TSTP Solution File: LCL362-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL362-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:51:44 EDT 2022
% Result : Unsatisfiable 2.44s 2.61s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 5
% Syntax : Number of clauses : 90 ( 52 unt; 0 nHn; 28 RR)
% Number of literals : 137 ( 0 equ; 48 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 245 ( 49 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_11,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(implies(not(y),y),y)),implies(implies(not(y),y),y))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(X_4256)
| ~ is_a_theorem(implies(X_4256,implies(X_4255,X_4256)))
| is_a_theorem(implies(X_4255,X_4256)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_4256)),bind(Y,$fot(implies(X_4255,X_4256)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(not(implies(X_4254,implies(X_4253,X_4254))),implies(X_4254,implies(X_4253,X_4254))))
| is_a_theorem(implies(X_4254,implies(X_4253,X_4254))) ),
inference(subst,[],[refute_0_3:[bind(X_7,$fot(implies(X_4254,implies(X_4253,X_4254))))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34)))
| ~ is_a_theorem(implies(implies(not(X_33),X_32),X_34))
| is_a_theorem(implies(X_33,X_34)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_33),X_32),X_34))),bind(Y,$fot(implies(X_33,X_34)))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(X_27,implies(not(X_27),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_7,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_8,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(X_27,implies(not(X_27),Y)))
| is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_27)),bind(Y,$fot(implies(not(X_27),Y))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(not(X_27),Y),X_29),implies(X_27,X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(X_27,implies(not(X_27),Y))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34))),
inference(subst,[],[refute_0_10:[bind(Y,$fot(X_32)),bind(X_27,$fot(X_33)),bind(X_29,$fot(X_34))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(not(X_33),X_32),X_34))
| is_a_theorem(implies(X_33,X_34)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_33),X_32),X_34),implies(X_33,X_34))) )],[refute_0_11,refute_0_5]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(not(X_33),not(X_4244)),implies(X_4246,implies(X_4244,X_4246))))
| is_a_theorem(implies(X_33,implies(X_4246,implies(X_4244,X_4246)))) ),
inference(subst,[],[refute_0_12:[bind(X_32,$fot(not(X_4244))),bind(X_34,$fot(implies(X_4246,implies(X_4244,X_4246))))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44))
| ~ is_a_theorem(implies(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44),implies(implies(X_41,X_42),X_44)))
| is_a_theorem(implies(implies(X_41,X_42),X_44)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44))),bind(Y,$fot(implies(implies(X_41,X_42),X_44)))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_29),implies(implies(X,Y),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_15]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44),implies(implies(X_41,X_42),X_44))),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X_43)),bind(X_29,$fot(X_44))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44))
| is_a_theorem(implies(implies(X_41,X_42),X_44)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44),implies(implies(X_41,X_42),X_44))) )],[refute_0_17,refute_0_14]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_1431,X_1430),X_1430),implies(X_41,X_1430)),implies(X_1430,implies(X_41,X_1430))))
| is_a_theorem(implies(implies(X_41,implies(X_1431,X_1430)),implies(X_1430,implies(X_41,X_1430)))) ),
inference(subst,[],[refute_0_18:[bind(X_42,$fot(implies(X_1431,X_1430))),bind(X_43,$fot(X_1430)),bind(X_44,$fot(implies(X_1430,implies(X_41,X_1430))))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53)))
| ~ is_a_theorem(implies(implies(implies(not(X_54),X_54),X_55),X_53))
| is_a_theorem(implies(implies(X_54,X_55),X_53)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_54),X_54),X_55),X_53))),bind(Y,$fot(implies(implies(X_54,X_55),X_53)))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31)))
| is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),Z),implies(implies(X_30,X_31),Z))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_30,X_31))),bind(Y,$fot(implies(implies(not(X_30),X_30),X_31)))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(not(X_28),X_28),X_28)),
inference(subst,[],[cn_2:[bind(X,$fot(X_28))]]) ).
cnf(refute_0_23,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_8:[bind(X,$fot(implies(not(X_28),X_28))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_28),X_28),X_28)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))),
inference(subst,[],[refute_0_24:[bind(X_28,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).
cnf(refute_0_26,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,[$cnf( is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53))),
inference(subst,[],[refute_0_26:[bind(Z,$fot(X_53)),bind(X_30,$fot(X_54)),bind(X_31,$fot(X_55))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_54),X_54),X_55),X_53))
| is_a_theorem(implies(implies(X_54,X_55),X_53)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53))) )],[refute_0_27,refute_0_20]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(X_1428,X_1426),X_1426)),implies(implies(X_1428,X_1426),X_1426)),X_1425),implies(X_1426,X_1425)))
| is_a_theorem(implies(implies(implies(implies(X_1428,X_1426),X_1426),X_1425),implies(X_1426,X_1425))) ),
inference(subst,[],[refute_0_28:[bind(X_53,$fot(implies(X_1426,X_1425))),bind(X_54,$fot(implies(implies(X_1428,X_1426),X_1426))),bind(X_55,$fot(X_1425))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(X_1261,implies(X_1262,implies(implies(X_1263,X_1261),X_1261))))
| is_a_theorem(implies(implies(implies(X_1262,implies(implies(X_1263,X_1261),X_1261)),Z),implies(X_1261,Z))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_1261)),bind(Y,$fot(implies(X_1262,implies(implies(X_1263,X_1261),X_1261))))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(not(X_1258),X_1260),implies(X_1259,implies(implies(X_1260,X_1258),X_1258))))
| is_a_theorem(implies(X_1258,implies(X_1259,implies(implies(X_1260,X_1258),X_1258)))) ),
inference(subst,[],[refute_0_12:[bind(X_32,$fot(X_1260)),bind(X_33,$fot(X_1258)),bind(X_34,$fot(implies(X_1259,implies(implies(X_1260,X_1258),X_1258))))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(implies(X_42,X_1255),implies(not(X_1255),X_1255)),implies(X_1256,implies(implies(X_42,X_1255),X_1255))))
| is_a_theorem(implies(implies(not(X_1255),X_42),implies(X_1256,implies(implies(X_42,X_1255),X_1255)))) ),
inference(subst,[],[refute_0_18:[bind(X_41,$fot(not(X_1255))),bind(X_43,$fot(X_1255)),bind(X_44,$fot(implies(X_1256,implies(implies(X_42,X_1255),X_1255))))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1222),X_1222),X_1222),implies(X_41,X_1222)),implies(X_1223,implies(X_41,X_1222))))
| is_a_theorem(implies(implies(X_41,implies(not(X_1222),X_1222)),implies(X_1223,implies(X_41,X_1222)))) ),
inference(subst,[],[refute_0_18:[bind(X_42,$fot(implies(not(X_1222),X_1222))),bind(X_43,$fot(X_1222)),bind(X_44,$fot(implies(X_1223,implies(X_41,X_1222))))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(X_194,implies(not(implies(implies(not(X_192),X_192),X_192)),X_193)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_192),X_192),X_192)),X_193),Z),implies(X_194,Z))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_194)),bind(Y,$fot(implies(not(implies(implies(not(X_192),X_192),X_192)),X_193)))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_36,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_37,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_37:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_28)),
inference(subst,[],[refute_0_39:[bind(X_9,$fot(X_28))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_28))
| is_a_theorem(implies(implies(X_28,X_29),implies(not(implies(implies(not(X),X),X)),X_29))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_28)),bind(Z,$fot(X_29))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(not(implies(implies(not(X),X),X)),X_29))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_28)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(not(X_174),X_173),implies(not(implies(implies(not(X),X),X)),X_173))),
inference(subst,[],[refute_0_42:[bind(X_28,$fot(not(X_174))),bind(X_29,$fot(X_173))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(implies(not(X_174),X_173),implies(not(implies(implies(not(X),X),X)),X_173)))
| is_a_theorem(implies(X_174,implies(not(implies(implies(not(X),X),X)),X_173))) ),
inference(subst,[],[refute_0_12:[bind(X_32,$fot(X_173)),bind(X_33,$fot(X_174)),bind(X_34,$fot(implies(not(implies(implies(not(X),X),X)),X_173)))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(X_174,implies(not(implies(implies(not(X),X),X)),X_173))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_174),X_173),implies(not(implies(implies(not(X),X),X)),X_173))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(X_194,implies(not(implies(implies(not(X_192),X_192),X_192)),X_193))),
inference(subst,[],[refute_0_45:[bind(X,$fot(X_192)),bind(X_173,$fot(X_193)),bind(X_174,$fot(X_194))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_192),X_192),X_192)),X_193),Z),implies(X_194,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_194,implies(not(implies(implies(not(X_192),X_192),X_192)),X_193))) )],[refute_0_46,refute_0_34]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_192),X_192),X_192)),implies(implies(not(X_192),X_192),X_192)),X_1202),implies(X_194,X_1202))),
inference(subst,[],[refute_0_47:[bind(Z,$fot(X_1202)),bind(X_193,$fot(implies(implies(not(X_192),X_192),X_192)))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_192),X_192),X_192)),implies(implies(not(X_192),X_192),X_192)),X_1202),implies(X_194,X_1202)))
| is_a_theorem(implies(implies(implies(implies(not(X_192),X_192),X_192),X_1202),implies(X_194,X_1202))) ),
inference(subst,[],[refute_0_28:[bind(X_53,$fot(implies(X_194,X_1202))),bind(X_54,$fot(implies(implies(not(X_192),X_192),X_192))),bind(X_55,$fot(X_1202))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(implies(implies(not(X_192),X_192),X_192),X_1202),implies(X_194,X_1202))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_192),X_192),X_192)),implies(implies(not(X_192),X_192),X_192)),X_1202),implies(X_194,X_1202))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1222),X_1222),X_1222),implies(X_41,X_1222)),implies(X_1223,implies(X_41,X_1222)))),
inference(subst,[],[refute_0_50:[bind(X_1202,$fot(implies(X_41,X_1222))),bind(X_192,$fot(X_1222)),bind(X_194,$fot(X_1223))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(X_41,implies(not(X_1222),X_1222)),implies(X_1223,implies(X_41,X_1222)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1222),X_1222),X_1222),implies(X_41,X_1222)),implies(X_1223,implies(X_41,X_1222)))) )],[refute_0_51,refute_0_33]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(X_42,X_1255),implies(not(X_1255),X_1255)),implies(X_1256,implies(implies(X_42,X_1255),X_1255)))),
inference(subst,[],[refute_0_52:[bind(X_1222,$fot(X_1255)),bind(X_1223,$fot(X_1256)),bind(X_41,$fot(implies(X_42,X_1255)))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(not(X_1255),X_42),implies(X_1256,implies(implies(X_42,X_1255),X_1255)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_42,X_1255),implies(not(X_1255),X_1255)),implies(X_1256,implies(implies(X_42,X_1255),X_1255)))) )],[refute_0_53,refute_0_32]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(not(X_1258),X_1260),implies(X_1259,implies(implies(X_1260,X_1258),X_1258)))),
inference(subst,[],[refute_0_54:[bind(X_1255,$fot(X_1258)),bind(X_1256,$fot(X_1259)),bind(X_42,$fot(X_1260))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(X_1258,implies(X_1259,implies(implies(X_1260,X_1258),X_1258)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_1258),X_1260),implies(X_1259,implies(implies(X_1260,X_1258),X_1258)))) )],[refute_0_55,refute_0_31]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(X_1261,implies(X_1262,implies(implies(X_1263,X_1261),X_1261)))),
inference(subst,[],[refute_0_56:[bind(X_1258,$fot(X_1261)),bind(X_1259,$fot(X_1262)),bind(X_1260,$fot(X_1263))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(X_1262,implies(implies(X_1263,X_1261),X_1261)),Z),implies(X_1261,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1261,implies(X_1262,implies(implies(X_1263,X_1261),X_1261)))) )],[refute_0_57,refute_0_30]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(X_1428,X_1426),X_1426)),implies(implies(X_1428,X_1426),X_1426)),X_1425),implies(X_1426,X_1425))),
inference(subst,[],[refute_0_58:[bind(Z,$fot(X_1425)),bind(X_1261,$fot(X_1426)),bind(X_1262,$fot(not(implies(implies(X_1428,X_1426),X_1426)))),bind(X_1263,$fot(X_1428))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(implies(X_1428,X_1426),X_1426),X_1425),implies(X_1426,X_1425))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(X_1428,X_1426),X_1426)),implies(implies(X_1428,X_1426),X_1426)),X_1425),implies(X_1426,X_1425))) )],[refute_0_59,refute_0_29]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(implies(X_1431,X_1430),X_1430),implies(X_41,X_1430)),implies(X_1430,implies(X_41,X_1430)))),
inference(subst,[],[refute_0_60:[bind(X_1425,$fot(implies(X_41,X_1430))),bind(X_1426,$fot(X_1430)),bind(X_1428,$fot(X_1431))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(X_41,implies(X_1431,X_1430)),implies(X_1430,implies(X_41,X_1430)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_1431,X_1430),X_1430),implies(X_41,X_1430)),implies(X_1430,implies(X_41,X_1430)))) )],[refute_0_61,refute_0_19]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(X_4240,implies(X_4241,X_4242)),implies(X_4242,implies(X_4240,X_4242)))),
inference(subst,[],[refute_0_62:[bind(X_1430,$fot(X_4242)),bind(X_1431,$fot(X_4241)),bind(X_41,$fot(X_4240))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(implies(X_2233,implies(X_2234,X_2235)),X_2232))
| ~ is_a_theorem(implies(implies(implies(X_2233,implies(X_2234,X_2235)),X_2232),implies(implies(X_2234,not(X_2233)),X_2232)))
| is_a_theorem(implies(implies(X_2234,not(X_2233)),X_2232)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_2233,implies(X_2234,X_2235)),X_2232))),bind(Y,$fot(implies(implies(X_2234,not(X_2233)),X_2232)))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(X_299,not(X_298)),implies(X_298,implies(X_299,X_300))))
| is_a_theorem(implies(implies(implies(X_298,implies(X_299,X_300)),Z),implies(implies(X_299,not(X_298)),Z))) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(implies(X_299,not(X_298)))),bind(Y,$fot(implies(X_298,implies(X_299,X_300))))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(not(X_27),X_296),implies(X_294,X_296)),implies(X_27,implies(X_294,X_296)))),
inference(subst,[],[refute_0_10:[bind(Y,$fot(X_296)),bind(X_29,$fot(implies(X_294,X_296)))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_27),X_296),implies(X_294,X_296)),implies(X_27,implies(X_294,X_296))))
| is_a_theorem(implies(implies(X_294,not(X_27)),implies(X_27,implies(X_294,X_296)))) ),
inference(subst,[],[refute_0_18:[bind(X_41,$fot(X_294)),bind(X_42,$fot(not(X_27))),bind(X_43,$fot(X_296)),bind(X_44,$fot(implies(X_27,implies(X_294,X_296))))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(X_294,not(X_27)),implies(X_27,implies(X_294,X_296)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_27),X_296),implies(X_294,X_296)),implies(X_27,implies(X_294,X_296)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(X_299,not(X_298)),implies(X_298,implies(X_299,X_300)))),
inference(subst,[],[refute_0_68:[bind(X_27,$fot(X_298)),bind(X_294,$fot(X_299)),bind(X_296,$fot(X_300))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(X_298,implies(X_299,X_300)),Z),implies(implies(X_299,not(X_298)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_299,not(X_298)),implies(X_298,implies(X_299,X_300)))) )],[refute_0_69,refute_0_65]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(implies(X_2233,implies(X_2234,X_2235)),X_2232),implies(implies(X_2234,not(X_2233)),X_2232))),
inference(subst,[],[refute_0_70:[bind(Z,$fot(X_2232)),bind(X_298,$fot(X_2233)),bind(X_299,$fot(X_2234)),bind(X_300,$fot(X_2235))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(X_2233,implies(X_2234,X_2235)),X_2232))
| is_a_theorem(implies(implies(X_2234,not(X_2233)),X_2232)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_2233,implies(X_2234,X_2235)),X_2232),implies(implies(X_2234,not(X_2233)),X_2232))) )],[refute_0_71,refute_0_64]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(implies(X_4240,implies(X_4241,X_4242)),implies(X_4242,implies(X_4240,X_4242))))
| is_a_theorem(implies(implies(X_4241,not(X_4240)),implies(X_4242,implies(X_4240,X_4242)))) ),
inference(subst,[],[refute_0_72:[bind(X_2232,$fot(implies(X_4242,implies(X_4240,X_4242)))),bind(X_2233,$fot(X_4240)),bind(X_2234,$fot(X_4241)),bind(X_2235,$fot(X_4242))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(X_4241,not(X_4240)),implies(X_4242,implies(X_4240,X_4242)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_4240,implies(X_4241,X_4242)),implies(X_4242,implies(X_4240,X_4242)))) )],[refute_0_63,refute_0_73]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(not(X_33),not(X_4244)),implies(X_4246,implies(X_4244,X_4246)))),
inference(subst,[],[refute_0_74:[bind(X_4240,$fot(X_4244)),bind(X_4241,$fot(not(X_33))),bind(X_4242,$fot(X_4246))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(X_33,implies(X_4246,implies(X_4244,X_4246)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_33),not(X_4244)),implies(X_4246,implies(X_4244,X_4246)))) )],[refute_0_75,refute_0_13]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(not(implies(X_4254,implies(X_4253,X_4254))),implies(X_4254,implies(X_4253,X_4254)))),
inference(subst,[],[refute_0_76:[bind(X_33,$fot(not(implies(X_4254,implies(X_4253,X_4254))))),bind(X_4244,$fot(X_4253)),bind(X_4246,$fot(X_4254))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(X_4254,implies(X_4253,X_4254))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_4254,implies(X_4253,X_4254))),implies(X_4254,implies(X_4253,X_4254)))) )],[refute_0_77,refute_0_4]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(X_4256,implies(X_4255,X_4256))),
inference(subst,[],[refute_0_78:[bind(X_4253,$fot(X_4255)),bind(X_4254,$fot(X_4256))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(X_4256)
| is_a_theorem(implies(X_4255,X_4256)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_4256,implies(X_4255,X_4256))) )],[refute_0_79,refute_0_0]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(X_4675,implies(implies(not(X),X),X))) ),
inference(subst,[],[refute_0_80:[bind(X_4255,$fot(X_4675)),bind(X_4256,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(X_4675,implies(implies(not(X),X),X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(x,implies(implies(not(y),y),y)),implies(implies(not(y),y),y))),
inference(subst,[],[refute_0_82:[bind(X,$fot(y)),bind(X_4675,$fot(implies(x,implies(implies(not(y),y),y))))]]) ).
cnf(refute_0_84,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(x,implies(implies(not(y),y),y)),implies(implies(not(y),y),y))) )],[refute_0_83,prove_cn_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL362-1 : TPTP v8.1.0. Released v2.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.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 : Mon Jul 4 17:47:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.44/2.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.44/2.61
% 2.44/2.61 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.44/2.62
%------------------------------------------------------------------------------