TSTP Solution File: LCL056-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL056-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:49:06 EDT 2022
% Result : Unsatisfiable 4.59s 4.77s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 5
% Syntax : Number of clauses : 143 ( 82 unt; 0 nHn; 46 RR)
% Number of literals : 218 ( 0 equ; 76 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 338 ( 54 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_39,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(not(X_399),X_398)),X_397),X_396),implies(X_399,X_396)))
| ~ is_a_theorem(implies(implies(not(implies(not(X_399),X_398)),X_397),X_396))
| is_a_theorem(implies(X_399,X_396)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(not(X_399),X_398)),X_397),X_396))),bind(Y,$fot(implies(X_399,X_396)))]]) ).
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,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X_116,implies(not(implies(not(X_116),X_115)),X_114)))
| is_a_theorem(implies(implies(implies(not(implies(not(X_116),X_115)),X_114),Z),implies(X_116,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_116)),bind(Y,$fot(implies(not(implies(not(X_116),X_115)),X_114)))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(not(X_104),X_103),implies(not(implies(not(X_104),X_103)),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(implies(not(X_104),X_103)))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_30),X_29),X_31),implies(X_30,X_31)))
| ~ is_a_theorem(implies(implies(not(X_30),X_29),X_31))
| is_a_theorem(implies(X_30,X_31)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_30),X_29),X_31))),bind(Y,$fot(implies(X_30,X_31)))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(X_24,implies(not(X_24),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(X_24,implies(not(X_24),Y)))
| is_a_theorem(implies(implies(implies(not(X_24),Y),X_26),implies(X_24,X_26))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(implies(not(X_24),Y))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(not(X_24),Y),X_26),implies(X_24,X_26))),
inference(resolve,[$cnf( is_a_theorem(implies(X_24,implies(not(X_24),Y))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(implies(not(X_30),X_29),X_31),implies(X_30,X_31))),
inference(subst,[],[refute_0_8:[bind(Y,$fot(X_29)),bind(X_24,$fot(X_30)),bind(X_26,$fot(X_31))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(not(X_30),X_29),X_31))
| is_a_theorem(implies(X_30,X_31)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_30),X_29),X_31),implies(X_30,X_31))) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(not(X_104),X_103),implies(not(implies(not(X_104),X_103)),Y)))
| is_a_theorem(implies(X_104,implies(not(implies(not(X_104),X_103)),Y))) ),
inference(subst,[],[refute_0_10:[bind(X_29,$fot(X_103)),bind(X_30,$fot(X_104)),bind(X_31,$fot(implies(not(implies(not(X_104),X_103)),Y)))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(X_104,implies(not(implies(not(X_104),X_103)),Y))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_104),X_103),implies(not(implies(not(X_104),X_103)),Y))) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(X_116,implies(not(implies(not(X_116),X_115)),X_114))),
inference(subst,[],[refute_0_12:[bind(Y,$fot(X_114)),bind(X_103,$fot(X_115)),bind(X_104,$fot(X_116))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(not(implies(not(X_116),X_115)),X_114),Z),implies(X_116,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_116,implies(not(implies(not(X_116),X_115)),X_114))) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(not(implies(not(X_399),X_398)),X_397),X_396),implies(X_399,X_396))),
inference(subst,[],[refute_0_14:[bind(Z,$fot(X_396)),bind(X_114,$fot(X_397)),bind(X_115,$fot(X_398)),bind(X_116,$fot(X_399))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(X_399),X_398)),X_397),X_396))
| is_a_theorem(implies(X_399,X_396)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(not(X_399),X_398)),X_397),X_396),implies(X_399,X_396))) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(not(implies(not(not(not(X_6712))),not(not(X_6712)))),X_6712),X_6712))
| is_a_theorem(implies(not(not(X_6712)),X_6712)) ),
inference(subst,[],[refute_0_16:[bind(X_396,$fot(X_6712)),bind(X_397,$fot(X_6712)),bind(X_398,$fot(not(not(X_6712)))),bind(X_399,$fot(not(not(X_6712))))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(not(X_1484),X_1485),implies(implies(X_1485,X_1484),X_1484)))
| ~ is_a_theorem(implies(not(X_1484),X_1485))
| is_a_theorem(implies(implies(X_1485,X_1484),X_1484)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_1484),X_1485))),bind(Y,$fot(implies(implies(X_1485,X_1484),X_1484)))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35))
| ~ is_a_theorem(implies(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35),implies(implies(X_32,X_33),X_35)))
| is_a_theorem(implies(implies(X_32,X_33),X_35)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35))),bind(Y,$fot(implies(implies(X_32,X_33),X_35)))]]) ).
cnf(refute_0_20,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_26),implies(implies(X,Y),X_26))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_26),implies(implies(X,Y),X_26))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35),implies(implies(X_32,X_33),X_35))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_32)),bind(Y,$fot(X_33)),bind(Z,$fot(X_34)),bind(X_26,$fot(X_35))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35))
| is_a_theorem(implies(implies(X_32,X_33),X_35)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_33,X_34),implies(X_32,X_34)),X_35),implies(implies(X_32,X_33),X_35))) )],[refute_0_22,refute_0_19]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(implies(X_33,X_1483),implies(not(X_1483),X_1483)),implies(implies(X_33,X_1483),X_1483)))
| is_a_theorem(implies(implies(not(X_1483),X_33),implies(implies(X_33,X_1483),X_1483))) ),
inference(subst,[],[refute_0_23:[bind(X_32,$fot(not(X_1483))),bind(X_34,$fot(X_1483)),bind(X_35,$fot(implies(implies(X_33,X_1483),X_1483)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_687)),X_686),X_687),X_687))
| ~ is_a_theorem(implies(implies(not(not(X_687)),X_686),X_687))
| is_a_theorem(X_687) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_687)),X_686),X_687))),bind(Y,$fot(X_687))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(not(not(X_684)),X_683),X_684),X_684)),implies(implies(implies(not(not(X_684)),X_683),X_684),X_684)))
| is_a_theorem(implies(implies(implies(not(not(X_684)),X_683),X_684),X_684)) ),
inference(subst,[],[refute_0_28:[bind(X_7,$fot(implies(implies(implies(not(not(X_684)),X_683),X_684),X_684)))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_30),X_29),X_31),implies(X_30,X_31)))
| is_a_theorem(implies(implies(implies(X_30,X_31),Z),implies(implies(implies(not(X_30),X_29),X_31),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(not(X_30),X_29),X_31))),bind(Y,$fot(implies(X_30,X_31)))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(X_30,X_31),Z),implies(implies(implies(not(X_30),X_29),X_31),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_30),X_29),X_31),implies(X_30,X_31))) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(not(X_592),X_592),X_593),implies(implies(implies(not(not(X_592)),X_29),X_592),X_593))),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_593)),bind(X_30,$fot(not(X_592))),bind(X_31,$fot(X_592))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),implies(implies(X_71,X_72),X_70)))
| ~ is_a_theorem(implies(implies(implies(not(X_71),X_71),X_72),X_70))
| is_a_theorem(implies(implies(X_71,X_72),X_70)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_71),X_71),X_72),X_70))),bind(Y,$fot(implies(implies(X_71,X_72),X_70)))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(X_27,X_28),implies(implies(not(X_27),X_27),X_28)))
| is_a_theorem(implies(implies(implies(implies(not(X_27),X_27),X_28),Z),implies(implies(X_27,X_28),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_27,X_28))),bind(Y,$fot(implies(implies(not(X_27),X_27),X_28)))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(implies(not(X_25),X_25),X_25)),
inference(subst,[],[cn_2:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(not(X_25),X_25),X_25))
| is_a_theorem(implies(implies(X_25,X_26),implies(implies(not(X_25),X_25),X_26))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_25),X_25))),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(X_25,X_26),implies(implies(not(X_25),X_25),X_26))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_25),X_25),X_25)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(X_27,X_28),implies(implies(not(X_27),X_27),X_28))),
inference(subst,[],[refute_0_37:[bind(X_25,$fot(X_27)),bind(X_26,$fot(X_28))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(implies(not(X_27),X_27),X_28),Z),implies(implies(X_27,X_28),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_27,X_28),implies(implies(not(X_27),X_27),X_28))) )],[refute_0_38,refute_0_34]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),implies(implies(X_71,X_72),X_70))),
inference(subst,[],[refute_0_39:[bind(Z,$fot(X_70)),bind(X_27,$fot(X_71)),bind(X_28,$fot(X_72))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_71),X_71),X_72),X_70))
| is_a_theorem(implies(implies(X_71,X_72),X_70)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),implies(implies(X_71,X_72),X_70))) )],[refute_0_40,refute_0_33]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_592),X_592),X_593),implies(implies(implies(not(not(X_592)),X_29),X_592),X_593)))
| is_a_theorem(implies(implies(X_592,X_593),implies(implies(implies(not(not(X_592)),X_29),X_592),X_593))) ),
inference(subst,[],[refute_0_41:[bind(X_70,$fot(implies(implies(implies(not(not(X_592)),X_29),X_592),X_593))),bind(X_71,$fot(X_592)),bind(X_72,$fot(X_593))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_592,X_593),implies(implies(implies(not(not(X_592)),X_29),X_592),X_593))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_592),X_592),X_593),implies(implies(implies(not(not(X_592)),X_29),X_592),X_593))) )],[refute_0_32,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(X_643,X_643),implies(implies(implies(not(not(X_643)),X_29),X_643),X_643))),
inference(subst,[],[refute_0_43:[bind(X_592,$fot(X_643)),bind(X_593,$fot(X_643))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(X_594,X_594),X_596))
| ~ is_a_theorem(implies(implies(implies(X_594,X_594),X_596),implies(X_595,X_596)))
| is_a_theorem(implies(X_595,X_596)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_594,X_594),X_596))),bind(Y,$fot(implies(X_595,X_596)))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(X_119,implies(not(implies(X_118,X_118)),X_117)))
| is_a_theorem(implies(implies(implies(not(implies(X_118,X_118)),X_117),Z),implies(X_119,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_119)),bind(Y,$fot(implies(not(implies(X_118,X_118)),X_117)))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(not(X_30),X_109),implies(not(implies(X_111,X_111)),X_109)))
| is_a_theorem(implies(X_30,implies(not(implies(X_111,X_111)),X_109))) ),
inference(subst,[],[refute_0_10:[bind(X_29,$fot(X_109)),bind(X_31,$fot(implies(not(implies(X_111,X_111)),X_109)))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(not(implies(X_108,X_108)),X_107))
| is_a_theorem(implies(implies(X_107,Z),implies(not(implies(X_108,X_108)),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(X_108,X_108)))),bind(Y,$fot(X_107))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_50,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_51,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(X_106,X_106))
| is_a_theorem(implies(not(implies(X_106,X_106)),Y)) ),
inference(subst,[],[refute_0_51:[bind(X_6,$fot(implies(X_106,X_106)))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(not(X_105),X_105),X_105)),
inference(subst,[],[cn_2:[bind(X,$fot(X_105))]]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(implies(not(X_105),X_105),X_105))
| is_a_theorem(implies(X_105,X_105)) ),
inference(subst,[],[refute_0_10:[bind(X_29,$fot(X_105)),bind(X_30,$fot(X_105)),bind(X_31,$fot(X_105))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(X_105,X_105)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_105),X_105),X_105)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(X_106,X_106)),
inference(subst,[],[refute_0_55:[bind(X_105,$fot(X_106))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(not(implies(X_106,X_106)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_106,X_106)) )],[refute_0_56,refute_0_52]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(not(implies(X_108,X_108)),X_107)),
inference(subst,[],[refute_0_57:[bind(Y,$fot(X_107)),bind(X_106,$fot(X_108))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(implies(X_107,Z),implies(not(implies(X_108,X_108)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_108,X_108)),X_107)) )],[refute_0_58,refute_0_48]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(not(X_30),X_109),implies(not(implies(X_111,X_111)),X_109))),
inference(subst,[],[refute_0_59:[bind(Z,$fot(X_109)),bind(X_107,$fot(not(X_30))),bind(X_108,$fot(X_111))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(X_30,implies(not(implies(X_111,X_111)),X_109))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_30),X_109),implies(not(implies(X_111,X_111)),X_109))) )],[refute_0_60,refute_0_47]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(X_119,implies(not(implies(X_118,X_118)),X_117))),
inference(subst,[],[refute_0_61:[bind(X_109,$fot(X_117)),bind(X_111,$fot(X_118)),bind(X_30,$fot(X_119))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(implies(not(implies(X_118,X_118)),X_117),Z),implies(X_119,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_119,implies(not(implies(X_118,X_118)),X_117))) )],[refute_0_62,refute_0_46]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(implies(not(implies(X_118,X_118)),implies(X_118,X_118)),X_593),implies(X_119,X_593))),
inference(subst,[],[refute_0_63:[bind(Z,$fot(X_593)),bind(X_117,$fot(implies(X_118,X_118)))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_118,X_118)),implies(X_118,X_118)),X_593),implies(X_119,X_593)))
| is_a_theorem(implies(implies(implies(X_118,X_118),X_593),implies(X_119,X_593))) ),
inference(subst,[],[refute_0_41:[bind(X_70,$fot(implies(X_119,X_593))),bind(X_71,$fot(implies(X_118,X_118))),bind(X_72,$fot(X_593))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(X_118,X_118),X_593),implies(X_119,X_593))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_118,X_118)),implies(X_118,X_118)),X_593),implies(X_119,X_593))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(implies(X_594,X_594),X_596),implies(X_595,X_596))),
inference(subst,[],[refute_0_66:[bind(X_118,$fot(X_594)),bind(X_119,$fot(X_595)),bind(X_593,$fot(X_596))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(X_594,X_594),X_596))
| is_a_theorem(implies(X_595,X_596)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_594,X_594),X_596),implies(X_595,X_596))) )],[refute_0_67,refute_0_45]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(implies(X_643,X_643),implies(implies(implies(not(not(X_643)),X_29),X_643),X_643)))
| is_a_theorem(implies(X_644,implies(implies(implies(not(not(X_643)),X_29),X_643),X_643))) ),
inference(subst,[],[refute_0_68:[bind(X_594,$fot(X_643)),bind(X_595,$fot(X_644)),bind(X_596,$fot(implies(implies(implies(not(not(X_643)),X_29),X_643),X_643)))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(X_644,implies(implies(implies(not(not(X_643)),X_29),X_643),X_643))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_643,X_643),implies(implies(implies(not(not(X_643)),X_29),X_643),X_643))) )],[refute_0_44,refute_0_69]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(not(implies(implies(implies(not(not(X_684)),X_683),X_684),X_684)),implies(implies(implies(not(not(X_684)),X_683),X_684),X_684))),
inference(subst,[],[refute_0_70:[bind(X_29,$fot(X_683)),bind(X_643,$fot(X_684)),bind(X_644,$fot(not(implies(implies(implies(not(not(X_684)),X_683),X_684),X_684))))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(implies(not(not(X_684)),X_683),X_684),X_684)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(not(not(X_684)),X_683),X_684),X_684)),implies(implies(implies(not(not(X_684)),X_683),X_684),X_684))) )],[refute_0_71,refute_0_29]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(implies(not(not(X_687)),X_686),X_687),X_687)),
inference(subst,[],[refute_0_72:[bind(X_683,$fot(X_686)),bind(X_684,$fot(X_687))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(implies(not(not(X_687)),X_686),X_687))
| is_a_theorem(X_687) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_687)),X_686),X_687),X_687)) )],[refute_0_73,refute_0_25]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1014,X_1014),X_1013),X_1013))),X_686),implies(implies(implies(X_1014,X_1014),X_1013),X_1013)))
| is_a_theorem(implies(implies(implies(X_1014,X_1014),X_1013),X_1013)) ),
inference(subst,[],[refute_0_74:[bind(X_687,$fot(implies(implies(implies(X_1014,X_1014),X_1013),X_1013)))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(X_1010,X_1010),implies(implies(implies(X_1011,X_1011),X_1010),X_1010)))
| is_a_theorem(implies(X_595,implies(implies(implies(X_1011,X_1011),X_1010),X_1010))) ),
inference(subst,[],[refute_0_68:[bind(X_594,$fot(X_1010)),bind(X_596,$fot(implies(implies(implies(X_1011,X_1011),X_1010),X_1010)))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1009),X_1009),X_1006),implies(implies(implies(X_1007,X_1007),X_1009),X_1006)))
| is_a_theorem(implies(implies(X_1009,X_1006),implies(implies(implies(X_1007,X_1007),X_1009),X_1006))) ),
inference(subst,[],[refute_0_41:[bind(X_70,$fot(implies(implies(implies(X_1007,X_1007),X_1009),X_1006))),bind(X_71,$fot(X_1009)),bind(X_72,$fot(X_1006))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(implies(X_594,X_594),X_596),implies(X_595,X_596)))
| is_a_theorem(implies(implies(implies(X_595,X_596),Z),implies(implies(implies(X_594,X_594),X_596),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(X_594,X_594),X_596))),bind(Y,$fot(implies(X_595,X_596)))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(implies(X_595,X_596),Z),implies(implies(implies(X_594,X_594),X_596),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_594,X_594),X_596),implies(X_595,X_596))) )],[refute_0_67,refute_0_78]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(implies(implies(not(X_1009),X_1009),X_1006),implies(implies(implies(X_1007,X_1007),X_1009),X_1006))),
inference(subst,[],[refute_0_79:[bind(Z,$fot(X_1006)),bind(X_594,$fot(X_1007)),bind(X_595,$fot(not(X_1009))),bind(X_596,$fot(X_1009))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(X_1009,X_1006),implies(implies(implies(X_1007,X_1007),X_1009),X_1006))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1009),X_1009),X_1006),implies(implies(implies(X_1007,X_1007),X_1009),X_1006))) )],[refute_0_80,refute_0_77]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(X_1010,X_1010),implies(implies(implies(X_1011,X_1011),X_1010),X_1010))),
inference(subst,[],[refute_0_81:[bind(X_1006,$fot(X_1010)),bind(X_1007,$fot(X_1011)),bind(X_1009,$fot(X_1010))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(X_595,implies(implies(implies(X_1011,X_1011),X_1010),X_1010))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1010,X_1010),implies(implies(implies(X_1011,X_1011),X_1010),X_1010))) )],[refute_0_82,refute_0_76]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1014,X_1014),X_1013),X_1013))),X_686),implies(implies(implies(X_1014,X_1014),X_1013),X_1013))),
inference(subst,[],[refute_0_83:[bind(X_1010,$fot(X_1013)),bind(X_1011,$fot(X_1014)),bind(X_595,$fot(implies(not(not(implies(implies(implies(X_1014,X_1014),X_1013),X_1013))),X_686)))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(implies(X_1014,X_1014),X_1013),X_1013)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1014,X_1014),X_1013),X_1013))),X_686),implies(implies(implies(X_1014,X_1014),X_1013),X_1013))) )],[refute_0_84,refute_0_75]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(implies(X_1088,X_1088),X_1085),X_1085)),
inference(subst,[],[refute_0_85:[bind(X_1013,$fot(X_1085)),bind(X_1014,$fot(X_1088))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(implies(X_467,X_468),X_466),X_465))
| ~ is_a_theorem(implies(implies(implies(implies(X_467,X_468),X_466),X_465),implies(implies(implies(implies(not(X_467),X_467),X_468),X_466),X_465)))
| is_a_theorem(implies(implies(implies(implies(not(X_467),X_467),X_468),X_466),X_465)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_467,X_468),X_466),X_465))),bind(Y,$fot(implies(implies(implies(implies(not(X_467),X_467),X_468),X_466),X_465)))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),implies(implies(X_71,X_72),X_70)))
| is_a_theorem(implies(implies(implies(implies(X_71,X_72),X_70),Z),implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(implies(not(X_71),X_71),X_72),X_70))),bind(Y,$fot(implies(implies(X_71,X_72),X_70)))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(implies(implies(implies(X_71,X_72),X_70),Z),implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_71),X_71),X_72),X_70),implies(implies(X_71,X_72),X_70))) )],[refute_0_40,refute_0_88]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(implies(implies(X_467,X_468),X_466),X_465),implies(implies(implies(implies(not(X_467),X_467),X_468),X_466),X_465))),
inference(subst,[],[refute_0_89:[bind(Z,$fot(X_465)),bind(X_70,$fot(X_466)),bind(X_71,$fot(X_467)),bind(X_72,$fot(X_468))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(implies(implies(X_467,X_468),X_466),X_465))
| is_a_theorem(implies(implies(implies(implies(not(X_467),X_467),X_468),X_466),X_465)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_467,X_468),X_466),X_465),implies(implies(implies(implies(not(X_467),X_467),X_468),X_466),X_465))) )],[refute_0_90,refute_0_87]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(implies(implies(implies(X_1088,X_1088),X_1085),X_1085))
| is_a_theorem(implies(implies(implies(implies(not(X_1088),X_1088),X_1088),X_1085),X_1085)) ),
inference(subst,[],[refute_0_91:[bind(X_465,$fot(X_1085)),bind(X_466,$fot(X_1085)),bind(X_467,$fot(X_1088)),bind(X_468,$fot(X_1088))]]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1088),X_1088),X_1088),X_1085),X_1085)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1088,X_1088),X_1085),X_1085)) )],[refute_0_86,refute_0_92]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1472),X_1472),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))),
inference(subst,[],[refute_0_93:[bind(X_1085,$fot(implies(X_1470,X_1472))),bind(X_1088,$fot(X_1472))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1472),X_1472),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472)))
| is_a_theorem(implies(implies(X_1470,implies(not(X_1472),X_1472)),implies(X_1470,X_1472))) ),
inference(subst,[],[refute_0_23:[bind(X_32,$fot(X_1470)),bind(X_33,$fot(implies(not(X_1472),X_1472))),bind(X_34,$fot(X_1472)),bind(X_35,$fot(implies(X_1470,X_1472)))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(implies(X_1470,implies(not(X_1472),X_1472)),implies(X_1470,X_1472))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1472),X_1472),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(implies(X_33,X_1483),implies(not(X_1483),X_1483)),implies(implies(X_33,X_1483),X_1483))),
inference(subst,[],[refute_0_96:[bind(X_1470,$fot(implies(X_33,X_1483))),bind(X_1472,$fot(X_1483))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(not(X_1483),X_33),implies(implies(X_33,X_1483),X_1483))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_33,X_1483),implies(not(X_1483),X_1483)),implies(implies(X_33,X_1483),X_1483))) )],[refute_0_97,refute_0_24]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(not(X_1484),X_1485),implies(implies(X_1485,X_1484),X_1484))),
inference(subst,[],[refute_0_98:[bind(X_1483,$fot(X_1484)),bind(X_33,$fot(X_1485))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(not(X_1484),X_1485))
| is_a_theorem(implies(implies(X_1485,X_1484),X_1484)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_1484),X_1485),implies(implies(X_1485,X_1484),X_1484))) )],[refute_0_99,refute_0_18]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(not(X_1484),not(implies(not(not(not(X_1484))),not(not(X_1484))))))
| is_a_theorem(implies(implies(not(implies(not(not(not(X_1484))),not(not(X_1484)))),X_1484),X_1484)) ),
inference(subst,[],[refute_0_100:[bind(X_1485,$fot(not(implies(not(not(not(X_1484))),not(not(X_1484))))))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(implies(not(X_30),not(implies(not(not(X_30)),not(X_30)))),not(implies(not(not(X_30)),not(X_30)))))
| is_a_theorem(implies(X_30,not(implies(not(not(X_30)),not(X_30))))) ),
inference(subst,[],[refute_0_10:[bind(X_29,$fot(not(implies(not(not(X_30)),not(X_30))))),bind(X_31,$fot(not(implies(not(not(X_30)),not(X_30)))))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(implies(not(not(implies(not(X_6372),X_6372))),X_6372))
| is_a_theorem(implies(implies(X_6372,not(implies(not(X_6372),X_6372))),not(implies(not(X_6372),X_6372)))) ),
inference(subst,[],[refute_0_100:[bind(X_1484,$fot(not(implies(not(X_6372),X_6372)))),bind(X_1485,$fot(X_6372))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(implies(not(not(not(implies(not(X_6371),X_6371)))),not(not(X_6371))),X_6371))
| is_a_theorem(implies(not(not(implies(not(X_6371),X_6371))),X_6371)) ),
inference(subst,[],[refute_0_10:[bind(X_29,$fot(not(not(X_6371)))),bind(X_30,$fot(not(not(implies(not(X_6371),X_6371))))),bind(X_31,$fot(X_6371))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_6369)),not(not(implies(not(X_6369),X_6369)))),implies(not(not(not(implies(not(X_6369),X_6369)))),not(not(implies(not(X_6369),X_6369))))),X_6369))
| is_a_theorem(implies(implies(not(not(not(implies(not(X_6369),X_6369)))),not(not(X_6369))),X_6369)) ),
inference(subst,[],[refute_0_23:[bind(X_32,$fot(not(not(not(implies(not(X_6369),X_6369)))))),bind(X_33,$fot(not(not(X_6369)))),bind(X_34,$fot(not(not(implies(not(X_6369),X_6369))))),bind(X_35,$fot(X_6369))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(X_1482,implies(not(X_1483),X_1483)))
| ~ is_a_theorem(implies(implies(X_1482,implies(not(X_1483),X_1483)),implies(X_1482,X_1483)))
| is_a_theorem(implies(X_1482,X_1483)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1482,implies(not(X_1483),X_1483)))),bind(Y,$fot(implies(X_1482,X_1483)))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(implies(X_1482,implies(not(X_1483),X_1483)),implies(X_1482,X_1483))),
inference(subst,[],[refute_0_96:[bind(X_1470,$fot(X_1482)),bind(X_1472,$fot(X_1483))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(X_1482,implies(not(X_1483),X_1483)))
| is_a_theorem(implies(X_1482,X_1483)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1482,implies(not(X_1483),X_1483)),implies(X_1482,X_1483))) )],[refute_0_107,refute_0_106]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(implies(not(X_1697),implies(not(not(not(implies(not(X_1697),X_1697)))),not(not(implies(not(X_1697),X_1697))))),implies(not(X_1697),X_1697)))
| is_a_theorem(implies(implies(not(X_1697),implies(not(not(not(implies(not(X_1697),X_1697)))),not(not(implies(not(X_1697),X_1697))))),X_1697)) ),
inference(subst,[],[refute_0_108:[bind(X_1482,$fot(implies(not(X_1697),implies(not(not(not(implies(not(X_1697),X_1697)))),not(not(implies(not(X_1697),X_1697))))))),bind(X_1483,$fot(X_1697))]]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(implies(implies(not(not(X_1085)),X_1088),X_1085),X_1085)),
inference(subst,[],[refute_0_72:[bind(X_683,$fot(X_1088)),bind(X_684,$fot(X_1085))]]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_1085)),X_1088),X_1085),X_1085))
| is_a_theorem(implies(implies(implies(implies(not(not(not(X_1085))),not(not(X_1085))),X_1088),X_1085),X_1085)) ),
inference(subst,[],[refute_0_91:[bind(X_465,$fot(X_1085)),bind(X_466,$fot(X_1085)),bind(X_467,$fot(not(not(X_1085)))),bind(X_468,$fot(X_1088))]]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(implies(implies(not(not(not(X_1085))),not(not(X_1085))),X_1088),X_1085),X_1085)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_1085)),X_1088),X_1085),X_1085)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(implies(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))),
inference(subst,[],[refute_0_112:[bind(X_1085,$fot(implies(X_1470,X_1472))),bind(X_1088,$fot(X_1472))]]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472)))
| is_a_theorem(implies(implies(X_1470,implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472))))),implies(X_1470,X_1472))) ),
inference(subst,[],[refute_0_23:[bind(X_32,$fot(X_1470)),bind(X_33,$fot(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))))),bind(X_34,$fot(X_1472)),bind(X_35,$fot(implies(X_1470,X_1472)))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(X_1470,implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472))))),implies(X_1470,X_1472))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(not(implies(X_1470,X_1472)))),not(not(implies(X_1470,X_1472)))),X_1472),implies(X_1470,X_1472)),implies(X_1470,X_1472))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(not(X_1697),implies(not(not(not(implies(not(X_1697),X_1697)))),not(not(implies(not(X_1697),X_1697))))),implies(not(X_1697),X_1697))),
inference(subst,[],[refute_0_115:[bind(X_1470,$fot(not(X_1697))),bind(X_1472,$fot(X_1697))]]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(not(X_1697),implies(not(not(not(implies(not(X_1697),X_1697)))),not(not(implies(not(X_1697),X_1697))))),X_1697)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_1697),implies(not(not(not(implies(not(X_1697),X_1697)))),not(not(implies(not(X_1697),X_1697))))),implies(not(X_1697),X_1697))) )],[refute_0_116,refute_0_109]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(not(X_6351),implies(not(not(not(implies(not(X_6351),X_6351)))),not(not(implies(not(X_6351),X_6351))))),X_6351)),
inference(subst,[],[refute_0_117:[bind(X_1697,$fot(X_6351))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(implies(X_93,X_94),X_91))
| ~ is_a_theorem(implies(implies(implies(X_93,X_94),X_91),implies(implies(implies(not(X_93),X_92),X_94),X_91)))
| is_a_theorem(implies(implies(implies(not(X_93),X_92),X_94),X_91)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_93,X_94),X_91))),bind(Y,$fot(implies(implies(implies(not(X_93),X_92),X_94),X_91)))]]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(implies(implies(X_93,X_94),X_91),implies(implies(implies(not(X_93),X_92),X_94),X_91))),
inference(subst,[],[refute_0_31:[bind(Z,$fot(X_91)),bind(X_29,$fot(X_92)),bind(X_30,$fot(X_93)),bind(X_31,$fot(X_94))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(implies(X_93,X_94),X_91))
| is_a_theorem(implies(implies(implies(not(X_93),X_92),X_94),X_91)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_93,X_94),X_91),implies(implies(implies(not(X_93),X_92),X_94),X_91))) )],[refute_0_120,refute_0_119]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(not(X_6351),implies(not(not(not(implies(not(X_6351),X_6351)))),not(not(implies(not(X_6351),X_6351))))),X_6351))
| is_a_theorem(implies(implies(implies(not(not(X_6351)),X_6352),implies(not(not(not(implies(not(X_6351),X_6351)))),not(not(implies(not(X_6351),X_6351))))),X_6351)) ),
inference(subst,[],[refute_0_121:[bind(X_91,$fot(X_6351)),bind(X_92,$fot(X_6352)),bind(X_93,$fot(not(X_6351))),bind(X_94,$fot(implies(not(not(not(implies(not(X_6351),X_6351)))),not(not(implies(not(X_6351),X_6351))))))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(implies(not(not(X_6351)),X_6352),implies(not(not(not(implies(not(X_6351),X_6351)))),not(not(implies(not(X_6351),X_6351))))),X_6351)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_6351),implies(not(not(not(implies(not(X_6351),X_6351)))),not(not(implies(not(X_6351),X_6351))))),X_6351)) )],[refute_0_118,refute_0_122]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(implies(not(not(X_6369)),not(not(implies(not(X_6369),X_6369)))),implies(not(not(not(implies(not(X_6369),X_6369)))),not(not(implies(not(X_6369),X_6369))))),X_6369)),
inference(subst,[],[refute_0_123:[bind(X_6351,$fot(X_6369)),bind(X_6352,$fot(not(not(implies(not(X_6369),X_6369)))))]]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(implies(not(not(not(implies(not(X_6369),X_6369)))),not(not(X_6369))),X_6369)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_6369)),not(not(implies(not(X_6369),X_6369)))),implies(not(not(not(implies(not(X_6369),X_6369)))),not(not(implies(not(X_6369),X_6369))))),X_6369)) )],[refute_0_124,refute_0_105]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(not(not(not(implies(not(X_6371),X_6371)))),not(not(X_6371))),X_6371)),
inference(subst,[],[refute_0_125:[bind(X_6369,$fot(X_6371))]]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(not(not(implies(not(X_6371),X_6371))),X_6371)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(implies(not(X_6371),X_6371)))),not(not(X_6371))),X_6371)) )],[refute_0_126,refute_0_104]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(not(not(implies(not(X_6372),X_6372))),X_6372)),
inference(subst,[],[refute_0_127:[bind(X_6371,$fot(X_6372))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_6372,not(implies(not(X_6372),X_6372))),not(implies(not(X_6372),X_6372)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(X_6372),X_6372))),X_6372)) )],[refute_0_128,refute_0_103]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(not(X_30),not(implies(not(not(X_30)),not(X_30)))),not(implies(not(not(X_30)),not(X_30))))),
inference(subst,[],[refute_0_129:[bind(X_6372,$fot(not(X_30)))]]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(X_30,not(implies(not(not(X_30)),not(X_30))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_30),not(implies(not(not(X_30)),not(X_30)))),not(implies(not(not(X_30)),not(X_30))))) )],[refute_0_130,refute_0_102]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(not(X_1484),not(implies(not(not(not(X_1484))),not(not(X_1484)))))),
inference(subst,[],[refute_0_131:[bind(X_30,$fot(not(X_1484)))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(not(implies(not(not(not(X_1484))),not(not(X_1484)))),X_1484),X_1484)),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1484),not(implies(not(not(not(X_1484))),not(not(X_1484)))))) )],[refute_0_132,refute_0_101]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(not(implies(not(not(not(X_6712))),not(not(X_6712)))),X_6712),X_6712)),
inference(subst,[],[refute_0_133:[bind(X_1484,$fot(X_6712))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(not(not(X_6712)),X_6712)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(not(not(not(X_6712))),not(not(X_6712)))),X_6712),X_6712)) )],[refute_0_134,refute_0_17]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(not(not(a)),a)),
inference(subst,[],[refute_0_135:[bind(X_6712,$fot(a))]]) ).
cnf(refute_0_137,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(not(not(a)),a)) )],[refute_0_136,prove_cn_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL056-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 2 11:42:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.59/4.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.59/4.77
% 4.59/4.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.62/4.79
%------------------------------------------------------------------------------