TSTP Solution File: LCL059-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL059-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 4.35s 4.56s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of clauses : 74 ( 41 unt; 0 nHn; 21 RR)
% Number of literals : 116 ( 0 equ; 43 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 : 194 ( 30 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_49,negated_conjecture,
~ is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(X_115,X_116),implies(X_114,X_116)),X_117))
| ~ is_a_theorem(implies(implies(implies(implies(X_115,X_116),implies(X_114,X_116)),X_117),implies(implies(X_114,X_115),X_117)))
| is_a_theorem(implies(implies(X_114,X_115),X_117)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_115,X_116),implies(X_114,X_116)),X_117))),bind(Y,$fot(implies(implies(X_114,X_115),X_117)))]]) ).
cnf(refute_0_1,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_2,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_35),implies(implies(X,Y),X_35))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_35),implies(implies(X,Y),X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(X_115,X_116),implies(X_114,X_116)),X_117),implies(implies(X_114,X_115),X_117))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_114)),bind(Y,$fot(X_115)),bind(Z,$fot(X_116)),bind(X_35,$fot(X_117))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(X_115,X_116),implies(X_114,X_116)),X_117))
| is_a_theorem(implies(implies(X_114,X_115),X_117)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_115,X_116),implies(X_114,X_116)),X_117),implies(implies(X_114,X_115),X_117))) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_5426),X_5424),implies(not(X_5424),X_5424)),implies(X_5426,X_5424)))
| is_a_theorem(implies(implies(not(X_5424),not(X_5426)),implies(X_5426,X_5424))) ),
inference(subst,[],[refute_0_6:[bind(X_114,$fot(not(X_5424))),bind(X_115,$fot(not(X_5426))),bind(X_116,$fot(X_5424)),bind(X_117,$fot(implies(X_5426,X_5424)))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867)),implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867)))
| is_a_theorem(implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867)) ),
inference(subst,[],[refute_0_10:[bind(X_7,$fot(implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_504),X_504),X_504),X_506),implies(X_505,X_506)))
| ~ is_a_theorem(implies(implies(implies(not(X_504),X_504),X_504),X_506))
| is_a_theorem(implies(X_505,X_506)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_504),X_504),X_504),X_506))),bind(Y,$fot(implies(X_505,X_506)))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(X_141,implies(not(implies(implies(not(X_139),X_139),X_139)),X_140)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_139),X_139),X_139)),X_140),Z),implies(X_141,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_141)),bind(Y,$fot(implies(not(implies(implies(not(X_139),X_139),X_139)),X_140)))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_15,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_16,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_16:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_34)),
inference(subst,[],[refute_0_18:[bind(X_9,$fot(X_34))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_34))
| is_a_theorem(implies(implies(X_34,X_35),implies(not(implies(implies(not(X),X),X)),X_35))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_34,X_35),implies(not(implies(implies(not(X),X),X)),X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_34)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(not(X_121),X_120),implies(not(implies(implies(not(X),X),X)),X_120))),
inference(subst,[],[refute_0_21:[bind(X_34,$fot(not(X_121))),bind(X_35,$fot(X_120))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_42),X_41),X_43),implies(X_42,X_43)))
| ~ is_a_theorem(implies(implies(not(X_42),X_41),X_43))
| is_a_theorem(implies(X_42,X_43)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_42),X_41),X_43))),bind(Y,$fot(implies(X_42,X_43)))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(X_33,implies(not(X_33),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(X_33,implies(not(X_33),Y)))
| is_a_theorem(implies(implies(implies(not(X_33),Y),X_35),implies(X_33,X_35))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_33)),bind(Y,$fot(implies(not(X_33),Y))),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(implies(not(X_33),Y),X_35),implies(X_33,X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(X_33,implies(not(X_33),Y))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(not(X_42),X_41),X_43),implies(X_42,X_43))),
inference(subst,[],[refute_0_26:[bind(Y,$fot(X_41)),bind(X_33,$fot(X_42)),bind(X_35,$fot(X_43))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(not(X_42),X_41),X_43))
| is_a_theorem(implies(X_42,X_43)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_42),X_41),X_43),implies(X_42,X_43))) )],[refute_0_27,refute_0_23]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(not(X_121),X_120),implies(not(implies(implies(not(X),X),X)),X_120)))
| is_a_theorem(implies(X_121,implies(not(implies(implies(not(X),X),X)),X_120))) ),
inference(subst,[],[refute_0_28:[bind(X_41,$fot(X_120)),bind(X_42,$fot(X_121)),bind(X_43,$fot(implies(not(implies(implies(not(X),X),X)),X_120)))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(X_121,implies(not(implies(implies(not(X),X),X)),X_120))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_121),X_120),implies(not(implies(implies(not(X),X),X)),X_120))) )],[refute_0_22,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(X_141,implies(not(implies(implies(not(X_139),X_139),X_139)),X_140))),
inference(subst,[],[refute_0_30:[bind(X,$fot(X_139)),bind(X_120,$fot(X_140)),bind(X_121,$fot(X_141))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_139),X_139),X_139)),X_140),Z),implies(X_141,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_141,implies(not(implies(implies(not(X_139),X_139),X_139)),X_140))) )],[refute_0_31,refute_0_13]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_139),X_139),X_139)),implies(implies(not(X_139),X_139),X_139)),X_487),implies(X_141,X_487))),
inference(subst,[],[refute_0_32:[bind(Z,$fot(X_487)),bind(X_140,$fot(implies(implies(not(X_139),X_139),X_139)))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_68),X_68),X_69),X_67),implies(implies(X_68,X_69),X_67)))
| ~ is_a_theorem(implies(implies(implies(not(X_68),X_68),X_69),X_67))
| is_a_theorem(implies(implies(X_68,X_69),X_67)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_68),X_68),X_69),X_67))),bind(Y,$fot(implies(implies(X_68,X_69),X_67)))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(X_36,X_37),implies(implies(not(X_36),X_36),X_37)))
| is_a_theorem(implies(implies(implies(implies(not(X_36),X_36),X_37),Z),implies(implies(X_36,X_37),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_36,X_37))),bind(Y,$fot(implies(implies(not(X_36),X_36),X_37)))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(not(X_34),X_34),X_34)),
inference(subst,[],[cn_2:[bind(X,$fot(X_34))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(not(X_34),X_34),X_34))
| is_a_theorem(implies(implies(X_34,X_35),implies(implies(not(X_34),X_34),X_35))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_34),X_34))),bind(Y,$fot(X_34)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(X_34,X_35),implies(implies(not(X_34),X_34),X_35))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_34),X_34),X_34)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(X_36,X_37),implies(implies(not(X_36),X_36),X_37))),
inference(subst,[],[refute_0_38:[bind(X_34,$fot(X_36)),bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(implies(not(X_36),X_36),X_37),Z),implies(implies(X_36,X_37),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_36,X_37),implies(implies(not(X_36),X_36),X_37))) )],[refute_0_39,refute_0_35]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(implies(implies(not(X_68),X_68),X_69),X_67),implies(implies(X_68,X_69),X_67))),
inference(subst,[],[refute_0_40:[bind(Z,$fot(X_67)),bind(X_36,$fot(X_68)),bind(X_37,$fot(X_69))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_68),X_68),X_69),X_67))
| is_a_theorem(implies(implies(X_68,X_69),X_67)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_68),X_68),X_69),X_67),implies(implies(X_68,X_69),X_67))) )],[refute_0_41,refute_0_34]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_139),X_139),X_139)),implies(implies(not(X_139),X_139),X_139)),X_487),implies(X_141,X_487)))
| is_a_theorem(implies(implies(implies(implies(not(X_139),X_139),X_139),X_487),implies(X_141,X_487))) ),
inference(subst,[],[refute_0_42:[bind(X_67,$fot(implies(X_141,X_487))),bind(X_68,$fot(implies(implies(not(X_139),X_139),X_139))),bind(X_69,$fot(X_487))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(implies(implies(not(X_139),X_139),X_139),X_487),implies(X_141,X_487))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_139),X_139),X_139)),implies(implies(not(X_139),X_139),X_139)),X_487),implies(X_141,X_487))) )],[refute_0_33,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(implies(not(X_504),X_504),X_504),X_506),implies(X_505,X_506))),
inference(subst,[],[refute_0_44:[bind(X_139,$fot(X_504)),bind(X_141,$fot(X_505)),bind(X_487,$fot(X_506))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_504),X_504),X_504),X_506))
| is_a_theorem(implies(X_505,X_506)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_504),X_504),X_504),X_506),implies(X_505,X_506))) )],[refute_0_45,refute_0_12]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1863),X_1863),X_1863),implies(implies(implies(implies(not(X_1864),X_1864),X_1864),X_1863),X_1863)))
| is_a_theorem(implies(X_505,implies(implies(implies(implies(not(X_1864),X_1864),X_1864),X_1863),X_1863))) ),
inference(subst,[],[refute_0_46:[bind(X_504,$fot(X_1863)),bind(X_506,$fot(implies(implies(implies(implies(not(X_1864),X_1864),X_1864),X_1863),X_1863)))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_504),X_504),X_504),X_506),implies(X_505,X_506)))
| is_a_theorem(implies(implies(implies(X_505,X_506),Z),implies(implies(implies(implies(not(X_504),X_504),X_504),X_506),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(implies(not(X_504),X_504),X_504),X_506))),bind(Y,$fot(implies(X_505,X_506)))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(X_505,X_506),Z),implies(implies(implies(implies(not(X_504),X_504),X_504),X_506),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_504),X_504),X_504),X_506),implies(X_505,X_506))) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(implies(not(X_1863),X_1863),X_1863),implies(implies(implies(implies(not(X_1864),X_1864),X_1864),X_1863),X_1863))),
inference(subst,[],[refute_0_49:[bind(Z,$fot(X_1863)),bind(X_504,$fot(X_1864)),bind(X_505,$fot(not(X_1863))),bind(X_506,$fot(X_1863))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(X_505,implies(implies(implies(implies(not(X_1864),X_1864),X_1864),X_1863),X_1863))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1863),X_1863),X_1863),implies(implies(implies(implies(not(X_1864),X_1864),X_1864),X_1863),X_1863))) )],[refute_0_50,refute_0_47]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867)),implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867))),
inference(subst,[],[refute_0_51:[bind(X_1863,$fot(X_1867)),bind(X_1864,$fot(X_1868)),bind(X_505,$fot(not(implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867))))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867)),implies(implies(implies(implies(not(X_1868),X_1868),X_1868),X_1867),X_1867))) )],[refute_0_52,refute_0_11]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(implies(not(X_2182),X_2182),X_2182),implies(X_2180,X_2182)),implies(X_2180,X_2182))),
inference(subst,[],[refute_0_53:[bind(X_1867,$fot(implies(X_2180,X_2182))),bind(X_1868,$fot(X_2182))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_2182),X_2182),X_2182),implies(X_2180,X_2182)),implies(X_2180,X_2182)))
| is_a_theorem(implies(implies(X_2180,implies(not(X_2182),X_2182)),implies(X_2180,X_2182))) ),
inference(subst,[],[refute_0_6:[bind(X_114,$fot(X_2180)),bind(X_115,$fot(implies(not(X_2182),X_2182))),bind(X_116,$fot(X_2182)),bind(X_117,$fot(implies(X_2180,X_2182)))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(X_2180,implies(not(X_2182),X_2182)),implies(X_2180,X_2182))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_2182),X_2182),X_2182),implies(X_2180,X_2182)),implies(X_2180,X_2182))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(X_5392,implies(not(X_2182),X_2182)),implies(X_5392,X_2182))),
inference(subst,[],[refute_0_56:[bind(X_2180,$fot(X_5392))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(X_57,X_58),X_55))
| ~ is_a_theorem(implies(implies(implies(X_57,X_58),X_55),implies(implies(implies(not(X_57),X_56),X_58),X_55)))
| is_a_theorem(implies(implies(implies(not(X_57),X_56),X_58),X_55)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_57,X_58),X_55))),bind(Y,$fot(implies(implies(implies(not(X_57),X_56),X_58),X_55)))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_42),X_41),X_43),implies(X_42,X_43)))
| is_a_theorem(implies(implies(implies(X_42,X_43),Z),implies(implies(implies(not(X_42),X_41),X_43),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(not(X_42),X_41),X_43))),bind(Y,$fot(implies(X_42,X_43)))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(X_42,X_43),Z),implies(implies(implies(not(X_42),X_41),X_43),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_42),X_41),X_43),implies(X_42,X_43))) )],[refute_0_27,refute_0_59]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(X_57,X_58),X_55),implies(implies(implies(not(X_57),X_56),X_58),X_55))),
inference(subst,[],[refute_0_60:[bind(Z,$fot(X_55)),bind(X_41,$fot(X_56)),bind(X_42,$fot(X_57)),bind(X_43,$fot(X_58))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(implies(X_57,X_58),X_55))
| is_a_theorem(implies(implies(implies(not(X_57),X_56),X_58),X_55)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_57,X_58),X_55),implies(implies(implies(not(X_57),X_56),X_58),X_55))) )],[refute_0_61,refute_0_58]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(X_5392,implies(not(X_2182),X_2182)),implies(X_5392,X_2182)))
| is_a_theorem(implies(implies(implies(not(X_5392),X_5391),implies(not(X_2182),X_2182)),implies(X_5392,X_2182))) ),
inference(subst,[],[refute_0_62:[bind(X_55,$fot(implies(X_5392,X_2182))),bind(X_56,$fot(X_5391)),bind(X_57,$fot(X_5392)),bind(X_58,$fot(implies(not(X_2182),X_2182)))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(implies(not(X_5392),X_5391),implies(not(X_2182),X_2182)),implies(X_5392,X_2182))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_5392,implies(not(X_2182),X_2182)),implies(X_5392,X_2182))) )],[refute_0_57,refute_0_63]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(implies(not(X_5426),X_5424),implies(not(X_5424),X_5424)),implies(X_5426,X_5424))),
inference(subst,[],[refute_0_64:[bind(X_2182,$fot(X_5424)),bind(X_5391,$fot(X_5424)),bind(X_5392,$fot(X_5426))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(not(X_5424),not(X_5426)),implies(X_5426,X_5424))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_5426),X_5424),implies(not(X_5424),X_5424)),implies(X_5426,X_5424))) )],[refute_0_65,refute_0_7]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))),
inference(subst,[],[refute_0_66:[bind(X_5424,$fot(a)),bind(X_5426,$fot(b))]]) ).
cnf(refute_0_68,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(a),not(b)),implies(b,a))) )],[refute_0_67,prove_cn_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL059-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.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 04:47:59 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.35/4.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.35/4.56
% 4.35/4.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.35/4.57
%------------------------------------------------------------------------------