TSTP Solution File: LCL057-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL057-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:49:07 EDT 2022
% Result : Unsatisfiable 5.99s 6.17s
% Output : CNFRefutation 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 5
% Syntax : Number of clauses : 152 ( 88 unt; 0 nHn; 48 RR)
% Number of literals : 230 ( 0 equ; 79 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 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 : 365 ( 55 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_40,negated_conjecture,
~ is_a_theorem(implies(a,not(not(a)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_37),X_36),X_38),implies(X_37,X_38)))
| ~ is_a_theorem(implies(implies(not(X_37),X_36),X_38))
| is_a_theorem(implies(X_37,X_38)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_37),X_36),X_38))),bind(Y,$fot(implies(X_37,X_38)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_27,implies(not(X_27),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_27,implies(not(X_27),Y)))
| is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_27)),bind(Y,$fot(implies(not(X_27),Y))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(X_27,implies(not(X_27),Y))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(not(X_37),X_36),X_38),implies(X_37,X_38))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_36)),bind(X_27,$fot(X_37)),bind(X_29,$fot(X_38))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(not(X_37),X_36),X_38))
| is_a_theorem(implies(X_37,X_38)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_37),X_36),X_38),implies(X_37,X_38))) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(not(X_37),not(not(X_37))),not(not(X_37))))
| is_a_theorem(implies(X_37,not(not(X_37)))) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(not(not(X_37)))),bind(X_38,$fot(not(not(X_37))))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(not(X_1487),X_1488),implies(implies(X_1488,X_1487),X_1487)))
| ~ is_a_theorem(implies(not(X_1487),X_1488))
| is_a_theorem(implies(implies(X_1488,X_1487),X_1487)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_1487),X_1488))),bind(Y,$fot(implies(implies(X_1488,X_1487),X_1487)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35))
| ~ is_a_theorem(implies(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35),implies(implies(X_32,X_33),X_35)))
| is_a_theorem(implies(implies(X_32,X_33),X_35)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35))),bind(Y,$fot(implies(implies(X_32,X_33),X_35)))]]) ).
cnf(refute_0_11,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_29),implies(implies(X,Y),X_29))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35),implies(implies(X_32,X_33),X_35))),
inference(subst,[],[refute_0_12:[bind(X,$fot(X_32)),bind(Y,$fot(X_33)),bind(Z,$fot(X_34)),bind(X_29,$fot(X_35))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35))
| is_a_theorem(implies(implies(X_32,X_33),X_35)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35),implies(implies(X_32,X_33),X_35))) )],[refute_0_13,refute_0_10]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(X_33,X_1482),implies(not(X_1482),X_1482)),implies(implies(X_33,X_1482),X_1482)))
| is_a_theorem(implies(implies(not(X_1482),X_33),implies(implies(X_33,X_1482),X_1482))) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(not(X_1482))),bind(X_34,$fot(X_1482)),bind(X_35,$fot(implies(implies(X_33,X_1482),X_1482)))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_71,X_72),X_70),X_69))
| ~ is_a_theorem(implies(implies(implies(implies(X_71,X_72),X_70),X_69),implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),X_69)))
| is_a_theorem(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),X_69)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_71,X_72),X_70),X_69))),bind(Y,$fot(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),X_69)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46)))
| is_a_theorem(implies(implies(implies(implies(X_47,X_48),X_46),Z),implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(implies(not(X_47),X_47),X_48),X_46))),bind(Y,$fot(implies(implies(X_47,X_48),X_46)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31)))
| is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),Z),implies(implies(X_30,X_31),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X_30,X_31))),bind(Y,$fot(implies(implies(not(X_30),X_30),X_31)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(not(X_28),X_28),X_28)),
inference(subst,[],[cn_2:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(not(X_28),X_28),X_28))
| is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(not(X_28),X_28))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_28),X_28),X_28)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))),
inference(subst,[],[refute_0_21:[bind(X_28,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),Z),implies(implies(X_30,X_31),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46))),
inference(subst,[],[refute_0_23:[bind(Z,$fot(X_46)),bind(X_30,$fot(X_47)),bind(X_31,$fot(X_48))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(implies(implies(X_47,X_48),X_46),Z),implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46))) )],[refute_0_24,refute_0_17]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(implies(implies(X_71,X_72),X_70),X_69),implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),X_69))),
inference(subst,[],[refute_0_25:[bind(Z,$fot(X_69)),bind(X_46,$fot(X_70)),bind(X_47,$fot(X_71)),bind(X_48,$fot(X_72))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(X_71,X_72),X_70),X_69))
| is_a_theorem(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),X_69)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_71,X_72),X_70),X_69),implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),X_69))) )],[refute_0_26,refute_0_16]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(implies(X_998,X_998),X_999),X_999))
| is_a_theorem(implies(implies(implies(implies(not(X_998),X_998),X_998),X_999),X_999)) ),
inference(subst,[],[refute_0_27:[bind(X_69,$fot(X_999)),bind(X_70,$fot(X_999)),bind(X_71,$fot(X_998)),bind(X_72,$fot(X_998))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_30,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_31,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(X_995,X_995),X_996),X_996)),implies(implies(implies(X_995,X_995),X_996),X_996)))
| is_a_theorem(implies(implies(implies(X_995,X_995),X_996),X_996)) ),
inference(subst,[],[refute_0_31:[bind(X_7,$fot(implies(implies(implies(X_995,X_995),X_996),X_996)))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46)))
| ~ is_a_theorem(implies(implies(implies(not(X_47),X_47),X_48),X_46))
| is_a_theorem(implies(implies(X_47,X_48),X_46)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_47),X_47),X_48),X_46))),bind(Y,$fot(implies(implies(X_47,X_48),X_46)))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_47),X_47),X_48),X_46))
| is_a_theorem(implies(implies(X_47,X_48),X_46)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_47),X_47),X_48),X_46),implies(implies(X_47,X_48),X_46))) )],[refute_0_24,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_854),X_854),X_851),implies(implies(implies(X_852,X_852),X_854),X_851)))
| is_a_theorem(implies(implies(X_854,X_851),implies(implies(implies(X_852,X_852),X_854),X_851))) ),
inference(subst,[],[refute_0_34:[bind(X_46,$fot(implies(implies(implies(X_852,X_852),X_854),X_851))),bind(X_47,$fot(X_854)),bind(X_48,$fot(X_851))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(implies(X_848,X_848),X_850),implies(X_849,X_850)))
| is_a_theorem(implies(implies(implies(X_849,X_850),Z),implies(implies(implies(X_848,X_848),X_850),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(X_848,X_848),X_850))),bind(Y,$fot(implies(X_849,X_850)))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(X_173,implies(not(implies(X_172,X_172)),X_171)))
| is_a_theorem(implies(implies(implies(not(implies(X_172,X_172)),X_171),Z),implies(X_173,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_173)),bind(Y,$fot(implies(not(implies(X_172,X_172)),X_171)))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(not(X_37),X_168),implies(not(implies(X_170,X_170)),X_168)))
| is_a_theorem(implies(X_37,implies(not(implies(X_170,X_170)),X_168))) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(X_168)),bind(X_38,$fot(implies(not(implies(X_170,X_170)),X_168)))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(not(implies(X_132,X_132)),X_131))
| is_a_theorem(implies(implies(X_131,Z),implies(not(implies(X_132,X_132)),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(X_132,X_132)))),bind(Y,$fot(X_131))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(X_130,X_130))
| is_a_theorem(implies(not(implies(X_130,X_130)),Y)) ),
inference(subst,[],[refute_0_42:[bind(X_6,$fot(implies(X_130,X_130)))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(not(X_129),X_129),X_129)),
inference(subst,[],[cn_2:[bind(X,$fot(X_129))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(not(X_129),X_129),X_129))
| is_a_theorem(implies(X_129,X_129)) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(X_129)),bind(X_37,$fot(X_129)),bind(X_38,$fot(X_129))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(X_129,X_129)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_129),X_129),X_129)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(X_130,X_130)),
inference(subst,[],[refute_0_46:[bind(X_129,$fot(X_130))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(not(implies(X_130,X_130)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_130,X_130)) )],[refute_0_47,refute_0_43]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(not(implies(X_132,X_132)),X_131)),
inference(subst,[],[refute_0_48:[bind(Y,$fot(X_131)),bind(X_130,$fot(X_132))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(X_131,Z),implies(not(implies(X_132,X_132)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_132,X_132)),X_131)) )],[refute_0_49,refute_0_39]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(not(X_37),X_168),implies(not(implies(X_170,X_170)),X_168))),
inference(subst,[],[refute_0_50:[bind(Z,$fot(X_168)),bind(X_131,$fot(not(X_37))),bind(X_132,$fot(X_170))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(X_37,implies(not(implies(X_170,X_170)),X_168))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_37),X_168),implies(not(implies(X_170,X_170)),X_168))) )],[refute_0_51,refute_0_38]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_173,implies(not(implies(X_172,X_172)),X_171))),
inference(subst,[],[refute_0_52:[bind(X_168,$fot(X_171)),bind(X_170,$fot(X_172)),bind(X_37,$fot(X_173))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(not(implies(X_172,X_172)),X_171),Z),implies(X_173,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_173,implies(not(implies(X_172,X_172)),X_171))) )],[refute_0_53,refute_0_37]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(not(implies(X_172,X_172)),implies(X_172,X_172)),X_847),implies(X_173,X_847))),
inference(subst,[],[refute_0_54:[bind(Z,$fot(X_847)),bind(X_171,$fot(implies(X_172,X_172)))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_172,X_172)),implies(X_172,X_172)),X_847),implies(X_173,X_847)))
| is_a_theorem(implies(implies(implies(X_172,X_172),X_847),implies(X_173,X_847))) ),
inference(subst,[],[refute_0_34:[bind(X_46,$fot(implies(X_173,X_847))),bind(X_47,$fot(implies(X_172,X_172))),bind(X_48,$fot(X_847))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(implies(X_172,X_172),X_847),implies(X_173,X_847))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_172,X_172)),implies(X_172,X_172)),X_847),implies(X_173,X_847))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(X_848,X_848),X_850),implies(X_849,X_850))),
inference(subst,[],[refute_0_57:[bind(X_172,$fot(X_848)),bind(X_173,$fot(X_849)),bind(X_847,$fot(X_850))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(implies(implies(X_849,X_850),Z),implies(implies(implies(X_848,X_848),X_850),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_848,X_848),X_850),implies(X_849,X_850))) )],[refute_0_58,refute_0_36]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(not(X_854),X_854),X_851),implies(implies(implies(X_852,X_852),X_854),X_851))),
inference(subst,[],[refute_0_59:[bind(Z,$fot(X_851)),bind(X_848,$fot(X_852)),bind(X_849,$fot(not(X_854))),bind(X_850,$fot(X_854))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(X_854,X_851),implies(implies(implies(X_852,X_852),X_854),X_851))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_854),X_854),X_851),implies(implies(implies(X_852,X_852),X_854),X_851))) )],[refute_0_60,refute_0_35]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(X_975,X_975),implies(implies(implies(X_852,X_852),X_975),X_975))),
inference(subst,[],[refute_0_61:[bind(X_851,$fot(X_975)),bind(X_854,$fot(X_975))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(X_848,X_848),X_850))
| ~ is_a_theorem(implies(implies(implies(X_848,X_848),X_850),implies(X_849,X_850)))
| is_a_theorem(implies(X_849,X_850)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_848,X_848),X_850))),bind(Y,$fot(implies(X_849,X_850)))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(implies(X_848,X_848),X_850))
| is_a_theorem(implies(X_849,X_850)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_848,X_848),X_850),implies(X_849,X_850))) )],[refute_0_58,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(X_975,X_975),implies(implies(implies(X_852,X_852),X_975),X_975)))
| is_a_theorem(implies(X_976,implies(implies(implies(X_852,X_852),X_975),X_975))) ),
inference(subst,[],[refute_0_64:[bind(X_848,$fot(X_975)),bind(X_849,$fot(X_976)),bind(X_850,$fot(implies(implies(implies(X_852,X_852),X_975),X_975)))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(X_976,implies(implies(implies(X_852,X_852),X_975),X_975))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_975,X_975),implies(implies(implies(X_852,X_852),X_975),X_975))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(not(implies(implies(implies(X_995,X_995),X_996),X_996)),implies(implies(implies(X_995,X_995),X_996),X_996))),
inference(subst,[],[refute_0_66:[bind(X_852,$fot(X_995)),bind(X_975,$fot(X_996)),bind(X_976,$fot(not(implies(implies(implies(X_995,X_995),X_996),X_996))))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(implies(X_995,X_995),X_996),X_996)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(X_995,X_995),X_996),X_996)),implies(implies(implies(X_995,X_995),X_996),X_996))) )],[refute_0_67,refute_0_32]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(implies(X_998,X_998),X_999),X_999)),
inference(subst,[],[refute_0_68:[bind(X_995,$fot(X_998)),bind(X_996,$fot(X_999))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(implies(not(X_998),X_998),X_998),X_999),X_999)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_998,X_998),X_999),X_999)) )],[refute_0_69,refute_0_28]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1472),X_1472),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))),
inference(subst,[],[refute_0_70:[bind(X_998,$fot(X_1472)),bind(X_999,$fot(implies(X_1470,X_1472)))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1472),X_1472),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472)))
| is_a_theorem(implies(implies(X_1470,implies(not(X_1472),X_1472)),implies(X_1470,X_1472))) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(X_1470)),bind(X_33,$fot(implies(not(X_1472),X_1472))),bind(X_34,$fot(X_1472)),bind(X_35,$fot(implies(X_1470,X_1472)))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(X_1470,implies(not(X_1472),X_1472)),implies(X_1470,X_1472))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1472),X_1472),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(implies(X_33,X_1482),implies(not(X_1482),X_1482)),implies(implies(X_33,X_1482),X_1482))),
inference(subst,[],[refute_0_73:[bind(X_1470,$fot(implies(X_33,X_1482))),bind(X_1472,$fot(X_1482))]]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(not(X_1482),X_33),implies(implies(X_33,X_1482),X_1482))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_33,X_1482),implies(not(X_1482),X_1482)),implies(implies(X_33,X_1482),X_1482))) )],[refute_0_74,refute_0_15]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(not(X_1487),X_1488),implies(implies(X_1488,X_1487),X_1487))),
inference(subst,[],[refute_0_75:[bind(X_1482,$fot(X_1487)),bind(X_33,$fot(X_1488))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(not(X_1487),X_1488))
| is_a_theorem(implies(implies(X_1488,X_1487),X_1487)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_1487),X_1488),implies(implies(X_1488,X_1487),X_1487))) )],[refute_0_76,refute_0_9]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(not(not(X_6111)),X_6111))
| is_a_theorem(implies(implies(X_6111,not(X_6111)),not(X_6111))) ),
inference(subst,[],[refute_0_77:[bind(X_1487,$fot(not(X_6111))),bind(X_1488,$fot(X_6111))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(not(X_484),X_483)),X_482),X_481),implies(X_484,X_481)))
| ~ is_a_theorem(implies(implies(not(implies(not(X_484),X_483)),X_482),X_481))
| is_a_theorem(implies(X_484,X_481)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(not(X_484),X_483)),X_482),X_481))),bind(Y,$fot(implies(X_484,X_481)))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(X_137,implies(not(implies(not(X_137),X_136)),X_135)))
| is_a_theorem(implies(implies(implies(not(implies(not(X_137),X_136)),X_135),Z),implies(X_137,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_137)),bind(Y,$fot(implies(not(implies(not(X_137),X_136)),X_135)))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(not(X_128),X_127),implies(not(implies(not(X_128),X_127)),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(implies(not(X_128),X_127)))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(implies(not(X_128),X_127),implies(not(implies(not(X_128),X_127)),Y)))
| is_a_theorem(implies(X_128,implies(not(implies(not(X_128),X_127)),Y))) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(X_127)),bind(X_37,$fot(X_128)),bind(X_38,$fot(implies(not(implies(not(X_128),X_127)),Y)))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(X_128,implies(not(implies(not(X_128),X_127)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_128),X_127),implies(not(implies(not(X_128),X_127)),Y))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(X_137,implies(not(implies(not(X_137),X_136)),X_135))),
inference(subst,[],[refute_0_83:[bind(Y,$fot(X_135)),bind(X_127,$fot(X_136)),bind(X_128,$fot(X_137))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(implies(not(implies(not(X_137),X_136)),X_135),Z),implies(X_137,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_137,implies(not(implies(not(X_137),X_136)),X_135))) )],[refute_0_84,refute_0_80]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(implies(not(implies(not(X_484),X_483)),X_482),X_481),implies(X_484,X_481))),
inference(subst,[],[refute_0_85:[bind(Z,$fot(X_481)),bind(X_135,$fot(X_482)),bind(X_136,$fot(X_483)),bind(X_137,$fot(X_484))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(X_484),X_483)),X_482),X_481))
| is_a_theorem(implies(X_484,X_481)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(not(X_484),X_483)),X_482),X_481),implies(X_484,X_481))) )],[refute_0_86,refute_0_79]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(not(not(X_6110))),not(not(X_6110)))),X_6110),X_6110))
| is_a_theorem(implies(not(not(X_6110)),X_6110)) ),
inference(subst,[],[refute_0_87:[bind(X_481,$fot(X_6110)),bind(X_482,$fot(X_6110)),bind(X_483,$fot(not(not(X_6110)))),bind(X_484,$fot(not(not(X_6110))))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(implies(not(X_1487),not(implies(not(not(not(X_1487))),not(not(X_1487))))))
| is_a_theorem(implies(implies(not(implies(not(not(not(X_1487))),not(not(X_1487)))),X_1487),X_1487)) ),
inference(subst,[],[refute_0_77:[bind(X_1488,$fot(not(implies(not(not(not(X_1487))),not(not(X_1487))))))]]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(implies(implies(not(X_37),not(implies(not(not(X_37)),not(X_37)))),not(implies(not(not(X_37)),not(X_37)))))
| is_a_theorem(implies(X_37,not(implies(not(not(X_37)),not(X_37))))) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(not(implies(not(not(X_37)),not(X_37))))),bind(X_38,$fot(not(implies(not(not(X_37)),not(X_37)))))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(not(not(implies(not(X_6090),X_6090))),X_6090))
| is_a_theorem(implies(implies(X_6090,not(implies(not(X_6090),X_6090))),not(implies(not(X_6090),X_6090)))) ),
inference(subst,[],[refute_0_77:[bind(X_1487,$fot(not(implies(not(X_6090),X_6090)))),bind(X_1488,$fot(X_6090))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(implies(implies(implies(X_592,X_591),implies(not(X_593),X_591)),X_590))
| ~ is_a_theorem(implies(implies(implies(implies(X_592,X_591),implies(not(X_593),X_591)),X_590),implies(X_593,X_590)))
| is_a_theorem(implies(X_593,X_590)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_592,X_591),implies(not(X_593),X_591)),X_590))),bind(Y,$fot(implies(X_593,X_590)))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(X_149,implies(implies(X_148,X_147),implies(not(X_149),X_147))))
| is_a_theorem(implies(implies(implies(implies(X_148,X_147),implies(not(X_149),X_147)),Z),implies(X_149,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_149)),bind(Y,$fot(implies(implies(X_148,X_147),implies(not(X_149),X_147))))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(not(X_128),X_127),implies(implies(X_127,Z),implies(not(X_128),Z)))),
inference(subst,[],[cn_1:[bind(X,$fot(not(X_128))),bind(Y,$fot(X_127))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(implies(not(X_128),X_127),implies(implies(X_127,Z),implies(not(X_128),Z))))
| is_a_theorem(implies(X_128,implies(implies(X_127,Z),implies(not(X_128),Z)))) ),
inference(subst,[],[refute_0_7:[bind(X_36,$fot(X_127)),bind(X_37,$fot(X_128)),bind(X_38,$fot(implies(implies(X_127,Z),implies(not(X_128),Z))))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(X_128,implies(implies(X_127,Z),implies(not(X_128),Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_128),X_127),implies(implies(X_127,Z),implies(not(X_128),Z)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(X_149,implies(implies(X_148,X_147),implies(not(X_149),X_147)))),
inference(subst,[],[refute_0_96:[bind(Z,$fot(X_147)),bind(X_127,$fot(X_148)),bind(X_128,$fot(X_149))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(implies(implies(X_148,X_147),implies(not(X_149),X_147)),Z),implies(X_149,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_149,implies(implies(X_148,X_147),implies(not(X_149),X_147)))) )],[refute_0_97,refute_0_93]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(implies(implies(X_592,X_591),implies(not(X_593),X_591)),X_590),implies(X_593,X_590))),
inference(subst,[],[refute_0_98:[bind(Z,$fot(X_590)),bind(X_147,$fot(X_591)),bind(X_148,$fot(X_592)),bind(X_149,$fot(X_593))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(implies(implies(X_592,X_591),implies(not(X_593),X_591)),X_590))
| is_a_theorem(implies(X_593,X_590)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_592,X_591),implies(not(X_593),X_591)),X_590),implies(X_593,X_590))) )],[refute_0_99,refute_0_92]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_6088)),not(not(implies(not(X_6088),X_6088)))),implies(not(not(not(implies(not(X_6088),X_6088)))),not(not(implies(not(X_6088),X_6088))))),X_6088))
| is_a_theorem(implies(not(not(implies(not(X_6088),X_6088))),X_6088)) ),
inference(subst,[],[refute_0_100:[bind(X_590,$fot(X_6088)),bind(X_591,$fot(not(not(implies(not(X_6088),X_6088))))),bind(X_592,$fot(not(not(X_6088)))),bind(X_593,$fot(not(not(implies(not(X_6088),X_6088)))))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_1037)),X_1036),X_1037),X_1037))
| is_a_theorem(implies(implies(implies(implies(not(not(not(X_1037))),not(not(X_1037))),X_1036),X_1037),X_1037)) ),
inference(subst,[],[refute_0_27:[bind(X_69,$fot(X_1037)),bind(X_70,$fot(X_1037)),bind(X_71,$fot(not(not(X_1037)))),bind(X_72,$fot(X_1036))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034)),implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034)))
| is_a_theorem(implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034)) ),
inference(subst,[],[refute_0_31:[bind(X_7,$fot(implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034)))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_37),X_36),X_38),implies(X_37,X_38)))
| is_a_theorem(implies(implies(implies(X_37,X_38),Z),implies(implies(implies(not(X_37),X_36),X_38),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(X_37),X_36),X_38))),bind(Y,$fot(implies(X_37,X_38)))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(implies(implies(X_37,X_38),Z),implies(implies(implies(not(X_37),X_36),X_38),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_37),X_36),X_38),implies(X_37,X_38))) )],[refute_0_6,refute_0_104]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(implies(implies(not(X_846),X_846),X_847),implies(implies(implies(not(not(X_846)),X_36),X_846),X_847))),
inference(subst,[],[refute_0_105:[bind(Z,$fot(X_847)),bind(X_37,$fot(not(X_846))),bind(X_38,$fot(X_846))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_846),X_846),X_847),implies(implies(implies(not(not(X_846)),X_36),X_846),X_847)))
| is_a_theorem(implies(implies(X_846,X_847),implies(implies(implies(not(not(X_846)),X_36),X_846),X_847))) ),
inference(subst,[],[refute_0_34:[bind(X_46,$fot(implies(implies(implies(not(not(X_846)),X_36),X_846),X_847))),bind(X_47,$fot(X_846)),bind(X_48,$fot(X_847))]]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(implies(X_846,X_847),implies(implies(implies(not(not(X_846)),X_36),X_846),X_847))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_846),X_846),X_847),implies(implies(implies(not(not(X_846)),X_36),X_846),X_847))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(implies(X_975,X_975),implies(implies(implies(not(not(X_975)),X_36),X_975),X_975))),
inference(subst,[],[refute_0_108:[bind(X_846,$fot(X_975)),bind(X_847,$fot(X_975))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(implies(X_975,X_975),implies(implies(implies(not(not(X_975)),X_36),X_975),X_975)))
| is_a_theorem(implies(X_976,implies(implies(implies(not(not(X_975)),X_36),X_975),X_975))) ),
inference(subst,[],[refute_0_64:[bind(X_848,$fot(X_975)),bind(X_849,$fot(X_976)),bind(X_850,$fot(implies(implies(implies(not(not(X_975)),X_36),X_975),X_975)))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(X_976,implies(implies(implies(not(not(X_975)),X_36),X_975),X_975))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_975,X_975),implies(implies(implies(not(not(X_975)),X_36),X_975),X_975))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(not(implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034)),implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034))),
inference(subst,[],[refute_0_111:[bind(X_36,$fot(X_1033)),bind(X_975,$fot(X_1034)),bind(X_976,$fot(not(implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034))))]]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034)),implies(implies(implies(not(not(X_1034)),X_1033),X_1034),X_1034))) )],[refute_0_112,refute_0_103]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(implies(not(not(X_1037)),X_1036),X_1037),X_1037)),
inference(subst,[],[refute_0_113:[bind(X_1033,$fot(X_1036)),bind(X_1034,$fot(X_1037))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(implies(implies(not(not(not(X_1037))),not(not(X_1037))),X_1036),X_1037),X_1037)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_1037)),X_1036),X_1037),X_1037)) )],[refute_0_114,refute_0_102]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(implies(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))),
inference(subst,[],[refute_0_115:[bind(X_1036,$fot(X_1472)),bind(X_1037,$fot(implies(X_1470,X_1472)))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472)))
| is_a_theorem(implies(implies(X_1470,implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472))))),implies(X_1470,X_1472))) ),
inference(subst,[],[refute_0_14:[bind(X_32,$fot(X_1470)),bind(X_33,$fot(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))))),bind(X_34,$fot(X_1472)),bind(X_35,$fot(implies(X_1470,X_1472)))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(X_1470,implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472))))),implies(X_1470,X_1472))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(not(X_2442),implies(not(not(not(implies(not(X_2442),X_2442)))),not(not(implies(not(X_2442),X_2442))))),implies(not(X_2442),X_2442))),
inference(subst,[],[refute_0_118:[bind(X_1470,$fot(not(X_2442))),bind(X_1472,$fot(X_2442))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(X_1481,implies(not(X_1482),X_1482)))
| ~ is_a_theorem(implies(implies(X_1481,implies(not(X_1482),X_1482)),implies(X_1481,X_1482)))
| is_a_theorem(implies(X_1481,X_1482)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1481,implies(not(X_1482),X_1482)))),bind(Y,$fot(implies(X_1481,X_1482)))]]) ).
cnf(refute_0_121,plain,
is_a_theorem(implies(implies(X_1481,implies(not(X_1482),X_1482)),implies(X_1481,X_1482))),
inference(subst,[],[refute_0_73:[bind(X_1470,$fot(X_1481)),bind(X_1472,$fot(X_1482))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(X_1481,implies(not(X_1482),X_1482)))
| is_a_theorem(implies(X_1481,X_1482)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1481,implies(not(X_1482),X_1482)),implies(X_1481,X_1482))) )],[refute_0_121,refute_0_120]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(implies(not(X_2442),implies(not(not(not(implies(not(X_2442),X_2442)))),not(not(implies(not(X_2442),X_2442))))),implies(not(X_2442),X_2442)))
| is_a_theorem(implies(implies(not(X_2442),implies(not(not(not(implies(not(X_2442),X_2442)))),not(not(implies(not(X_2442),X_2442))))),X_2442)) ),
inference(subst,[],[refute_0_122:[bind(X_1481,$fot(implies(not(X_2442),implies(not(not(not(implies(not(X_2442),X_2442)))),not(not(implies(not(X_2442),X_2442))))))),bind(X_1482,$fot(X_2442))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(not(X_2442),implies(not(not(not(implies(not(X_2442),X_2442)))),not(not(implies(not(X_2442),X_2442))))),X_2442)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_2442),implies(not(not(not(implies(not(X_2442),X_2442)))),not(not(implies(not(X_2442),X_2442))))),implies(not(X_2442),X_2442))) )],[refute_0_119,refute_0_123]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(implies(not(X_5787),implies(not(not(not(implies(not(X_5787),X_5787)))),not(not(implies(not(X_5787),X_5787))))),X_5787)),
inference(subst,[],[refute_0_124:[bind(X_2442,$fot(X_5787))]]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(implies(implies(X_120,X_121),X_118))
| ~ is_a_theorem(implies(implies(implies(X_120,X_121),X_118),implies(implies(implies(not(X_120),X_119),X_121),X_118)))
| is_a_theorem(implies(implies(implies(not(X_120),X_119),X_121),X_118)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_120,X_121),X_118))),bind(Y,$fot(implies(implies(implies(not(X_120),X_119),X_121),X_118)))]]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(implies(X_120,X_121),X_118),implies(implies(implies(not(X_120),X_119),X_121),X_118))),
inference(subst,[],[refute_0_105:[bind(Z,$fot(X_118)),bind(X_36,$fot(X_119)),bind(X_37,$fot(X_120)),bind(X_38,$fot(X_121))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(implies(X_120,X_121),X_118))
| is_a_theorem(implies(implies(implies(not(X_120),X_119),X_121),X_118)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_120,X_121),X_118),implies(implies(implies(not(X_120),X_119),X_121),X_118))) )],[refute_0_127,refute_0_126]) ).
cnf(refute_0_129,plain,
( ~ is_a_theorem(implies(implies(not(X_5787),implies(not(not(not(implies(not(X_5787),X_5787)))),not(not(implies(not(X_5787),X_5787))))),X_5787))
| is_a_theorem(implies(implies(implies(not(not(X_5787)),X_5788),implies(not(not(not(implies(not(X_5787),X_5787)))),not(not(implies(not(X_5787),X_5787))))),X_5787)) ),
inference(subst,[],[refute_0_128:[bind(X_118,$fot(X_5787)),bind(X_119,$fot(X_5788)),bind(X_120,$fot(not(X_5787))),bind(X_121,$fot(implies(not(not(not(implies(not(X_5787),X_5787)))),not(not(implies(not(X_5787),X_5787))))))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(implies(not(not(X_5787)),X_5788),implies(not(not(not(implies(not(X_5787),X_5787)))),not(not(implies(not(X_5787),X_5787))))),X_5787)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_5787),implies(not(not(not(implies(not(X_5787),X_5787)))),not(not(implies(not(X_5787),X_5787))))),X_5787)) )],[refute_0_125,refute_0_129]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(implies(not(not(X_6088)),not(not(implies(not(X_6088),X_6088)))),implies(not(not(not(implies(not(X_6088),X_6088)))),not(not(implies(not(X_6088),X_6088))))),X_6088)),
inference(subst,[],[refute_0_130:[bind(X_5787,$fot(X_6088)),bind(X_5788,$fot(not(not(implies(not(X_6088),X_6088)))))]]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(not(not(implies(not(X_6088),X_6088))),X_6088)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_6088)),not(not(implies(not(X_6088),X_6088)))),implies(not(not(not(implies(not(X_6088),X_6088)))),not(not(implies(not(X_6088),X_6088))))),X_6088)) )],[refute_0_131,refute_0_101]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(not(not(implies(not(X_6090),X_6090))),X_6090)),
inference(subst,[],[refute_0_132:[bind(X_6088,$fot(X_6090))]]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(X_6090,not(implies(not(X_6090),X_6090))),not(implies(not(X_6090),X_6090)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(X_6090),X_6090))),X_6090)) )],[refute_0_133,refute_0_91]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(not(X_37),not(implies(not(not(X_37)),not(X_37)))),not(implies(not(not(X_37)),not(X_37))))),
inference(subst,[],[refute_0_134:[bind(X_6090,$fot(not(X_37)))]]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(X_37,not(implies(not(not(X_37)),not(X_37))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_37),not(implies(not(not(X_37)),not(X_37)))),not(implies(not(not(X_37)),not(X_37))))) )],[refute_0_135,refute_0_90]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(not(X_1487),not(implies(not(not(not(X_1487))),not(not(X_1487)))))),
inference(subst,[],[refute_0_136:[bind(X_37,$fot(not(X_1487)))]]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(implies(not(implies(not(not(not(X_1487))),not(not(X_1487)))),X_1487),X_1487)),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1487),not(implies(not(not(not(X_1487))),not(not(X_1487)))))) )],[refute_0_137,refute_0_89]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(implies(not(implies(not(not(not(X_6110))),not(not(X_6110)))),X_6110),X_6110)),
inference(subst,[],[refute_0_138:[bind(X_1487,$fot(X_6110))]]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(not(not(X_6110)),X_6110)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(not(not(not(X_6110))),not(not(X_6110)))),X_6110),X_6110)) )],[refute_0_139,refute_0_88]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(not(not(X_6111)),X_6111)),
inference(subst,[],[refute_0_140:[bind(X_6110,$fot(X_6111))]]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(implies(X_6111,not(X_6111)),not(X_6111))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_6111)),X_6111)) )],[refute_0_141,refute_0_78]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(implies(not(X_37),not(not(X_37))),not(not(X_37)))),
inference(subst,[],[refute_0_142:[bind(X_6111,$fot(not(X_37)))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(X_37,not(not(X_37)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_37),not(not(X_37))),not(not(X_37)))) )],[refute_0_143,refute_0_8]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(a,not(not(a)))),
inference(subst,[],[refute_0_144:[bind(X_37,$fot(a))]]) ).
cnf(refute_0_146,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,not(not(a)))) )],[refute_0_145,prove_cn_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL057-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 11:19:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.99/6.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.99/6.17
% 5.99/6.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.99/6.19
%------------------------------------------------------------------------------