TSTP Solution File: LCL381-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL381-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 12:51:51 EDT 2022
% Result : Unsatisfiable 37.47s 37.64s
% Output : CNFRefutation 37.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 5
% Syntax : Number of clauses : 207 ( 119 unt; 0 nHn; 55 RR)
% Number of literals : 313 ( 0 equ; 107 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 534 ( 108 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_42,negated_conjecture,
~ is_a_theorem(implies(implies(implies(not(not(x)),y),z),implies(implies(x,y),z))) ).
cnf(refute_0_0,plain,
is_a_theorem(implies(implies(implies(X_1899,X_1900),implies(X_1898,X_1900)),implies(implies(implies(X_1898,X_1900),Z),implies(implies(X_1899,X_1900),Z)))),
inference(subst,[],[cn_1:[bind(X,$fot(implies(X_1899,X_1900))),bind(Y,$fot(implies(X_1898,X_1900)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(implies(X_70,X_71),implies(X_69,X_71)),X_72))
| ~ is_a_theorem(implies(implies(implies(implies(X_70,X_71),implies(X_69,X_71)),X_72),implies(implies(X_69,X_70),X_72)))
| is_a_theorem(implies(implies(X_69,X_70),X_72)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_70,X_71),implies(X_69,X_71)),X_72))),bind(Y,$fot(implies(implies(X_69,X_70),X_72)))]]) ).
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,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_31),implies(implies(X,Y),X_31))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_31),implies(implies(X,Y),X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(implies(X_70,X_71),implies(X_69,X_71)),X_72),implies(implies(X_69,X_70),X_72))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_69)),bind(Y,$fot(X_70)),bind(Z,$fot(X_71)),bind(X_31,$fot(X_72))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(X_70,X_71),implies(X_69,X_71)),X_72))
| is_a_theorem(implies(implies(X_69,X_70),X_72)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_70,X_71),implies(X_69,X_71)),X_72),implies(implies(X_69,X_70),X_72))) )],[refute_0_6,refute_0_1]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(X_1899,X_1900),implies(X_1898,X_1900)),implies(implies(implies(X_1898,X_1900),Z),implies(implies(X_1899,X_1900),Z))))
| is_a_theorem(implies(implies(X_1898,X_1899),implies(implies(implies(X_1898,X_1900),Z),implies(implies(X_1899,X_1900),Z)))) ),
inference(subst,[],[refute_0_7:[bind(X_69,$fot(X_1898)),bind(X_70,$fot(X_1899)),bind(X_71,$fot(X_1900)),bind(X_72,$fot(implies(implies(implies(X_1898,X_1900),Z),implies(implies(X_1899,X_1900),Z))))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(X_1898,X_1899),implies(implies(implies(X_1898,X_1900),Z),implies(implies(X_1899,X_1900),Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1899,X_1900),implies(X_1898,X_1900)),implies(implies(implies(X_1898,X_1900),Z),implies(implies(X_1899,X_1900),Z)))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(not(not(X_26001)),X_26001),implies(implies(implies(not(not(X_26001)),X_1900),Z),implies(implies(X_26001,X_1900),Z)))),
inference(subst,[],[refute_0_9:[bind(X_1898,$fot(not(not(X_26001)))),bind(X_1899,$fot(X_26001))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_16935)),X_16935),X_16934),X_16934))
| ~ is_a_theorem(implies(implies(not(not(X_16935)),X_16935),X_16934))
| is_a_theorem(X_16934) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_16935)),X_16935),X_16934))),bind(Y,$fot(X_16934))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_5548),X_5548),X_5548),X_5547),X_5547))
| ~ is_a_theorem(implies(implies(implies(not(X_5548),X_5548),X_5548),X_5547))
| is_a_theorem(X_5547) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_5548),X_5548),X_5548),X_5547))),bind(Y,$fot(X_5547))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_297)),X_298),X_297),X_297))
| ~ is_a_theorem(implies(implies(not(not(X_297)),X_298),X_297))
| is_a_theorem(X_297) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_297)),X_298),X_297))),bind(Y,$fot(X_297))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(not(X_291),X_291),X_291)),
inference(subst,[],[cn_2:[bind(X,$fot(X_291))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(X_39,X_40),X_37))
| ~ is_a_theorem(implies(implies(implies(X_39,X_40),X_37),implies(implies(implies(not(X_39),X_38),X_40),X_37)))
| is_a_theorem(implies(implies(implies(not(X_39),X_38),X_40),X_37)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_39,X_40),X_37))),bind(Y,$fot(implies(implies(implies(not(X_39),X_38),X_40),X_37)))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36)))
| is_a_theorem(implies(implies(implies(X_35,X_36),Z),implies(implies(implies(not(X_35),X_34),X_36),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(X_35),X_34),X_36))),bind(Y,$fot(implies(X_35,X_36)))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(X_29,implies(not(X_29),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(X_29,implies(not(X_29),Y)))
| is_a_theorem(implies(implies(implies(not(X_29),Y),X_31),implies(X_29,X_31))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_29)),bind(Y,$fot(implies(not(X_29),Y))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(not(X_29),Y),X_31),implies(X_29,X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(X_29,implies(not(X_29),Y))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36))),
inference(subst,[],[refute_0_19:[bind(Y,$fot(X_34)),bind(X_29,$fot(X_35)),bind(X_31,$fot(X_36))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(implies(X_35,X_36),Z),implies(implies(implies(not(X_35),X_34),X_36),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36))) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(X_39,X_40),X_37),implies(implies(implies(not(X_39),X_38),X_40),X_37))),
inference(subst,[],[refute_0_21:[bind(Z,$fot(X_37)),bind(X_34,$fot(X_38)),bind(X_35,$fot(X_39)),bind(X_36,$fot(X_40))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(X_39,X_40),X_37))
| is_a_theorem(implies(implies(implies(not(X_39),X_38),X_40),X_37)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_39,X_40),X_37),implies(implies(implies(not(X_39),X_38),X_40),X_37))) )],[refute_0_22,refute_0_15]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(not(X_291),X_291),X_291))
| is_a_theorem(implies(implies(implies(not(not(X_291)),X_292),X_291),X_291)) ),
inference(subst,[],[refute_0_23:[bind(X_37,$fot(X_291)),bind(X_38,$fot(X_292)),bind(X_39,$fot(not(X_291))),bind(X_40,$fot(X_291))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(implies(not(not(X_291)),X_292),X_291),X_291)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_291),X_291),X_291)) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(implies(not(not(X_297)),X_298),X_297),X_297)),
inference(subst,[],[refute_0_25:[bind(X_291,$fot(X_297)),bind(X_292,$fot(X_298))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(not(not(X_297)),X_298),X_297))
| is_a_theorem(X_297) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_297)),X_298),X_297),X_297)) )],[refute_0_26,refute_0_13]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545))),X_298),implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545)))
| is_a_theorem(implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545)) ),
inference(subst,[],[refute_0_27:[bind(X_297,$fot(implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545)))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023),implies(X_1022,X_1023)))
| ~ is_a_theorem(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023))
| is_a_theorem(implies(X_1022,X_1023)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023))),bind(Y,$fot(implies(X_1022,X_1023)))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(X_181,implies(not(implies(implies(not(X_179),X_179),X_179)),X_180)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_180),Z),implies(X_181,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_181)),bind(Y,$fot(implies(not(implies(implies(not(X_179),X_179),X_179)),X_180)))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_32,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_33,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_34]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_30)),
inference(subst,[],[refute_0_35:[bind(X_9,$fot(X_30))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_30))
| is_a_theorem(implies(implies(X_30,X_31),implies(not(implies(implies(not(X),X),X)),X_31))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(not(implies(implies(not(X),X),X)),X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_30)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(not(X_152),X_151),implies(not(implies(implies(not(X),X),X)),X_151))),
inference(subst,[],[refute_0_38:[bind(X_30,$fot(not(X_152))),bind(X_31,$fot(X_151))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36)))
| ~ is_a_theorem(implies(implies(not(X_35),X_34),X_36))
| is_a_theorem(implies(X_35,X_36)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_35),X_34),X_36))),bind(Y,$fot(implies(X_35,X_36)))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(not(X_35),X_34),X_36))
| is_a_theorem(implies(X_35,X_36)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36))) )],[refute_0_20,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(not(X_152),X_151),implies(not(implies(implies(not(X),X),X)),X_151)))
| is_a_theorem(implies(X_152,implies(not(implies(implies(not(X),X),X)),X_151))) ),
inference(subst,[],[refute_0_41:[bind(X_34,$fot(X_151)),bind(X_35,$fot(X_152)),bind(X_36,$fot(implies(not(implies(implies(not(X),X),X)),X_151)))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(X_152,implies(not(implies(implies(not(X),X),X)),X_151))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_152),X_151),implies(not(implies(implies(not(X),X),X)),X_151))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(X_181,implies(not(implies(implies(not(X_179),X_179),X_179)),X_180))),
inference(subst,[],[refute_0_43:[bind(X,$fot(X_179)),bind(X_151,$fot(X_180)),bind(X_152,$fot(X_181))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_180),Z),implies(X_181,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_181,implies(not(implies(implies(not(X_179),X_179),X_179)),X_180))) )],[refute_0_44,refute_0_30]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),implies(implies(not(X_179),X_179),X_179)),X_998),implies(X_181,X_998))),
inference(subst,[],[refute_0_45:[bind(Z,$fot(X_998)),bind(X_180,$fot(implies(implies(not(X_179),X_179),X_179)))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_42),X_42),X_43),X_41),implies(implies(X_42,X_43),X_41)))
| ~ is_a_theorem(implies(implies(implies(not(X_42),X_42),X_43),X_41))
| is_a_theorem(implies(implies(X_42,X_43),X_41)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_42),X_42),X_43),X_41))),bind(Y,$fot(implies(implies(X_42,X_43),X_41)))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33)))
| is_a_theorem(implies(implies(implies(implies(not(X_32),X_32),X_33),Z),implies(implies(X_32,X_33),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X_32,X_33))),bind(Y,$fot(implies(implies(not(X_32),X_32),X_33)))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(not(X_30),X_30),X_30)),
inference(subst,[],[cn_2:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(implies(not(X_30),X_30),X_30))
| is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(not(X_30),X_30))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_30),X_30),X_30)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33))),
inference(subst,[],[refute_0_51:[bind(X_30,$fot(X_32)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(implies(not(X_32),X_32),X_33),Z),implies(implies(X_32,X_33),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33))) )],[refute_0_52,refute_0_48]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(implies(not(X_42),X_42),X_43),X_41),implies(implies(X_42,X_43),X_41))),
inference(subst,[],[refute_0_53:[bind(Z,$fot(X_41)),bind(X_32,$fot(X_42)),bind(X_33,$fot(X_43))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_42),X_42),X_43),X_41))
| is_a_theorem(implies(implies(X_42,X_43),X_41)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_42),X_42),X_43),X_41),implies(implies(X_42,X_43),X_41))) )],[refute_0_54,refute_0_47]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),implies(implies(not(X_179),X_179),X_179)),X_998),implies(X_181,X_998)))
| is_a_theorem(implies(implies(implies(implies(not(X_179),X_179),X_179),X_998),implies(X_181,X_998))) ),
inference(subst,[],[refute_0_55:[bind(X_41,$fot(implies(X_181,X_998))),bind(X_42,$fot(implies(implies(not(X_179),X_179),X_179))),bind(X_43,$fot(X_998))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(implies(implies(not(X_179),X_179),X_179),X_998),implies(X_181,X_998))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),implies(implies(not(X_179),X_179),X_179)),X_998),implies(X_181,X_998))) )],[refute_0_46,refute_0_56]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023),implies(X_1022,X_1023))),
inference(subst,[],[refute_0_57:[bind(X_179,$fot(X_1021)),bind(X_181,$fot(X_1022)),bind(X_998,$fot(X_1023))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023))
| is_a_theorem(implies(X_1022,X_1023)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023),implies(X_1022,X_1023))) )],[refute_0_58,refute_0_29]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_5536),X_5536),X_5536),implies(implies(implies(implies(not(X_5537),X_5537),X_5537),X_5536),X_5536)))
| is_a_theorem(implies(X_1022,implies(implies(implies(implies(not(X_5537),X_5537),X_5537),X_5536),X_5536))) ),
inference(subst,[],[refute_0_59:[bind(X_1021,$fot(X_5536)),bind(X_1023,$fot(implies(implies(implies(implies(not(X_5537),X_5537),X_5537),X_5536),X_5536)))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023),implies(X_1022,X_1023)))
| is_a_theorem(implies(implies(implies(X_1022,X_1023),Z),implies(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023))),bind(Y,$fot(implies(X_1022,X_1023)))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(implies(X_1022,X_1023),Z),implies(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1021),X_1021),X_1021),X_1023),implies(X_1022,X_1023))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(implies(not(X_5536),X_5536),X_5536),implies(implies(implies(implies(not(X_5537),X_5537),X_5537),X_5536),X_5536))),
inference(subst,[],[refute_0_62:[bind(Z,$fot(X_5536)),bind(X_1021,$fot(X_5537)),bind(X_1022,$fot(not(X_5536))),bind(X_1023,$fot(X_5536))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(X_1022,implies(implies(implies(implies(not(X_5537),X_5537),X_5537),X_5536),X_5536))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_5536),X_5536),X_5536),implies(implies(implies(implies(not(X_5537),X_5537),X_5537),X_5536),X_5536))) )],[refute_0_63,refute_0_60]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545))),X_298),implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545))),
inference(subst,[],[refute_0_64:[bind(X_1022,$fot(implies(not(not(implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545))),X_298))),bind(X_5536,$fot(X_5545)),bind(X_5537,$fot(X_5546))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545))),X_298),implies(implies(implies(implies(not(X_5546),X_5546),X_5546),X_5545),X_5545))) )],[refute_0_65,refute_0_28]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(implies(implies(not(X_5548),X_5548),X_5548),X_5547),X_5547)),
inference(subst,[],[refute_0_66:[bind(X_5545,$fot(X_5547)),bind(X_5546,$fot(X_5548))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_5548),X_5548),X_5548),X_5547))
| is_a_theorem(X_5547) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_5548),X_5548),X_5548),X_5547),X_5547)) )],[refute_0_67,refute_0_12]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_16930),X_16930),X_16930),implies(implies(implies(not(not(X_16931)),X_16931),X_16930),X_16930)))
| is_a_theorem(implies(implies(implies(not(not(X_16931)),X_16931),X_16930),X_16930)) ),
inference(subst,[],[refute_0_68:[bind(X_5547,$fot(implies(implies(implies(not(not(X_16931)),X_16931),X_16930),X_16930))),bind(X_5548,$fot(X_16930))]]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_16506)),X_16506),X_16508),implies(X_16507,X_16508)))
| is_a_theorem(implies(implies(implies(X_16507,X_16508),Z),implies(implies(implies(not(not(X_16506)),X_16506),X_16508),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(not(X_16506)),X_16506),X_16508))),bind(Y,$fot(implies(X_16507,X_16508)))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(X_5579)
| ~ is_a_theorem(implies(X_5579,implies(X_5580,X_5579)))
| is_a_theorem(implies(X_5580,X_5579)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_5579)),bind(Y,$fot(implies(X_5580,X_5579)))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(not(X_5575),not(X_5576)),implies(X_5576,X_5575)))
| is_a_theorem(implies(X_5575,implies(X_5576,X_5575))) ),
inference(subst,[],[refute_0_41:[bind(X_34,$fot(not(X_5576))),bind(X_35,$fot(X_5575)),bind(X_36,$fot(implies(X_5576,X_5575)))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_5574),X_5573),implies(not(X_5573),X_5573)),implies(X_5574,X_5573)))
| is_a_theorem(implies(implies(not(X_5573),not(X_5574)),implies(X_5574,X_5573))) ),
inference(subst,[],[refute_0_7:[bind(X_69,$fot(not(X_5573))),bind(X_70,$fot(not(X_5574))),bind(X_71,$fot(X_5573)),bind(X_72,$fot(implies(X_5574,X_5573)))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(implies(X_5550,implies(not(X_5549),X_5549)),implies(X_5550,X_5549)))
| is_a_theorem(implies(implies(implies(not(X_5550),X_38),implies(not(X_5549),X_5549)),implies(X_5550,X_5549))) ),
inference(subst,[],[refute_0_23:[bind(X_37,$fot(implies(X_5550,X_5549))),bind(X_39,$fot(X_5550)),bind(X_40,$fot(implies(not(X_5549),X_5549)))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_5548),X_5548),X_5548),implies(X_69,X_5548)),implies(X_69,X_5548)))
| is_a_theorem(implies(implies(X_69,implies(not(X_5548),X_5548)),implies(X_69,X_5548))) ),
inference(subst,[],[refute_0_7:[bind(X_70,$fot(implies(not(X_5548),X_5548))),bind(X_71,$fot(X_5548)),bind(X_72,$fot(implies(X_69,X_5548)))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(implies(implies(not(X_5548),X_5548),X_5548),implies(X_69,X_5548)),implies(X_69,X_5548))),
inference(subst,[],[refute_0_66:[bind(X_5545,$fot(implies(X_69,X_5548))),bind(X_5546,$fot(X_5548))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(X_69,implies(not(X_5548),X_5548)),implies(X_69,X_5548))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_5548),X_5548),X_5548),implies(X_69,X_5548)),implies(X_69,X_5548))) )],[refute_0_76,refute_0_75]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(X_5550,implies(not(X_5549),X_5549)),implies(X_5550,X_5549))),
inference(subst,[],[refute_0_77:[bind(X_5548,$fot(X_5549)),bind(X_69,$fot(X_5550))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(implies(not(X_5550),X_38),implies(not(X_5549),X_5549)),implies(X_5550,X_5549))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_5550,implies(not(X_5549),X_5549)),implies(X_5550,X_5549))) )],[refute_0_78,refute_0_74]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(implies(implies(not(X_5574),X_5573),implies(not(X_5573),X_5573)),implies(X_5574,X_5573))),
inference(subst,[],[refute_0_79:[bind(X_38,$fot(X_5573)),bind(X_5549,$fot(X_5573)),bind(X_5550,$fot(X_5574))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(not(X_5573),not(X_5574)),implies(X_5574,X_5573))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_5574),X_5573),implies(not(X_5573),X_5573)),implies(X_5574,X_5573))) )],[refute_0_80,refute_0_73]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(not(X_5575),not(X_5576)),implies(X_5576,X_5575))),
inference(subst,[],[refute_0_81:[bind(X_5573,$fot(X_5575)),bind(X_5574,$fot(X_5576))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(X_5575,implies(X_5576,X_5575))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_5575),not(X_5576)),implies(X_5576,X_5575))) )],[refute_0_82,refute_0_72]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(X_5579,implies(X_5580,X_5579))),
inference(subst,[],[refute_0_83:[bind(X_5575,$fot(X_5579)),bind(X_5576,$fot(X_5580))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(X_5579)
| is_a_theorem(implies(X_5580,X_5579)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_5579,implies(X_5580,X_5579))) )],[refute_0_84,refute_0_71]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(X_11173,implies(not(not(X_11172)),X_11172)))
| is_a_theorem(implies(X_5580,implies(X_11173,implies(not(not(X_11172)),X_11172)))) ),
inference(subst,[],[refute_0_85:[bind(X_5579,$fot(implies(X_11173,implies(not(not(X_11172)),X_11172))))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(not(not(X_11169)),X_11169))
| is_a_theorem(implies(X_5580,implies(not(not(X_11169)),X_11169))) ),
inference(subst,[],[refute_0_85:[bind(X_5579,$fot(implies(not(not(X_11169)),X_11169)))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_224)),not(X_224)),X_223),X_222),implies(X_224,X_222)))
| ~ is_a_theorem(implies(implies(implies(not(not(X_224)),not(X_224)),X_223),X_222))
| is_a_theorem(implies(X_224,X_222)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(not(X_224)),not(X_224)),X_223),X_222))),bind(Y,$fot(implies(X_224,X_222)))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(implies(X_158,implies(implies(not(not(X_158)),not(X_158)),X_157)))
| is_a_theorem(implies(implies(implies(implies(not(not(X_158)),not(X_158)),X_157),Z),implies(X_158,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_158)),bind(Y,$fot(implies(implies(not(not(X_158)),not(X_158)),X_157)))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(not(X_152),X_151),implies(implies(not(not(X_152)),not(X_152)),X_151))),
inference(subst,[],[refute_0_51:[bind(X_30,$fot(not(X_152))),bind(X_31,$fot(X_151))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(implies(not(X_152),X_151),implies(implies(not(not(X_152)),not(X_152)),X_151)))
| is_a_theorem(implies(X_152,implies(implies(not(not(X_152)),not(X_152)),X_151))) ),
inference(subst,[],[refute_0_41:[bind(X_34,$fot(X_151)),bind(X_35,$fot(X_152)),bind(X_36,$fot(implies(implies(not(not(X_152)),not(X_152)),X_151)))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(X_152,implies(implies(not(not(X_152)),not(X_152)),X_151))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_152),X_151),implies(implies(not(not(X_152)),not(X_152)),X_151))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(X_158,implies(implies(not(not(X_158)),not(X_158)),X_157))),
inference(subst,[],[refute_0_92:[bind(X_151,$fot(X_157)),bind(X_152,$fot(X_158))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_158)),not(X_158)),X_157),Z),implies(X_158,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_158,implies(implies(not(not(X_158)),not(X_158)),X_157))) )],[refute_0_93,refute_0_89]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_224)),not(X_224)),X_223),X_222),implies(X_224,X_222))),
inference(subst,[],[refute_0_94:[bind(Z,$fot(X_222)),bind(X_157,$fot(X_223)),bind(X_158,$fot(X_224))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_224)),not(X_224)),X_223),X_222))
| is_a_theorem(implies(X_224,X_222)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_224)),not(X_224)),X_223),X_222),implies(X_224,X_222))) )],[refute_0_95,refute_0_88]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(not(not(X_11167)))),not(not(not(X_11167)))),not(not(X_11167))),X_11167))
| is_a_theorem(implies(not(not(X_11167)),X_11167)) ),
inference(subst,[],[refute_0_96:[bind(X_222,$fot(X_11167)),bind(X_223,$fot(not(not(X_11167)))),bind(X_224,$fot(not(not(X_11167))))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_11163),X_11163),X_11163),implies(implies(implies(not(not(not(not(X_11163)))),X_11164),not(not(X_11163))),X_11163)))
| is_a_theorem(implies(implies(implies(not(not(not(not(X_11163)))),X_11164),not(not(X_11163))),X_11163)) ),
inference(subst,[],[refute_0_68:[bind(X_5547,$fot(implies(implies(implies(not(not(not(not(X_11163)))),X_11164),not(not(X_11163))),X_11163))),bind(X_5548,$fot(X_11163))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(not(X_11082))),X_11080),not(X_11082)),implies(X_11082,X_11081)))
| is_a_theorem(implies(implies(implies(X_11082,X_11081),Z),implies(implies(implies(not(not(not(X_11082))),X_11080),not(X_11082)),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(not(not(X_11082))),X_11080),not(X_11082)))),bind(Y,$fot(implies(X_11082,X_11081)))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(implies(not(not(X_4089)),not(X_4089)),implies(X_4089,X_4088)))
| is_a_theorem(implies(not(X_4089),implies(X_4089,X_4088))) ),
inference(subst,[],[refute_0_41:[bind(X_34,$fot(not(X_4089))),bind(X_35,$fot(not(X_4089))),bind(X_36,$fot(implies(X_4089,X_4088)))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(not(X_4085)),not(X_4085))),X_4084),implies(X_4085,X_4084)))
| is_a_theorem(implies(implies(not(not(X_4085)),not(X_4085)),implies(X_4085,X_4084))) ),
inference(subst,[],[refute_0_41:[bind(X_34,$fot(X_4084)),bind(X_35,$fot(implies(not(not(X_4085)),not(X_4085)))),bind(X_36,$fot(implies(X_4085,X_4084)))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(X_4083,not(implies(not(not(X_4083)),not(X_4083)))))
| is_a_theorem(implies(implies(not(implies(not(not(X_4083)),not(X_4083))),Z),implies(X_4083,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_4083)),bind(Y,$fot(not(implies(not(not(X_4083)),not(X_4083)))))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(implies(not(X_4082),X_4082),not(implies(not(not(X_4082)),not(X_4082)))))
| is_a_theorem(implies(X_4082,not(implies(not(not(X_4082)),not(X_4082))))) ),
inference(subst,[],[refute_0_41:[bind(X_34,$fot(X_4082)),bind(X_35,$fot(X_4082)),bind(X_36,$fot(not(implies(not(not(X_4082)),not(X_4082)))))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081)))))),X_298),implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081))))))
| is_a_theorem(implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081))))) ),
inference(subst,[],[refute_0_27:[bind(X_297,$fot(implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081))))))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(implies(not(not(X_4079)),not(X_4079)))),not(implies(not(not(X_4079)),not(X_4079)))),not(implies(not(not(X_4079)),not(X_4079)))),implies(implies(not(X_4079),X_4079),not(implies(not(not(X_4079)),not(X_4079))))))
| is_a_theorem(implies(X_1022,implies(implies(not(X_4079),X_4079),not(implies(not(not(X_4079)),not(X_4079)))))) ),
inference(subst,[],[refute_0_59:[bind(X_1021,$fot(not(implies(not(not(X_4079)),not(X_4079))))),bind(X_1023,$fot(implies(implies(not(X_4079),X_4079),not(implies(not(not(X_4079)),not(X_4079))))))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(implies(not(X_3870),X_3870),implies(not(not(implies(not(not(X_3870)),not(X_3870)))),X_3869)))
| is_a_theorem(implies(implies(implies(not(not(implies(not(not(X_3870)),not(X_3870)))),X_3869),Z),implies(implies(not(X_3870),X_3870),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(not(X_3870),X_3870))),bind(Y,$fot(implies(not(not(implies(not(not(X_3870)),not(X_3870)))),X_3869)))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_128,X_129)),implies(X_128,X_129)),implies(implies(not(X_128),X_128),X_129)))
| ~ is_a_theorem(implies(not(implies(X_128,X_129)),implies(X_128,X_129)))
| is_a_theorem(implies(implies(not(X_128),X_128),X_129)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(implies(X_128,X_129)),implies(X_128,X_129)))),bind(Y,$fot(implies(implies(not(X_128),X_128),X_129)))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(X_32,X_33))
| ~ is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33)))
| is_a_theorem(implies(implies(not(X_32),X_32),X_33)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_32,X_33))),bind(Y,$fot(implies(implies(not(X_32),X_32),X_33)))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(X_32,X_33))
| is_a_theorem(implies(implies(not(X_32),X_32),X_33)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33))) )],[refute_0_52,refute_0_108]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31)))
| is_a_theorem(implies(implies(not(implies(X_30,X_31)),implies(X_30,X_31)),implies(implies(not(X_30),X_30),X_31))) ),
inference(subst,[],[refute_0_109:[bind(X_32,$fot(implies(X_30,X_31))),bind(X_33,$fot(implies(implies(not(X_30),X_30),X_31)))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(not(implies(X_30,X_31)),implies(X_30,X_31)),implies(implies(not(X_30),X_30),X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) )],[refute_0_51,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(not(implies(X_128,X_129)),implies(X_128,X_129)),implies(implies(not(X_128),X_128),X_129))),
inference(subst,[],[refute_0_111:[bind(X_30,$fot(X_128)),bind(X_31,$fot(X_129))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(not(implies(X_128,X_129)),implies(X_128,X_129)))
| is_a_theorem(implies(implies(not(X_128),X_128),X_129)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(X_128,X_129)),implies(X_128,X_129)),implies(implies(not(X_128),X_128),X_129))) )],[refute_0_112,refute_0_107]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(not(implies(X_3868,implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867))),implies(X_3868,implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867))))
| is_a_theorem(implies(implies(not(X_3868),X_3868),implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867))) ),
inference(subst,[],[refute_0_113:[bind(X_128,$fot(X_3868)),bind(X_129,$fot(implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867)))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(X_2777),X_2777))),X_2777))),X_298),implies(not(not(implies(not(X_2777),X_2777))),X_2777)))
| is_a_theorem(implies(not(not(implies(not(X_2777),X_2777))),X_2777)) ),
inference(subst,[],[refute_0_27:[bind(X_297,$fot(implies(not(not(implies(not(X_2777),X_2777))),X_2777)))]]) ).
cnf(refute_0_116,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_2773),X_2773),X_2773),implies(not(not(implies(not(X_2773),X_2773))),X_2773)))
| is_a_theorem(implies(X_1022,implies(not(not(implies(not(X_2773),X_2773))),X_2773))) ),
inference(subst,[],[refute_0_59:[bind(X_1021,$fot(X_2773)),bind(X_1023,$fot(implies(not(not(implies(not(X_2773),X_2773))),X_2773)))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_2317,X_2318)),implies(X_2317,X_2318)),X_2315),implies(not(not(implies(X_2317,X_2318))),X_2315)))
| is_a_theorem(implies(implies(implies(X_2317,X_2318),X_2315),implies(not(not(implies(X_2317,X_2318))),X_2315))) ),
inference(subst,[],[refute_0_55:[bind(X_41,$fot(implies(not(not(implies(X_2317,X_2318))),X_2315))),bind(X_42,$fot(implies(X_2317,X_2318))),bind(X_43,$fot(X_2315))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(not(X_2302),implies(X_2302,implies(X_2303,X_2304))))
| is_a_theorem(implies(implies(implies(X_2302,implies(X_2303,X_2304)),Z),implies(not(X_2302),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(X_2302))),bind(Y,$fot(implies(X_2302,implies(X_2303,X_2304))))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(implies(not(not(X_2191)),not(X_2192)),implies(X_2191,implies(X_2192,X_2193))))
| is_a_theorem(implies(not(X_2191),implies(X_2191,implies(X_2192,X_2193)))) ),
inference(subst,[],[refute_0_41:[bind(X_34,$fot(not(X_2192))),bind(X_35,$fot(not(X_2191))),bind(X_36,$fot(implies(X_2191,implies(X_2192,X_2193))))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_2188),not(X_2187)),implies(not(not(X_2187)),not(X_2187))),implies(X_2187,implies(X_2188,X_2189))))
| is_a_theorem(implies(implies(not(not(X_2187)),not(X_2188)),implies(X_2187,implies(X_2188,X_2189)))) ),
inference(subst,[],[refute_0_7:[bind(X_69,$fot(not(not(X_2187)))),bind(X_70,$fot(not(X_2188))),bind(X_71,$fot(not(X_2187))),bind(X_72,$fot(implies(X_2187,implies(X_2188,X_2189))))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(implies(X_2042,implies(not(not(X_2041)),not(X_2041))),implies(X_2041,implies(X_2042,X_2043))))
| is_a_theorem(implies(implies(implies(not(X_2042),X_38),implies(not(not(X_2041)),not(X_2041))),implies(X_2041,implies(X_2042,X_2043)))) ),
inference(subst,[],[refute_0_23:[bind(X_37,$fot(implies(X_2041,implies(X_2042,X_2043)))),bind(X_39,$fot(X_2042)),bind(X_40,$fot(implies(not(not(X_2041)),not(X_2041))))]]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_158)),not(X_158)),X_1900),implies(X_1898,X_1900)),implies(X_158,implies(X_1898,X_1900)))),
inference(subst,[],[refute_0_94:[bind(Z,$fot(implies(X_1898,X_1900))),bind(X_157,$fot(X_1900))]]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_158)),not(X_158)),X_1900),implies(X_1898,X_1900)),implies(X_158,implies(X_1898,X_1900))))
| is_a_theorem(implies(implies(X_1898,implies(not(not(X_158)),not(X_158))),implies(X_158,implies(X_1898,X_1900)))) ),
inference(subst,[],[refute_0_7:[bind(X_69,$fot(X_1898)),bind(X_70,$fot(implies(not(not(X_158)),not(X_158)))),bind(X_71,$fot(X_1900)),bind(X_72,$fot(implies(X_158,implies(X_1898,X_1900))))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(X_1898,implies(not(not(X_158)),not(X_158))),implies(X_158,implies(X_1898,X_1900)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_158)),not(X_158)),X_1900),implies(X_1898,X_1900)),implies(X_158,implies(X_1898,X_1900)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(implies(X_2042,implies(not(not(X_2041)),not(X_2041))),implies(X_2041,implies(X_2042,X_2043)))),
inference(subst,[],[refute_0_124:[bind(X_158,$fot(X_2041)),bind(X_1898,$fot(X_2042)),bind(X_1900,$fot(X_2043))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(implies(not(X_2042),X_38),implies(not(not(X_2041)),not(X_2041))),implies(X_2041,implies(X_2042,X_2043)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2042,implies(not(not(X_2041)),not(X_2041))),implies(X_2041,implies(X_2042,X_2043)))) )],[refute_0_125,refute_0_121]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(implies(not(X_2188),not(X_2187)),implies(not(not(X_2187)),not(X_2187))),implies(X_2187,implies(X_2188,X_2189)))),
inference(subst,[],[refute_0_126:[bind(X_2041,$fot(X_2187)),bind(X_2042,$fot(X_2188)),bind(X_2043,$fot(X_2189)),bind(X_38,$fot(not(X_2187)))]]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(not(not(X_2187)),not(X_2188)),implies(X_2187,implies(X_2188,X_2189)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_2188),not(X_2187)),implies(not(not(X_2187)),not(X_2187))),implies(X_2187,implies(X_2188,X_2189)))) )],[refute_0_127,refute_0_120]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(not(not(X_2191)),not(X_2192)),implies(X_2191,implies(X_2192,X_2193)))),
inference(subst,[],[refute_0_128:[bind(X_2187,$fot(X_2191)),bind(X_2188,$fot(X_2192)),bind(X_2189,$fot(X_2193))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(not(X_2191),implies(X_2191,implies(X_2192,X_2193)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_2191)),not(X_2192)),implies(X_2191,implies(X_2192,X_2193)))) )],[refute_0_129,refute_0_119]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(not(X_2302),implies(X_2302,implies(X_2303,X_2304)))),
inference(subst,[],[refute_0_130:[bind(X_2191,$fot(X_2302)),bind(X_2192,$fot(X_2303)),bind(X_2193,$fot(X_2304))]]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(implies(X_2302,implies(X_2303,X_2304)),Z),implies(not(X_2302),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_2302),implies(X_2302,implies(X_2303,X_2304)))) )],[refute_0_131,refute_0_118]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(implies(not(implies(X_2317,X_2318)),implies(X_2317,X_2318)),X_2315),implies(not(not(implies(X_2317,X_2318))),X_2315))),
inference(subst,[],[refute_0_132:[bind(Z,$fot(X_2315)),bind(X_2302,$fot(not(implies(X_2317,X_2318)))),bind(X_2303,$fot(X_2317)),bind(X_2304,$fot(X_2318))]]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(implies(X_2317,X_2318),X_2315),implies(not(not(implies(X_2317,X_2318))),X_2315))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_2317,X_2318)),implies(X_2317,X_2318)),X_2315),implies(not(not(implies(X_2317,X_2318))),X_2315))) )],[refute_0_133,refute_0_117]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(implies(not(X_2773),X_2773),X_2773),implies(not(not(implies(not(X_2773),X_2773))),X_2773))),
inference(subst,[],[refute_0_134:[bind(X_2315,$fot(X_2773)),bind(X_2317,$fot(not(X_2773))),bind(X_2318,$fot(X_2773))]]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(X_1022,implies(not(not(implies(not(X_2773),X_2773))),X_2773))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_2773),X_2773),X_2773),implies(not(not(implies(not(X_2773),X_2773))),X_2773))) )],[refute_0_135,refute_0_116]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(X_2777),X_2777))),X_2777))),X_298),implies(not(not(implies(not(X_2777),X_2777))),X_2777))),
inference(subst,[],[refute_0_136:[bind(X_1022,$fot(implies(not(not(implies(not(not(implies(not(X_2777),X_2777))),X_2777))),X_298))),bind(X_2773,$fot(X_2777))]]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(not(not(implies(not(X_2777),X_2777))),X_2777)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(X_2777),X_2777))),X_2777))),X_298),implies(not(not(implies(not(X_2777),X_2777))),X_2777))) )],[refute_0_137,refute_0_115]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(not(not(implies(not(not(X_3848)),not(X_3848)))),not(X_3848))),
inference(subst,[],[refute_0_138:[bind(X_2777,$fot(not(X_3848)))]]) ).
cnf(refute_0_140,plain,
( ~ is_a_theorem(implies(X_1939,not(X_1941)))
| ~ is_a_theorem(implies(implies(X_1939,not(X_1941)),implies(not(implies(X_1941,implies(X_1939,X_1940))),X_1938)))
| is_a_theorem(implies(not(implies(X_1941,implies(X_1939,X_1940))),X_1938)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1939,not(X_1941)))),bind(Y,$fot(implies(not(implies(X_1941,implies(X_1939,X_1940))),X_1938)))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(implies(X_293,X_294),implies(not(implies(X_293,X_294)),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(implies(X_293,X_294)))]]) ).
cnf(refute_0_142,plain,
( ~ is_a_theorem(implies(implies(X_293,X_294),implies(not(implies(X_293,X_294)),Y)))
| is_a_theorem(implies(implies(implies(not(X_293),X_292),X_294),implies(not(implies(X_293,X_294)),Y))) ),
inference(subst,[],[refute_0_23:[bind(X_37,$fot(implies(not(implies(X_293,X_294)),Y))),bind(X_38,$fot(X_292)),bind(X_39,$fot(X_293)),bind(X_40,$fot(X_294))]]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(implies(implies(not(X_293),X_292),X_294),implies(not(implies(X_293,X_294)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_293,X_294),implies(not(implies(X_293,X_294)),Y))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(implies(implies(not(X_293),X_1900),implies(X_1898,X_1900)),implies(not(implies(X_293,implies(X_1898,X_1900))),Y))),
inference(subst,[],[refute_0_143:[bind(X_292,$fot(X_1900)),bind(X_294,$fot(implies(X_1898,X_1900)))]]) ).
cnf(refute_0_145,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_293),X_1900),implies(X_1898,X_1900)),implies(not(implies(X_293,implies(X_1898,X_1900))),Y)))
| is_a_theorem(implies(implies(X_1898,not(X_293)),implies(not(implies(X_293,implies(X_1898,X_1900))),Y))) ),
inference(subst,[],[refute_0_7:[bind(X_69,$fot(X_1898)),bind(X_70,$fot(not(X_293))),bind(X_71,$fot(X_1900)),bind(X_72,$fot(implies(not(implies(X_293,implies(X_1898,X_1900))),Y)))]]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(X_1898,not(X_293)),implies(not(implies(X_293,implies(X_1898,X_1900))),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_293),X_1900),implies(X_1898,X_1900)),implies(not(implies(X_293,implies(X_1898,X_1900))),Y))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(X_1939,not(X_1941)),implies(not(implies(X_1941,implies(X_1939,X_1940))),X_1938))),
inference(subst,[],[refute_0_146:[bind(Y,$fot(X_1938)),bind(X_1898,$fot(X_1939)),bind(X_1900,$fot(X_1940)),bind(X_293,$fot(X_1941))]]) ).
cnf(refute_0_148,plain,
( ~ is_a_theorem(implies(X_1939,not(X_1941)))
| is_a_theorem(implies(not(implies(X_1941,implies(X_1939,X_1940))),X_1938)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1939,not(X_1941)),implies(not(implies(X_1941,implies(X_1939,X_1940))),X_1938))) )],[refute_0_147,refute_0_140]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(not(not(implies(not(not(X_3848)),not(X_3848)))),not(X_3848)))
| is_a_theorem(implies(not(implies(X_3848,implies(not(not(implies(not(not(X_3848)),not(X_3848)))),X_3847))),X_3845)) ),
inference(subst,[],[refute_0_148:[bind(X_1938,$fot(X_3845)),bind(X_1939,$fot(not(not(implies(not(not(X_3848)),not(X_3848)))))),bind(X_1940,$fot(X_3847)),bind(X_1941,$fot(X_3848))]]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(not(implies(X_3848,implies(not(not(implies(not(not(X_3848)),not(X_3848)))),X_3847))),X_3845)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(not(X_3848)),not(X_3848)))),not(X_3848))) )],[refute_0_139,refute_0_149]) ).
cnf(refute_0_151,plain,
is_a_theorem(implies(not(implies(X_3868,implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867))),implies(X_3868,implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867)))),
inference(subst,[],[refute_0_150:[bind(X_3845,$fot(implies(X_3868,implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867)))),bind(X_3847,$fot(X_3867)),bind(X_3848,$fot(X_3868))]]) ).
cnf(refute_0_152,plain,
is_a_theorem(implies(implies(not(X_3868),X_3868),implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_3868,implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867))),implies(X_3868,implies(not(not(implies(not(not(X_3868)),not(X_3868)))),X_3867)))) )],[refute_0_151,refute_0_114]) ).
cnf(refute_0_153,plain,
is_a_theorem(implies(implies(not(X_3870),X_3870),implies(not(not(implies(not(not(X_3870)),not(X_3870)))),X_3869))),
inference(subst,[],[refute_0_152:[bind(X_3867,$fot(X_3869)),bind(X_3868,$fot(X_3870))]]) ).
cnf(refute_0_154,plain,
is_a_theorem(implies(implies(implies(not(not(implies(not(not(X_3870)),not(X_3870)))),X_3869),Z),implies(implies(not(X_3870),X_3870),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_3870),X_3870),implies(not(not(implies(not(not(X_3870)),not(X_3870)))),X_3869))) )],[refute_0_153,refute_0_106]) ).
cnf(refute_0_155,plain,
is_a_theorem(implies(implies(implies(not(not(implies(not(not(X_4079)),not(X_4079)))),not(implies(not(not(X_4079)),not(X_4079)))),not(implies(not(not(X_4079)),not(X_4079)))),implies(implies(not(X_4079),X_4079),not(implies(not(not(X_4079)),not(X_4079)))))),
inference(subst,[],[refute_0_154:[bind(Z,$fot(not(implies(not(not(X_4079)),not(X_4079))))),bind(X_3869,$fot(not(implies(not(not(X_4079)),not(X_4079))))),bind(X_3870,$fot(X_4079))]]) ).
cnf(refute_0_156,plain,
is_a_theorem(implies(X_1022,implies(implies(not(X_4079),X_4079),not(implies(not(not(X_4079)),not(X_4079)))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(implies(not(not(X_4079)),not(X_4079)))),not(implies(not(not(X_4079)),not(X_4079)))),not(implies(not(not(X_4079)),not(X_4079)))),implies(implies(not(X_4079),X_4079),not(implies(not(not(X_4079)),not(X_4079)))))) )],[refute_0_155,refute_0_105]) ).
cnf(refute_0_157,plain,
is_a_theorem(implies(implies(not(not(implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081)))))),X_298),implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081)))))),
inference(subst,[],[refute_0_156:[bind(X_1022,$fot(implies(not(not(implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081)))))),X_298))),bind(X_4079,$fot(X_4081))]]) ).
cnf(refute_0_158,plain,
is_a_theorem(implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081)))))),X_298),implies(implies(not(X_4081),X_4081),not(implies(not(not(X_4081)),not(X_4081)))))) )],[refute_0_157,refute_0_104]) ).
cnf(refute_0_159,plain,
is_a_theorem(implies(implies(not(X_4082),X_4082),not(implies(not(not(X_4082)),not(X_4082))))),
inference(subst,[],[refute_0_158:[bind(X_4081,$fot(X_4082))]]) ).
cnf(refute_0_160,plain,
is_a_theorem(implies(X_4082,not(implies(not(not(X_4082)),not(X_4082))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_4082),X_4082),not(implies(not(not(X_4082)),not(X_4082))))) )],[refute_0_159,refute_0_103]) ).
cnf(refute_0_161,plain,
is_a_theorem(implies(X_4083,not(implies(not(not(X_4083)),not(X_4083))))),
inference(subst,[],[refute_0_160:[bind(X_4082,$fot(X_4083))]]) ).
cnf(refute_0_162,plain,
is_a_theorem(implies(implies(not(implies(not(not(X_4083)),not(X_4083))),Z),implies(X_4083,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4083,not(implies(not(not(X_4083)),not(X_4083))))) )],[refute_0_161,refute_0_102]) ).
cnf(refute_0_163,plain,
is_a_theorem(implies(implies(not(implies(not(not(X_4085)),not(X_4085))),X_4084),implies(X_4085,X_4084))),
inference(subst,[],[refute_0_162:[bind(Z,$fot(X_4084)),bind(X_4083,$fot(X_4085))]]) ).
cnf(refute_0_164,plain,
is_a_theorem(implies(implies(not(not(X_4085)),not(X_4085)),implies(X_4085,X_4084))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(not(not(X_4085)),not(X_4085))),X_4084),implies(X_4085,X_4084))) )],[refute_0_163,refute_0_101]) ).
cnf(refute_0_165,plain,
is_a_theorem(implies(implies(not(not(X_4089)),not(X_4089)),implies(X_4089,X_4088))),
inference(subst,[],[refute_0_164:[bind(X_4084,$fot(X_4088)),bind(X_4085,$fot(X_4089))]]) ).
cnf(refute_0_166,plain,
is_a_theorem(implies(not(X_4089),implies(X_4089,X_4088))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_4089)),not(X_4089)),implies(X_4089,X_4088))) )],[refute_0_165,refute_0_100]) ).
cnf(refute_0_167,plain,
( ~ is_a_theorem(implies(X_318,X_317))
| ~ is_a_theorem(implies(implies(X_318,X_317),implies(implies(implies(not(not(X_318)),X_319),X_318),X_317)))
| is_a_theorem(implies(implies(implies(not(not(X_318)),X_319),X_318),X_317)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_318,X_317))),bind(Y,$fot(implies(implies(implies(not(not(X_318)),X_319),X_318),X_317)))]]) ).
cnf(refute_0_168,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_297)),X_298),X_297),X_297))
| is_a_theorem(implies(implies(X_297,Z),implies(implies(implies(not(not(X_297)),X_298),X_297),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(not(X_297)),X_298),X_297))),bind(Y,$fot(X_297))]]) ).
cnf(refute_0_169,plain,
is_a_theorem(implies(implies(X_297,Z),implies(implies(implies(not(not(X_297)),X_298),X_297),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_297)),X_298),X_297),X_297)) )],[refute_0_26,refute_0_168]) ).
cnf(refute_0_170,plain,
is_a_theorem(implies(implies(X_318,X_317),implies(implies(implies(not(not(X_318)),X_319),X_318),X_317))),
inference(subst,[],[refute_0_169:[bind(Z,$fot(X_317)),bind(X_297,$fot(X_318)),bind(X_298,$fot(X_319))]]) ).
cnf(refute_0_171,plain,
( ~ is_a_theorem(implies(X_318,X_317))
| is_a_theorem(implies(implies(implies(not(not(X_318)),X_319),X_318),X_317)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_318,X_317),implies(implies(implies(not(not(X_318)),X_319),X_318),X_317))) )],[refute_0_170,refute_0_167]) ).
cnf(refute_0_172,plain,
( ~ is_a_theorem(implies(not(X_4089),implies(X_4089,X_4088)))
| is_a_theorem(implies(implies(implies(not(not(not(X_4089))),X_11079),not(X_4089)),implies(X_4089,X_4088))) ),
inference(subst,[],[refute_0_171:[bind(X_317,$fot(implies(X_4089,X_4088))),bind(X_318,$fot(not(X_4089))),bind(X_319,$fot(X_11079))]]) ).
cnf(refute_0_173,plain,
is_a_theorem(implies(implies(implies(not(not(not(X_4089))),X_11079),not(X_4089)),implies(X_4089,X_4088))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_4089),implies(X_4089,X_4088))) )],[refute_0_166,refute_0_172]) ).
cnf(refute_0_174,plain,
is_a_theorem(implies(implies(implies(not(not(not(X_11082))),X_11080),not(X_11082)),implies(X_11082,X_11081))),
inference(subst,[],[refute_0_173:[bind(X_11079,$fot(X_11080)),bind(X_4088,$fot(X_11081)),bind(X_4089,$fot(X_11082))]]) ).
cnf(refute_0_175,plain,
is_a_theorem(implies(implies(implies(X_11082,X_11081),Z),implies(implies(implies(not(not(not(X_11082))),X_11080),not(X_11082)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(not(X_11082))),X_11080),not(X_11082)),implies(X_11082,X_11081))) )],[refute_0_174,refute_0_99]) ).
cnf(refute_0_176,plain,
is_a_theorem(implies(implies(implies(not(X_11163),X_11163),X_11163),implies(implies(implies(not(not(not(not(X_11163)))),X_11164),not(not(X_11163))),X_11163))),
inference(subst,[],[refute_0_175:[bind(Z,$fot(X_11163)),bind(X_11080,$fot(X_11164)),bind(X_11081,$fot(X_11163)),bind(X_11082,$fot(not(X_11163)))]]) ).
cnf(refute_0_177,plain,
is_a_theorem(implies(implies(implies(not(not(not(not(X_11163)))),X_11164),not(not(X_11163))),X_11163)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_11163),X_11163),X_11163),implies(implies(implies(not(not(not(not(X_11163)))),X_11164),not(not(X_11163))),X_11163))) )],[refute_0_176,refute_0_98]) ).
cnf(refute_0_178,plain,
is_a_theorem(implies(implies(implies(not(not(not(not(X_11167)))),not(not(not(X_11167)))),not(not(X_11167))),X_11167)),
inference(subst,[],[refute_0_177:[bind(X_11163,$fot(X_11167)),bind(X_11164,$fot(not(not(not(X_11167)))))]]) ).
cnf(refute_0_179,plain,
is_a_theorem(implies(not(not(X_11167)),X_11167)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(not(not(X_11167)))),not(not(not(X_11167)))),not(not(X_11167))),X_11167)) )],[refute_0_178,refute_0_97]) ).
cnf(refute_0_180,plain,
is_a_theorem(implies(not(not(X_11169)),X_11169)),
inference(subst,[],[refute_0_179:[bind(X_11167,$fot(X_11169))]]) ).
cnf(refute_0_181,plain,
is_a_theorem(implies(X_5580,implies(not(not(X_11169)),X_11169))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_11169)),X_11169)) )],[refute_0_180,refute_0_87]) ).
cnf(refute_0_182,plain,
is_a_theorem(implies(X_11173,implies(not(not(X_11172)),X_11172))),
inference(subst,[],[refute_0_181:[bind(X_11169,$fot(X_11172)),bind(X_5580,$fot(X_11173))]]) ).
cnf(refute_0_183,plain,
is_a_theorem(implies(X_5580,implies(X_11173,implies(not(not(X_11172)),X_11172)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_11173,implies(not(not(X_11172)),X_11172))) )],[refute_0_182,refute_0_86]) ).
cnf(refute_0_184,plain,
is_a_theorem(implies(not(implies(X_16472,implies(not(not(X_11172)),X_11172))),implies(X_16472,implies(not(not(X_11172)),X_11172)))),
inference(subst,[],[refute_0_183:[bind(X_11173,$fot(X_16472)),bind(X_5580,$fot(not(implies(X_16472,implies(not(not(X_11172)),X_11172)))))]]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_288,X_289)),implies(X_288,X_289)),implies(implies(X_289,X_290),implies(X_288,X_290))))
| ~ is_a_theorem(implies(not(implies(X_288,X_289)),implies(X_288,X_289)))
| is_a_theorem(implies(implies(X_289,X_290),implies(X_288,X_290))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(implies(X_288,X_289)),implies(X_288,X_289)))),bind(Y,$fot(implies(implies(X_289,X_290),implies(X_288,X_290))))]]) ).
cnf(refute_0_186,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(not(implies(X,Y)),implies(X,Y)),implies(implies(Y,Z),implies(X,Z)))) ),
inference(subst,[],[refute_0_109:[bind(X_32,$fot(implies(X,Y))),bind(X_33,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_187,plain,
is_a_theorem(implies(implies(not(implies(X,Y)),implies(X,Y)),implies(implies(Y,Z),implies(X,Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_186]) ).
cnf(refute_0_188,plain,
is_a_theorem(implies(implies(not(implies(X_288,X_289)),implies(X_288,X_289)),implies(implies(X_289,X_290),implies(X_288,X_290)))),
inference(subst,[],[refute_0_187:[bind(X,$fot(X_288)),bind(Y,$fot(X_289)),bind(Z,$fot(X_290))]]) ).
cnf(refute_0_189,plain,
( ~ is_a_theorem(implies(not(implies(X_288,X_289)),implies(X_288,X_289)))
| is_a_theorem(implies(implies(X_289,X_290),implies(X_288,X_290))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(X_288,X_289)),implies(X_288,X_289)),implies(implies(X_289,X_290),implies(X_288,X_290)))) )],[refute_0_188,refute_0_185]) ).
cnf(refute_0_190,plain,
( ~ is_a_theorem(implies(not(implies(X_16472,implies(not(not(X_11172)),X_11172))),implies(X_16472,implies(not(not(X_11172)),X_11172))))
| is_a_theorem(implies(implies(implies(not(not(X_11172)),X_11172),X_16474),implies(X_16472,X_16474))) ),
inference(subst,[],[refute_0_189:[bind(X_288,$fot(X_16472)),bind(X_289,$fot(implies(not(not(X_11172)),X_11172))),bind(X_290,$fot(X_16474))]]) ).
cnf(refute_0_191,plain,
is_a_theorem(implies(implies(implies(not(not(X_11172)),X_11172),X_16474),implies(X_16472,X_16474))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_16472,implies(not(not(X_11172)),X_11172))),implies(X_16472,implies(not(not(X_11172)),X_11172)))) )],[refute_0_184,refute_0_190]) ).
cnf(refute_0_192,plain,
is_a_theorem(implies(implies(implies(not(not(X_16506)),X_16506),X_16508),implies(X_16507,X_16508))),
inference(subst,[],[refute_0_191:[bind(X_11172,$fot(X_16506)),bind(X_16472,$fot(X_16507)),bind(X_16474,$fot(X_16508))]]) ).
cnf(refute_0_193,plain,
is_a_theorem(implies(implies(implies(X_16507,X_16508),Z),implies(implies(implies(not(not(X_16506)),X_16506),X_16508),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_16506)),X_16506),X_16508),implies(X_16507,X_16508))) )],[refute_0_192,refute_0_70]) ).
cnf(refute_0_194,plain,
is_a_theorem(implies(implies(implies(not(X_16930),X_16930),X_16930),implies(implies(implies(not(not(X_16931)),X_16931),X_16930),X_16930))),
inference(subst,[],[refute_0_193:[bind(Z,$fot(X_16930)),bind(X_16506,$fot(X_16931)),bind(X_16507,$fot(not(X_16930))),bind(X_16508,$fot(X_16930))]]) ).
cnf(refute_0_195,plain,
is_a_theorem(implies(implies(implies(not(not(X_16931)),X_16931),X_16930),X_16930)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_16930),X_16930),X_16930),implies(implies(implies(not(not(X_16931)),X_16931),X_16930),X_16930))) )],[refute_0_194,refute_0_69]) ).
cnf(refute_0_196,plain,
is_a_theorem(implies(implies(implies(not(not(X_16935)),X_16935),X_16934),X_16934)),
inference(subst,[],[refute_0_195:[bind(X_16930,$fot(X_16934)),bind(X_16931,$fot(X_16935))]]) ).
cnf(refute_0_197,plain,
( ~ is_a_theorem(implies(implies(not(not(X_16935)),X_16935),X_16934))
| is_a_theorem(X_16934) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_16935)),X_16935),X_16934),X_16934)) )],[refute_0_196,refute_0_11]) ).
cnf(refute_0_198,plain,
( ~ is_a_theorem(implies(implies(not(not(X_26001)),X_26001),implies(implies(implies(not(not(X_26001)),X_1900),Z),implies(implies(X_26001,X_1900),Z))))
| is_a_theorem(implies(implies(implies(not(not(X_26001)),X_1900),Z),implies(implies(X_26001,X_1900),Z))) ),
inference(subst,[],[refute_0_197:[bind(X_16934,$fot(implies(implies(implies(not(not(X_26001)),X_1900),Z),implies(implies(X_26001,X_1900),Z)))),bind(X_16935,$fot(X_26001))]]) ).
cnf(refute_0_199,plain,
is_a_theorem(implies(implies(implies(not(not(X_26001)),X_1900),Z),implies(implies(X_26001,X_1900),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_26001)),X_26001),implies(implies(implies(not(not(X_26001)),X_1900),Z),implies(implies(X_26001,X_1900),Z)))) )],[refute_0_10,refute_0_198]) ).
cnf(refute_0_200,plain,
is_a_theorem(implies(implies(implies(not(not(x)),y),z),implies(implies(x,y),z))),
inference(subst,[],[refute_0_199:[bind(Z,$fot(z)),bind(X_1900,$fot(y)),bind(X_26001,$fot(x))]]) ).
cnf(refute_0_201,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(x)),y),z),implies(implies(x,y),z))) )],[refute_0_200,prove_cn_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL381-1 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 14:31:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 37.47/37.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.47/37.64
% 37.47/37.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.47/37.66
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