TSTP Solution File: LCL053-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL053-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:49:05 EDT 2022
% Result : Unsatisfiable 18.45s 18.62s
% Output : CNFRefutation 18.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 5
% Syntax : Number of clauses : 159 ( 92 unt; 0 nHn; 45 RR)
% Number of literals : 240 ( 0 equ; 82 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 : 449 ( 88 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_30,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))) ).
cnf(refute_0_0,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_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,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_31),implies(implies(X,Y),X_31))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_31),implies(implies(X,Y),X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_3]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44),implies(implies(X_41,X_42),X_44))),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(X_43)),bind(X_31,$fot(X_44))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(X_42,X_43),implies(X_41,X_43)),X_44))
| is_a_theorem(implies(implies(X_41,X_42),X_44)) ),
inference(resolve,[$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_5,refute_0_0]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_41,X_21411),X_21411),implies(X_41,X_21411)),implies(X_41,X_21411)))
| is_a_theorem(implies(implies(X_41,implies(X_41,X_21411)),implies(X_41,X_21411))) ),
inference(subst,[],[refute_0_6:[bind(X_42,$fot(implies(X_41,X_21411))),bind(X_43,$fot(X_21411)),bind(X_44,$fot(implies(X_41,X_21411)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_70),X_70),X_71),X_69),implies(implies(X_70,X_71),X_69)))
| ~ is_a_theorem(implies(implies(implies(not(X_70),X_70),X_71),X_69))
| is_a_theorem(implies(implies(X_70,X_71),X_69)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_70),X_70),X_71),X_69))),bind(Y,$fot(implies(implies(X_70,X_71),X_69)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33)))
| is_a_theorem(implies(implies(implies(implies(not(X_32),X_32),X_33),Z),implies(implies(X_32,X_33),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_32,X_33))),bind(Y,$fot(implies(implies(not(X_32),X_32),X_33)))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(not(X_30),X_30),X_30)),
inference(subst,[],[cn_2:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(not(X_30),X_30),X_30))
| is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_30),X_30))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(implies(not(X_30),X_30),X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_30),X_30),X_30)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33))),
inference(subst,[],[refute_0_12:[bind(X_30,$fot(X_32)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(implies(not(X_32),X_32),X_33),Z),implies(implies(X_32,X_33),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33))) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(implies(not(X_70),X_70),X_71),X_69),implies(implies(X_70,X_71),X_69))),
inference(subst,[],[refute_0_14:[bind(Z,$fot(X_69)),bind(X_32,$fot(X_70)),bind(X_33,$fot(X_71))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_70),X_70),X_71),X_69))
| is_a_theorem(implies(implies(X_70,X_71),X_69)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_70),X_70),X_71),X_69),implies(implies(X_70,X_71),X_69))) )],[refute_0_15,refute_0_8]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_21407,X_21408)),implies(X_21407,X_21408)),X_21407),X_21407))
| is_a_theorem(implies(implies(implies(X_21407,X_21408),X_21407),X_21407)) ),
inference(subst,[],[refute_0_16:[bind(X_69,$fot(X_21407)),bind(X_70,$fot(implies(X_21407,X_21408))),bind(X_71,$fot(X_21407))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(X_4140,implies(not(X_4141),X_4141)))
| ~ is_a_theorem(implies(implies(X_4140,implies(not(X_4141),X_4141)),implies(X_4140,X_4141)))
| is_a_theorem(implies(X_4140,X_4141)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_4140,implies(not(X_4141),X_4141)))),bind(Y,$fot(implies(X_4140,X_4141)))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_4139),X_4139),X_4139),implies(X_41,X_4139)),implies(X_41,X_4139)))
| is_a_theorem(implies(implies(X_41,implies(not(X_4139),X_4139)),implies(X_41,X_4139))) ),
inference(subst,[],[refute_0_6:[bind(X_42,$fot(implies(not(X_4139),X_4139))),bind(X_43,$fot(X_4139)),bind(X_44,$fot(implies(X_41,X_4139)))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(implies(X_745,X_746),X_744),X_743))
| ~ is_a_theorem(implies(implies(implies(implies(X_745,X_746),X_744),X_743),implies(implies(implies(implies(not(X_745),X_745),X_746),X_744),X_743)))
| is_a_theorem(implies(implies(implies(implies(not(X_745),X_745),X_746),X_744),X_743)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_745,X_746),X_744),X_743))),bind(Y,$fot(implies(implies(implies(implies(not(X_745),X_745),X_746),X_744),X_743)))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_70),X_70),X_71),X_69),implies(implies(X_70,X_71),X_69)))
| is_a_theorem(implies(implies(implies(implies(X_70,X_71),X_69),Z),implies(implies(implies(implies(not(X_70),X_70),X_71),X_69),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(implies(not(X_70),X_70),X_71),X_69))),bind(Y,$fot(implies(implies(X_70,X_71),X_69)))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(implies(X_70,X_71),X_69),Z),implies(implies(implies(implies(not(X_70),X_70),X_71),X_69),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_70),X_70),X_71),X_69),implies(implies(X_70,X_71),X_69))) )],[refute_0_15,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(implies(X_745,X_746),X_744),X_743),implies(implies(implies(implies(not(X_745),X_745),X_746),X_744),X_743))),
inference(subst,[],[refute_0_22:[bind(Z,$fot(X_743)),bind(X_69,$fot(X_744)),bind(X_70,$fot(X_745)),bind(X_71,$fot(X_746))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(implies(X_745,X_746),X_744),X_743))
| is_a_theorem(implies(implies(implies(implies(not(X_745),X_745),X_746),X_744),X_743)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_745,X_746),X_744),X_743),implies(implies(implies(implies(not(X_745),X_745),X_746),X_744),X_743))) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(X_4137,X_4137),X_4136),X_4136))
| is_a_theorem(implies(implies(implies(implies(not(X_4137),X_4137),X_4137),X_4136),X_4136)) ),
inference(subst,[],[refute_0_24:[bind(X_743,$fot(X_4136)),bind(X_744,$fot(X_4136)),bind(X_745,$fot(X_4137)),bind(X_746,$fot(X_4137))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_1600)),X_1601),X_1600),X_1600))
| ~ is_a_theorem(implies(implies(not(not(X_1600)),X_1601),X_1600))
| is_a_theorem(X_1600) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_1600)),X_1601),X_1600))),bind(Y,$fot(X_1600))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_28,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_29,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597)),implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597)))
| is_a_theorem(implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597)) ),
inference(subst,[],[refute_0_29:[bind(X_7,$fot(implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597)))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_824,X_824)),X_823),X_822),implies(X_825,X_822)))
| ~ is_a_theorem(implies(implies(not(implies(X_824,X_824)),X_823),X_822))
| is_a_theorem(implies(X_825,X_822)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(X_824,X_824)),X_823),X_822))),bind(Y,$fot(implies(X_825,X_822)))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(X_132,implies(not(implies(X_131,X_131)),X_130)))
| is_a_theorem(implies(implies(implies(not(implies(X_131,X_131)),X_130),Z),implies(X_132,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_132)),bind(Y,$fot(implies(not(implies(X_131,X_131)),X_130)))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36)))
| ~ is_a_theorem(implies(implies(not(X_35),X_34),X_36))
| is_a_theorem(implies(X_35,X_36)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_35),X_34),X_36))),bind(Y,$fot(implies(X_35,X_36)))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(X_29,implies(not(X_29),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(X_29,implies(not(X_29),Y)))
| is_a_theorem(implies(implies(implies(not(X_29),Y),X_31),implies(X_29,X_31))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_29)),bind(Y,$fot(implies(not(X_29),Y))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(implies(not(X_29),Y),X_31),implies(X_29,X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(X_29,implies(not(X_29),Y))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36))),
inference(subst,[],[refute_0_36:[bind(Y,$fot(X_34)),bind(X_29,$fot(X_35)),bind(X_31,$fot(X_36))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(implies(not(X_35),X_34),X_36))
| is_a_theorem(implies(X_35,X_36)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36))) )],[refute_0_37,refute_0_33]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(not(X_35),X_127),implies(not(implies(X_129,X_129)),X_127)))
| is_a_theorem(implies(X_35,implies(not(implies(X_129,X_129)),X_127))) ),
inference(subst,[],[refute_0_38:[bind(X_34,$fot(X_127)),bind(X_36,$fot(implies(not(implies(X_129,X_129)),X_127)))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(not(implies(X_84,X_84)),X_83))
| is_a_theorem(implies(implies(X_83,Z),implies(not(implies(X_84,X_84)),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(X_84,X_84)))),bind(Y,$fot(X_83))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_42,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_43,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(X_82,X_82))
| is_a_theorem(implies(not(implies(X_82,X_82)),Y)) ),
inference(subst,[],[refute_0_43:[bind(X_6,$fot(implies(X_82,X_82)))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(not(X_81),X_81),X_81)),
inference(subst,[],[cn_2:[bind(X,$fot(X_81))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(not(X_81),X_81),X_81))
| is_a_theorem(implies(X_81,X_81)) ),
inference(subst,[],[refute_0_38:[bind(X_34,$fot(X_81)),bind(X_35,$fot(X_81)),bind(X_36,$fot(X_81))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(X_81,X_81)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_81),X_81),X_81)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(X_82,X_82)),
inference(subst,[],[refute_0_47:[bind(X_81,$fot(X_82))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(not(implies(X_82,X_82)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_82,X_82)) )],[refute_0_48,refute_0_44]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(not(implies(X_84,X_84)),X_83)),
inference(subst,[],[refute_0_49:[bind(Y,$fot(X_83)),bind(X_82,$fot(X_84))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(X_83,Z),implies(not(implies(X_84,X_84)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_84,X_84)),X_83)) )],[refute_0_50,refute_0_40]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(not(X_35),X_127),implies(not(implies(X_129,X_129)),X_127))),
inference(subst,[],[refute_0_51:[bind(Z,$fot(X_127)),bind(X_83,$fot(not(X_35))),bind(X_84,$fot(X_129))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_35,implies(not(implies(X_129,X_129)),X_127))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_35),X_127),implies(not(implies(X_129,X_129)),X_127))) )],[refute_0_52,refute_0_39]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(X_132,implies(not(implies(X_131,X_131)),X_130))),
inference(subst,[],[refute_0_53:[bind(X_127,$fot(X_130)),bind(X_129,$fot(X_131)),bind(X_35,$fot(X_132))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(not(implies(X_131,X_131)),X_130),Z),implies(X_132,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_132,implies(not(implies(X_131,X_131)),X_130))) )],[refute_0_54,refute_0_32]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(implies(not(implies(X_824,X_824)),X_823),X_822),implies(X_825,X_822))),
inference(subst,[],[refute_0_55:[bind(Z,$fot(X_822)),bind(X_130,$fot(X_823)),bind(X_131,$fot(X_824)),bind(X_132,$fot(X_825))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_824,X_824)),X_823),X_822))
| is_a_theorem(implies(X_825,X_822)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_824,X_824)),X_823),X_822),implies(X_825,X_822))) )],[refute_0_56,refute_0_31]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_1595,X_1595)),implies(X_1595,X_1595)),implies(implies(implies(not(not(X_1595)),X_1596),X_1595),X_1595)))
| is_a_theorem(implies(X_825,implies(implies(implies(not(not(X_1595)),X_1596),X_1595),X_1595))) ),
inference(subst,[],[refute_0_57:[bind(X_822,$fot(implies(implies(implies(not(not(X_1595)),X_1596),X_1595),X_1595))),bind(X_823,$fot(implies(X_1595,X_1595))),bind(X_824,$fot(X_1595))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(X_32,X_33))
| ~ is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33)))
| is_a_theorem(implies(implies(not(X_32),X_32),X_33)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_32,X_33))),bind(Y,$fot(implies(implies(not(X_32),X_32),X_33)))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(X_32,X_33))
| is_a_theorem(implies(implies(not(X_32),X_32),X_33)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_32,X_33),implies(implies(not(X_32),X_32),X_33))) )],[refute_0_13,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(X_1358,X_1359),implies(implies(implies(not(not(X_1358)),X_1360),X_1358),X_1359)))
| is_a_theorem(implies(implies(not(implies(X_1358,X_1359)),implies(X_1358,X_1359)),implies(implies(implies(not(not(X_1358)),X_1360),X_1358),X_1359))) ),
inference(subst,[],[refute_0_60:[bind(X_32,$fot(implies(X_1358,X_1359))),bind(X_33,$fot(implies(implies(implies(not(not(X_1358)),X_1360),X_1358),X_1359)))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36)))
| is_a_theorem(implies(implies(implies(X_35,X_36),Z),implies(implies(implies(not(X_35),X_34),X_36),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(not(X_35),X_34),X_36))),bind(Y,$fot(implies(X_35,X_36)))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(implies(X_35,X_36),Z),implies(implies(implies(not(X_35),X_34),X_36),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_35),X_34),X_36),implies(X_35,X_36))) )],[refute_0_37,refute_0_62]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(implies(not(X_1339),X_1339),X_1340),implies(implies(implies(not(not(X_1339)),X_34),X_1339),X_1340))),
inference(subst,[],[refute_0_63:[bind(Z,$fot(X_1340)),bind(X_35,$fot(not(X_1339))),bind(X_36,$fot(X_1339))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1339),X_1339),X_1340),implies(implies(implies(not(not(X_1339)),X_34),X_1339),X_1340)))
| is_a_theorem(implies(implies(X_1339,X_1340),implies(implies(implies(not(not(X_1339)),X_34),X_1339),X_1340))) ),
inference(subst,[],[refute_0_16:[bind(X_69,$fot(implies(implies(implies(not(not(X_1339)),X_34),X_1339),X_1340))),bind(X_70,$fot(X_1339)),bind(X_71,$fot(X_1340))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(X_1339,X_1340),implies(implies(implies(not(not(X_1339)),X_34),X_1339),X_1340))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1339),X_1339),X_1340),implies(implies(implies(not(not(X_1339)),X_34),X_1339),X_1340))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(X_1358,X_1359),implies(implies(implies(not(not(X_1358)),X_1360),X_1358),X_1359))),
inference(subst,[],[refute_0_66:[bind(X_1339,$fot(X_1358)),bind(X_1340,$fot(X_1359)),bind(X_34,$fot(X_1360))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(not(implies(X_1358,X_1359)),implies(X_1358,X_1359)),implies(implies(implies(not(not(X_1358)),X_1360),X_1358),X_1359))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1358,X_1359),implies(implies(implies(not(not(X_1358)),X_1360),X_1358),X_1359))) )],[refute_0_67,refute_0_61]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(not(implies(X_1595,X_1595)),implies(X_1595,X_1595)),implies(implies(implies(not(not(X_1595)),X_1596),X_1595),X_1595))),
inference(subst,[],[refute_0_68:[bind(X_1358,$fot(X_1595)),bind(X_1359,$fot(X_1595)),bind(X_1360,$fot(X_1596))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(X_825,implies(implies(implies(not(not(X_1595)),X_1596),X_1595),X_1595))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(X_1595,X_1595)),implies(X_1595,X_1595)),implies(implies(implies(not(not(X_1595)),X_1596),X_1595),X_1595))) )],[refute_0_69,refute_0_58]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(not(implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597)),implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597))),
inference(subst,[],[refute_0_70:[bind(X_1595,$fot(X_1597)),bind(X_1596,$fot(X_1598)),bind(X_825,$fot(not(implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597))))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597)),implies(implies(implies(not(not(X_1597)),X_1598),X_1597),X_1597))) )],[refute_0_71,refute_0_30]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(implies(not(not(X_1600)),X_1601),X_1600),X_1600)),
inference(subst,[],[refute_0_72:[bind(X_1597,$fot(X_1600)),bind(X_1598,$fot(X_1601))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(implies(not(not(X_1600)),X_1601),X_1600))
| is_a_theorem(X_1600) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_1600)),X_1601),X_1600),X_1600)) )],[refute_0_73,refute_0_26]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(X_4134,X_4134),X_4133),X_4133))),X_1601),implies(implies(implies(X_4134,X_4134),X_4133),X_4133)))
| is_a_theorem(implies(implies(implies(X_4134,X_4134),X_4133),X_4133)) ),
inference(subst,[],[refute_0_74:[bind(X_1600,$fot(implies(implies(implies(X_4134,X_4134),X_4133),X_4133)))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(not(implies(X_4130,X_4130)),implies(X_4130,X_4130)),implies(implies(implies(X_4132,X_4132),X_4130),X_4130)))
| is_a_theorem(implies(X_825,implies(implies(implies(X_4132,X_4132),X_4130),X_4130))) ),
inference(subst,[],[refute_0_57:[bind(X_822,$fot(implies(implies(implies(X_4132,X_4132),X_4130),X_4130))),bind(X_823,$fot(implies(X_4130,X_4130))),bind(X_824,$fot(X_4130))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(X_4079,X_4078),implies(implies(implies(X_4080,X_4080),X_4079),X_4078)))
| is_a_theorem(implies(implies(not(implies(X_4079,X_4078)),implies(X_4079,X_4078)),implies(implies(implies(X_4080,X_4080),X_4079),X_4078))) ),
inference(subst,[],[refute_0_60:[bind(X_32,$fot(implies(X_4079,X_4078))),bind(X_33,$fot(implies(implies(implies(X_4080,X_4080),X_4079),X_4078)))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_4071),X_4071),X_4070),implies(implies(implies(X_4073,X_4073),X_4071),X_4070)))
| is_a_theorem(implies(implies(X_4071,X_4070),implies(implies(implies(X_4073,X_4073),X_4071),X_4070))) ),
inference(subst,[],[refute_0_16:[bind(X_69,$fot(implies(implies(implies(X_4073,X_4073),X_4071),X_4070))),bind(X_70,$fot(X_4071)),bind(X_71,$fot(X_4070))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(implies(implies(X_502,X_502),X_500),implies(X_501,X_500)))
| is_a_theorem(implies(implies(implies(X_501,X_500),Z),implies(implies(implies(X_502,X_502),X_500),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(X_502,X_502),X_500))),bind(Y,$fot(implies(X_501,X_500)))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(X_495,implies(X_496,X_496)))
| is_a_theorem(implies(implies(implies(X_496,X_496),Z),implies(X_495,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_495)),bind(Y,$fot(implies(X_496,X_496)))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(not(X_35),implies(implies(not(X_493),X_493),X_493)),implies(X_493,X_493)))
| is_a_theorem(implies(X_35,implies(X_493,X_493))) ),
inference(subst,[],[refute_0_38:[bind(X_34,$fot(implies(implies(not(X_493),X_493),X_493))),bind(X_36,$fot(implies(X_493,X_493)))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),Y),X_31),implies(X_29,X_31)))
| is_a_theorem(implies(implies(not(implies(implies(not(X_29),Y),X_31)),implies(implies(not(X_29),Y),X_31)),implies(X_29,X_31))) ),
inference(subst,[],[refute_0_60:[bind(X_32,$fot(implies(implies(not(X_29),Y),X_31))),bind(X_33,$fot(implies(X_29,X_31)))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(not(implies(implies(not(X_29),Y),X_31)),implies(implies(not(X_29),Y),X_31)),implies(X_29,X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),Y),X_31),implies(X_29,X_31))) )],[refute_0_36,refute_0_82]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(implies(not(implies(implies(not(X_483),X_483),X_483)),implies(implies(not(X_483),X_483),X_483)),implies(X_483,X_483))),
inference(subst,[],[refute_0_83:[bind(Y,$fot(X_483)),bind(X_29,$fot(X_483)),bind(X_31,$fot(X_483))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_66),X_66),X_66)),X_68),X_65),implies(implies(X_67,X_68),X_65)))
| ~ is_a_theorem(implies(implies(not(implies(implies(not(X_66),X_66),X_66)),X_68),X_65))
| is_a_theorem(implies(implies(X_67,X_68),X_65)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(implies(not(X_66),X_66),X_66)),X_68),X_65))),bind(Y,$fot(implies(implies(X_67,X_68),X_65)))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(implies(X_46,X_47),implies(not(implies(implies(not(X_45),X_45),X_45)),X_47)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_45),X_45),X_45)),X_47),Z),implies(implies(X_46,X_47),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_46,X_47))),bind(Y,$fot(implies(not(implies(implies(not(X_45),X_45),X_45)),X_47)))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_43:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_87]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_30)),
inference(subst,[],[refute_0_88:[bind(X_9,$fot(X_30))]]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_30))
| is_a_theorem(implies(implies(X_30,X_31),implies(not(implies(implies(not(X),X),X)),X_31))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(X_30,X_31),implies(not(implies(implies(not(X),X),X)),X_31))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_30)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(X_46,X_47),implies(not(implies(implies(not(X_45),X_45),X_45)),X_47))),
inference(subst,[],[refute_0_91:[bind(X,$fot(X_45)),bind(X_30,$fot(X_46)),bind(X_31,$fot(X_47))]]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_45),X_45),X_45)),X_47),Z),implies(implies(X_46,X_47),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_46,X_47),implies(not(implies(implies(not(X_45),X_45),X_45)),X_47))) )],[refute_0_92,refute_0_86]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_66),X_66),X_66)),X_68),X_65),implies(implies(X_67,X_68),X_65))),
inference(subst,[],[refute_0_93:[bind(Z,$fot(X_65)),bind(X_45,$fot(X_66)),bind(X_46,$fot(X_67)),bind(X_47,$fot(X_68))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_66),X_66),X_66)),X_68),X_65))
| is_a_theorem(implies(implies(X_67,X_68),X_65)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_66),X_66),X_66)),X_68),X_65),implies(implies(X_67,X_68),X_65))) )],[refute_0_94,refute_0_85]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_483),X_483),X_483)),implies(implies(not(X_483),X_483),X_483)),implies(X_483,X_483)))
| is_a_theorem(implies(implies(X_484,implies(implies(not(X_483),X_483),X_483)),implies(X_483,X_483))) ),
inference(subst,[],[refute_0_95:[bind(X_65,$fot(implies(X_483,X_483))),bind(X_66,$fot(X_483)),bind(X_67,$fot(X_484)),bind(X_68,$fot(implies(implies(not(X_483),X_483),X_483)))]]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(X_484,implies(implies(not(X_483),X_483),X_483)),implies(X_483,X_483))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(not(X_483),X_483),X_483)),implies(implies(not(X_483),X_483),X_483)),implies(X_483,X_483))) )],[refute_0_84,refute_0_96]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(not(X_35),implies(implies(not(X_493),X_493),X_493)),implies(X_493,X_493))),
inference(subst,[],[refute_0_97:[bind(X_483,$fot(X_493)),bind(X_484,$fot(not(X_35)))]]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(X_35,implies(X_493,X_493))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_35),implies(implies(not(X_493),X_493),X_493)),implies(X_493,X_493))) )],[refute_0_98,refute_0_81]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(X_495,implies(X_496,X_496))),
inference(subst,[],[refute_0_99:[bind(X_35,$fot(X_495)),bind(X_493,$fot(X_496))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(implies(X_496,X_496),Z),implies(X_495,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_495,implies(X_496,X_496))) )],[refute_0_100,refute_0_80]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(implies(implies(X_502,X_502),X_500),implies(X_501,X_500))),
inference(subst,[],[refute_0_101:[bind(Z,$fot(X_500)),bind(X_495,$fot(X_501)),bind(X_496,$fot(X_502))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(implies(X_501,X_500),Z),implies(implies(implies(X_502,X_502),X_500),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_502,X_502),X_500),implies(X_501,X_500))) )],[refute_0_102,refute_0_79]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(implies(implies(not(X_4071),X_4071),X_4070),implies(implies(implies(X_4073,X_4073),X_4071),X_4070))),
inference(subst,[],[refute_0_103:[bind(Z,$fot(X_4070)),bind(X_500,$fot(X_4071)),bind(X_501,$fot(not(X_4071))),bind(X_502,$fot(X_4073))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(implies(X_4071,X_4070),implies(implies(implies(X_4073,X_4073),X_4071),X_4070))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_4071),X_4071),X_4070),implies(implies(implies(X_4073,X_4073),X_4071),X_4070))) )],[refute_0_104,refute_0_78]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(implies(X_4079,X_4078),implies(implies(implies(X_4080,X_4080),X_4079),X_4078))),
inference(subst,[],[refute_0_105:[bind(X_4070,$fot(X_4078)),bind(X_4071,$fot(X_4079)),bind(X_4073,$fot(X_4080))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(implies(not(implies(X_4079,X_4078)),implies(X_4079,X_4078)),implies(implies(implies(X_4080,X_4080),X_4079),X_4078))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_4079,X_4078),implies(implies(implies(X_4080,X_4080),X_4079),X_4078))) )],[refute_0_106,refute_0_77]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(implies(not(implies(X_4130,X_4130)),implies(X_4130,X_4130)),implies(implies(implies(X_4132,X_4132),X_4130),X_4130))),
inference(subst,[],[refute_0_107:[bind(X_4078,$fot(X_4130)),bind(X_4079,$fot(X_4130)),bind(X_4080,$fot(X_4132))]]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(X_825,implies(implies(implies(X_4132,X_4132),X_4130),X_4130))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(X_4130,X_4130)),implies(X_4130,X_4130)),implies(implies(implies(X_4132,X_4132),X_4130),X_4130))) )],[refute_0_108,refute_0_76]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(X_4134,X_4134),X_4133),X_4133))),X_1601),implies(implies(implies(X_4134,X_4134),X_4133),X_4133))),
inference(subst,[],[refute_0_109:[bind(X_4130,$fot(X_4133)),bind(X_4132,$fot(X_4134)),bind(X_825,$fot(implies(not(not(implies(implies(implies(X_4134,X_4134),X_4133),X_4133))),X_1601)))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(implies(X_4134,X_4134),X_4133),X_4133)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(X_4134,X_4134),X_4133),X_4133))),X_1601),implies(implies(implies(X_4134,X_4134),X_4133),X_4133))) )],[refute_0_110,refute_0_75]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(implies(X_4137,X_4137),X_4136),X_4136)),
inference(subst,[],[refute_0_111:[bind(X_4133,$fot(X_4136)),bind(X_4134,$fot(X_4137))]]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(implies(implies(not(X_4137),X_4137),X_4137),X_4136),X_4136)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_4137,X_4137),X_4136),X_4136)) )],[refute_0_112,refute_0_25]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(implies(implies(not(X_4139),X_4139),X_4139),implies(X_41,X_4139)),implies(X_41,X_4139))),
inference(subst,[],[refute_0_113:[bind(X_4136,$fot(implies(X_41,X_4139))),bind(X_4137,$fot(X_4139))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(X_41,implies(not(X_4139),X_4139)),implies(X_41,X_4139))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_4139),X_4139),X_4139),implies(X_41,X_4139)),implies(X_41,X_4139))) )],[refute_0_114,refute_0_19]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(X_4140,implies(not(X_4141),X_4141)),implies(X_4140,X_4141))),
inference(subst,[],[refute_0_115:[bind(X_41,$fot(X_4140)),bind(X_4139,$fot(X_4141))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(X_4140,implies(not(X_4141),X_4141)))
| is_a_theorem(implies(X_4140,X_4141)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_4140,implies(not(X_4141),X_4141)),implies(X_4140,X_4141))) )],[refute_0_116,refute_0_18]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(implies(implies(X_21405,implies(X_21403,X_21404)),X_21403),implies(not(X_21403),X_21403)))
| is_a_theorem(implies(implies(implies(X_21405,implies(X_21403,X_21404)),X_21403),X_21403)) ),
inference(subst,[],[refute_0_117:[bind(X_4140,$fot(implies(implies(X_21405,implies(X_21403,X_21404)),X_21403))),bind(X_4141,$fot(X_21403))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(not(X_21390),implies(X_21389,implies(X_21390,X_21388))))
| is_a_theorem(implies(implies(implies(X_21389,implies(X_21390,X_21388)),Z),implies(not(X_21390),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(X_21390))),bind(Y,$fot(implies(X_21389,implies(X_21390,X_21388))))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(not(not(X_21387)),not(X_21387)),implies(X_21386,implies(X_21387,X_21385))))
| is_a_theorem(implies(not(X_21387),implies(X_21386,implies(X_21387,X_21385)))) ),
inference(subst,[],[refute_0_38:[bind(X_34,$fot(not(X_21387))),bind(X_35,$fot(not(X_21387))),bind(X_36,$fot(implies(X_21386,implies(X_21387,X_21385))))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_21384),not(X_21384)),implies(not(not(X_21384)),not(X_21384))),implies(X_21383,implies(X_21384,X_21381))))
| is_a_theorem(implies(implies(not(not(X_21384)),not(X_21384)),implies(X_21383,implies(X_21384,X_21381)))) ),
inference(subst,[],[refute_0_6:[bind(X_41,$fot(not(not(X_21384)))),bind(X_42,$fot(not(X_21384))),bind(X_43,$fot(not(X_21384))),bind(X_44,$fot(implies(X_21383,implies(X_21384,X_21381))))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_21380)),not(X_21380)),X_21376),implies(implies(X_21377,X_21377),X_21376)),implies(X_21378,implies(X_21380,X_21376))))
| is_a_theorem(implies(implies(implies(X_21377,X_21377),implies(not(not(X_21380)),not(X_21380))),implies(X_21378,implies(X_21380,X_21376)))) ),
inference(subst,[],[refute_0_6:[bind(X_41,$fot(implies(X_21377,X_21377))),bind(X_42,$fot(implies(not(not(X_21380)),not(X_21380)))),bind(X_43,$fot(X_21376)),bind(X_44,$fot(implies(X_21378,implies(X_21380,X_21376))))]]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_21375),X_21374),implies(implies(X_21372,X_21372),X_21371)),implies(X_21373,implies(X_21375,X_21371))))
| is_a_theorem(implies(implies(implies(implies(not(not(X_21375)),not(X_21375)),X_21374),implies(implies(X_21372,X_21372),X_21371)),implies(X_21373,implies(X_21375,X_21371)))) ),
inference(subst,[],[refute_0_24:[bind(X_743,$fot(implies(X_21373,implies(X_21375,X_21371)))),bind(X_744,$fot(implies(implies(X_21372,X_21372),X_21371))),bind(X_745,$fot(not(X_21375))),bind(X_746,$fot(X_21374))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_4166,X_4166),X_4165),X_4165),implies(X_41,X_4165)),implies(X_4167,implies(X_41,X_4165))))
| is_a_theorem(implies(implies(X_41,implies(implies(X_4166,X_4166),X_4165)),implies(X_4167,implies(X_41,X_4165)))) ),
inference(subst,[],[refute_0_6:[bind(X_42,$fot(implies(implies(X_4166,X_4166),X_4165))),bind(X_43,$fot(X_4165)),bind(X_44,$fot(implies(X_4167,implies(X_41,X_4165))))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(X_4135,implies(implies(implies(X_4134,X_4134),X_4133),X_4133)))
| is_a_theorem(implies(implies(implies(implies(implies(X_4134,X_4134),X_4133),X_4133),Z),implies(X_4135,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_4135)),bind(Y,$fot(implies(implies(implies(X_4134,X_4134),X_4133),X_4133)))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(X_4135,implies(implies(implies(X_4134,X_4134),X_4133),X_4133))),
inference(subst,[],[refute_0_109:[bind(X_4130,$fot(X_4133)),bind(X_4132,$fot(X_4134)),bind(X_825,$fot(X_4135))]]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_4134,X_4134),X_4133),X_4133),Z),implies(X_4135,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_4135,implies(implies(implies(X_4134,X_4134),X_4133),X_4133))) )],[refute_0_126,refute_0_125]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_4166,X_4166),X_4165),X_4165),implies(X_41,X_4165)),implies(X_4167,implies(X_41,X_4165)))),
inference(subst,[],[refute_0_127:[bind(Z,$fot(implies(X_41,X_4165))),bind(X_4133,$fot(X_4165)),bind(X_4134,$fot(X_4166)),bind(X_4135,$fot(X_4167))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_41,implies(implies(X_4166,X_4166),X_4165)),implies(X_4167,implies(X_41,X_4165)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_4166,X_4166),X_4165),X_4165),implies(X_41,X_4165)),implies(X_4167,implies(X_41,X_4165)))) )],[refute_0_128,refute_0_124]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(X_6851,implies(implies(X_4166,X_4166),X_4165)),implies(X_4167,implies(X_6851,X_4165)))),
inference(subst,[],[refute_0_129:[bind(X_41,$fot(X_6851))]]) ).
cnf(refute_0_131,plain,
( ~ is_a_theorem(implies(implies(X_54,X_55),X_52))
| ~ is_a_theorem(implies(implies(implies(X_54,X_55),X_52),implies(implies(implies(not(X_54),X_53),X_55),X_52)))
| is_a_theorem(implies(implies(implies(not(X_54),X_53),X_55),X_52)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_54,X_55),X_52))),bind(Y,$fot(implies(implies(implies(not(X_54),X_53),X_55),X_52)))]]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(implies(X_54,X_55),X_52),implies(implies(implies(not(X_54),X_53),X_55),X_52))),
inference(subst,[],[refute_0_63:[bind(Z,$fot(X_52)),bind(X_34,$fot(X_53)),bind(X_35,$fot(X_54)),bind(X_36,$fot(X_55))]]) ).
cnf(refute_0_133,plain,
( ~ is_a_theorem(implies(implies(X_54,X_55),X_52))
| is_a_theorem(implies(implies(implies(not(X_54),X_53),X_55),X_52)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_54,X_55),X_52),implies(implies(implies(not(X_54),X_53),X_55),X_52))) )],[refute_0_132,refute_0_131]) ).
cnf(refute_0_134,plain,
( ~ is_a_theorem(implies(implies(X_6851,implies(implies(X_4166,X_4166),X_4165)),implies(X_4167,implies(X_6851,X_4165))))
| is_a_theorem(implies(implies(implies(not(X_6851),X_6850),implies(implies(X_4166,X_4166),X_4165)),implies(X_4167,implies(X_6851,X_4165)))) ),
inference(subst,[],[refute_0_133:[bind(X_52,$fot(implies(X_4167,implies(X_6851,X_4165)))),bind(X_53,$fot(X_6850)),bind(X_54,$fot(X_6851)),bind(X_55,$fot(implies(implies(X_4166,X_4166),X_4165)))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(implies(not(X_6851),X_6850),implies(implies(X_4166,X_4166),X_4165)),implies(X_4167,implies(X_6851,X_4165)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_6851,implies(implies(X_4166,X_4166),X_4165)),implies(X_4167,implies(X_6851,X_4165)))) )],[refute_0_130,refute_0_134]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(implies(implies(not(X_21375),X_21374),implies(implies(X_21372,X_21372),X_21371)),implies(X_21373,implies(X_21375,X_21371)))),
inference(subst,[],[refute_0_135:[bind(X_4165,$fot(X_21371)),bind(X_4166,$fot(X_21372)),bind(X_4167,$fot(X_21373)),bind(X_6850,$fot(X_21374)),bind(X_6851,$fot(X_21375))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_21375)),not(X_21375)),X_21374),implies(implies(X_21372,X_21372),X_21371)),implies(X_21373,implies(X_21375,X_21371)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_21375),X_21374),implies(implies(X_21372,X_21372),X_21371)),implies(X_21373,implies(X_21375,X_21371)))) )],[refute_0_136,refute_0_123]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_21380)),not(X_21380)),X_21376),implies(implies(X_21377,X_21377),X_21376)),implies(X_21378,implies(X_21380,X_21376)))),
inference(subst,[],[refute_0_137:[bind(X_21371,$fot(X_21376)),bind(X_21372,$fot(X_21377)),bind(X_21373,$fot(X_21378)),bind(X_21374,$fot(X_21376)),bind(X_21375,$fot(X_21380))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(implies(implies(X_21377,X_21377),implies(not(not(X_21380)),not(X_21380))),implies(X_21378,implies(X_21380,X_21376)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_21380)),not(X_21380)),X_21376),implies(implies(X_21377,X_21377),X_21376)),implies(X_21378,implies(X_21380,X_21376)))) )],[refute_0_138,refute_0_122]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(implies(implies(not(X_21384),not(X_21384)),implies(not(not(X_21384)),not(X_21384))),implies(X_21383,implies(X_21384,X_21381)))),
inference(subst,[],[refute_0_139:[bind(X_21376,$fot(X_21381)),bind(X_21377,$fot(not(X_21384))),bind(X_21378,$fot(X_21383)),bind(X_21380,$fot(X_21384))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(implies(not(not(X_21384)),not(X_21384)),implies(X_21383,implies(X_21384,X_21381)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_21384),not(X_21384)),implies(not(not(X_21384)),not(X_21384))),implies(X_21383,implies(X_21384,X_21381)))) )],[refute_0_140,refute_0_121]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(implies(not(not(X_21387)),not(X_21387)),implies(X_21386,implies(X_21387,X_21385)))),
inference(subst,[],[refute_0_141:[bind(X_21381,$fot(X_21385)),bind(X_21383,$fot(X_21386)),bind(X_21384,$fot(X_21387))]]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(not(X_21387),implies(X_21386,implies(X_21387,X_21385)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_21387)),not(X_21387)),implies(X_21386,implies(X_21387,X_21385)))) )],[refute_0_142,refute_0_120]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(not(X_21390),implies(X_21389,implies(X_21390,X_21388)))),
inference(subst,[],[refute_0_143:[bind(X_21385,$fot(X_21388)),bind(X_21386,$fot(X_21389)),bind(X_21387,$fot(X_21390))]]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(implies(implies(X_21389,implies(X_21390,X_21388)),Z),implies(not(X_21390),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_21390),implies(X_21389,implies(X_21390,X_21388)))) )],[refute_0_144,refute_0_119]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(implies(X_21405,implies(X_21403,X_21404)),X_21403),implies(not(X_21403),X_21403))),
inference(subst,[],[refute_0_145:[bind(Z,$fot(X_21403)),bind(X_21388,$fot(X_21404)),bind(X_21389,$fot(X_21405)),bind(X_21390,$fot(X_21403))]]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(implies(X_21405,implies(X_21403,X_21404)),X_21403),X_21403)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_21405,implies(X_21403,X_21404)),X_21403),implies(not(X_21403),X_21403))) )],[refute_0_146,refute_0_118]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(implies(not(implies(X_21407,X_21408)),implies(X_21407,X_21408)),X_21407),X_21407)),
inference(subst,[],[refute_0_147:[bind(X_21403,$fot(X_21407)),bind(X_21404,$fot(X_21408)),bind(X_21405,$fot(not(implies(X_21407,X_21408))))]]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(implies(implies(X_21407,X_21408),X_21407),X_21407)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_21407,X_21408)),implies(X_21407,X_21408)),X_21407),X_21407)) )],[refute_0_148,refute_0_17]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(implies(implies(implies(X_41,X_21411),X_21411),implies(X_41,X_21411)),implies(X_41,X_21411))),
inference(subst,[],[refute_0_149:[bind(X_21407,$fot(implies(X_41,X_21411))),bind(X_21408,$fot(X_21411))]]) ).
cnf(refute_0_151,plain,
is_a_theorem(implies(implies(X_41,implies(X_41,X_21411)),implies(X_41,X_21411))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_41,X_21411),X_21411),implies(X_41,X_21411)),implies(X_41,X_21411))) )],[refute_0_150,refute_0_7]) ).
cnf(refute_0_152,plain,
is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))),
inference(subst,[],[refute_0_151:[bind(X_21411,$fot(b)),bind(X_41,$fot(a))]]) ).
cnf(refute_0_153,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))) )],[refute_0_152,prove_cn_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL053-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.30 % Computer : n004.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Sat Jul 2 11:28:08 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 18.45/18.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.45/18.62
% 18.45/18.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.45/18.64
%------------------------------------------------------------------------------