_15233,implies(X_15233,X_15232)))),bind(X_13961,$fot(X_15233))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(X_15082,X_15081),implies(implies(X_15082,not(X_15081)),not(X_15082))))
| is_a_theorem(implies(implies(X_15082,implies(X_15082,X_15081)),implies(implies(X_15082,not(X_15081)),not(X_15082)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(implies(X_15082,not(X_15081)))),bind(X_111,$fot(X_15082)),bind(X_112,$fot(implies(X_15082,X_15081)))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(X_15035,implies(implies(X_15036,not(X_15035)),not(X_15036))))
| is_a_theorem(implies(implies(X_15036,X_15035),implies(implies(X_15036,not(X_15035)),not(X_15036)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(implies(X_15036,not(X_15035)))),bind(X_111,$fot(X_15036)),bind(X_112,$fot(X_15035))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(not(X_3609),implies(implies(implies(X_3610,X_3611),X_3609),not(X_3611))))
| is_a_theorem(implies(implies(X_3611,not(X_3609)),implies(implies(implies(X_3610,X_3611),X_3609),not(X_3611)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(implies(implies(X_3610,X_3611),X_3609))),bind(X_111,$fot(X_3611)),bind(X_112,$fot(not(X_3609)))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(X_3606,not(X_3608)),implies(implies(implies(X_3607,X_3608),X_3606),not(X_3608))))
| is_a_theorem(implies(not(X_3606),implies(implies(implies(X_3607,X_3608),X_3606),not(X_3608)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_3606)),bind(Y,$fot(not(X_3608))),bind(Z,$fot(implies(implies(implies(X_3607,X_3608),X_3606),not(X_3608))))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(not(implies(X_3377,X_3378)),not(X_3378)))
| is_a_theorem(implies(implies(Y,not(X_3378)),implies(implies(implies(X_3377,X_3378),Y),not(X_3378)))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(implies(X_3377,X_3378))),bind(Z,$fot(not(X_3378)))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(X_625,not(implies(X_624,X_623))))
| ~ is_a_theorem(implies(implies(X_625,not(implies(X_624,X_623))),implies(not(X_624),not(X_625))))
| is_a_theorem(implies(not(X_624),not(X_625))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_625,not(implies(X_624,X_623))))),bind(Y,$fot(implies(not(X_624),not(X_625))))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(implies(implies(X,Y),X_38),implies(not(X),X_38))),
inference(subst,[],[cn_37:[bind(Z,$fot(X_38))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_38),implies(not(X),X_38)))
| is_a_theorem(implies(not(implies(X,Y)),implies(not(X),X_38))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_38)),bind(Z,$fot(implies(not(X),X_38)))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(not(implies(X,Y)),implies(not(X),X_38))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_38),implies(not(X),X_38))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(not(implies(X_618,Y)),implies(not(X_618),not(X_619)))),
inference(subst,[],[refute_0_89:[bind(X,$fot(X_618)),bind(X_38,$fot(not(X_619)))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(X_88,implies(not(X_86),not(X_87))))
| ~ is_a_theorem(implies(implies(X_88,implies(not(X_86),not(X_87))),implies(implies(X_87,X_88),implies(not(X_86),not(X_87)))))
| is_a_theorem(implies(implies(X_87,X_88),implies(not(X_86),not(X_87)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_88,implies(not(X_86),not(X_87))))),bind(Y,$fot(implies(implies(X_87,X_88),implies(not(X_86),not(X_87)))))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(implies(X,Y),X_12),implies(not(X),X_12))),
inference(subst,[],[cn_37:[bind(Z,$fot(X_12))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_12),implies(not(X),X_12)))
| is_a_theorem(implies(X_12,implies(not(X),X_12))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_12)),bind(Z,$fot(implies(not(X),X_12)))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(X_12,implies(not(X),X_12))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_12),implies(not(X),X_12))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(not(X_71),implies(not(X),not(X_71)))),
inference(subst,[],[refute_0_94:[bind(X_12,$fot(not(X_71)))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(not(X_71),implies(not(X),not(X_71))))
| is_a_theorem(implies(implies(X_72,implies(not(X),not(X_71))),implies(implies(X_71,X_72),implies(not(X),not(X_71))))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_71)),bind(Y,$fot(X_72)),bind(Z,$fot(implies(not(X),not(X_71))))]]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(X_72,implies(not(X),not(X_71))),implies(implies(X_71,X_72),implies(not(X),not(X_71))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_71),implies(not(X),not(X_71)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(X_88,implies(not(X_86),not(X_87))),implies(implies(X_87,X_88),implies(not(X_86),not(X_87))))),
inference(subst,[],[refute_0_97:[bind(X,$fot(X_86)),bind(X_71,$fot(X_87)),bind(X_72,$fot(X_88))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(X_88,implies(not(X_86),not(X_87))))
| is_a_theorem(implies(implies(X_87,X_88),implies(not(X_86),not(X_87)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_88,implies(not(X_86),not(X_87))),implies(implies(X_87,X_88),implies(not(X_86),not(X_87))))) )],[refute_0_98,refute_0_91]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(not(implies(X_618,Y)),implies(not(X_618),not(X_619))))
| is_a_theorem(implies(implies(X_619,not(implies(X_618,Y))),implies(not(X_618),not(X_619)))) ),
inference(subst,[],[refute_0_99:[bind(X_86,$fot(X_618)),bind(X_87,$fot(X_619)),bind(X_88,$fot(not(implies(X_618,Y))))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(X_619,not(implies(X_618,Y))),implies(not(X_618),not(X_619)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_618,Y)),implies(not(X_618),not(X_619)))) )],[refute_0_90,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(implies(X_625,not(implies(X_624,X_623))),implies(not(X_624),not(X_625)))),
inference(subst,[],[refute_0_101:[bind(Y,$fot(X_623)),bind(X_618,$fot(X_624)),bind(X_619,$fot(X_625))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(X_625,not(implies(X_624,X_623))))
| is_a_theorem(implies(not(X_624),not(X_625))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_625,not(implies(X_624,X_623))),implies(not(X_624),not(X_625)))) )],[refute_0_102,refute_0_86]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(X_3376,not(implies(implies(X_3375,X_3376),not(implies(X_3374,implies(X_3373,X_3374)))))))
| is_a_theorem(implies(not(implies(X_3375,X_3376)),not(X_3376))) ),
inference(subst,[],[refute_0_103:[bind(X_623,$fot(not(implies(X_3374,implies(X_3373,X_3374))))),bind(X_624,$fot(implies(X_3375,X_3376))),bind(X_625,$fot(X_3376))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(not(X_115),implies(implies(X_114,X_115),implies(X_113,not(X_114)))))
| ~ is_a_theorem(not(X_115))
| is_a_theorem(implies(implies(X_114,X_115),implies(X_113,not(X_114)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(not(X_115))),bind(Y,$fot(implies(implies(X_114,X_115),implies(X_113,not(X_114)))))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(implies(X_112,implies(X_110,not(X_111))),implies(implies(X_111,X_112),implies(X_110,not(X_111)))))
| is_a_theorem(implies(not(X_112),implies(implies(X_111,X_112),implies(X_110,not(X_111))))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_112)),bind(Y,$fot(implies(X_110,not(X_111)))),bind(Z,$fot(implies(implies(X_111,X_112),implies(X_110,not(X_111)))))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(not(X_112),implies(implies(X_111,X_112),implies(X_110,not(X_111))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_112,implies(X_110,not(X_111))),implies(implies(X_111,X_112),implies(X_110,not(X_111))))) )],[refute_0_61,refute_0_106]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(not(X_115),implies(implies(X_114,X_115),implies(X_113,not(X_114))))),
inference(subst,[],[refute_0_107:[bind(X_110,$fot(X_113)),bind(X_111,$fot(X_114)),bind(X_112,$fot(X_115))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(not(X_115))
| is_a_theorem(implies(implies(X_114,X_115),implies(X_113,not(X_114)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_115),implies(implies(X_114,X_115),implies(X_113,not(X_114))))) )],[refute_0_108,refute_0_105]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(not(not(implies(X_1134,implies(X_1133,X_1134)))))
| is_a_theorem(implies(implies(X_114,not(implies(X_1134,implies(X_1133,X_1134)))),implies(X_113,not(X_114)))) ),
inference(subst,[],[refute_0_109:[bind(X_115,$fot(not(implies(X_1134,implies(X_1133,X_1134)))))]]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(X_1118)
| ~ is_a_theorem(implies(X_1118,not(not(X_1118))))
| is_a_theorem(not(not(X_1118))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1118)),bind(Y,$fot(not(not(X_1118))))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(implies(implies(X_1041,not(not(X_1043))),implies(implies(implies(X_1042,not(X_1043)),X_1041),not(not(X_1043)))))
| is_a_theorem(implies(not(X_1041),implies(implies(implies(X_1042,not(X_1043)),X_1041),not(not(X_1043))))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_1041)),bind(Y,$fot(not(not(X_1043)))),bind(Z,$fot(implies(implies(implies(X_1042,not(X_1043)),X_1041),not(not(X_1043)))))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(not(implies(X_886,not(X_887))),not(not(X_887))))
| is_a_theorem(implies(implies(Y,not(not(X_887))),implies(implies(implies(X_886,not(X_887)),Y),not(not(X_887))))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(implies(X_886,not(X_887)))),bind(Z,$fot(not(not(X_887))))]]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(X_636,not(implies(X_634,not(X_635)))))
| ~ is_a_theorem(implies(implies(X_636,not(implies(X_634,not(X_635)))),implies(not(X_635),not(X_636))))
| is_a_theorem(implies(not(X_635),not(X_636))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_636,not(implies(X_634,not(X_635)))))),bind(Y,$fot(implies(not(X_635),not(X_636))))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(not(implies(X,not(X_618))),implies(not(X_618),not(X_619)))),
inference(subst,[],[refute_0_10:[bind(Y,$fot(not(X_618))),bind(X_38,$fot(not(X_619)))]]) ).
cnf(refute_0_116,plain,
( ~ is_a_theorem(implies(not(implies(X,not(X_618))),implies(not(X_618),not(X_619))))
| is_a_theorem(implies(implies(X_619,not(implies(X,not(X_618)))),implies(not(X_618),not(X_619)))) ),
inference(subst,[],[refute_0_99:[bind(X_86,$fot(X_618)),bind(X_87,$fot(X_619)),bind(X_88,$fot(not(implies(X,not(X_618)))))]]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(X_619,not(implies(X,not(X_618)))),implies(not(X_618),not(X_619)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,not(X_618))),implies(not(X_618),not(X_619)))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(X_636,not(implies(X_634,not(X_635)))),implies(not(X_635),not(X_636)))),
inference(subst,[],[refute_0_117:[bind(X,$fot(X_634)),bind(X_618,$fot(X_635)),bind(X_619,$fot(X_636))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(X_636,not(implies(X_634,not(X_635)))))
| is_a_theorem(implies(not(X_635),not(X_636))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_636,not(implies(X_634,not(X_635)))),implies(not(X_635),not(X_636)))) )],[refute_0_118,refute_0_114]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(not(X_885),not(implies(implies(X_884,not(X_885)),not(implies(X_884,not(X_885)))))))
| is_a_theorem(implies(not(implies(X_884,not(X_885))),not(not(X_885)))) ),
inference(subst,[],[refute_0_119:[bind(X_634,$fot(implies(X_884,not(X_885)))),bind(X_635,$fot(implies(X_884,not(X_885)))),bind(X_636,$fot(not(X_885)))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(X_680,implies(X_680,not(implies(X_678,not(X_679))))))
| ~ is_a_theorem(implies(implies(X_680,implies(X_680,not(implies(X_678,not(X_679))))),implies(not(X_679),not(X_680))))
| is_a_theorem(implies(not(X_679),not(X_680))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_680,implies(X_680,not(implies(X_678,not(X_679))))))),bind(Y,$fot(implies(not(X_679),not(X_680))))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(X_636,not(implies(X_634,not(X_635)))),implies(not(X_635),not(X_636))))
| is_a_theorem(implies(implies(X_636,implies(X_636,not(implies(X_634,not(X_635))))),implies(not(X_635),not(X_636)))) ),
inference(subst,[],[refute_0_99:[bind(X_86,$fot(X_635)),bind(X_87,$fot(X_636)),bind(X_88,$fot(implies(X_636,not(implies(X_634,not(X_635))))))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(X_636,implies(X_636,not(implies(X_634,not(X_635))))),implies(not(X_635),not(X_636)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_636,not(implies(X_634,not(X_635)))),implies(not(X_635),not(X_636)))) )],[refute_0_118,refute_0_122]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(X_680,implies(X_680,not(implies(X_678,not(X_679))))),implies(not(X_679),not(X_680)))),
inference(subst,[],[refute_0_123:[bind(X_634,$fot(X_678)),bind(X_635,$fot(X_679)),bind(X_636,$fot(X_680))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(X_680,implies(X_680,not(implies(X_678,not(X_679))))))
| is_a_theorem(implies(not(X_679),not(X_680))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_680,implies(X_680,not(implies(X_678,not(X_679))))),implies(not(X_679),not(X_680)))) )],[refute_0_124,refute_0_121]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(implies(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679)))),implies(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679)))),not(implies(X_678,not(X_679))))))
| is_a_theorem(implies(not(X_679),not(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679))))))) ),
inference(subst,[],[refute_0_125:[bind(X_680,$fot(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679))))))]]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(not(X_874),implies(X_873,not(X_874)))),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_873)),bind(X_12,$fot(not(X_874)))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(not(X_874),implies(X_873,not(X_874))))
| is_a_theorem(implies(implies(X_874,not(X_874)),implies(X_873,not(X_874)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(X_873)),bind(X_111,$fot(X_874)),bind(X_112,$fot(not(X_874)))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_874,not(X_874)),implies(X_873,not(X_874)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_874),implies(X_873,not(X_874)))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679)))),implies(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679)))),not(implies(X_678,not(X_679)))))),
inference(subst,[],[refute_0_129:[bind(X_873,$fot(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679)))))),bind(X_874,$fot(implies(X_678,not(X_679))))]]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(not(X_679),not(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679)))),implies(implies(implies(X_678,not(X_679)),not(implies(X_678,not(X_679)))),not(implies(X_678,not(X_679)))))) )],[refute_0_130,refute_0_126]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(not(X_885),not(implies(implies(X_884,not(X_885)),not(implies(X_884,not(X_885))))))),
inference(subst,[],[refute_0_131:[bind(X_678,$fot(X_884)),bind(X_679,$fot(X_885))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(not(implies(X_884,not(X_885))),not(not(X_885)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_885),not(implies(implies(X_884,not(X_885)),not(implies(X_884,not(X_885))))))) )],[refute_0_132,refute_0_120]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(not(implies(X_886,not(X_887))),not(not(X_887)))),
inference(subst,[],[refute_0_133:[bind(X_884,$fot(X_886)),bind(X_885,$fot(X_887))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(Y,not(not(X_887))),implies(implies(implies(X_886,not(X_887)),Y),not(not(X_887))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_886,not(X_887))),not(not(X_887)))) )],[refute_0_134,refute_0_113]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(implies(X_1041,not(not(X_1043))),implies(implies(implies(X_1042,not(X_1043)),X_1041),not(not(X_1043))))),
inference(subst,[],[refute_0_135:[bind(Y,$fot(X_1041)),bind(X_886,$fot(X_1042)),bind(X_887,$fot(X_1043))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(not(X_1041),implies(implies(implies(X_1042,not(X_1043)),X_1041),not(not(X_1043))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1041,not(not(X_1043))),implies(implies(implies(X_1042,not(X_1043)),X_1041),not(not(X_1043))))) )],[refute_0_136,refute_0_112]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(not(X_1116),implies(implies(implies(X_1042,not(X_1116)),X_1116),not(not(X_1116))))),
inference(subst,[],[refute_0_137:[bind(X_1041,$fot(X_1116)),bind(X_1043,$fot(X_1116))]]) ).
cnf(refute_0_139,plain,
( ~ is_a_theorem(implies(not(X_1116),implies(implies(implies(X_1042,not(X_1116)),X_1116),not(not(X_1116)))))
| is_a_theorem(implies(X_1116,not(not(X_1116)))) ),
inference(subst,[],[refute_0_66:[bind(X_878,$fot(implies(X_1042,not(X_1116)))),bind(X_879,$fot(X_1116)),bind(X_880,$fot(not(X_1116)))]]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(X_1116,not(not(X_1116)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1116),implies(implies(implies(X_1042,not(X_1116)),X_1116),not(not(X_1116))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(X_1118,not(not(X_1118)))),
inference(subst,[],[refute_0_140:[bind(X_1116,$fot(X_1118))]]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(X_1118)
| is_a_theorem(not(not(X_1118))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1118,not(not(X_1118)))) )],[refute_0_141,refute_0_111]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(implies(X_12,implies(Y,X_12)))
| is_a_theorem(not(not(implies(X_12,implies(Y,X_12))))) ),
inference(subst,[],[refute_0_142:[bind(X_1118,$fot(implies(X_12,implies(Y,X_12))))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(not(not(implies(X_12,implies(Y,X_12))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_12,implies(Y,X_12))) )],[refute_0_27,refute_0_143]) ).
cnf(refute_0_145,plain,
is_a_theorem(not(not(implies(X_1134,implies(X_1133,X_1134))))),
inference(subst,[],[refute_0_144:[bind(Y,$fot(X_1133)),bind(X_12,$fot(X_1134))]]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(X_114,not(implies(X_1134,implies(X_1133,X_1134)))),implies(X_113,not(X_114)))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(X_1134,implies(X_1133,X_1134))))) )],[refute_0_145,refute_0_110]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134)))),implies(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134)))),not(implies(X_3370,X_3371))))),
inference(subst,[],[refute_0_146:[bind(X_113,$fot(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134)))))),bind(X_114,$fot(implies(X_3370,X_3371)))]]) ).
cnf(refute_0_148,plain,
( ~ is_a_theorem(implies(X_902,implies(X_902,not(implies(X_900,X_901)))))
| ~ is_a_theorem(implies(implies(X_902,implies(X_902,not(implies(X_900,X_901)))),implies(X_901,not(X_902))))
| is_a_theorem(implies(X_901,not(X_902))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_902,implies(X_902,not(implies(X_900,X_901)))))),bind(Y,$fot(implies(X_901,not(X_902))))]]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(implies(X_883,not(implies(X_881,X_882))),implies(X_882,not(X_883))))
| is_a_theorem(implies(implies(X_883,implies(X_883,not(implies(X_881,X_882)))),implies(X_882,not(X_883)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(X_882)),bind(X_111,$fot(X_883)),bind(X_112,$fot(implies(X_883,not(implies(X_881,X_882)))))]]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(not(implies(X,X_873)),implies(X_873,not(X_874)))),
inference(subst,[],[refute_0_10:[bind(Y,$fot(X_873)),bind(X_38,$fot(not(X_874)))]]) ).
cnf(refute_0_151,plain,
( ~ is_a_theorem(implies(not(implies(X,X_873)),implies(X_873,not(X_874))))
| is_a_theorem(implies(implies(X_874,not(implies(X,X_873))),implies(X_873,not(X_874)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(X_873)),bind(X_111,$fot(X_874)),bind(X_112,$fot(not(implies(X,X_873))))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(implies(implies(X_874,not(implies(X,X_873))),implies(X_873,not(X_874)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,X_873)),implies(X_873,not(X_874)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
is_a_theorem(implies(implies(X_883,not(implies(X_881,X_882))),implies(X_882,not(X_883)))),
inference(subst,[],[refute_0_152:[bind(X,$fot(X_881)),bind(X_873,$fot(X_882)),bind(X_874,$fot(X_883))]]) ).
cnf(refute_0_154,plain,
is_a_theorem(implies(implies(X_883,implies(X_883,not(implies(X_881,X_882)))),implies(X_882,not(X_883)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_883,not(implies(X_881,X_882))),implies(X_882,not(X_883)))) )],[refute_0_153,refute_0_149]) ).
cnf(refute_0_155,plain,
is_a_theorem(implies(implies(X_902,implies(X_902,not(implies(X_900,X_901)))),implies(X_901,not(X_902)))),
inference(subst,[],[refute_0_154:[bind(X_881,$fot(X_900)),bind(X_882,$fot(X_901)),bind(X_883,$fot(X_902))]]) ).
cnf(refute_0_156,plain,
( ~ is_a_theorem(implies(X_902,implies(X_902,not(implies(X_900,X_901)))))
| is_a_theorem(implies(X_901,not(X_902))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_902,implies(X_902,not(implies(X_900,X_901)))),implies(X_901,not(X_902)))) )],[refute_0_155,refute_0_148]) ).
cnf(refute_0_157,plain,
( ~ is_a_theorem(implies(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134)))),implies(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134)))),not(implies(X_3370,X_3371)))))
| is_a_theorem(implies(X_3371,not(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134))))))) ),
inference(subst,[],[refute_0_156:[bind(X_900,$fot(X_3370)),bind(X_901,$fot(X_3371)),bind(X_902,$fot(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134))))))]]) ).
cnf(refute_0_158,plain,
is_a_theorem(implies(X_3371,not(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134)))),implies(implies(implies(X_3370,X_3371),not(implies(X_1134,implies(X_1133,X_1134)))),not(implies(X_3370,X_3371))))) )],[refute_0_147,refute_0_157]) ).
cnf(refute_0_159,plain,
is_a_theorem(implies(X_3376,not(implies(implies(X_3375,X_3376),not(implies(X_3374,implies(X_3373,X_3374))))))),
inference(subst,[],[refute_0_158:[bind(X_1133,$fot(X_3373)),bind(X_1134,$fot(X_3374)),bind(X_3370,$fot(X_3375)),bind(X_3371,$fot(X_3376))]]) ).
cnf(refute_0_160,plain,
is_a_theorem(implies(not(implies(X_3375,X_3376)),not(X_3376))),
inference(resolve,[$cnf( is_a_theorem(implies(X_3376,not(implies(implies(X_3375,X_3376),not(implies(X_3374,implies(X_3373,X_3374))))))) )],[refute_0_159,refute_0_104]) ).
cnf(refute_0_161,plain,
is_a_theorem(implies(not(implies(X_3377,X_3378)),not(X_3378))),
inference(subst,[],[refute_0_160:[bind(X_3375,$fot(X_3377)),bind(X_3376,$fot(X_3378))]]) ).
cnf(refute_0_162,plain,
is_a_theorem(implies(implies(Y,not(X_3378)),implies(implies(implies(X_3377,X_3378),Y),not(X_3378)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_3377,X_3378)),not(X_3378))) )],[refute_0_161,refute_0_85]) ).
cnf(refute_0_163,plain,
is_a_theorem(implies(implies(X_3606,not(X_3608)),implies(implies(implies(X_3607,X_3608),X_3606),not(X_3608)))),
inference(subst,[],[refute_0_162:[bind(Y,$fot(X_3606)),bind(X_3377,$fot(X_3607)),bind(X_3378,$fot(X_3608))]]) ).
cnf(refute_0_164,plain,
is_a_theorem(implies(not(X_3606),implies(implies(implies(X_3607,X_3608),X_3606),not(X_3608)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_3606,not(X_3608)),implies(implies(implies(X_3607,X_3608),X_3606),not(X_3608)))) )],[refute_0_163,refute_0_84]) ).
cnf(refute_0_165,plain,
is_a_theorem(implies(not(X_3609),implies(implies(implies(X_3610,X_3611),X_3609),not(X_3611)))),
inference(subst,[],[refute_0_164:[bind(X_3606,$fot(X_3609)),bind(X_3607,$fot(X_3610)),bind(X_3608,$fot(X_3611))]]) ).
cnf(refute_0_166,plain,
is_a_theorem(implies(implies(X_3611,not(X_3609)),implies(implies(implies(X_3610,X_3611),X_3609),not(X_3611)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_3609),implies(implies(implies(X_3610,X_3611),X_3609),not(X_3611)))) )],[refute_0_165,refute_0_83]) ).
cnf(refute_0_167,plain,
is_a_theorem(implies(implies(X_3611,not(X_15027)),implies(implies(implies(X_3610,X_3611),X_15027),not(X_3611)))),
inference(subst,[],[refute_0_166:[bind(X_3609,$fot(X_15027))]]) ).
cnf(refute_0_168,plain,
( ~ is_a_theorem(implies(implies(X_3611,not(X_15027)),implies(implies(implies(X_3610,X_3611),X_15027),not(X_3611))))
| is_a_theorem(implies(X_15027,implies(implies(X_3611,not(X_15027)),not(X_3611)))) ),
inference(subst,[],[refute_0_79:[bind(X_13958,$fot(X_15027)),bind(X_13959,$fot(not(X_3611))),bind(X_13960,$fot(implies(X_3611,not(X_15027)))),bind(X_13961,$fot(implies(X_3610,X_3611)))]]) ).
cnf(refute_0_169,plain,
is_a_theorem(implies(X_15027,implies(implies(X_3611,not(X_15027)),not(X_3611)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_3611,not(X_15027)),implies(implies(implies(X_3610,X_3611),X_15027),not(X_3611)))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
is_a_theorem(implies(X_15035,implies(implies(X_15036,not(X_15035)),not(X_15036)))),
inference(subst,[],[refute_0_169:[bind(X_15027,$fot(X_15035)),bind(X_3611,$fot(X_15036))]]) ).
cnf(refute_0_171,plain,
is_a_theorem(implies(implies(X_15036,X_15035),implies(implies(X_15036,not(X_15035)),not(X_15036)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_15035,implies(implies(X_15036,not(X_15035)),not(X_15036)))) )],[refute_0_170,refute_0_82]) ).
cnf(refute_0_172,plain,
is_a_theorem(implies(implies(X_15082,X_15081),implies(implies(X_15082,not(X_15081)),not(X_15082)))),
inference(subst,[],[refute_0_171:[bind(X_15035,$fot(X_15081)),bind(X_15036,$fot(X_15082))]]) ).
cnf(refute_0_173,plain,
is_a_theorem(implies(implies(X_15082,implies(X_15082,X_15081)),implies(implies(X_15082,not(X_15081)),not(X_15082)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_15082,X_15081),implies(implies(X_15082,not(X_15081)),not(X_15082)))) )],[refute_0_172,refute_0_81]) ).
cnf(refute_0_174,plain,
is_a_theorem(implies(implies(X_15233,implies(X_15233,X_15232)),implies(implies(X_15233,not(X_15232)),not(X_15233)))),
inference(subst,[],[refute_0_173:[bind(X_15081,$fot(X_15232)),bind(X_15082,$fot(X_15233))]]) ).
cnf(refute_0_175,plain,
is_a_theorem(implies(not(X_15232),implies(implies(X_15233,implies(X_15233,X_15232)),not(X_15233)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_15233,implies(X_15233,X_15232)),implies(implies(X_15233,not(X_15232)),not(X_15233)))) )],[refute_0_174,refute_0_80]) ).
cnf(refute_0_176,plain,
is_a_theorem(implies(not(X_15234),implies(implies(not(X_15234),implies(not(X_15234),X_15234)),not(not(X_15234))))),
inference(subst,[],[refute_0_175:[bind(X_15232,$fot(X_15234)),bind(X_15233,$fot(not(X_15234)))]]) ).
cnf(refute_0_177,plain,
is_a_theorem(implies(implies(not(X_15234),X_15234),not(not(X_15234)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_15234),implies(implies(not(X_15234),implies(not(X_15234),X_15234)),not(not(X_15234))))) )],[refute_0_176,refute_0_67]) ).
cnf(refute_0_178,plain,
is_a_theorem(implies(implies(not(X_15236),X_15236),not(not(X_15236)))),
inference(subst,[],[refute_0_177:[bind(X_15234,$fot(X_15236))]]) ).
cnf(refute_0_179,plain,
( ~ is_a_theorem(implies(not(X_15236),X_15236))
| is_a_theorem(not(not(X_15236))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_15236),X_15236),not(not(X_15236)))) )],[refute_0_178,refute_0_54]) ).
cnf(refute_0_180,plain,
( ~ is_a_theorem(implies(not(implies(not(not(X_43094)),X_43094)),implies(not(not(X_43094)),X_43094)))
| is_a_theorem(not(not(implies(not(not(X_43094)),X_43094)))) ),
inference(subst,[],[refute_0_179:[bind(X_15236,$fot(implies(not(not(X_43094)),X_43094)))]]) ).
cnf(refute_0_181,plain,
( ~ is_a_theorem(implies(implies(implies(X_43091,not(not(X_43091))),not(implies(X_43089,X_43088))),implies(not(not(X_43088)),X_43090)))
| is_a_theorem(implies(not(implies(X_43089,X_43088)),implies(not(not(X_43088)),X_43090))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(implies(X_43091,not(not(X_43091))))),bind(Y,$fot(not(implies(X_43089,X_43088)))),bind(Z,$fot(implies(not(not(X_43088)),X_43090)))]]) ).
cnf(refute_0_182,plain,
( ~ is_a_theorem(implies(implies(not(X_25046),X_25046),not(not(implies(X_25047,X_25046)))))
| is_a_theorem(implies(not(not(X_25046)),not(not(implies(X_25047,X_25046))))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(not(X_25046))),bind(Y,$fot(X_25046)),bind(Z,$fot(not(not(implies(X_25047,X_25046)))))]]) ).
cnf(refute_0_183,plain,
is_a_theorem(implies(not(implies(X_3375,X_24932)),not(X_24932))),
inference(subst,[],[refute_0_160:[bind(X_3376,$fot(X_24932))]]) ).
cnf(refute_0_184,plain,
( ~ is_a_theorem(implies(X_20732,not(X_20733)))
| ~ is_a_theorem(implies(implies(X_20732,not(X_20733)),implies(implies(not(X_20733),X_20733),not(X_20732))))
| is_a_theorem(implies(implies(not(X_20733),X_20733),not(X_20732))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_20732,not(X_20733)))),bind(Y,$fot(implies(implies(not(X_20733),X_20733),not(X_20732))))]]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(implies(not(X_20730),implies(implies(not(X_20730),X_20730),not(X_111))))
| is_a_theorem(implies(implies(X_111,not(X_20730)),implies(implies(not(X_20730),X_20730),not(X_111)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(implies(not(X_20730),X_20730))),bind(X_112,$fot(not(X_20730)))]]) ).
cnf(refute_0_186,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_20720),X_20720),not(X_20720)),implies(implies(not(X_20720),X_20720),X_20721)))
| is_a_theorem(implies(not(X_20720),implies(implies(not(X_20720),X_20720),X_20721))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(implies(not(X_20720),X_20720))),bind(Y,$fot(not(X_20720))),bind(Z,$fot(implies(implies(not(X_20720),X_20720),X_20721)))]]) ).
cnf(refute_0_187,plain,
( ~ is_a_theorem(implies(X_13434,not(X_13435)))
| ~ is_a_theorem(implies(implies(X_13434,not(X_13435)),implies(implies(X_13434,X_13435),implies(X_13434,X_13433))))
| is_a_theorem(implies(implies(X_13434,X_13435),implies(X_13434,X_13433))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_13434,not(X_13435)))),bind(Y,$fot(implies(implies(X_13434,X_13435),implies(X_13434,X_13433))))]]) ).
cnf(refute_0_188,plain,
( ~ is_a_theorem(implies(implies(X_7471,implies(X_7472,X_7473)),implies(implies(X_7472,X_7471),implies(X_7472,X_7473))))
| is_a_theorem(implies(not(X_7471),implies(implies(X_7472,X_7471),implies(X_7472,X_7473)))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_7471)),bind(Y,$fot(implies(X_7472,X_7473))),bind(Z,$fot(implies(implies(X_7472,X_7471),implies(X_7472,X_7473))))]]) ).
cnf(refute_0_189,plain,
( ~ is_a_theorem(implies(not(X_6979),implies(X_6979,X_6980)))
| is_a_theorem(implies(implies(Y,implies(X_6979,X_6980)),implies(implies(X_6979,Y),implies(X_6979,X_6980)))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_6979)),bind(Z,$fot(implies(X_6979,X_6980)))]]) ).
cnf(refute_0_190,plain,
is_a_theorem(implies(not(X_37),implies(X_6070,implies(X_37,X_38)))),
inference(subst,[],[refute_0_30:[bind(Y,$fot(X_6070))]]) ).
cnf(refute_0_191,plain,
( ~ is_a_theorem(implies(not(X_37),implies(X_6070,implies(X_37,X_38))))
| is_a_theorem(implies(implies(implies(X_6069,X_6070),not(X_37)),implies(X_6070,implies(X_37,X_38)))) ),
inference(subst,[],[refute_0_16:[bind(X_201,$fot(X_6069)),bind(X_202,$fot(X_6070)),bind(X_203,$fot(implies(X_37,X_38))),bind(X_204,$fot(not(X_37)))]]) ).
cnf(refute_0_192,plain,
is_a_theorem(implies(implies(implies(X_6069,X_6070),not(X_37)),implies(X_6070,implies(X_37,X_38)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_37),implies(X_6070,implies(X_37,X_38)))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
is_a_theorem(implies(implies(implies(X_6069,implies(X_6962,not(X_37))),not(X_37)),implies(implies(X_6962,not(X_37)),implies(X_37,X_38)))),
inference(subst,[],[refute_0_192:[bind(X_6070,$fot(implies(X_6962,not(X_37))))]]) ).
cnf(refute_0_194,plain,
( ~ is_a_theorem(implies(implies(implies(X_6069,implies(X_6962,not(X_37))),not(X_37)),implies(implies(X_6962,not(X_37)),implies(X_37,X_38))))
| is_a_theorem(implies(not(X_37),implies(X_37,X_38))) ),
inference(subst,[],[refute_0_20:[bind(X_6081,$fot(X_6962)),bind(X_6082,$fot(implies(X_6069,implies(X_6962,not(X_37))))),bind(X_6083,$fot(not(X_37))),bind(X_6084,$fot(implies(X_37,X_38)))]]) ).
cnf(refute_0_195,plain,
is_a_theorem(implies(not(X_37),implies(X_37,X_38))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_6069,implies(X_6962,not(X_37))),not(X_37)),implies(implies(X_6962,not(X_37)),implies(X_37,X_38)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
is_a_theorem(implies(not(X_6979),implies(X_6979,X_6980))),
inference(subst,[],[refute_0_195:[bind(X_37,$fot(X_6979)),bind(X_38,$fot(X_6980))]]) ).
cnf(refute_0_197,plain,
is_a_theorem(implies(implies(Y,implies(X_6979,X_6980)),implies(implies(X_6979,Y),implies(X_6979,X_6980)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_6979),implies(X_6979,X_6980))) )],[refute_0_196,refute_0_189]) ).
cnf(refute_0_198,plain,
is_a_theorem(implies(implies(X_7471,implies(X_7472,X_7473)),implies(implies(X_7472,X_7471),implies(X_7472,X_7473)))),
inference(subst,[],[refute_0_197:[bind(Y,$fot(X_7471)),bind(X_6979,$fot(X_7472)),bind(X_6980,$fot(X_7473))]]) ).
cnf(refute_0_199,plain,
is_a_theorem(implies(not(X_7471),implies(implies(X_7472,X_7471),implies(X_7472,X_7473)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_7471,implies(X_7472,X_7473)),implies(implies(X_7472,X_7471),implies(X_7472,X_7473)))) )],[refute_0_198,refute_0_188]) ).
cnf(refute_0_200,plain,
is_a_theorem(implies(not(X_7471),implies(implies(X_13341,X_7471),implies(X_13341,X_13340)))),
inference(subst,[],[refute_0_199:[bind(X_7472,$fot(X_13341)),bind(X_7473,$fot(X_13340))]]) ).
cnf(refute_0_201,plain,
( ~ is_a_theorem(implies(not(X_7471),implies(implies(X_13341,X_7471),implies(X_13341,X_13340))))
| is_a_theorem(implies(implies(X_13341,not(X_7471)),implies(implies(X_13341,X_7471),implies(X_13341,X_13340)))) ),
inference(subst,[],[refute_0_35:[bind(X_82,$fot(implies(X_13341,X_7471))),bind(X_83,$fot(X_13340)),bind(X_84,$fot(X_13341)),bind(X_85,$fot(not(X_7471)))]]) ).
cnf(refute_0_202,plain,
is_a_theorem(implies(implies(X_13341,not(X_7471)),implies(implies(X_13341,X_7471),implies(X_13341,X_13340)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_7471),implies(implies(X_13341,X_7471),implies(X_13341,X_13340)))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
is_a_theorem(implies(implies(X_13434,not(X_13435)),implies(implies(X_13434,X_13435),implies(X_13434,X_13433)))),
inference(subst,[],[refute_0_202:[bind(X_13340,$fot(X_13433)),bind(X_13341,$fot(X_13434)),bind(X_7471,$fot(X_13435))]]) ).
cnf(refute_0_204,plain,
( ~ is_a_theorem(implies(X_13434,not(X_13435)))
| is_a_theorem(implies(implies(X_13434,X_13435),implies(X_13434,X_13433))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13434,not(X_13435)),implies(implies(X_13434,X_13435),implies(X_13434,X_13433)))) )],[refute_0_203,refute_0_187]) ).
cnf(refute_0_205,plain,
( ~ is_a_theorem(implies(implies(not(X_15234),X_15234),not(not(X_15234))))
| is_a_theorem(implies(implies(implies(not(X_15234),X_15234),not(X_15234)),implies(implies(not(X_15234),X_15234),X_20374))) ),
inference(subst,[],[refute_0_204:[bind(X_13433,$fot(X_20374)),bind(X_13434,$fot(implies(not(X_15234),X_15234))),bind(X_13435,$fot(not(X_15234)))]]) ).
cnf(refute_0_206,plain,
is_a_theorem(implies(implies(implies(not(X_15234),X_15234),not(X_15234)),implies(implies(not(X_15234),X_15234),X_20374))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_15234),X_15234),not(not(X_15234)))) )],[refute_0_177,refute_0_205]) ).
cnf(refute_0_207,plain,
is_a_theorem(implies(implies(implies(not(X_20720),X_20720),not(X_20720)),implies(implies(not(X_20720),X_20720),X_20721))),
inference(subst,[],[refute_0_206:[bind(X_15234,$fot(X_20720)),bind(X_20374,$fot(X_20721))]]) ).
cnf(refute_0_208,plain,
is_a_theorem(implies(not(X_20720),implies(implies(not(X_20720),X_20720),X_20721))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_20720),X_20720),not(X_20720)),implies(implies(not(X_20720),X_20720),X_20721))) )],[refute_0_207,refute_0_186]) ).
cnf(refute_0_209,plain,
is_a_theorem(implies(not(X_20730),implies(implies(not(X_20730),X_20730),not(X_111)))),
inference(subst,[],[refute_0_208:[bind(X_20720,$fot(X_20730)),bind(X_20721,$fot(not(X_111)))]]) ).
cnf(refute_0_210,plain,
is_a_theorem(implies(implies(X_111,not(X_20730)),implies(implies(not(X_20730),X_20730),not(X_111)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_20730),implies(implies(not(X_20730),X_20730),not(X_111)))) )],[refute_0_209,refute_0_185]) ).
cnf(refute_0_211,plain,
is_a_theorem(implies(implies(X_20732,not(X_20733)),implies(implies(not(X_20733),X_20733),not(X_20732)))),
inference(subst,[],[refute_0_210:[bind(X_111,$fot(X_20732)),bind(X_20730,$fot(X_20733))]]) ).
cnf(refute_0_212,plain,
( ~ is_a_theorem(implies(X_20732,not(X_20733)))
| is_a_theorem(implies(implies(not(X_20733),X_20733),not(X_20732))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_20732,not(X_20733)),implies(implies(not(X_20733),X_20733),not(X_20732)))) )],[refute_0_211,refute_0_184]) ).
cnf(refute_0_213,plain,
( ~ is_a_theorem(implies(not(implies(X_3375,X_24932)),not(X_24932)))
| is_a_theorem(implies(implies(not(X_24932),X_24932),not(not(implies(X_3375,X_24932))))) ),
inference(subst,[],[refute_0_212:[bind(X_20732,$fot(not(implies(X_3375,X_24932)))),bind(X_20733,$fot(X_24932))]]) ).
cnf(refute_0_214,plain,
is_a_theorem(implies(implies(not(X_24932),X_24932),not(not(implies(X_3375,X_24932))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_3375,X_24932)),not(X_24932))) )],[refute_0_183,refute_0_213]) ).
cnf(refute_0_215,plain,
is_a_theorem(implies(implies(not(X_25046),X_25046),not(not(implies(X_25047,X_25046))))),
inference(subst,[],[refute_0_214:[bind(X_24932,$fot(X_25046)),bind(X_3375,$fot(X_25047))]]) ).
cnf(refute_0_216,plain,
is_a_theorem(implies(not(not(X_25046)),not(not(implies(X_25047,X_25046))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_25046),X_25046),not(not(implies(X_25047,X_25046))))) )],[refute_0_215,refute_0_182]) ).
cnf(refute_0_217,plain,
( ~ is_a_theorem(implies(X_13401,not(X_13403)))
| ~ is_a_theorem(implies(implies(X_13401,not(X_13403)),implies(implies(implies(X_13402,not(not(X_13402))),X_13403),implies(X_13401,X_13400))))
| is_a_theorem(implies(implies(implies(X_13402,not(not(X_13402))),X_13403),implies(X_13401,X_13400))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_13401,not(X_13403)))),bind(Y,$fot(implies(implies(implies(X_13402,not(not(X_13402))),X_13403),implies(X_13401,X_13400))))]]) ).
cnf(refute_0_218,plain,
( ~ is_a_theorem(implies(implies(X_3963,X_3964),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),X_3964)))
| is_a_theorem(implies(not(X_3963),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),X_3964))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_3963)),bind(Y,$fot(X_3964)),bind(Z,$fot(implies(implies(implies(X_3962,not(not(X_3962))),X_3963),X_3964)))]]) ).
cnf(refute_0_219,plain,
( ~ is_a_theorem(not(not(implies(X_1124,not(not(X_1124))))))
| is_a_theorem(implies(implies(X_54,X_55),implies(implies(implies(X_1124,not(not(X_1124))),X_54),X_55))) ),
inference(subst,[],[refute_0_52:[bind(X_53,$fot(implies(X_1124,not(not(X_1124)))))]]) ).
cnf(refute_0_220,plain,
( ~ is_a_theorem(implies(X_1116,not(not(X_1116))))
| is_a_theorem(not(not(implies(X_1116,not(not(X_1116)))))) ),
inference(subst,[],[refute_0_142:[bind(X_1118,$fot(implies(X_1116,not(not(X_1116)))))]]) ).
cnf(refute_0_221,plain,
is_a_theorem(not(not(implies(X_1116,not(not(X_1116)))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1116,not(not(X_1116)))) )],[refute_0_140,refute_0_220]) ).
cnf(refute_0_222,plain,
is_a_theorem(not(not(implies(X_1124,not(not(X_1124)))))),
inference(subst,[],[refute_0_221:[bind(X_1116,$fot(X_1124))]]) ).
cnf(refute_0_223,plain,
is_a_theorem(implies(implies(X_54,X_55),implies(implies(implies(X_1124,not(not(X_1124))),X_54),X_55))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(X_1124,not(not(X_1124)))))) )],[refute_0_222,refute_0_219]) ).
cnf(refute_0_224,plain,
is_a_theorem(implies(implies(X_3963,X_3964),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),X_3964))),
inference(subst,[],[refute_0_223:[bind(X_1124,$fot(X_3962)),bind(X_54,$fot(X_3963)),bind(X_55,$fot(X_3964))]]) ).
cnf(refute_0_225,plain,
is_a_theorem(implies(not(X_3963),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),X_3964))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_3963,X_3964),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),X_3964))) )],[refute_0_224,refute_0_218]) ).
cnf(refute_0_226,plain,
is_a_theorem(implies(not(X_3963),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),implies(X_13341,X_13340)))),
inference(subst,[],[refute_0_225:[bind(X_3964,$fot(implies(X_13341,X_13340)))]]) ).
cnf(refute_0_227,plain,
( ~ is_a_theorem(implies(not(X_3963),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),implies(X_13341,X_13340))))
| is_a_theorem(implies(implies(X_13341,not(X_3963)),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),implies(X_13341,X_13340)))) ),
inference(subst,[],[refute_0_35:[bind(X_82,$fot(implies(implies(X_3962,not(not(X_3962))),X_3963))),bind(X_83,$fot(X_13340)),bind(X_84,$fot(X_13341)),bind(X_85,$fot(not(X_3963)))]]) ).
cnf(refute_0_228,plain,
is_a_theorem(implies(implies(X_13341,not(X_3963)),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),implies(X_13341,X_13340)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_3963),implies(implies(implies(X_3962,not(not(X_3962))),X_3963),implies(X_13341,X_13340)))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
is_a_theorem(implies(implies(X_13401,not(X_13403)),implies(implies(implies(X_13402,not(not(X_13402))),X_13403),implies(X_13401,X_13400)))),
inference(subst,[],[refute_0_228:[bind(X_13340,$fot(X_13400)),bind(X_13341,$fot(X_13401)),bind(X_3962,$fot(X_13402)),bind(X_3963,$fot(X_13403))]]) ).
cnf(refute_0_230,plain,
( ~ is_a_theorem(implies(X_13401,not(X_13403)))
| is_a_theorem(implies(implies(implies(X_13402,not(not(X_13402))),X_13403),implies(X_13401,X_13400))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_13401,not(X_13403)),implies(implies(implies(X_13402,not(not(X_13402))),X_13403),implies(X_13401,X_13400)))) )],[refute_0_229,refute_0_217]) ).
cnf(refute_0_231,plain,
( ~ is_a_theorem(implies(not(not(X_25046)),not(not(implies(X_25047,X_25046)))))
| is_a_theorem(implies(implies(implies(X_43025,not(not(X_43025))),not(implies(X_25047,X_25046))),implies(not(not(X_25046)),X_43023))) ),
inference(subst,[],[refute_0_230:[bind(X_13400,$fot(X_43023)),bind(X_13401,$fot(not(not(X_25046)))),bind(X_13402,$fot(X_43025)),bind(X_13403,$fot(not(implies(X_25047,X_25046))))]]) ).
cnf(refute_0_232,plain,
is_a_theorem(implies(implies(implies(X_43025,not(not(X_43025))),not(implies(X_25047,X_25046))),implies(not(not(X_25046)),X_43023))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_25046)),not(not(implies(X_25047,X_25046))))) )],[refute_0_216,refute_0_231]) ).
cnf(refute_0_233,plain,
is_a_theorem(implies(implies(implies(X_43091,not(not(X_43091))),not(implies(X_43089,X_43088))),implies(not(not(X_43088)),X_43090))),
inference(subst,[],[refute_0_232:[bind(X_25046,$fot(X_43088)),bind(X_25047,$fot(X_43089)),bind(X_43023,$fot(X_43090)),bind(X_43025,$fot(X_43091))]]) ).
cnf(refute_0_234,plain,
is_a_theorem(implies(not(implies(X_43089,X_43088)),implies(not(not(X_43088)),X_43090))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_43091,not(not(X_43091))),not(implies(X_43089,X_43088))),implies(not(not(X_43088)),X_43090))) )],[refute_0_233,refute_0_181]) ).
cnf(refute_0_235,plain,
is_a_theorem(implies(not(implies(not(not(X_43094)),X_43094)),implies(not(not(X_43094)),X_43094))),
inference(subst,[],[refute_0_234:[bind(X_43088,$fot(X_43094)),bind(X_43089,$fot(not(not(X_43094)))),bind(X_43090,$fot(X_43094))]]) ).
cnf(refute_0_236,plain,
is_a_theorem(not(not(implies(not(not(X_43094)),X_43094)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(not(not(X_43094)),X_43094)),implies(not(not(X_43094)),X_43094))) )],[refute_0_235,refute_0_180]) ).
cnf(refute_0_237,plain,
is_a_theorem(not(not(implies(not(not(X_43095)),X_43095)))),
inference(subst,[],[refute_0_236:[bind(X_43094,$fot(X_43095))]]) ).
cnf(refute_0_238,plain,
is_a_theorem(implies(implies(X_54,X_55),implies(implies(implies(not(not(X_43095)),X_43095),X_54),X_55))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(not(not(X_43095)),X_43095)))) )],[refute_0_237,refute_0_53]) ).
cnf(refute_0_239,plain,
is_a_theorem(implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(not(not(X_43504)),X_43504)))),
inference(subst,[],[refute_0_238:[bind(X_43095,$fot(X_43504)),bind(X_54,$fot(implies(not(not(X_43504)),X_43504))),bind(X_55,$fot(implies(not(not(X_43504)),X_43504)))]]) ).
cnf(refute_0_240,plain,
is_a_theorem(implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(not(not(X_43504)),X_43504))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(implies(implies(not(not(X_43504)),X_43504),implies(not(not(X_43504)),X_43504)),implies(not(not(X_43504)),X_43504)))) )],[refute_0_239,refute_0_46]) ).
cnf(refute_0_241,plain,
is_a_theorem(implies(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507)),implies(not(not(X_43507)),X_43507))),
inference(subst,[],[refute_0_240:[bind(X_43504,$fot(X_43507))]]) ).
cnf(refute_0_242,plain,
( ~ is_a_theorem(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507)))
| is_a_theorem(implies(not(not(X_43507)),X_43507)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507)),implies(not(not(X_43507)),X_43507))) )],[refute_0_241,refute_0_1]) ).
cnf(refute_0_243,plain,
is_a_theorem(implies(implies(implies(X,implies(X_6962,X_6965)),X_6965),implies(implies(X_6962,X_6965),X_6965))),
inference(subst,[],[cn_19:[bind(Y,$fot(implies(X_6962,X_6965))),bind(Z,$fot(X_6965))]]) ).
cnf(refute_0_244,plain,
( ~ is_a_theorem(implies(implies(implies(X,implies(X_6962,X_6965)),X_6965),implies(implies(X_6962,X_6965),X_6965)))
| is_a_theorem(implies(X_6965,X_6965)) ),
inference(subst,[],[refute_0_20:[bind(X_6081,$fot(X_6962)),bind(X_6082,$fot(implies(X,implies(X_6962,X_6965)))),bind(X_6083,$fot(X_6965)),bind(X_6084,$fot(X_6965))]]) ).
cnf(refute_0_245,plain,
is_a_theorem(implies(X_6965,X_6965)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,implies(X_6962,X_6965)),X_6965),implies(implies(X_6962,X_6965),X_6965))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
is_a_theorem(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507))),
inference(subst,[],[refute_0_245:[bind(X_6965,$fot(implies(not(not(X_43507)),X_43507)))]]) ).
cnf(refute_0_247,plain,
is_a_theorem(implies(not(not(X_43507)),X_43507)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_43507)),X_43507),implies(not(not(X_43507)),X_43507))) )],[refute_0_246,refute_0_242]) ).
cnf(refute_0_248,plain,
is_a_theorem(implies(not(not(X_43508)),X_43508)),
inference(subst,[],[refute_0_247:[bind(X_43507,$fot(X_43508))]]) ).
cnf(refute_0_249,plain,
( ~ is_a_theorem(not(not(X_43508)))
| is_a_theorem(X_43508) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_43508)),X_43508)) )],[refute_0_248,refute_0_0]) ).
cnf(refute_0_250,plain,
( ~ is_a_theorem(not(not(implies(implies(not(X_43575),X_43575),X_43575))))
| is_a_theorem(implies(implies(not(X_43575),X_43575),X_43575)) ),
inference(subst,[],[refute_0_249:[bind(X_43508,$fot(implies(implies(not(X_43575),X_43575),X_43575)))]]) ).
cnf(refute_0_251,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X_43574),X_43574),X_43574)),implies(implies(not(X_43574),X_43574),X_43574)))
| is_a_theorem(not(not(implies(implies(not(X_43574),X_43574),X_43574)))) ),
inference(subst,[],[refute_0_179:[bind(X_15236,$fot(implies(implies(not(X_43574),X_43574),X_43574)))]]) ).
cnf(refute_0_252,plain,
( ~ is_a_theorem(implies(implies(X_43567,not(implies(X_43566,X_43567))),implies(implies(not(X_43567),X_43567),X_43568)))
| is_a_theorem(implies(not(implies(X_43566,X_43567)),implies(implies(not(X_43567),X_43567),X_43568))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_43567)),bind(Y,$fot(not(implies(X_43566,X_43567)))),bind(Z,$fot(implies(implies(not(X_43567),X_43567),X_43568)))]]) ).
cnf(refute_0_253,plain,
( ~ is_a_theorem(implies(implies(implies(X_43565,not(not(X_43565))),implies(X_43563,not(implies(X_43562,X_43563)))),implies(implies(not(X_43563),X_43563),X_43564)))
| is_a_theorem(implies(implies(X_43563,not(implies(X_43562,X_43563))),implies(implies(not(X_43563),X_43563),X_43564))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(implies(X_43565,not(not(X_43565))))),bind(Y,$fot(implies(X_43563,not(implies(X_43562,X_43563))))),bind(Z,$fot(implies(implies(not(X_43563),X_43563),X_43564)))]]) ).
cnf(refute_0_254,plain,
( ~ is_a_theorem(implies(X_15528,implies(implies(implies(X_15527,implies(X_15526,X_15528)),implies(X_15528,not(implies(X_15526,X_15528)))),not(X_15528))))
| is_a_theorem(implies(implies(X_15528,not(implies(X_15526,X_15528))),not(X_15528))) ),
inference(subst,[],[refute_0_66:[bind(X_878,$fot(implies(X_15527,implies(X_15526,X_15528)))),bind(X_879,$fot(implies(X_15528,not(implies(X_15526,X_15528))))),bind(X_880,$fot(X_15528))]]) ).
cnf(refute_0_255,plain,
( ~ is_a_theorem(implies(implies(X_6996,not(X_6997)),implies(X_6997,not(X_6996))))
| is_a_theorem(implies(implies(implies(X_201,X_6997),implies(X_6996,not(X_6997))),implies(X_6997,not(X_6996)))) ),
inference(subst,[],[refute_0_16:[bind(X_202,$fot(X_6997)),bind(X_203,$fot(not(X_6996))),bind(X_204,$fot(implies(X_6996,not(X_6997))))]]) ).
cnf(refute_0_256,plain,
( ~ is_a_theorem(implies(not(X_6979),implies(X_6979,not(X_111))))
| is_a_theorem(implies(implies(X_111,not(X_6979)),implies(X_6979,not(X_111)))) ),
inference(subst,[],[refute_0_62:[bind(X_110,$fot(X_6979)),bind(X_112,$fot(not(X_6979)))]]) ).
cnf(refute_0_257,plain,
is_a_theorem(implies(not(X_6979),implies(X_6979,not(X_111)))),
inference(subst,[],[refute_0_195:[bind(X_37,$fot(X_6979)),bind(X_38,$fot(not(X_111)))]]) ).
cnf(refute_0_258,plain,
is_a_theorem(implies(implies(X_111,not(X_6979)),implies(X_6979,not(X_111)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_6979),implies(X_6979,not(X_111)))) )],[refute_0_257,refute_0_256]) ).
cnf(refute_0_259,plain,
is_a_theorem(implies(implies(X_6996,not(X_6997)),implies(X_6997,not(X_6996)))),
inference(subst,[],[refute_0_258:[bind(X_111,$fot(X_6996)),bind(X_6979,$fot(X_6997))]]) ).
cnf(refute_0_260,plain,
is_a_theorem(implies(implies(implies(X_201,X_6997),implies(X_6996,not(X_6997))),implies(X_6997,not(X_6996)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_6996,not(X_6997)),implies(X_6997,not(X_6996)))) )],[refute_0_259,refute_0_255]) ).
cnf(refute_0_261,plain,
is_a_theorem(implies(implies(implies(X_201,implies(X_15030,X_15027)),implies(X_6996,not(implies(X_15030,X_15027)))),implies(implies(X_15030,X_15027),not(X_6996)))),
inference(subst,[],[refute_0_260:[bind(X_6997,$fot(implies(X_15030,X_15027)))]]) ).
cnf(refute_0_262,plain,
( ~ is_a_theorem(implies(implies(implies(X_201,implies(X_15030,X_15027)),implies(X_6996,not(implies(X_15030,X_15027)))),implies(implies(X_15030,X_15027),not(X_6996))))
| is_a_theorem(implies(X_15027,implies(implies(implies(X_201,implies(X_15030,X_15027)),implies(X_6996,not(implies(X_15030,X_15027)))),not(X_6996)))) ),
inference(subst,[],[refute_0_79:[bind(X_13958,$fot(X_15027)),bind(X_13959,$fot(not(X_6996))),bind(X_13960,$fot(implies(implies(X_201,implies(X_15030,X_15027)),implies(X_6996,not(implies(X_15030,X_15027)))))),bind(X_13961,$fot(X_15030))]]) ).
cnf(refute_0_263,plain,
is_a_theorem(implies(X_15027,implies(implies(implies(X_201,implies(X_15030,X_15027)),implies(X_6996,not(implies(X_15030,X_15027)))),not(X_6996)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_201,implies(X_15030,X_15027)),implies(X_6996,not(implies(X_15030,X_15027)))),implies(implies(X_15030,X_15027),not(X_6996)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
is_a_theorem(implies(X_15528,implies(implies(implies(X_15527,implies(X_15526,X_15528)),implies(X_15528,not(implies(X_15526,X_15528)))),not(X_15528)))),
inference(subst,[],[refute_0_263:[bind(X_15027,$fot(X_15528)),bind(X_15030,$fot(X_15526)),bind(X_201,$fot(X_15527)),bind(X_6996,$fot(X_15528))]]) ).
cnf(refute_0_265,plain,
is_a_theorem(implies(implies(X_15528,not(implies(X_15526,X_15528))),not(X_15528))),
inference(resolve,[$cnf( is_a_theorem(implies(X_15528,implies(implies(implies(X_15527,implies(X_15526,X_15528)),implies(X_15528,not(implies(X_15526,X_15528)))),not(X_15528)))) )],[refute_0_264,refute_0_254]) ).
cnf(refute_0_266,plain,
is_a_theorem(implies(implies(X_24932,not(implies(X_15526,X_24932))),not(X_24932))),
inference(subst,[],[refute_0_265:[bind(X_15528,$fot(X_24932))]]) ).
cnf(refute_0_267,plain,
( ~ is_a_theorem(implies(implies(X_24932,not(implies(X_15526,X_24932))),not(X_24932)))
| is_a_theorem(implies(implies(not(X_24932),X_24932),not(implies(X_24932,not(implies(X_15526,X_24932)))))) ),
inference(subst,[],[refute_0_212:[bind(X_20732,$fot(implies(X_24932,not(implies(X_15526,X_24932))))),bind(X_20733,$fot(X_24932))]]) ).
cnf(refute_0_268,plain,
is_a_theorem(implies(implies(not(X_24932),X_24932),not(implies(X_24932,not(implies(X_15526,X_24932)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_24932,not(implies(X_15526,X_24932))),not(X_24932))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
( ~ is_a_theorem(implies(implies(not(X_24932),X_24932),not(implies(X_24932,not(implies(X_15526,X_24932))))))
| is_a_theorem(implies(implies(implies(X_43025,not(not(X_43025))),implies(X_24932,not(implies(X_15526,X_24932)))),implies(implies(not(X_24932),X_24932),X_43023))) ),
inference(subst,[],[refute_0_230:[bind(X_13400,$fot(X_43023)),bind(X_13401,$fot(implies(not(X_24932),X_24932))),bind(X_13402,$fot(X_43025)),bind(X_13403,$fot(implies(X_24932,not(implies(X_15526,X_24932)))))]]) ).
cnf(refute_0_270,plain,
is_a_theorem(implies(implies(implies(X_43025,not(not(X_43025))),implies(X_24932,not(implies(X_15526,X_24932)))),implies(implies(not(X_24932),X_24932),X_43023))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_24932),X_24932),not(implies(X_24932,not(implies(X_15526,X_24932)))))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
is_a_theorem(implies(implies(implies(X_43565,not(not(X_43565))),implies(X_43563,not(implies(X_43562,X_43563)))),implies(implies(not(X_43563),X_43563),X_43564))),
inference(subst,[],[refute_0_270:[bind(X_15526,$fot(X_43562)),bind(X_24932,$fot(X_43563)),bind(X_43023,$fot(X_43564)),bind(X_43025,$fot(X_43565))]]) ).
cnf(refute_0_272,plain,
is_a_theorem(implies(implies(X_43563,not(implies(X_43562,X_43563))),implies(implies(not(X_43563),X_43563),X_43564))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_43565,not(not(X_43565))),implies(X_43563,not(implies(X_43562,X_43563)))),implies(implies(not(X_43563),X_43563),X_43564))) )],[refute_0_271,refute_0_253]) ).
cnf(refute_0_273,plain,
is_a_theorem(implies(implies(X_43567,not(implies(X_43566,X_43567))),implies(implies(not(X_43567),X_43567),X_43568))),
inference(subst,[],[refute_0_272:[bind(X_43562,$fot(X_43566)),bind(X_43563,$fot(X_43567)),bind(X_43564,$fot(X_43568))]]) ).
cnf(refute_0_274,plain,
is_a_theorem(implies(not(implies(X_43566,X_43567)),implies(implies(not(X_43567),X_43567),X_43568))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_43567,not(implies(X_43566,X_43567))),implies(implies(not(X_43567),X_43567),X_43568))) )],[refute_0_273,refute_0_252]) ).
cnf(refute_0_275,plain,
is_a_theorem(implies(not(implies(implies(not(X_43574),X_43574),X_43574)),implies(implies(not(X_43574),X_43574),X_43574))),
inference(subst,[],[refute_0_274:[bind(X_43566,$fot(implies(not(X_43574),X_43574))),bind(X_43567,$fot(X_43574)),bind(X_43568,$fot(X_43574))]]) ).
cnf(refute_0_276,plain,
is_a_theorem(not(not(implies(implies(not(X_43574),X_43574),X_43574)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X_43574),X_43574),X_43574)),implies(implies(not(X_43574),X_43574),X_43574))) )],[refute_0_275,refute_0_251]) ).
cnf(refute_0_277,plain,
is_a_theorem(not(not(implies(implies(not(X_43575),X_43575),X_43575)))),
inference(subst,[],[refute_0_276:[bind(X_43574,$fot(X_43575))]]) ).
cnf(refute_0_278,plain,
is_a_theorem(implies(implies(not(X_43575),X_43575),X_43575)),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(implies(not(X_43575),X_43575),X_43575)))) )],[refute_0_277,refute_0_250]) ).
cnf(refute_0_279,plain,
is_a_theorem(implies(implies(not(a),a),a)),
inference(subst,[],[refute_0_278:[bind(X_43575,$fot(a))]]) ).
cnf(refute_0_280,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(a),a),a)) )],[refute_0_279,prove_cn_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL068-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 17:25:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 57.95/58.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.95/58.12
% 57.95/58.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.95/58.16
%------------------------------------------------------------------------------