TSTP Solution File: LCL399-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL399-1 : TPTP v8.1.0. Released v2.3.0.
% 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 12:51:58 EDT 2022
% Result : Unsatisfiable 6.02s 6.23s
% Output : CNFRefutation 6.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of clauses : 92 ( 53 unt; 0 nHn; 24 RR)
% Number of literals : 140 ( 0 equ; 49 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 : 255 ( 41 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_65,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),not(implies(y,y))),x)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(X_75,X_76),implies(X_74,X_76)),X_77))
| ~ is_a_theorem(implies(implies(implies(implies(X_75,X_76),implies(X_74,X_76)),X_77),implies(implies(X_74,X_75),X_77)))
| is_a_theorem(implies(implies(X_74,X_75),X_77)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_75,X_76),implies(X_74,X_76)),X_77))),bind(Y,$fot(implies(implies(X_74,X_75),X_77)))]]) ).
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,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_20),implies(implies(X,Y),X_20))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_20),implies(implies(X,Y),X_20))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(X_75,X_76),implies(X_74,X_76)),X_77),implies(implies(X_74,X_75),X_77))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_74)),bind(Y,$fot(X_75)),bind(Z,$fot(X_76)),bind(X_20,$fot(X_77))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(X_75,X_76),implies(X_74,X_76)),X_77))
| is_a_theorem(implies(implies(X_74,X_75),X_77)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_75,X_76),implies(X_74,X_76)),X_77),implies(implies(X_74,X_75),X_77))) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_6115,X_6115)),X_6116),implies(not(X_6116),X_6116)),X_6116))
| is_a_theorem(implies(implies(not(X_6116),not(implies(X_6115,X_6115))),X_6116)) ),
inference(subst,[],[refute_0_6:[bind(X_74,$fot(not(X_6116))),bind(X_75,$fot(not(implies(X_6115,X_6115)))),bind(X_76,$fot(X_6116)),bind(X_77,$fot(X_6116))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(X_718,X_719),X_716)),implies(implies(X_718,X_719),X_716)),implies(implies(implies(not(X_718),X_717),X_719),X_716)))
| ~ is_a_theorem(implies(not(implies(implies(X_718,X_719),X_716)),implies(implies(X_718,X_719),X_716)))
| is_a_theorem(implies(implies(implies(not(X_718),X_717),X_719),X_716)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(implies(implies(X_718,X_719),X_716)),implies(implies(X_718,X_719),X_716)))),bind(Y,$fot(implies(implies(implies(not(X_718),X_717),X_719),X_716)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(X_21,X_22))
| ~ is_a_theorem(implies(implies(X_21,X_22),implies(implies(not(X_21),X_21),X_22)))
| is_a_theorem(implies(implies(not(X_21),X_21),X_22)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_21,X_22))),bind(Y,$fot(implies(implies(not(X_21),X_21),X_22)))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(not(X_19),X_19),X_19)),
inference(subst,[],[cn_2:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(not(X_19),X_19),X_19))
| is_a_theorem(implies(implies(X_19,X_20),implies(implies(not(X_19),X_19),X_20))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_19),X_19))),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(X_19,X_20),implies(implies(not(X_19),X_19),X_20))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_19),X_19),X_19)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(X_21,X_22),implies(implies(not(X_21),X_21),X_22))),
inference(subst,[],[refute_0_12:[bind(X_19,$fot(X_21)),bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(X_21,X_22))
| is_a_theorem(implies(implies(not(X_21),X_21),X_22)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_21,X_22),implies(implies(not(X_21),X_21),X_22))) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(X_96,X_97),X_94),implies(implies(implies(not(X_96),X_95),X_97),X_94)))
| is_a_theorem(implies(implies(not(implies(implies(X_96,X_97),X_94)),implies(implies(X_96,X_97),X_94)),implies(implies(implies(not(X_96),X_95),X_97),X_94))) ),
inference(subst,[],[refute_0_14:[bind(X_21,$fot(implies(implies(X_96,X_97),X_94))),bind(X_22,$fot(implies(implies(implies(not(X_96),X_95),X_97),X_94)))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_24),X_23),X_25),implies(X_24,X_25)))
| is_a_theorem(implies(implies(implies(X_24,X_25),Z),implies(implies(implies(not(X_24),X_23),X_25),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(not(X_24),X_23),X_25))),bind(Y,$fot(implies(X_24,X_25)))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(X_18,implies(not(X_18),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(X_18,implies(not(X_18),Y)))
| is_a_theorem(implies(implies(implies(not(X_18),Y),X_20),implies(X_18,X_20))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_18)),bind(Y,$fot(implies(not(X_18),Y))),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(not(X_18),Y),X_20),implies(X_18,X_20))),
inference(resolve,[$cnf( is_a_theorem(implies(X_18,implies(not(X_18),Y))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(implies(not(X_24),X_23),X_25),implies(X_24,X_25))),
inference(subst,[],[refute_0_19:[bind(Y,$fot(X_23)),bind(X_18,$fot(X_24)),bind(X_20,$fot(X_25))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(implies(X_24,X_25),Z),implies(implies(implies(not(X_24),X_23),X_25),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_24),X_23),X_25),implies(X_24,X_25))) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(X_96,X_97),X_94),implies(implies(implies(not(X_96),X_95),X_97),X_94))),
inference(subst,[],[refute_0_21:[bind(Z,$fot(X_94)),bind(X_23,$fot(X_95)),bind(X_24,$fot(X_96)),bind(X_25,$fot(X_97))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(not(implies(implies(X_96,X_97),X_94)),implies(implies(X_96,X_97),X_94)),implies(implies(implies(not(X_96),X_95),X_97),X_94))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_96,X_97),X_94),implies(implies(implies(not(X_96),X_95),X_97),X_94))) )],[refute_0_22,refute_0_15]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(not(implies(implies(X_718,X_719),X_716)),implies(implies(X_718,X_719),X_716)),implies(implies(implies(not(X_718),X_717),X_719),X_716))),
inference(subst,[],[refute_0_23:[bind(X_94,$fot(X_716)),bind(X_95,$fot(X_717)),bind(X_96,$fot(X_718)),bind(X_97,$fot(X_719))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(not(implies(implies(X_718,X_719),X_716)),implies(implies(X_718,X_719),X_716)))
| is_a_theorem(implies(implies(implies(not(X_718),X_717),X_719),X_716)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(X_718,X_719),X_716)),implies(implies(X_718,X_719),X_716)),implies(implies(implies(not(X_718),X_717),X_719),X_716))) )],[refute_0_24,refute_0_8]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(X_6113,X_6113),implies(not(X_6114),X_6114)),X_6114)),implies(implies(implies(X_6113,X_6113),implies(not(X_6114),X_6114)),X_6114)))
| is_a_theorem(implies(implies(implies(not(implies(X_6113,X_6113)),X_717),implies(not(X_6114),X_6114)),X_6114)) ),
inference(subst,[],[refute_0_25:[bind(X_716,$fot(X_6114)),bind(X_718,$fot(implies(X_6113,X_6113))),bind(X_719,$fot(implies(not(X_6114),X_6114)))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_24),X_23),X_25),implies(X_24,X_25)))
| ~ is_a_theorem(implies(implies(not(X_24),X_23),X_25))
| is_a_theorem(implies(X_24,X_25)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_24),X_23),X_25))),bind(Y,$fot(implies(X_24,X_25)))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(not(X_24),X_23),X_25))
| is_a_theorem(implies(X_24,X_25)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_24),X_23),X_25),implies(X_24,X_25))) )],[refute_0_20,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(not(X_24),implies(implies(not(X_6108),X_6108),X_6108)),implies(implies(implies(X_6107,X_6107),implies(not(X_6108),X_6108)),X_6108)))
| is_a_theorem(implies(X_24,implies(implies(implies(X_6107,X_6107),implies(not(X_6108),X_6108)),X_6108))) ),
inference(subst,[],[refute_0_28:[bind(X_23,$fot(implies(implies(not(X_6108),X_6108),X_6108))),bind(X_25,$fot(implies(implies(implies(X_6107,X_6107),implies(not(X_6108),X_6108)),X_6108)))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(X_5274,X_5273),implies(implies(implies(X_5275,X_5275),X_5274),X_5273)))
| is_a_theorem(implies(implies(not(implies(X_5274,X_5273)),implies(X_5274,X_5273)),implies(implies(implies(X_5275,X_5275),X_5274),X_5273))) ),
inference(subst,[],[refute_0_14:[bind(X_21,$fot(implies(X_5274,X_5273))),bind(X_22,$fot(implies(implies(implies(X_5275,X_5275),X_5274),X_5273)))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),X_29),implies(implies(X_30,X_31),X_29)))
| ~ is_a_theorem(implies(implies(implies(not(X_30),X_30),X_31),X_29))
| is_a_theorem(implies(implies(X_30,X_31),X_29)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_30),X_30),X_31),X_29))),bind(Y,$fot(implies(implies(X_30,X_31),X_29)))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(X_21,X_22),implies(implies(not(X_21),X_21),X_22)))
| is_a_theorem(implies(implies(implies(implies(not(X_21),X_21),X_22),Z),implies(implies(X_21,X_22),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_21,X_22))),bind(Y,$fot(implies(implies(not(X_21),X_21),X_22)))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(implies(implies(not(X_21),X_21),X_22),Z),implies(implies(X_21,X_22),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_21,X_22),implies(implies(not(X_21),X_21),X_22))) )],[refute_0_13,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),X_29),implies(implies(X_30,X_31),X_29))),
inference(subst,[],[refute_0_33:[bind(Z,$fot(X_29)),bind(X_21,$fot(X_30)),bind(X_22,$fot(X_31))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_30),X_30),X_31),X_29))
| is_a_theorem(implies(implies(X_30,X_31),X_29)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_30),X_30),X_31),X_29),implies(implies(X_30,X_31),X_29))) )],[refute_0_34,refute_0_31]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_5270),X_5270),X_5269),implies(implies(implies(X_5271,X_5271),X_5270),X_5269)))
| is_a_theorem(implies(implies(X_5270,X_5269),implies(implies(implies(X_5271,X_5271),X_5270),X_5269))) ),
inference(subst,[],[refute_0_35:[bind(X_29,$fot(implies(implies(implies(X_5271,X_5271),X_5270),X_5269))),bind(X_30,$fot(X_5270)),bind(X_31,$fot(X_5269))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(implies(X_666,X_666),X_665),implies(X_667,X_665)))
| is_a_theorem(implies(implies(implies(X_667,X_665),Z),implies(implies(implies(X_666,X_666),X_665),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(X_666,X_666),X_665))),bind(Y,$fot(implies(X_667,X_665)))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_663,X_663)),implies(X_663,X_663)),X_661),implies(X_664,X_661)))
| is_a_theorem(implies(implies(implies(X_663,X_663),X_661),implies(X_664,X_661))) ),
inference(subst,[],[refute_0_35:[bind(X_29,$fot(implies(X_664,X_661))),bind(X_30,$fot(implies(X_663,X_663))),bind(X_31,$fot(X_661))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(X_199,implies(not(implies(X_198,X_198)),X_197)))
| is_a_theorem(implies(implies(implies(not(implies(X_198,X_198)),X_197),Z),implies(X_199,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_199)),bind(Y,$fot(implies(not(implies(X_198,X_198)),X_197)))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(not(X_24),X_194),implies(not(implies(X_196,X_196)),X_194)))
| is_a_theorem(implies(X_24,implies(not(implies(X_196,X_196)),X_194))) ),
inference(subst,[],[refute_0_28:[bind(X_23,$fot(X_194)),bind(X_25,$fot(implies(not(implies(X_196,X_196)),X_194)))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(not(implies(X_163,X_163)),X_162))
| is_a_theorem(implies(implies(X_162,Z),implies(not(implies(X_163,X_163)),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(X_163,X_163)))),bind(Y,$fot(X_162))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(X_161,X_161))
| is_a_theorem(implies(not(implies(X_161,X_161)),Y)) ),
inference(subst,[],[refute_0_44:[bind(X_6,$fot(implies(X_161,X_161)))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(not(X_160),X_160),X_160)),
inference(subst,[],[cn_2:[bind(X,$fot(X_160))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(not(X_160),X_160),X_160))
| is_a_theorem(implies(X_160,X_160)) ),
inference(subst,[],[refute_0_28:[bind(X_23,$fot(X_160)),bind(X_24,$fot(X_160)),bind(X_25,$fot(X_160))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(X_160,X_160)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_160),X_160),X_160)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(X_161,X_161)),
inference(subst,[],[refute_0_48:[bind(X_160,$fot(X_161))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(not(implies(X_161,X_161)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_161,X_161)) )],[refute_0_49,refute_0_45]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(not(implies(X_163,X_163)),X_162)),
inference(subst,[],[refute_0_50:[bind(Y,$fot(X_162)),bind(X_161,$fot(X_163))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(X_162,Z),implies(not(implies(X_163,X_163)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_163,X_163)),X_162)) )],[refute_0_51,refute_0_41]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(not(X_24),X_194),implies(not(implies(X_196,X_196)),X_194))),
inference(subst,[],[refute_0_52:[bind(Z,$fot(X_194)),bind(X_162,$fot(not(X_24))),bind(X_163,$fot(X_196))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(X_24,implies(not(implies(X_196,X_196)),X_194))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_24),X_194),implies(not(implies(X_196,X_196)),X_194))) )],[refute_0_53,refute_0_40]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(X_199,implies(not(implies(X_198,X_198)),X_197))),
inference(subst,[],[refute_0_54:[bind(X_194,$fot(X_197)),bind(X_196,$fot(X_198)),bind(X_24,$fot(X_199))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(implies(not(implies(X_198,X_198)),X_197),Z),implies(X_199,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_199,implies(not(implies(X_198,X_198)),X_197))) )],[refute_0_55,refute_0_39]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(implies(not(implies(X_663,X_663)),implies(X_663,X_663)),X_661),implies(X_664,X_661))),
inference(subst,[],[refute_0_56:[bind(Z,$fot(X_661)),bind(X_197,$fot(implies(X_663,X_663))),bind(X_198,$fot(X_663)),bind(X_199,$fot(X_664))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(X_663,X_663),X_661),implies(X_664,X_661))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_663,X_663)),implies(X_663,X_663)),X_661),implies(X_664,X_661))) )],[refute_0_57,refute_0_38]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(implies(implies(X_666,X_666),X_665),implies(X_667,X_665))),
inference(subst,[],[refute_0_58:[bind(X_661,$fot(X_665)),bind(X_663,$fot(X_666)),bind(X_664,$fot(X_667))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(X_667,X_665),Z),implies(implies(implies(X_666,X_666),X_665),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_666,X_666),X_665),implies(X_667,X_665))) )],[refute_0_59,refute_0_37]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(not(X_5270),X_5270),X_5269),implies(implies(implies(X_5271,X_5271),X_5270),X_5269))),
inference(subst,[],[refute_0_60:[bind(Z,$fot(X_5269)),bind(X_665,$fot(X_5270)),bind(X_666,$fot(X_5271)),bind(X_667,$fot(not(X_5270)))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(X_5270,X_5269),implies(implies(implies(X_5271,X_5271),X_5270),X_5269))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_5270),X_5270),X_5269),implies(implies(implies(X_5271,X_5271),X_5270),X_5269))) )],[refute_0_61,refute_0_36]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(X_5274,X_5273),implies(implies(implies(X_5275,X_5275),X_5274),X_5273))),
inference(subst,[],[refute_0_62:[bind(X_5269,$fot(X_5273)),bind(X_5270,$fot(X_5274)),bind(X_5271,$fot(X_5275))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(not(implies(X_5274,X_5273)),implies(X_5274,X_5273)),implies(implies(implies(X_5275,X_5275),X_5274),X_5273))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_5274,X_5273),implies(implies(implies(X_5275,X_5275),X_5274),X_5273))) )],[refute_0_63,refute_0_30]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(not(implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(implies(X_5275,X_5275),implies(not(X_5983),X_5983)),X_5983))),
inference(subst,[],[refute_0_64:[bind(X_5273,$fot(X_5983)),bind(X_5274,$fot(implies(not(X_5983),X_5983)))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_33),X_33),X_33)),X_35),X_32),implies(implies(X_34,X_35),X_32)))
| ~ is_a_theorem(implies(implies(not(implies(implies(not(X_33),X_33),X_33)),X_35),X_32))
| is_a_theorem(implies(implies(X_34,X_35),X_32)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(implies(not(X_33),X_33),X_33)),X_35),X_32))),bind(Y,$fot(implies(implies(X_34,X_35),X_32)))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(X_27,X_28),implies(not(implies(implies(not(X_26),X_26),X_26)),X_28)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_26),X_26),X_26)),X_28),Z),implies(implies(X_27,X_28),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_27,X_28))),bind(Y,$fot(implies(not(implies(implies(not(X_26),X_26),X_26)),X_28)))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_44:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_19)),
inference(subst,[],[refute_0_69:[bind(X_9,$fot(X_19))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_19))
| is_a_theorem(implies(implies(X_19,X_20),implies(not(implies(implies(not(X),X),X)),X_20))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_19)),bind(Z,$fot(X_20))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(X_19,X_20),implies(not(implies(implies(not(X),X),X)),X_20))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_19)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(X_27,X_28),implies(not(implies(implies(not(X_26),X_26),X_26)),X_28))),
inference(subst,[],[refute_0_72:[bind(X,$fot(X_26)),bind(X_19,$fot(X_27)),bind(X_20,$fot(X_28))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_26),X_26),X_26)),X_28),Z),implies(implies(X_27,X_28),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_27,X_28),implies(not(implies(implies(not(X_26),X_26),X_26)),X_28))) )],[refute_0_73,refute_0_67]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_33),X_33),X_33)),X_35),X_32),implies(implies(X_34,X_35),X_32))),
inference(subst,[],[refute_0_74:[bind(Z,$fot(X_32)),bind(X_26,$fot(X_33)),bind(X_27,$fot(X_34)),bind(X_28,$fot(X_35))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_33),X_33),X_33)),X_35),X_32))
| is_a_theorem(implies(implies(X_34,X_35),X_32)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_33),X_33),X_33)),X_35),X_32),implies(implies(X_34,X_35),X_32))) )],[refute_0_75,refute_0_66]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(implies(X_5275,X_5275),implies(not(X_5983),X_5983)),X_5983)))
| is_a_theorem(implies(implies(X_5984,implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(implies(X_5275,X_5275),implies(not(X_5983),X_5983)),X_5983))) ),
inference(subst,[],[refute_0_76:[bind(X_32,$fot(implies(implies(implies(X_5275,X_5275),implies(not(X_5983),X_5983)),X_5983))),bind(X_33,$fot(X_5983)),bind(X_34,$fot(X_5984)),bind(X_35,$fot(implies(implies(not(X_5983),X_5983),X_5983)))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(X_5984,implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(implies(X_5275,X_5275),implies(not(X_5983),X_5983)),X_5983))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(not(X_5983),X_5983),X_5983)),implies(implies(implies(X_5275,X_5275),implies(not(X_5983),X_5983)),X_5983))) )],[refute_0_65,refute_0_77]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(not(X_24),implies(implies(not(X_6108),X_6108),X_6108)),implies(implies(implies(X_6107,X_6107),implies(not(X_6108),X_6108)),X_6108))),
inference(subst,[],[refute_0_78:[bind(X_5275,$fot(X_6107)),bind(X_5983,$fot(X_6108)),bind(X_5984,$fot(not(X_24)))]]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(X_24,implies(implies(implies(X_6107,X_6107),implies(not(X_6108),X_6108)),X_6108))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_24),implies(implies(not(X_6108),X_6108),X_6108)),implies(implies(implies(X_6107,X_6107),implies(not(X_6108),X_6108)),X_6108))) )],[refute_0_79,refute_0_29]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(not(implies(implies(implies(X_6113,X_6113),implies(not(X_6114),X_6114)),X_6114)),implies(implies(implies(X_6113,X_6113),implies(not(X_6114),X_6114)),X_6114))),
inference(subst,[],[refute_0_80:[bind(X_24,$fot(not(implies(implies(implies(X_6113,X_6113),implies(not(X_6114),X_6114)),X_6114)))),bind(X_6107,$fot(X_6113)),bind(X_6108,$fot(X_6114))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(implies(not(implies(X_6113,X_6113)),X_717),implies(not(X_6114),X_6114)),X_6114)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(X_6113,X_6113),implies(not(X_6114),X_6114)),X_6114)),implies(implies(implies(X_6113,X_6113),implies(not(X_6114),X_6114)),X_6114))) )],[refute_0_81,refute_0_26]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(implies(not(implies(X_6115,X_6115)),X_6116),implies(not(X_6116),X_6116)),X_6116)),
inference(subst,[],[refute_0_82:[bind(X_6113,$fot(X_6115)),bind(X_6114,$fot(X_6116)),bind(X_717,$fot(X_6116))]]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(implies(not(X_6116),not(implies(X_6115,X_6115))),X_6116)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_6115,X_6115)),X_6116),implies(not(X_6116),X_6116)),X_6116)) )],[refute_0_83,refute_0_7]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(not(x),not(implies(y,y))),x)),
inference(subst,[],[refute_0_84:[bind(X_6115,$fot(y)),bind(X_6116,$fot(x))]]) ).
cnf(refute_0_86,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(x),not(implies(y,y))),x)) )],[refute_0_85,prove_cn_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL399-1 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : 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 : Mon Jul 4 03:40:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.02/6.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.02/6.23
% 6.02/6.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.02/6.25
%------------------------------------------------------------------------------