TSTP Solution File: LCL396-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL396-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:51:57 EDT 2022
% Result : Unsatisfiable 3.61s 3.79s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 5
% Syntax : Number of clauses : 156 ( 93 unt; 0 nHn; 46 RR)
% Number of literals : 231 ( 0 equ; 76 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 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 : 363 ( 57 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X),X),X)) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X,implies(not(X),Y))) ).
cnf(prove_cn_62,negated_conjecture,
~ is_a_theorem(implies(implies(not(not(x)),y),implies(x,y))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X_5568,not(not(X_5568))))
| is_a_theorem(implies(implies(not(not(X_5568)),Z),implies(X_5568,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_5568)),bind(Y,$fot(not(not(X_5568))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_39),X_38),X_40),implies(X_39,X_40)))
| ~ is_a_theorem(implies(implies(not(X_39),X_38),X_40))
| is_a_theorem(implies(X_39,X_40)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_39),X_38),X_40))),bind(Y,$fot(implies(X_39,X_40)))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(X_33,implies(not(X_33),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(X_33,implies(not(X_33),Y)))
| is_a_theorem(implies(implies(implies(not(X_33),Y),X_35),implies(X_33,X_35))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_33)),bind(Y,$fot(implies(not(X_33),Y))),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(not(X_33),Y),X_35),implies(X_33,X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(X_33,implies(not(X_33),Y))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(implies(not(X_39),X_38),X_40),implies(X_39,X_40))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(X_38)),bind(X_33,$fot(X_39)),bind(X_35,$fot(X_40))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(not(X_39),X_38),X_40))
| is_a_theorem(implies(X_39,X_40)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_39),X_38),X_40),implies(X_39,X_40))) )],[refute_0_7,refute_0_3]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(not(X_39),not(not(X_39))),not(not(X_39))))
| is_a_theorem(implies(X_39,not(not(X_39)))) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(not(not(X_39)))),bind(X_40,$fot(not(not(X_39))))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(not(X_2047),X_2048),implies(implies(X_2048,X_2047),X_2047)))
| ~ is_a_theorem(implies(not(X_2047),X_2048))
| is_a_theorem(implies(implies(X_2048,X_2047),X_2047)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_2047),X_2048))),bind(Y,$fot(implies(implies(X_2048,X_2047),X_2047)))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(implies(X_80,X_81),implies(X_79,X_81)),X_82))
| ~ is_a_theorem(implies(implies(implies(implies(X_80,X_81),implies(X_79,X_81)),X_82),implies(implies(X_79,X_80),X_82)))
| is_a_theorem(implies(implies(X_79,X_80),X_82)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_80,X_81),implies(X_79,X_81)),X_82))),bind(Y,$fot(implies(implies(X_79,X_80),X_82)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_35),implies(implies(X,Y),X_35))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_35),implies(implies(X,Y),X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(implies(X_80,X_81),implies(X_79,X_81)),X_82),implies(implies(X_79,X_80),X_82))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_79)),bind(Y,$fot(X_80)),bind(Z,$fot(X_81)),bind(X_35,$fot(X_82))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(X_80,X_81),implies(X_79,X_81)),X_82))
| is_a_theorem(implies(implies(X_79,X_80),X_82)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_80,X_81),implies(X_79,X_81)),X_82),implies(implies(X_79,X_80),X_82))) )],[refute_0_14,refute_0_11]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_80,X_2021),implies(not(X_2021),X_2021)),implies(implies(X_80,X_2021),X_2021)))
| is_a_theorem(implies(implies(not(X_2021),X_80),implies(implies(X_80,X_2021),X_2021))) ),
inference(subst,[],[refute_0_15:[bind(X_79,$fot(not(X_2021))),bind(X_81,$fot(X_2021)),bind(X_82,$fot(implies(implies(X_80,X_2021),X_2021)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_45),X_45),X_46),X_44),implies(implies(X_45,X_46),X_44)))
| ~ is_a_theorem(implies(implies(implies(not(X_45),X_45),X_46),X_44))
| is_a_theorem(implies(implies(X_45,X_46),X_44)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_45),X_45),X_46),X_44))),bind(Y,$fot(implies(implies(X_45,X_46),X_44)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(X_36,X_37),implies(implies(not(X_36),X_36),X_37)))
| is_a_theorem(implies(implies(implies(implies(not(X_36),X_36),X_37),Z),implies(implies(X_36,X_37),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X_36,X_37))),bind(Y,$fot(implies(implies(not(X_36),X_36),X_37)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(not(X_34),X_34),X_34)),
inference(subst,[],[cn_2:[bind(X,$fot(X_34))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(not(X_34),X_34),X_34))
| is_a_theorem(implies(implies(X_34,X_35),implies(implies(not(X_34),X_34),X_35))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(not(X_34),X_34))),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_34,X_35),implies(implies(not(X_34),X_34),X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_34),X_34),X_34)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(X_36,X_37),implies(implies(not(X_36),X_36),X_37))),
inference(subst,[],[refute_0_21:[bind(X_34,$fot(X_36)),bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(implies(not(X_36),X_36),X_37),Z),implies(implies(X_36,X_37),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_36,X_37),implies(implies(not(X_36),X_36),X_37))) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(implies(implies(not(X_45),X_45),X_46),X_44),implies(implies(X_45,X_46),X_44))),
inference(subst,[],[refute_0_23:[bind(Z,$fot(X_44)),bind(X_36,$fot(X_45)),bind(X_37,$fot(X_46))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_45),X_45),X_46),X_44))
| is_a_theorem(implies(implies(X_45,X_46),X_44)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_45),X_45),X_46),X_44),implies(implies(X_45,X_46),X_44))) )],[refute_0_24,refute_0_17]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_670),X_670),X_667),implies(implies(implies(implies(not(X_668),X_668),X_668),X_670),X_667)))
| is_a_theorem(implies(implies(X_670,X_667),implies(implies(implies(implies(not(X_668),X_668),X_668),X_670),X_667))) ),
inference(subst,[],[refute_0_25:[bind(X_44,$fot(implies(implies(implies(implies(not(X_668),X_668),X_668),X_670),X_667))),bind(X_45,$fot(X_670)),bind(X_46,$fot(X_667))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_648),X_648),X_648),X_650),implies(X_649,X_650)))
| is_a_theorem(implies(implies(implies(X_649,X_650),Z),implies(implies(implies(implies(not(X_648),X_648),X_648),X_650),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(implies(not(X_648),X_648),X_648),X_650))),bind(Y,$fot(implies(X_649,X_650)))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(X_147,implies(not(implies(implies(not(X_145),X_145),X_145)),X_146)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),X_146),Z),implies(X_147,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_147)),bind(Y,$fot(implies(not(implies(implies(not(X_145),X_145),X_145)),X_146)))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_34)),
inference(subst,[],[refute_0_33:[bind(X_9,$fot(X_34))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_34))
| is_a_theorem(implies(implies(X_34,X_35),implies(not(implies(implies(not(X),X),X)),X_35))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(X_34,X_35),implies(not(implies(implies(not(X),X),X)),X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_34)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(not(X_135),X_134),implies(not(implies(implies(not(X),X),X)),X_134))),
inference(subst,[],[refute_0_36:[bind(X_34,$fot(not(X_135))),bind(X_35,$fot(X_134))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(not(X_135),X_134),implies(not(implies(implies(not(X),X),X)),X_134)))
| is_a_theorem(implies(X_135,implies(not(implies(implies(not(X),X),X)),X_134))) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(X_134)),bind(X_39,$fot(X_135)),bind(X_40,$fot(implies(not(implies(implies(not(X),X),X)),X_134)))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(X_135,implies(not(implies(implies(not(X),X),X)),X_134))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_135),X_134),implies(not(implies(implies(not(X),X),X)),X_134))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(X_147,implies(not(implies(implies(not(X_145),X_145),X_145)),X_146))),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_145)),bind(X_134,$fot(X_146)),bind(X_135,$fot(X_147))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),X_146),Z),implies(X_147,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_147,implies(not(implies(implies(not(X_145),X_145),X_145)),X_146))) )],[refute_0_40,refute_0_28]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),implies(implies(not(X_145),X_145),X_145)),X_647),implies(X_147,X_647))),
inference(subst,[],[refute_0_41:[bind(Z,$fot(X_647)),bind(X_146,$fot(implies(implies(not(X_145),X_145),X_145)))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),implies(implies(not(X_145),X_145),X_145)),X_647),implies(X_147,X_647)))
| is_a_theorem(implies(implies(implies(implies(not(X_145),X_145),X_145),X_647),implies(X_147,X_647))) ),
inference(subst,[],[refute_0_25:[bind(X_44,$fot(implies(X_147,X_647))),bind(X_45,$fot(implies(implies(not(X_145),X_145),X_145))),bind(X_46,$fot(X_647))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(implies(implies(not(X_145),X_145),X_145),X_647),implies(X_147,X_647))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_145),X_145),X_145)),implies(implies(not(X_145),X_145),X_145)),X_647),implies(X_147,X_647))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(implies(not(X_648),X_648),X_648),X_650),implies(X_649,X_650))),
inference(subst,[],[refute_0_44:[bind(X_145,$fot(X_648)),bind(X_147,$fot(X_649)),bind(X_647,$fot(X_650))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(implies(X_649,X_650),Z),implies(implies(implies(implies(not(X_648),X_648),X_648),X_650),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_648),X_648),X_648),X_650),implies(X_649,X_650))) )],[refute_0_45,refute_0_27]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(implies(not(X_670),X_670),X_667),implies(implies(implies(implies(not(X_668),X_668),X_668),X_670),X_667))),
inference(subst,[],[refute_0_46:[bind(Z,$fot(X_667)),bind(X_648,$fot(X_668)),bind(X_649,$fot(not(X_670))),bind(X_650,$fot(X_670))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(X_670,X_667),implies(implies(implies(implies(not(X_668),X_668),X_668),X_670),X_667))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_670),X_670),X_667),implies(implies(implies(implies(not(X_668),X_668),X_668),X_670),X_667))) )],[refute_0_47,refute_0_26]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(X_1185,X_1185),implies(implies(implies(implies(not(X_668),X_668),X_668),X_1185),X_1185))),
inference(subst,[],[refute_0_48:[bind(X_667,$fot(X_1185)),bind(X_670,$fot(X_1185))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(implies(X_1159,X_1159),X_1158))
| ~ is_a_theorem(implies(implies(implies(X_1159,X_1159),X_1158),X_1158))
| is_a_theorem(X_1158) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1159,X_1159),X_1158))),bind(Y,$fot(X_1158))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(X_1156,X_1156),X_1155),X_1155)),implies(implies(implies(X_1156,X_1156),X_1155),X_1155)))
| is_a_theorem(implies(implies(implies(X_1156,X_1156),X_1155),X_1155)) ),
inference(subst,[],[refute_0_53:[bind(X_7,$fot(implies(implies(implies(X_1156,X_1156),X_1155),X_1155)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(implies(X_654,X_654),X_656))
| ~ is_a_theorem(implies(implies(implies(X_654,X_654),X_656),implies(X_655,X_656)))
| is_a_theorem(implies(X_655,X_656)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_654,X_654),X_656))),bind(Y,$fot(implies(X_655,X_656)))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(X_188,implies(not(implies(X_187,X_187)),X_186)))
| is_a_theorem(implies(implies(implies(not(implies(X_187,X_187)),X_186),Z),implies(X_188,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_188)),bind(Y,$fot(implies(not(implies(X_187,X_187)),X_186)))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(implies(not(X_39),X_170),implies(not(implies(X_172,X_172)),X_170)))
| is_a_theorem(implies(X_39,implies(not(implies(X_172,X_172)),X_170))) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(X_170)),bind(X_40,$fot(implies(not(implies(X_172,X_172)),X_170)))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(not(implies(X_139,X_139)),X_138))
| is_a_theorem(implies(implies(X_138,Z),implies(not(implies(X_139,X_139)),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(implies(X_139,X_139)))),bind(Y,$fot(X_138))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(X_137,X_137))
| is_a_theorem(implies(not(implies(X_137,X_137)),Y)) ),
inference(subst,[],[refute_0_31:[bind(X_6,$fot(implies(X_137,X_137)))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(not(X_136),X_136),X_136)),
inference(subst,[],[cn_2:[bind(X,$fot(X_136))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(not(X_136),X_136),X_136))
| is_a_theorem(implies(X_136,X_136)) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(X_136)),bind(X_39,$fot(X_136)),bind(X_40,$fot(X_136))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(X_136,X_136)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_136),X_136),X_136)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(X_137,X_137)),
inference(subst,[],[refute_0_62:[bind(X_136,$fot(X_137))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(not(implies(X_137,X_137)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_137,X_137)) )],[refute_0_63,refute_0_59]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(not(implies(X_139,X_139)),X_138)),
inference(subst,[],[refute_0_64:[bind(Y,$fot(X_138)),bind(X_137,$fot(X_139))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(X_138,Z),implies(not(implies(X_139,X_139)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_139,X_139)),X_138)) )],[refute_0_65,refute_0_58]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(not(X_39),X_170),implies(not(implies(X_172,X_172)),X_170))),
inference(subst,[],[refute_0_66:[bind(Z,$fot(X_170)),bind(X_138,$fot(not(X_39))),bind(X_139,$fot(X_172))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(X_39,implies(not(implies(X_172,X_172)),X_170))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_39),X_170),implies(not(implies(X_172,X_172)),X_170))) )],[refute_0_67,refute_0_57]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(X_188,implies(not(implies(X_187,X_187)),X_186))),
inference(subst,[],[refute_0_68:[bind(X_170,$fot(X_186)),bind(X_172,$fot(X_187)),bind(X_39,$fot(X_188))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(not(implies(X_187,X_187)),X_186),Z),implies(X_188,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_188,implies(not(implies(X_187,X_187)),X_186))) )],[refute_0_69,refute_0_56]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(implies(not(implies(X_187,X_187)),implies(X_187,X_187)),X_647),implies(X_188,X_647))),
inference(subst,[],[refute_0_70:[bind(Z,$fot(X_647)),bind(X_186,$fot(implies(X_187,X_187)))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_187,X_187)),implies(X_187,X_187)),X_647),implies(X_188,X_647)))
| is_a_theorem(implies(implies(implies(X_187,X_187),X_647),implies(X_188,X_647))) ),
inference(subst,[],[refute_0_25:[bind(X_44,$fot(implies(X_188,X_647))),bind(X_45,$fot(implies(X_187,X_187))),bind(X_46,$fot(X_647))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(implies(X_187,X_187),X_647),implies(X_188,X_647))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_187,X_187)),implies(X_187,X_187)),X_647),implies(X_188,X_647))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(implies(X_654,X_654),X_656),implies(X_655,X_656))),
inference(subst,[],[refute_0_73:[bind(X_187,$fot(X_654)),bind(X_188,$fot(X_655)),bind(X_647,$fot(X_656))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(X_654,X_654),X_656))
| is_a_theorem(implies(X_655,X_656)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_654,X_654),X_656),implies(X_655,X_656))) )],[refute_0_74,refute_0_55]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(X_1152,X_1152),implies(implies(implies(X_1153,X_1153),X_1152),X_1152)))
| is_a_theorem(implies(X_655,implies(implies(implies(X_1153,X_1153),X_1152),X_1152))) ),
inference(subst,[],[refute_0_75:[bind(X_654,$fot(X_1152)),bind(X_656,$fot(implies(implies(implies(X_1153,X_1153),X_1152),X_1152)))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1147),X_1147),X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144)))
| is_a_theorem(implies(implies(X_1147,X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144))) ),
inference(subst,[],[refute_0_25:[bind(X_44,$fot(implies(implies(implies(X_1145,X_1145),X_1147),X_1144))),bind(X_45,$fot(X_1147)),bind(X_46,$fot(X_1144))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(implies(X_654,X_654),X_656),implies(X_655,X_656)))
| is_a_theorem(implies(implies(implies(X_655,X_656),Z),implies(implies(implies(X_654,X_654),X_656),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(X_654,X_654),X_656))),bind(Y,$fot(implies(X_655,X_656)))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(implies(X_655,X_656),Z),implies(implies(implies(X_654,X_654),X_656),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_654,X_654),X_656),implies(X_655,X_656))) )],[refute_0_74,refute_0_78]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(implies(implies(not(X_1147),X_1147),X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144))),
inference(subst,[],[refute_0_79:[bind(Z,$fot(X_1144)),bind(X_654,$fot(X_1145)),bind(X_655,$fot(not(X_1147))),bind(X_656,$fot(X_1147))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(X_1147,X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1147),X_1147),X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144))) )],[refute_0_80,refute_0_77]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(X_1152,X_1152),implies(implies(implies(X_1153,X_1153),X_1152),X_1152))),
inference(subst,[],[refute_0_81:[bind(X_1144,$fot(X_1152)),bind(X_1145,$fot(X_1153)),bind(X_1147,$fot(X_1152))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(X_655,implies(implies(implies(X_1153,X_1153),X_1152),X_1152))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1152,X_1152),implies(implies(implies(X_1153,X_1153),X_1152),X_1152))) )],[refute_0_82,refute_0_76]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(not(implies(implies(implies(X_1156,X_1156),X_1155),X_1155)),implies(implies(implies(X_1156,X_1156),X_1155),X_1155))),
inference(subst,[],[refute_0_83:[bind(X_1152,$fot(X_1155)),bind(X_1153,$fot(X_1156)),bind(X_655,$fot(not(implies(implies(implies(X_1156,X_1156),X_1155),X_1155))))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(implies(X_1156,X_1156),X_1155),X_1155)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(X_1156,X_1156),X_1155),X_1155)),implies(implies(implies(X_1156,X_1156),X_1155),X_1155))) )],[refute_0_84,refute_0_54]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(implies(X_1159,X_1159),X_1158),X_1158)),
inference(subst,[],[refute_0_85:[bind(X_1155,$fot(X_1158)),bind(X_1156,$fot(X_1159))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(X_1159,X_1159),X_1158))
| is_a_theorem(X_1158) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1159,X_1159),X_1158),X_1158)) )],[refute_0_86,refute_0_50]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(X_1185,X_1185),implies(implies(implies(implies(not(X_668),X_668),X_668),X_1185),X_1185)))
| is_a_theorem(implies(implies(implies(implies(not(X_668),X_668),X_668),X_1185),X_1185)) ),
inference(subst,[],[refute_0_87:[bind(X_1158,$fot(implies(implies(implies(implies(not(X_668),X_668),X_668),X_1185),X_1185))),bind(X_1159,$fot(X_1185))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(implies(implies(implies(not(X_668),X_668),X_668),X_1185),X_1185)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1185,X_1185),implies(implies(implies(implies(not(X_668),X_668),X_668),X_1185),X_1185))) )],[refute_0_49,refute_0_88]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1996),X_1996),X_1996),implies(X_1994,X_1996)),implies(X_1994,X_1996))),
inference(subst,[],[refute_0_89:[bind(X_1185,$fot(implies(X_1994,X_1996))),bind(X_668,$fot(X_1996))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1996),X_1996),X_1996),implies(X_1994,X_1996)),implies(X_1994,X_1996)))
| is_a_theorem(implies(implies(X_1994,implies(not(X_1996),X_1996)),implies(X_1994,X_1996))) ),
inference(subst,[],[refute_0_15:[bind(X_79,$fot(X_1994)),bind(X_80,$fot(implies(not(X_1996),X_1996))),bind(X_81,$fot(X_1996)),bind(X_82,$fot(implies(X_1994,X_1996)))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(X_1994,implies(not(X_1996),X_1996)),implies(X_1994,X_1996))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1996),X_1996),X_1996),implies(X_1994,X_1996)),implies(X_1994,X_1996))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(implies(X_80,X_2021),implies(not(X_2021),X_2021)),implies(implies(X_80,X_2021),X_2021))),
inference(subst,[],[refute_0_92:[bind(X_1994,$fot(implies(X_80,X_2021))),bind(X_1996,$fot(X_2021))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(not(X_2021),X_80),implies(implies(X_80,X_2021),X_2021))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_80,X_2021),implies(not(X_2021),X_2021)),implies(implies(X_80,X_2021),X_2021))) )],[refute_0_93,refute_0_16]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(implies(not(X_2047),X_2048),implies(implies(X_2048,X_2047),X_2047))),
inference(subst,[],[refute_0_94:[bind(X_2021,$fot(X_2047)),bind(X_80,$fot(X_2048))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(not(X_2047),X_2048))
| is_a_theorem(implies(implies(X_2048,X_2047),X_2047)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_2047),X_2048),implies(implies(X_2048,X_2047),X_2047))) )],[refute_0_95,refute_0_10]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(not(not(X_5566)),X_5566))
| is_a_theorem(implies(implies(X_5566,not(X_5566)),not(X_5566))) ),
inference(subst,[],[refute_0_96:[bind(X_2047,$fot(not(X_5566))),bind(X_2048,$fot(X_5566))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(implies(not(not(not(X_5565))),not(not(X_5565))),X_5565))
| is_a_theorem(implies(not(not(X_5565)),X_5565)) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(not(not(X_5565)))),bind(X_39,$fot(not(not(X_5565)))),bind(X_40,$fot(X_5565))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(not(not(X_5564))),not(not(X_5564)))),X_5564),X_5564))
| is_a_theorem(implies(implies(not(not(not(X_5564))),not(not(X_5564))),X_5564)) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(X_5564)),bind(X_39,$fot(implies(not(not(not(X_5564))),not(not(X_5564))))),bind(X_40,$fot(X_5564))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(not(X_2047),not(implies(not(not(not(X_2047))),not(not(X_2047))))))
| is_a_theorem(implies(implies(not(implies(not(not(not(X_2047))),not(not(X_2047)))),X_2047),X_2047)) ),
inference(subst,[],[refute_0_96:[bind(X_2048,$fot(not(implies(not(not(not(X_2047))),not(not(X_2047))))))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(implies(not(X_39),not(implies(not(not(X_39)),not(X_39)))),not(implies(not(not(X_39)),not(X_39)))))
| is_a_theorem(implies(X_39,not(implies(not(not(X_39)),not(X_39))))) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(not(implies(not(not(X_39)),not(X_39))))),bind(X_40,$fot(not(implies(not(not(X_39)),not(X_39)))))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(not(not(implies(not(X_5553),X_5553))),X_5553))
| is_a_theorem(implies(implies(X_5553,not(implies(not(X_5553),X_5553))),not(implies(not(X_5553),X_5553)))) ),
inference(subst,[],[refute_0_96:[bind(X_2047,$fot(not(implies(not(X_5553),X_5553)))),bind(X_2048,$fot(X_5553))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(X_2020,implies(not(X_2021),X_2021)))
| ~ is_a_theorem(implies(implies(X_2020,implies(not(X_2021),X_2021)),implies(X_2020,X_2021)))
| is_a_theorem(implies(X_2020,X_2021)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_2020,implies(not(X_2021),X_2021)))),bind(Y,$fot(implies(X_2020,X_2021)))]]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(implies(X_2020,implies(not(X_2021),X_2021)),implies(X_2020,X_2021))),
inference(subst,[],[refute_0_92:[bind(X_1994,$fot(X_2020)),bind(X_1996,$fot(X_2021))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(X_2020,implies(not(X_2021),X_2021)))
| is_a_theorem(implies(X_2020,X_2021)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2020,implies(not(X_2021),X_2021)),implies(X_2020,X_2021))) )],[refute_0_104,refute_0_103]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(not(not(implies(not(X_5551),X_5551))),implies(not(X_5551),X_5551)))
| is_a_theorem(implies(not(not(implies(not(X_5551),X_5551))),X_5551)) ),
inference(subst,[],[refute_0_105:[bind(X_2020,$fot(not(not(implies(not(X_5551),X_5551))))),bind(X_2021,$fot(X_5551))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(not(not(implies(X_5546,X_5545))),implies(not(implies(X_5546,X_5545)),implies(X_5546,X_5545))))
| is_a_theorem(implies(not(not(implies(X_5546,X_5545))),implies(X_5546,X_5545))) ),
inference(subst,[],[refute_0_105:[bind(X_2020,$fot(not(not(implies(X_5546,X_5545))))),bind(X_2021,$fot(implies(X_5546,X_5545)))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(implies(not(not(X_5541)),not(X_5541)),implies(X_5541,implies(X_5543,X_5542))))
| is_a_theorem(implies(not(X_5541),implies(X_5541,implies(X_5543,X_5542)))) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(not(X_5541))),bind(X_39,$fot(not(X_5541))),bind(X_40,$fot(implies(X_5541,implies(X_5543,X_5542))))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_4703),not(X_4703)),implies(not(not(X_4703)),not(X_4703))),implies(X_4703,implies(X_4706,X_4704))))
| is_a_theorem(implies(implies(not(not(X_4703)),not(X_4703)),implies(X_4703,implies(X_4706,X_4704)))) ),
inference(subst,[],[refute_0_15:[bind(X_79,$fot(not(not(X_4703)))),bind(X_80,$fot(not(X_4703))),bind(X_81,$fot(not(X_4703))),bind(X_82,$fot(implies(X_4703,implies(X_4706,X_4704))))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(X_149,implies(implies(not(not(X_149)),not(X_149)),X_148)))
| is_a_theorem(implies(implies(implies(implies(not(not(X_149)),not(X_149)),X_148),Z),implies(X_149,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_149)),bind(Y,$fot(implies(implies(not(not(X_149)),not(X_149)),X_148)))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(not(X_135),X_134),implies(implies(not(not(X_135)),not(X_135)),X_134))),
inference(subst,[],[refute_0_21:[bind(X_34,$fot(not(X_135))),bind(X_35,$fot(X_134))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(implies(implies(not(X_135),X_134),implies(implies(not(not(X_135)),not(X_135)),X_134)))
| is_a_theorem(implies(X_135,implies(implies(not(not(X_135)),not(X_135)),X_134))) ),
inference(subst,[],[refute_0_8:[bind(X_38,$fot(X_134)),bind(X_39,$fot(X_135)),bind(X_40,$fot(implies(implies(not(not(X_135)),not(X_135)),X_134)))]]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(X_135,implies(implies(not(not(X_135)),not(X_135)),X_134))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_135),X_134),implies(implies(not(not(X_135)),not(X_135)),X_134))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(X_149,implies(implies(not(not(X_149)),not(X_149)),X_148))),
inference(subst,[],[refute_0_113:[bind(X_134,$fot(X_148)),bind(X_135,$fot(X_149))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_149)),not(X_149)),X_148),Z),implies(X_149,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_149,implies(implies(not(not(X_149)),not(X_149)),X_148))) )],[refute_0_114,refute_0_110]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_149)),not(X_149)),X_1996),implies(X_1994,X_1996)),implies(X_149,implies(X_1994,X_1996)))),
inference(subst,[],[refute_0_115:[bind(Z,$fot(implies(X_1994,X_1996))),bind(X_148,$fot(X_1996))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_149)),not(X_149)),X_1996),implies(X_1994,X_1996)),implies(X_149,implies(X_1994,X_1996))))
| is_a_theorem(implies(implies(X_1994,implies(not(not(X_149)),not(X_149))),implies(X_149,implies(X_1994,X_1996)))) ),
inference(subst,[],[refute_0_15:[bind(X_79,$fot(X_1994)),bind(X_80,$fot(implies(not(not(X_149)),not(X_149)))),bind(X_81,$fot(X_1996)),bind(X_82,$fot(implies(X_149,implies(X_1994,X_1996))))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(X_1994,implies(not(not(X_149)),not(X_149))),implies(X_149,implies(X_1994,X_1996)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_149)),not(X_149)),X_1996),implies(X_1994,X_1996)),implies(X_149,implies(X_1994,X_1996)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(X_4558,implies(not(not(X_149)),not(X_149))),implies(X_149,implies(X_4558,X_1996)))),
inference(subst,[],[refute_0_118:[bind(X_1994,$fot(X_4558))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(X_1146,X_1147),X_1144))
| ~ is_a_theorem(implies(implies(implies(X_1146,X_1147),X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144)))
| is_a_theorem(implies(implies(implies(X_1145,X_1145),X_1147),X_1144)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1146,X_1147),X_1144))),bind(Y,$fot(implies(implies(implies(X_1145,X_1145),X_1147),X_1144)))]]) ).
cnf(refute_0_121,plain,
is_a_theorem(implies(implies(implies(X_1146,X_1147),X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144))),
inference(subst,[],[refute_0_79:[bind(Z,$fot(X_1144)),bind(X_654,$fot(X_1145)),bind(X_655,$fot(X_1146)),bind(X_656,$fot(X_1147))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(X_1146,X_1147),X_1144))
| is_a_theorem(implies(implies(implies(X_1145,X_1145),X_1147),X_1144)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1146,X_1147),X_1144),implies(implies(implies(X_1145,X_1145),X_1147),X_1144))) )],[refute_0_121,refute_0_120]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(implies(X_4558,implies(not(not(X_149)),not(X_149))),implies(X_149,implies(X_4558,X_1996))))
| is_a_theorem(implies(implies(implies(X_4557,X_4557),implies(not(not(X_149)),not(X_149))),implies(X_149,implies(X_4558,X_1996)))) ),
inference(subst,[],[refute_0_122:[bind(X_1144,$fot(implies(X_149,implies(X_4558,X_1996)))),bind(X_1145,$fot(X_4557)),bind(X_1146,$fot(X_4558)),bind(X_1147,$fot(implies(not(not(X_149)),not(X_149))))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(implies(X_4557,X_4557),implies(not(not(X_149)),not(X_149))),implies(X_149,implies(X_4558,X_1996)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_4558,implies(not(not(X_149)),not(X_149))),implies(X_149,implies(X_4558,X_1996)))) )],[refute_0_119,refute_0_123]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(implies(implies(not(X_4703),not(X_4703)),implies(not(not(X_4703)),not(X_4703))),implies(X_4703,implies(X_4706,X_4704)))),
inference(subst,[],[refute_0_124:[bind(X_149,$fot(X_4703)),bind(X_1996,$fot(X_4704)),bind(X_4557,$fot(not(X_4703))),bind(X_4558,$fot(X_4706))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(not(not(X_4703)),not(X_4703)),implies(X_4703,implies(X_4706,X_4704)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_4703),not(X_4703)),implies(not(not(X_4703)),not(X_4703))),implies(X_4703,implies(X_4706,X_4704)))) )],[refute_0_125,refute_0_109]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(not(not(X_5541)),not(X_5541)),implies(X_5541,implies(X_5543,X_5542)))),
inference(subst,[],[refute_0_126:[bind(X_4703,$fot(X_5541)),bind(X_4704,$fot(X_5542)),bind(X_4706,$fot(X_5543))]]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(not(X_5541),implies(X_5541,implies(X_5543,X_5542)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_5541)),not(X_5541)),implies(X_5541,implies(X_5543,X_5542)))) )],[refute_0_127,refute_0_108]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(not(not(implies(X_5546,X_5545))),implies(not(implies(X_5546,X_5545)),implies(X_5546,X_5545)))),
inference(subst,[],[refute_0_128:[bind(X_5541,$fot(not(implies(X_5546,X_5545)))),bind(X_5542,$fot(X_5545)),bind(X_5543,$fot(X_5546))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(not(not(implies(X_5546,X_5545))),implies(X_5546,X_5545))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(X_5546,X_5545))),implies(not(implies(X_5546,X_5545)),implies(X_5546,X_5545)))) )],[refute_0_129,refute_0_107]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(not(not(implies(not(X_5551),X_5551))),implies(not(X_5551),X_5551))),
inference(subst,[],[refute_0_130:[bind(X_5545,$fot(X_5551)),bind(X_5546,$fot(not(X_5551)))]]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(not(not(implies(not(X_5551),X_5551))),X_5551)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(X_5551),X_5551))),implies(not(X_5551),X_5551))) )],[refute_0_131,refute_0_106]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(not(not(implies(not(X_5553),X_5553))),X_5553)),
inference(subst,[],[refute_0_132:[bind(X_5551,$fot(X_5553))]]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(X_5553,not(implies(not(X_5553),X_5553))),not(implies(not(X_5553),X_5553)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(X_5553),X_5553))),X_5553)) )],[refute_0_133,refute_0_102]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(not(X_39),not(implies(not(not(X_39)),not(X_39)))),not(implies(not(not(X_39)),not(X_39))))),
inference(subst,[],[refute_0_134:[bind(X_5553,$fot(not(X_39)))]]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(X_39,not(implies(not(not(X_39)),not(X_39))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_39),not(implies(not(not(X_39)),not(X_39)))),not(implies(not(not(X_39)),not(X_39))))) )],[refute_0_135,refute_0_101]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(not(X_2047),not(implies(not(not(not(X_2047))),not(not(X_2047)))))),
inference(subst,[],[refute_0_136:[bind(X_39,$fot(not(X_2047)))]]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(implies(not(implies(not(not(not(X_2047))),not(not(X_2047)))),X_2047),X_2047)),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_2047),not(implies(not(not(not(X_2047))),not(not(X_2047)))))) )],[refute_0_137,refute_0_100]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(implies(not(implies(not(not(not(X_5564))),not(not(X_5564)))),X_5564),X_5564)),
inference(subst,[],[refute_0_138:[bind(X_2047,$fot(X_5564))]]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(implies(not(not(not(X_5564))),not(not(X_5564))),X_5564)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(not(not(not(X_5564))),not(not(X_5564)))),X_5564),X_5564)) )],[refute_0_139,refute_0_99]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(implies(not(not(not(X_5565))),not(not(X_5565))),X_5565)),
inference(subst,[],[refute_0_140:[bind(X_5564,$fot(X_5565))]]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(not(not(X_5565)),X_5565)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(X_5565))),not(not(X_5565))),X_5565)) )],[refute_0_141,refute_0_98]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(not(not(X_5566)),X_5566)),
inference(subst,[],[refute_0_142:[bind(X_5565,$fot(X_5566))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(implies(X_5566,not(X_5566)),not(X_5566))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_5566)),X_5566)) )],[refute_0_143,refute_0_97]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(implies(not(X_39),not(not(X_39))),not(not(X_39)))),
inference(subst,[],[refute_0_144:[bind(X_5566,$fot(not(X_39)))]]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(X_39,not(not(X_39)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_39),not(not(X_39))),not(not(X_39)))) )],[refute_0_145,refute_0_9]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(X_5568,not(not(X_5568)))),
inference(subst,[],[refute_0_146:[bind(X_39,$fot(X_5568))]]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(not(not(X_5568)),Z),implies(X_5568,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_5568,not(not(X_5568)))) )],[refute_0_147,refute_0_2]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(implies(not(not(x)),y),implies(x,y))),
inference(subst,[],[refute_0_148:[bind(Z,$fot(y)),bind(X_5568,$fot(x))]]) ).
cnf(refute_0_150,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(x)),y),implies(x,y))) )],[refute_0_149,prove_cn_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL396-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 2 18:38:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.61/3.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.61/3.79
% 3.61/3.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.61/3.80
%------------------------------------------------------------------------------