TSTP Solution File: LCL072-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL072-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:49:12 EDT 2022
% Result : Unsatisfiable 99.97s 100.18s
% Output : CNFRefutation 99.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 5
% Syntax : Number of clauses : 157 ( 87 unt; 0 nHn; 52 RR)
% Number of literals : 245 ( 0 equ; 89 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 449 ( 85 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_60,axiom,
is_a_theorem(implies(implies(X,implies(not(Y),Z)),implies(X,implies(implies(U,Z),implies(implies(Y,U),Z))))) ).
cnf(prove_cn_3,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))) ).
cnf(refute_0_0,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_1,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| is_a_theorem(implies(Y,Z)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))) )],[cn_19,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(X_67741,not(not(X_67741))))),X_67742),implies(not(X_67742),X_67743)))
| is_a_theorem(implies(X_67742,implies(not(X_67742),X_67743))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(not(implies(X_67741,not(not(X_67741))))))),bind(Y,$fot(X_67742)),bind(Z,$fot(implies(not(X_67742),X_67743)))]]) ).
cnf(refute_0_3,plain,
is_a_theorem(implies(implies(implies(X,X_25238),not(X_25238)),implies(X_25238,not(X_25238)))),
inference(subst,[],[cn_19:[bind(Y,$fot(X_25238)),bind(Z,$fot(not(X_25238)))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(X_15707,X_15708),implies(X_15706,not(X_15706))))
| ~ is_a_theorem(implies(implies(implies(X_15707,X_15708),implies(X_15706,not(X_15706))),implies(X_15708,not(X_15706))))
| is_a_theorem(implies(X_15708,not(X_15706))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_15707,X_15708),implies(X_15706,not(X_15706))))),bind(Y,$fot(implies(X_15708,not(X_15706))))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(X,Y),X_9),implies(Y,X_9))),
inference(subst,[],[cn_19:[bind(Z,$fot(X_9))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_9),implies(Y,X_9)))
| is_a_theorem(implies(X_9,implies(Y,X_9))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_9)),bind(Z,$fot(implies(Y,X_9)))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(X_9,implies(Y,X_9))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_9),implies(Y,X_9))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(not(X_1507),implies(X_1505,not(X_1507)))),
inference(subst,[],[refute_0_7:[bind(Y,$fot(X_1505)),bind(X_9,$fot(not(X_1507)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(X_331,implies(X_330,not(X_332))))
| ~ is_a_theorem(implies(implies(X_331,implies(X_330,not(X_332))),implies(implies(X_332,X_331),implies(X_330,not(X_332)))))
| is_a_theorem(implies(implies(X_332,X_331),implies(X_330,not(X_332)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_331,implies(X_330,not(X_332))))),bind(Y,$fot(implies(implies(X_332,X_331),implies(X_330,not(X_332)))))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(X,Y),not(X_318)),implies(Y,not(X_318)))),
inference(subst,[],[cn_19:[bind(Z,$fot(not(X_318)))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(X_96,not(X_98)),X_99))
| ~ is_a_theorem(implies(implies(implies(X_96,not(X_98)),X_99),implies(implies(X_97,X_99),implies(implies(X_98,X_97),X_99))))
| is_a_theorem(implies(implies(X_97,X_99),implies(implies(X_98,X_97),X_99))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_96,not(X_98)),X_99))),bind(Y,$fot(implies(implies(X_97,X_99),implies(implies(X_98,X_97),X_99))))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(X,not(X_90)),X_91),implies(not(X_90),X_91))),
inference(subst,[],[cn_19:[bind(Y,$fot(not(X_90))),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(X_30,implies(not(X_31),X_32)))
| ~ is_a_theorem(implies(implies(X_30,implies(not(X_31),X_32)),implies(X_30,implies(implies(X_29,X_32),implies(implies(X_31,X_29),X_32)))))
| is_a_theorem(implies(X_30,implies(implies(X_29,X_32),implies(implies(X_31,X_29),X_32)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_30,implies(not(X_31),X_32)))),bind(Y,$fot(implies(X_30,implies(implies(X_29,X_32),implies(implies(X_31,X_29),X_32)))))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(X_30,implies(not(X_31),X_32)),implies(X_30,implies(implies(X_29,X_32),implies(implies(X_31,X_29),X_32))))),
inference(subst,[],[cn_60:[bind(U,$fot(X_29)),bind(X,$fot(X_30)),bind(Y,$fot(X_31)),bind(Z,$fot(X_32))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(X_30,implies(not(X_31),X_32)))
| is_a_theorem(implies(X_30,implies(implies(X_29,X_32),implies(implies(X_31,X_29),X_32)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_30,implies(not(X_31),X_32)),implies(X_30,implies(implies(X_29,X_32),implies(implies(X_31,X_29),X_32))))) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X,not(X_90)),X_91),implies(not(X_90),X_91)))
| is_a_theorem(implies(implies(implies(X,not(X_90)),X_91),implies(implies(X_88,X_91),implies(implies(X_90,X_88),X_91)))) ),
inference(subst,[],[refute_0_15:[bind(X_29,$fot(X_88)),bind(X_30,$fot(implies(implies(X,not(X_90)),X_91))),bind(X_31,$fot(X_90)),bind(X_32,$fot(X_91))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(X,not(X_90)),X_91),implies(implies(X_88,X_91),implies(implies(X_90,X_88),X_91)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,not(X_90)),X_91),implies(not(X_90),X_91))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(implies(X_96,not(X_98)),X_99),implies(implies(X_97,X_99),implies(implies(X_98,X_97),X_99)))),
inference(subst,[],[refute_0_17:[bind(X,$fot(X_96)),bind(X_88,$fot(X_97)),bind(X_90,$fot(X_98)),bind(X_91,$fot(X_99))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(X_96,not(X_98)),X_99))
| is_a_theorem(implies(implies(X_97,X_99),implies(implies(X_98,X_97),X_99))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_96,not(X_98)),X_99),implies(implies(X_97,X_99),implies(implies(X_98,X_97),X_99)))) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),not(X_318)),implies(Y,not(X_318))))
| is_a_theorem(implies(implies(X_317,implies(Y,not(X_318))),implies(implies(X_318,X_317),implies(Y,not(X_318))))) ),
inference(subst,[],[refute_0_19:[bind(X_96,$fot(implies(X,Y))),bind(X_97,$fot(X_317)),bind(X_98,$fot(X_318)),bind(X_99,$fot(implies(Y,not(X_318))))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_317,implies(Y,not(X_318))),implies(implies(X_318,X_317),implies(Y,not(X_318))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),not(X_318)),implies(Y,not(X_318)))) )],[refute_0_10,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(X_331,implies(X_330,not(X_332))),implies(implies(X_332,X_331),implies(X_330,not(X_332))))),
inference(subst,[],[refute_0_21:[bind(Y,$fot(X_330)),bind(X_317,$fot(X_331)),bind(X_318,$fot(X_332))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(X_331,implies(X_330,not(X_332))))
| is_a_theorem(implies(implies(X_332,X_331),implies(X_330,not(X_332)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_331,implies(X_330,not(X_332))),implies(implies(X_332,X_331),implies(X_330,not(X_332))))) )],[refute_0_22,refute_0_9]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(not(X_1507),implies(X_1505,not(X_1507))))
| is_a_theorem(implies(implies(X_1507,not(X_1507)),implies(X_1505,not(X_1507)))) ),
inference(subst,[],[refute_0_23:[bind(X_330,$fot(X_1505)),bind(X_331,$fot(not(X_1507))),bind(X_332,$fot(X_1507))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_1507,not(X_1507)),implies(X_1505,not(X_1507)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1507),implies(X_1505,not(X_1507)))) )],[refute_0_8,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(X_1507,not(X_1507)),implies(X_15645,not(X_1507)))),
inference(subst,[],[refute_0_25:[bind(X_1505,$fot(X_15645))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(X_968,implies(X_966,X_967)))
| ~ is_a_theorem(implies(implies(X_968,implies(X_966,X_967)),implies(implies(implies(X_965,X_966),X_968),implies(X_966,X_967))))
| is_a_theorem(implies(implies(implies(X_965,X_966),X_968),implies(X_966,X_967))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_968,implies(X_966,X_967)))),bind(Y,$fot(implies(implies(implies(X_965,X_966),X_968),implies(X_966,X_967))))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(X,Y),X_941),implies(Y,X_941))),
inference(subst,[],[cn_19:[bind(Z,$fot(X_941))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(X_236,X_234),X_237))
| ~ is_a_theorem(implies(implies(implies(X_236,X_234),X_237),implies(implies(X_235,X_237),implies(implies(X_236,X_235),X_237))))
| is_a_theorem(implies(implies(X_235,X_237),implies(implies(X_236,X_235),X_237))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_236,X_234),X_237))),bind(Y,$fot(implies(implies(X_235,X_237),implies(implies(X_236,X_235),X_237))))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(implies(X_90,Y),X_91),implies(not(X_90),X_91))),
inference(subst,[],[cn_37:[bind(X,$fot(X_90)),bind(Z,$fot(X_91))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(X_90,Y),X_91),implies(not(X_90),X_91)))
| is_a_theorem(implies(implies(implies(X_90,Y),X_91),implies(implies(X_88,X_91),implies(implies(X_90,X_88),X_91)))) ),
inference(subst,[],[refute_0_15:[bind(X_29,$fot(X_88)),bind(X_30,$fot(implies(implies(X_90,Y),X_91))),bind(X_31,$fot(X_90)),bind(X_32,$fot(X_91))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(X_90,Y),X_91),implies(implies(X_88,X_91),implies(implies(X_90,X_88),X_91)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_90,Y),X_91),implies(not(X_90),X_91))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(implies(X_236,X_234),X_237),implies(implies(X_235,X_237),implies(implies(X_236,X_235),X_237)))),
inference(subst,[],[refute_0_32:[bind(Y,$fot(X_234)),bind(X_88,$fot(X_235)),bind(X_90,$fot(X_236)),bind(X_91,$fot(X_237))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(X_236,X_234),X_237))
| is_a_theorem(implies(implies(X_235,X_237),implies(implies(X_236,X_235),X_237))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_236,X_234),X_237),implies(implies(X_235,X_237),implies(implies(X_236,X_235),X_237)))) )],[refute_0_33,refute_0_29]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_941),implies(Y,X_941)))
| is_a_theorem(implies(implies(X_942,implies(Y,X_941)),implies(implies(implies(X,Y),X_942),implies(Y,X_941)))) ),
inference(subst,[],[refute_0_34:[bind(X_234,$fot(X_941)),bind(X_235,$fot(X_942)),bind(X_236,$fot(implies(X,Y))),bind(X_237,$fot(implies(Y,X_941)))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(X_942,implies(Y,X_941)),implies(implies(implies(X,Y),X_942),implies(Y,X_941)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_941),implies(Y,X_941))) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(X_968,implies(X_966,X_967)),implies(implies(implies(X_965,X_966),X_968),implies(X_966,X_967)))),
inference(subst,[],[refute_0_36:[bind(X,$fot(X_965)),bind(Y,$fot(X_966)),bind(X_941,$fot(X_967)),bind(X_942,$fot(X_968))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(X_968,implies(X_966,X_967)))
| is_a_theorem(implies(implies(implies(X_965,X_966),X_968),implies(X_966,X_967))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_968,implies(X_966,X_967)),implies(implies(implies(X_965,X_966),X_968),implies(X_966,X_967)))) )],[refute_0_37,refute_0_27]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(X_1507,not(X_1507)),implies(X_15645,not(X_1507))))
| is_a_theorem(implies(implies(implies(X_15644,X_15645),implies(X_1507,not(X_1507))),implies(X_15645,not(X_1507)))) ),
inference(subst,[],[refute_0_38:[bind(X_965,$fot(X_15644)),bind(X_966,$fot(X_15645)),bind(X_967,$fot(not(X_1507))),bind(X_968,$fot(implies(X_1507,not(X_1507))))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(X_15644,X_15645),implies(X_1507,not(X_1507))),implies(X_15645,not(X_1507)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1507,not(X_1507)),implies(X_15645,not(X_1507)))) )],[refute_0_26,refute_0_39]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(implies(X_15707,X_15708),implies(X_15706,not(X_15706))),implies(X_15708,not(X_15706)))),
inference(subst,[],[refute_0_40:[bind(X_1507,$fot(X_15706)),bind(X_15644,$fot(X_15707)),bind(X_15645,$fot(X_15708))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(X_15707,X_15708),implies(X_15706,not(X_15706))))
| is_a_theorem(implies(X_15708,not(X_15706))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_15707,X_15708),implies(X_15706,not(X_15706))),implies(X_15708,not(X_15706)))) )],[refute_0_41,refute_0_4]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(implies(X,X_25238),not(X_25238)),implies(X_25238,not(X_25238))))
| is_a_theorem(implies(not(X_25238),not(X_25238))) ),
inference(subst,[],[refute_0_42:[bind(X_15706,$fot(X_25238)),bind(X_15707,$fot(implies(X,X_25238))),bind(X_15708,$fot(not(X_25238)))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(not(X_25238),not(X_25238))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,X_25238),not(X_25238)),implies(X_25238,not(X_25238)))) )],[refute_0_3,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(not(X_67729),not(X_67729))),
inference(subst,[],[refute_0_44:[bind(X_25238,$fot(X_67729))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(X_53088,not(X_53086)))
| ~ is_a_theorem(implies(implies(X_53088,not(X_53086)),implies(implies(not(not(implies(X_53085,not(not(X_53085))))),X_53086),implies(X_53088,X_53087))))
| is_a_theorem(implies(implies(not(not(implies(X_53085,not(not(X_53085))))),X_53086),implies(X_53088,X_53087))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_53088,not(X_53086)))),bind(Y,$fot(implies(implies(not(not(implies(X_53085,not(not(X_53085))))),X_53086),implies(X_53088,X_53087))))]]) ).
cnf(refute_0_47,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_48,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| is_a_theorem(implies(not(X),Z)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))) )],[cn_37,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(implies(X_28908,X_28909),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),X_28909)))
| is_a_theorem(implies(not(X_28908),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),X_28909))) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_28908)),bind(Y,$fot(X_28909)),bind(Z,$fot(implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),X_28909)))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(not(implies(X_92,not(X_94))),implies(implies(X_93,X_95),implies(implies(X_94,X_93),X_95))))
| ~ is_a_theorem(not(implies(X_92,not(X_94))))
| is_a_theorem(implies(implies(X_93,X_95),implies(implies(X_94,X_93),X_95))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(not(implies(X_92,not(X_94))))),bind(Y,$fot(implies(implies(X_93,X_95),implies(implies(X_94,X_93),X_95))))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(implies(X,Y),X_34),implies(Y,X_34))),
inference(subst,[],[cn_19:[bind(Z,$fot(X_34))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_34),implies(Y,X_34)))
| is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_34))) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_34)),bind(Z,$fot(implies(Y,X_34)))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_34))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_34),implies(Y,X_34))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(not(implies(X,not(X_90))),implies(not(X_90),X_91))),
inference(subst,[],[refute_0_53:[bind(Y,$fot(not(X_90))),bind(X_34,$fot(X_91))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(not(implies(X,not(X_90))),implies(not(X_90),X_91)))
| is_a_theorem(implies(not(implies(X,not(X_90))),implies(implies(X_88,X_91),implies(implies(X_90,X_88),X_91)))) ),
inference(subst,[],[refute_0_15:[bind(X_29,$fot(X_88)),bind(X_30,$fot(not(implies(X,not(X_90))))),bind(X_31,$fot(X_90)),bind(X_32,$fot(X_91))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(not(implies(X,not(X_90))),implies(implies(X_88,X_91),implies(implies(X_90,X_88),X_91)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,not(X_90))),implies(not(X_90),X_91))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(not(implies(X_92,not(X_94))),implies(implies(X_93,X_95),implies(implies(X_94,X_93),X_95)))),
inference(subst,[],[refute_0_56:[bind(X,$fot(X_92)),bind(X_88,$fot(X_93)),bind(X_90,$fot(X_94)),bind(X_91,$fot(X_95))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(not(implies(X_92,not(X_94))))
| is_a_theorem(implies(implies(X_93,X_95),implies(implies(X_94,X_93),X_95))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_92,not(X_94))),implies(implies(X_93,X_95),implies(implies(X_94,X_93),X_95)))) )],[refute_0_57,refute_0_50]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(not(implies(implies(X_27219,not(not(X_27219))),not(not(not(implies(X_27218,not(not(X_27218)))))))))
| is_a_theorem(implies(implies(X_93,X_95),implies(implies(not(not(implies(X_27218,not(not(X_27218))))),X_93),X_95))) ),
inference(subst,[],[refute_0_58:[bind(X_92,$fot(implies(X_27219,not(not(X_27219))))),bind(X_94,$fot(not(not(implies(X_27218,not(not(X_27218)))))))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(not(X_334),implies(implies(X_335,X_334),implies(X_333,not(X_335)))))
| ~ is_a_theorem(not(X_334))
| is_a_theorem(implies(implies(X_335,X_334),implies(X_333,not(X_335)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(not(X_334))),bind(Y,$fot(implies(implies(X_335,X_334),implies(X_333,not(X_335)))))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(X_331,implies(X_330,not(X_332))),implies(implies(X_332,X_331),implies(X_330,not(X_332)))))
| is_a_theorem(implies(not(X_331),implies(implies(X_332,X_331),implies(X_330,not(X_332))))) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_331)),bind(Y,$fot(implies(X_330,not(X_332)))),bind(Z,$fot(implies(implies(X_332,X_331),implies(X_330,not(X_332)))))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(not(X_331),implies(implies(X_332,X_331),implies(X_330,not(X_332))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_331,implies(X_330,not(X_332))),implies(implies(X_332,X_331),implies(X_330,not(X_332))))) )],[refute_0_22,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(not(X_334),implies(implies(X_335,X_334),implies(X_333,not(X_335))))),
inference(subst,[],[refute_0_62:[bind(X_330,$fot(X_333)),bind(X_331,$fot(X_334)),bind(X_332,$fot(X_335))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(not(X_334))
| is_a_theorem(implies(implies(X_335,X_334),implies(X_333,not(X_335)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_334),implies(implies(X_335,X_334),implies(X_333,not(X_335))))) )],[refute_0_63,refute_0_60]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(not(not(not(not(implies(X_1910,not(not(X_1910))))))))
| is_a_theorem(implies(implies(X_335,not(not(not(implies(X_1910,not(not(X_1910))))))),implies(X_333,not(X_335)))) ),
inference(subst,[],[refute_0_64:[bind(X_334,$fot(not(not(not(implies(X_1910,not(not(X_1910))))))))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(X_1897)
| ~ is_a_theorem(implies(X_1897,not(not(X_1897))))
| is_a_theorem(not(not(X_1897))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1897)),bind(Y,$fot(not(not(X_1897))))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(X_1740,not(X_1739)),implies(implies(implies(X_1738,X_1739),X_1740),not(X_1739))))
| is_a_theorem(implies(not(X_1740),implies(implies(implies(X_1738,X_1739),X_1740),not(X_1739)))) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_1740)),bind(Y,$fot(not(X_1739))),bind(Z,$fot(implies(implies(implies(X_1738,X_1739),X_1740),not(X_1739))))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(implies(X_1701,X_1702),not(implies(X_1701,X_1702))),not(X_1702)))
| is_a_theorem(implies(implies(X_235,not(X_1702)),implies(implies(implies(X_1701,X_1702),X_235),not(X_1702)))) ),
inference(subst,[],[refute_0_34:[bind(X_234,$fot(not(implies(X_1701,X_1702)))),bind(X_236,$fot(implies(X_1701,X_1702))),bind(X_237,$fot(not(X_1702)))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(X_1516,not(implies(X_1514,X_1515))))
| ~ is_a_theorem(implies(implies(X_1516,not(implies(X_1514,X_1515))),implies(X_1515,not(X_1516))))
| is_a_theorem(implies(X_1515,not(X_1516))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1516,not(implies(X_1514,X_1515))))),bind(Y,$fot(implies(X_1515,not(X_1516))))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(not(implies(X,X_1505)),implies(X_1505,not(X_1507)))),
inference(subst,[],[refute_0_53:[bind(Y,$fot(X_1505)),bind(X_34,$fot(not(X_1507)))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(not(implies(X,X_1505)),implies(X_1505,not(X_1507))))
| is_a_theorem(implies(implies(X_1507,not(implies(X,X_1505))),implies(X_1505,not(X_1507)))) ),
inference(subst,[],[refute_0_23:[bind(X_330,$fot(X_1505)),bind(X_331,$fot(not(implies(X,X_1505)))),bind(X_332,$fot(X_1507))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(X_1507,not(implies(X,X_1505))),implies(X_1505,not(X_1507)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,X_1505)),implies(X_1505,not(X_1507)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(X_1516,not(implies(X_1514,X_1515))),implies(X_1515,not(X_1516)))),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_1514)),bind(X_1505,$fot(X_1515)),bind(X_1507,$fot(X_1516))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(X_1516,not(implies(X_1514,X_1515))))
| is_a_theorem(implies(X_1515,not(X_1516))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1516,not(implies(X_1514,X_1515))),implies(X_1515,not(X_1516)))) )],[refute_0_73,refute_0_69]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(X_1683,not(implies(implies(X_1682,X_1683),implies(implies(X_1682,X_1683),not(implies(X_1682,X_1683)))))))
| is_a_theorem(implies(implies(implies(X_1682,X_1683),not(implies(X_1682,X_1683))),not(X_1683))) ),
inference(subst,[],[refute_0_74:[bind(X_1514,$fot(implies(X_1682,X_1683))),bind(X_1515,$fot(implies(implies(X_1682,X_1683),not(implies(X_1682,X_1683))))),bind(X_1516,$fot(X_1683))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(X_1509,not(X_1509)),implies(X_1508,not(X_1509))))
| is_a_theorem(implies(implies(X_1509,implies(X_1509,not(X_1509))),implies(X_1508,not(X_1509)))) ),
inference(subst,[],[refute_0_23:[bind(X_330,$fot(X_1508)),bind(X_331,$fot(implies(X_1509,not(X_1509)))),bind(X_332,$fot(X_1509))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(X_1509,not(X_1509)),implies(X_1508,not(X_1509)))),
inference(subst,[],[refute_0_25:[bind(X_1505,$fot(X_1508)),bind(X_1507,$fot(X_1509))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(X_1509,implies(X_1509,not(X_1509))),implies(X_1508,not(X_1509)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1509,not(X_1509)),implies(X_1508,not(X_1509)))) )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668)))),implies(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668)))),not(implies(X_1667,X_1668))))),
inference(subst,[],[refute_0_78:[bind(X_1508,$fot(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668)))))),bind(X_1509,$fot(implies(X_1667,X_1668)))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(X_1561,implies(X_1561,not(implies(X_1559,X_1560)))))
| ~ is_a_theorem(implies(implies(X_1561,implies(X_1561,not(implies(X_1559,X_1560)))),implies(X_1560,not(X_1561))))
| is_a_theorem(implies(X_1560,not(X_1561))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1561,implies(X_1561,not(implies(X_1559,X_1560)))))),bind(Y,$fot(implies(X_1560,not(X_1561))))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(X_1516,not(implies(X_1514,X_1515))),implies(X_1515,not(X_1516))))
| is_a_theorem(implies(implies(X_1516,implies(X_1516,not(implies(X_1514,X_1515)))),implies(X_1515,not(X_1516)))) ),
inference(subst,[],[refute_0_23:[bind(X_330,$fot(X_1515)),bind(X_331,$fot(implies(X_1516,not(implies(X_1514,X_1515))))),bind(X_332,$fot(X_1516))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(X_1516,implies(X_1516,not(implies(X_1514,X_1515)))),implies(X_1515,not(X_1516)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1516,not(implies(X_1514,X_1515))),implies(X_1515,not(X_1516)))) )],[refute_0_73,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(X_1561,implies(X_1561,not(implies(X_1559,X_1560)))),implies(X_1560,not(X_1561)))),
inference(subst,[],[refute_0_82:[bind(X_1514,$fot(X_1559)),bind(X_1515,$fot(X_1560)),bind(X_1516,$fot(X_1561))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(X_1561,implies(X_1561,not(implies(X_1559,X_1560)))))
| is_a_theorem(implies(X_1560,not(X_1561))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1561,implies(X_1561,not(implies(X_1559,X_1560)))),implies(X_1560,not(X_1561)))) )],[refute_0_83,refute_0_80]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668)))),implies(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668)))),not(implies(X_1667,X_1668)))))
| is_a_theorem(implies(X_1668,not(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668))))))) ),
inference(subst,[],[refute_0_84:[bind(X_1559,$fot(X_1667)),bind(X_1560,$fot(X_1668)),bind(X_1561,$fot(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668))))))]]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(X_1668,not(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668)))),implies(implies(implies(X_1667,X_1668),implies(implies(X_1667,X_1668),not(implies(X_1667,X_1668)))),not(implies(X_1667,X_1668))))) )],[refute_0_79,refute_0_85]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(X_1683,not(implies(implies(X_1682,X_1683),implies(implies(X_1682,X_1683),not(implies(X_1682,X_1683))))))),
inference(subst,[],[refute_0_86:[bind(X_1667,$fot(X_1682)),bind(X_1668,$fot(X_1683))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(implies(implies(X_1682,X_1683),not(implies(X_1682,X_1683))),not(X_1683))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1683,not(implies(implies(X_1682,X_1683),implies(implies(X_1682,X_1683),not(implies(X_1682,X_1683))))))) )],[refute_0_87,refute_0_75]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(implies(implies(X_1701,X_1702),not(implies(X_1701,X_1702))),not(X_1702))),
inference(subst,[],[refute_0_88:[bind(X_1682,$fot(X_1701)),bind(X_1683,$fot(X_1702))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(X_235,not(X_1702)),implies(implies(implies(X_1701,X_1702),X_235),not(X_1702)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1701,X_1702),not(implies(X_1701,X_1702))),not(X_1702))) )],[refute_0_89,refute_0_68]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(X_1740,not(X_1739)),implies(implies(implies(X_1738,X_1739),X_1740),not(X_1739)))),
inference(subst,[],[refute_0_90:[bind(X_1701,$fot(X_1738)),bind(X_1702,$fot(X_1739)),bind(X_235,$fot(X_1740))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(not(X_1740),implies(implies(implies(X_1738,X_1739),X_1740),not(X_1739)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1740,not(X_1739)),implies(implies(implies(X_1738,X_1739),X_1740),not(X_1739)))) )],[refute_0_91,refute_0_67]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(not(X_1895),implies(implies(implies(X_1738,not(X_1895)),X_1895),not(not(X_1895))))),
inference(subst,[],[refute_0_92:[bind(X_1739,$fot(not(X_1895))),bind(X_1740,$fot(X_1895))]]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(implies(X_1540,implies(implies(X_1538,X_1539),not(X_1540))))
| ~ is_a_theorem(implies(implies(X_1540,implies(implies(X_1538,X_1539),not(X_1540))),implies(X_1539,not(X_1540))))
| is_a_theorem(implies(X_1539,not(X_1540))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1540,implies(implies(X_1538,X_1539),not(X_1540))))),bind(Y,$fot(implies(X_1539,not(X_1540))))]]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(implies(implies(X,X_1505),not(X_1507)),implies(X_1505,not(X_1507)))),
inference(subst,[],[cn_19:[bind(Y,$fot(X_1505)),bind(Z,$fot(not(X_1507)))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(implies(implies(X,X_1505),not(X_1507)),implies(X_1505,not(X_1507))))
| is_a_theorem(implies(implies(X_1507,implies(implies(X,X_1505),not(X_1507))),implies(X_1505,not(X_1507)))) ),
inference(subst,[],[refute_0_23:[bind(X_330,$fot(X_1505)),bind(X_331,$fot(implies(implies(X,X_1505),not(X_1507)))),bind(X_332,$fot(X_1507))]]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(X_1507,implies(implies(X,X_1505),not(X_1507))),implies(X_1505,not(X_1507)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,X_1505),not(X_1507)),implies(X_1505,not(X_1507)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(X_1540,implies(implies(X_1538,X_1539),not(X_1540))),implies(X_1539,not(X_1540)))),
inference(subst,[],[refute_0_97:[bind(X,$fot(X_1538)),bind(X_1505,$fot(X_1539)),bind(X_1507,$fot(X_1540))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(X_1540,implies(implies(X_1538,X_1539),not(X_1540))))
| is_a_theorem(implies(X_1539,not(X_1540))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1540,implies(implies(X_1538,X_1539),not(X_1540))),implies(X_1539,not(X_1540)))) )],[refute_0_98,refute_0_94]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(not(X_1895),implies(implies(implies(X_1738,not(X_1895)),X_1895),not(not(X_1895)))))
| is_a_theorem(implies(X_1895,not(not(X_1895)))) ),
inference(subst,[],[refute_0_99:[bind(X_1538,$fot(implies(X_1738,not(X_1895)))),bind(X_1539,$fot(X_1895)),bind(X_1540,$fot(not(X_1895)))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(X_1895,not(not(X_1895)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1895),implies(implies(implies(X_1738,not(X_1895)),X_1895),not(not(X_1895))))) )],[refute_0_93,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(X_1897,not(not(X_1897)))),
inference(subst,[],[refute_0_101:[bind(X_1895,$fot(X_1897))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(X_1897)
| is_a_theorem(not(not(X_1897))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1897,not(not(X_1897)))) )],[refute_0_102,refute_0_66]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(not(not(implies(X_1905,not(not(X_1905))))))
| is_a_theorem(not(not(not(not(implies(X_1905,not(not(X_1905)))))))) ),
inference(subst,[],[refute_0_103:[bind(X_1897,$fot(not(not(implies(X_1905,not(not(X_1905)))))))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(X_1895,not(not(X_1895))))
| is_a_theorem(not(not(implies(X_1895,not(not(X_1895)))))) ),
inference(subst,[],[refute_0_103:[bind(X_1897,$fot(implies(X_1895,not(not(X_1895)))))]]) ).
cnf(refute_0_106,plain,
is_a_theorem(not(not(implies(X_1895,not(not(X_1895)))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1895,not(not(X_1895)))) )],[refute_0_101,refute_0_105]) ).
cnf(refute_0_107,plain,
is_a_theorem(not(not(implies(X_1905,not(not(X_1905)))))),
inference(subst,[],[refute_0_106:[bind(X_1895,$fot(X_1905))]]) ).
cnf(refute_0_108,plain,
is_a_theorem(not(not(not(not(implies(X_1905,not(not(X_1905)))))))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(X_1905,not(not(X_1905)))))) )],[refute_0_107,refute_0_104]) ).
cnf(refute_0_109,plain,
is_a_theorem(not(not(not(not(implies(X_1910,not(not(X_1910)))))))),
inference(subst,[],[refute_0_108:[bind(X_1905,$fot(X_1910))]]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(implies(X_335,not(not(not(implies(X_1910,not(not(X_1910))))))),implies(X_333,not(X_335)))),
inference(resolve,[$cnf( is_a_theorem(not(not(not(not(implies(X_1910,not(not(X_1910)))))))) )],[refute_0_109,refute_0_65]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(X_335,not(not(not(implies(X_1910,not(not(X_1910))))))),implies(X_15645,not(X_335)))),
inference(subst,[],[refute_0_110:[bind(X_333,$fot(X_15645))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(implies(implies(X_335,not(not(not(implies(X_1910,not(not(X_1910))))))),implies(X_15645,not(X_335))))
| is_a_theorem(implies(implies(implies(X_15644,X_15645),implies(X_335,not(not(not(implies(X_1910,not(not(X_1910)))))))),implies(X_15645,not(X_335)))) ),
inference(subst,[],[refute_0_38:[bind(X_965,$fot(X_15644)),bind(X_966,$fot(X_15645)),bind(X_967,$fot(not(X_335))),bind(X_968,$fot(implies(X_335,not(not(not(implies(X_1910,not(not(X_1910)))))))))]]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(implies(X_15644,X_15645),implies(X_335,not(not(not(implies(X_1910,not(not(X_1910)))))))),implies(X_15645,not(X_335)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_335,not(not(not(implies(X_1910,not(not(X_1910))))))),implies(X_15645,not(X_335)))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(implies(X_15644,X_25238),implies(X_25238,not(not(not(implies(X_1910,not(not(X_1910)))))))),implies(X_25238,not(X_25238)))),
inference(subst,[],[refute_0_113:[bind(X_15645,$fot(X_25238)),bind(X_335,$fot(X_25238))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(implies(implies(implies(X_15644,X_25238),implies(X_25238,not(not(not(implies(X_1910,not(not(X_1910)))))))),implies(X_25238,not(X_25238))))
| is_a_theorem(implies(implies(X_25238,not(not(not(implies(X_1910,not(not(X_1910))))))),not(X_25238))) ),
inference(subst,[],[refute_0_42:[bind(X_15706,$fot(X_25238)),bind(X_15707,$fot(implies(X_15644,X_25238))),bind(X_15708,$fot(implies(X_25238,not(not(not(implies(X_1910,not(not(X_1910)))))))))]]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(X_25238,not(not(not(implies(X_1910,not(not(X_1910))))))),not(X_25238))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_15644,X_25238),implies(X_25238,not(not(not(implies(X_1910,not(not(X_1910)))))))),implies(X_25238,not(X_25238)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(implies(X_27214,not(not(X_27214))),not(not(not(implies(X_1910,not(not(X_1910))))))),not(implies(X_27214,not(not(X_27214)))))),
inference(subst,[],[refute_0_116:[bind(X_25238,$fot(implies(X_27214,not(not(X_27214)))))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(X_25296,not(implies(X_25295,not(not(X_25295))))))
| ~ is_a_theorem(implies(implies(X_25296,not(implies(X_25295,not(not(X_25295))))),not(X_25296)))
| is_a_theorem(not(X_25296)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_25296,not(implies(X_25295,not(not(X_25295))))))),bind(Y,$fot(not(X_25296)))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(not(not(implies(X_1905,not(not(X_1905))))))
| is_a_theorem(implies(implies(X_335,not(implies(X_1905,not(not(X_1905))))),implies(X_333,not(X_335)))) ),
inference(subst,[],[refute_0_64:[bind(X_334,$fot(not(implies(X_1905,not(not(X_1905))))))]]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(implies(X_335,not(implies(X_1905,not(not(X_1905))))),implies(X_333,not(X_335)))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(X_1905,not(not(X_1905)))))) )],[refute_0_107,refute_0_119]) ).
cnf(refute_0_121,plain,
is_a_theorem(implies(implies(X_335,not(implies(X_1905,not(not(X_1905))))),implies(X_15645,not(X_335)))),
inference(subst,[],[refute_0_120:[bind(X_333,$fot(X_15645))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(X_335,not(implies(X_1905,not(not(X_1905))))),implies(X_15645,not(X_335))))
| is_a_theorem(implies(implies(implies(X_15644,X_15645),implies(X_335,not(implies(X_1905,not(not(X_1905)))))),implies(X_15645,not(X_335)))) ),
inference(subst,[],[refute_0_38:[bind(X_965,$fot(X_15644)),bind(X_966,$fot(X_15645)),bind(X_967,$fot(not(X_335))),bind(X_968,$fot(implies(X_335,not(implies(X_1905,not(not(X_1905)))))))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(implies(X_15644,X_15645),implies(X_335,not(implies(X_1905,not(not(X_1905)))))),implies(X_15645,not(X_335)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_335,not(implies(X_1905,not(not(X_1905))))),implies(X_15645,not(X_335)))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(implies(X_15644,X_25238),implies(X_25238,not(implies(X_1905,not(not(X_1905)))))),implies(X_25238,not(X_25238)))),
inference(subst,[],[refute_0_123:[bind(X_15645,$fot(X_25238)),bind(X_335,$fot(X_25238))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(implies(implies(X_15644,X_25238),implies(X_25238,not(implies(X_1905,not(not(X_1905)))))),implies(X_25238,not(X_25238))))
| is_a_theorem(implies(implies(X_25238,not(implies(X_1905,not(not(X_1905))))),not(X_25238))) ),
inference(subst,[],[refute_0_42:[bind(X_15706,$fot(X_25238)),bind(X_15707,$fot(implies(X_15644,X_25238))),bind(X_15708,$fot(implies(X_25238,not(implies(X_1905,not(not(X_1905)))))))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(X_25238,not(implies(X_1905,not(not(X_1905))))),not(X_25238))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_15644,X_25238),implies(X_25238,not(implies(X_1905,not(not(X_1905)))))),implies(X_25238,not(X_25238)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(X_25296,not(implies(X_25295,not(not(X_25295))))),not(X_25296))),
inference(subst,[],[refute_0_126:[bind(X_1905,$fot(X_25295)),bind(X_25238,$fot(X_25296))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(X_25296,not(implies(X_25295,not(not(X_25295))))))
| is_a_theorem(not(X_25296)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_25296,not(implies(X_25295,not(not(X_25295))))),not(X_25296))) )],[refute_0_127,refute_0_118]) ).
cnf(refute_0_129,plain,
( ~ is_a_theorem(implies(implies(implies(X_27214,not(not(X_27214))),not(not(not(implies(X_1910,not(not(X_1910))))))),not(implies(X_27214,not(not(X_27214))))))
| is_a_theorem(not(implies(implies(X_27214,not(not(X_27214))),not(not(not(implies(X_1910,not(not(X_1910))))))))) ),
inference(subst,[],[refute_0_128:[bind(X_25295,$fot(X_27214)),bind(X_25296,$fot(implies(implies(X_27214,not(not(X_27214))),not(not(not(implies(X_1910,not(not(X_1910)))))))))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(not(implies(implies(X_27214,not(not(X_27214))),not(not(not(implies(X_1910,not(not(X_1910))))))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_27214,not(not(X_27214))),not(not(not(implies(X_1910,not(not(X_1910))))))),not(implies(X_27214,not(not(X_27214)))))) )],[refute_0_117,refute_0_129]) ).
cnf(refute_0_131,plain,
is_a_theorem(not(implies(implies(X_27219,not(not(X_27219))),not(not(not(implies(X_27218,not(not(X_27218))))))))),
inference(subst,[],[refute_0_130:[bind(X_1910,$fot(X_27218)),bind(X_27214,$fot(X_27219))]]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(X_93,X_95),implies(implies(not(not(implies(X_27218,not(not(X_27218))))),X_93),X_95))),
inference(resolve,[$cnf( is_a_theorem(not(implies(implies(X_27219,not(not(X_27219))),not(not(not(implies(X_27218,not(not(X_27218))))))))) )],[refute_0_131,refute_0_59]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(X_28908,X_28909),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),X_28909))),
inference(subst,[],[refute_0_132:[bind(X_27218,$fot(X_28907)),bind(X_93,$fot(X_28908)),bind(X_95,$fot(X_28909))]]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(not(X_28908),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),X_28909))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_28908,X_28909),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),X_28909))) )],[refute_0_133,refute_0_49]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(not(X_28908),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),implies(X_49525,X_49523)))),
inference(subst,[],[refute_0_134:[bind(X_28909,$fot(implies(X_49525,X_49523)))]]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(implies(X_947,implies(X_945,implies(X_948,X_946))))
| ~ is_a_theorem(implies(implies(X_947,implies(X_945,implies(X_948,X_946))),implies(implies(X_948,X_947),implies(X_945,implies(X_948,X_946)))))
| is_a_theorem(implies(implies(X_948,X_947),implies(X_945,implies(X_948,X_946)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_947,implies(X_945,implies(X_948,X_946))))),bind(Y,$fot(implies(implies(X_948,X_947),implies(X_945,implies(X_948,X_946)))))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(implies(X_943,X_941),implies(Y,implies(X_943,X_941)))),
inference(subst,[],[refute_0_7:[bind(X_9,$fot(implies(X_943,X_941)))]]) ).
cnf(refute_0_138,plain,
( ~ is_a_theorem(implies(implies(X_943,X_941),implies(Y,implies(X_943,X_941))))
| is_a_theorem(implies(implies(X_942,implies(Y,implies(X_943,X_941))),implies(implies(X_943,X_942),implies(Y,implies(X_943,X_941))))) ),
inference(subst,[],[refute_0_34:[bind(X_234,$fot(X_941)),bind(X_235,$fot(X_942)),bind(X_236,$fot(X_943)),bind(X_237,$fot(implies(Y,implies(X_943,X_941))))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(implies(X_942,implies(Y,implies(X_943,X_941))),implies(implies(X_943,X_942),implies(Y,implies(X_943,X_941))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_943,X_941),implies(Y,implies(X_943,X_941)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(implies(X_947,implies(X_945,implies(X_948,X_946))),implies(implies(X_948,X_947),implies(X_945,implies(X_948,X_946))))),
inference(subst,[],[refute_0_139:[bind(Y,$fot(X_945)),bind(X_941,$fot(X_946)),bind(X_942,$fot(X_947)),bind(X_943,$fot(X_948))]]) ).
cnf(refute_0_141,plain,
( ~ is_a_theorem(implies(X_947,implies(X_945,implies(X_948,X_946))))
| is_a_theorem(implies(implies(X_948,X_947),implies(X_945,implies(X_948,X_946)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_947,implies(X_945,implies(X_948,X_946))),implies(implies(X_948,X_947),implies(X_945,implies(X_948,X_946))))) )],[refute_0_140,refute_0_136]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(implies(not(X_28908),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),implies(X_49525,X_49523))))
| is_a_theorem(implies(implies(X_49525,not(X_28908)),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),implies(X_49525,X_49523)))) ),
inference(subst,[],[refute_0_141:[bind(X_945,$fot(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908))),bind(X_946,$fot(X_49523)),bind(X_947,$fot(not(X_28908))),bind(X_948,$fot(X_49525))]]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(implies(X_49525,not(X_28908)),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),implies(X_49525,X_49523)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_28908),implies(implies(not(not(implies(X_28907,not(not(X_28907))))),X_28908),implies(X_49525,X_49523)))) )],[refute_0_135,refute_0_142]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(implies(X_53088,not(X_53086)),implies(implies(not(not(implies(X_53085,not(not(X_53085))))),X_53086),implies(X_53088,X_53087)))),
inference(subst,[],[refute_0_143:[bind(X_28907,$fot(X_53085)),bind(X_28908,$fot(X_53086)),bind(X_49523,$fot(X_53087)),bind(X_49525,$fot(X_53088))]]) ).
cnf(refute_0_145,plain,
( ~ is_a_theorem(implies(X_53088,not(X_53086)))
| is_a_theorem(implies(implies(not(not(implies(X_53085,not(not(X_53085))))),X_53086),implies(X_53088,X_53087))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_53088,not(X_53086)),implies(implies(not(not(implies(X_53085,not(not(X_53085))))),X_53086),implies(X_53088,X_53087)))) )],[refute_0_144,refute_0_46]) ).
cnf(refute_0_146,plain,
( ~ is_a_theorem(implies(not(X_67729),not(X_67729)))
| is_a_theorem(implies(implies(not(not(implies(X_67728,not(not(X_67728))))),X_67729),implies(not(X_67729),X_67730))) ),
inference(subst,[],[refute_0_145:[bind(X_53085,$fot(X_67728)),bind(X_53086,$fot(X_67729)),bind(X_53087,$fot(X_67730)),bind(X_53088,$fot(not(X_67729)))]]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(not(not(implies(X_67728,not(not(X_67728))))),X_67729),implies(not(X_67729),X_67730))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_67729),not(X_67729))) )],[refute_0_45,refute_0_146]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(not(not(implies(X_67741,not(not(X_67741))))),X_67742),implies(not(X_67742),X_67743))),
inference(subst,[],[refute_0_147:[bind(X_67728,$fot(X_67741)),bind(X_67729,$fot(X_67742)),bind(X_67730,$fot(X_67743))]]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(X_67742,implies(not(X_67742),X_67743))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(X_67741,not(not(X_67741))))),X_67742),implies(not(X_67742),X_67743))) )],[refute_0_148,refute_0_2]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(a,implies(not(a),b))),
inference(subst,[],[refute_0_149:[bind(X_67742,$fot(a)),bind(X_67743,$fot(b))]]) ).
cnf(refute_0_151,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(not(a),b))) )],[refute_0_150,prove_cn_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL072-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 2 10:28:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 99.97/100.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 99.97/100.18
% 99.97/100.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 99.97/100.20
%------------------------------------------------------------------------------