TSTP Solution File: LCL378-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL378-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:51:50 EDT 2022
% Result : Unsatisfiable 4.36s 4.58s
% Output : CNFRefutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 5
% Syntax : Number of clauses : 157 ( 93 unt; 0 nHn; 44 RR)
% Number of literals : 233 ( 0 equ; 77 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 372 ( 62 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_36,negated_conjecture,
~ is_a_theorem(implies(not(x),implies(x,y))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_34),X_33),X_35),implies(X_34,X_35)))
| ~ is_a_theorem(implies(implies(not(X_34),X_33),X_35))
| is_a_theorem(implies(X_34,X_35)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_34),X_33),X_35))),bind(Y,$fot(implies(X_34,X_35)))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_25,implies(not(X_25),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(X_25,implies(not(X_25),Y)))
| is_a_theorem(implies(implies(implies(not(X_25),Y),X_27),implies(X_25,X_27))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_25)),bind(Y,$fot(implies(not(X_25),Y))),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(implies(not(X_25),Y),X_27),implies(X_25,X_27))),
inference(resolve,[$cnf( is_a_theorem(implies(X_25,implies(not(X_25),Y))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(not(X_34),X_33),X_35),implies(X_34,X_35))),
inference(subst,[],[refute_0_5:[bind(Y,$fot(X_33)),bind(X_25,$fot(X_34)),bind(X_27,$fot(X_35))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(not(X_34),X_33),X_35))
| is_a_theorem(implies(X_34,X_35)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_34),X_33),X_35),implies(X_34,X_35))) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(not(not(X_6073)),X_6072),implies(X_6073,X_6072)))
| is_a_theorem(implies(not(X_6073),implies(X_6073,X_6072))) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(X_6072)),bind(X_34,$fot(not(X_6073))),bind(X_35,$fot(implies(X_6073,X_6072)))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(X_5910,not(not(X_5910))))
| is_a_theorem(implies(implies(not(not(X_5910)),Z),implies(X_5910,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_5910)),bind(Y,$fot(not(not(X_5910))))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(not(X_1927),not(X_1926)),implies(X_1926,X_1927)))
| ~ is_a_theorem(implies(not(X_1927),not(X_1926)))
| is_a_theorem(implies(X_1926,X_1927)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_1927),not(X_1926)))),bind(Y,$fot(implies(X_1926,X_1927)))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(implies(X_83,X_84),implies(X_82,X_84)),X_85))
| ~ is_a_theorem(implies(implies(implies(implies(X_83,X_84),implies(X_82,X_84)),X_85),implies(implies(X_82,X_83),X_85)))
| is_a_theorem(implies(implies(X_82,X_83),X_85)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_83,X_84),implies(X_82,X_84)),X_85))),bind(Y,$fot(implies(implies(X_82,X_83),X_85)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_27),implies(implies(X,Y),X_27))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_27),implies(implies(X,Y),X_27))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(implies(X_83,X_84),implies(X_82,X_84)),X_85),implies(implies(X_82,X_83),X_85))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(X_84)),bind(X_27,$fot(X_85))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(X_83,X_84),implies(X_82,X_84)),X_85))
| is_a_theorem(implies(implies(X_82,X_83),X_85)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_83,X_84),implies(X_82,X_84)),X_85),implies(implies(X_82,X_83),X_85))) )],[refute_0_14,refute_0_11]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1915),X_1916),implies(not(X_1916),X_1916)),implies(X_1915,X_1916)))
| is_a_theorem(implies(implies(not(X_1916),not(X_1915)),implies(X_1915,X_1916))) ),
inference(subst,[],[refute_0_15:[bind(X_82,$fot(not(X_1916))),bind(X_83,$fot(not(X_1915))),bind(X_84,$fot(X_1916)),bind(X_85,$fot(implies(X_1915,X_1916)))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(X_45,X_46),X_43))
| ~ is_a_theorem(implies(implies(implies(X_45,X_46),X_43),implies(implies(implies(not(X_45),X_44),X_46),X_43)))
| is_a_theorem(implies(implies(implies(not(X_45),X_44),X_46),X_43)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_45,X_46),X_43))),bind(Y,$fot(implies(implies(implies(not(X_45),X_44),X_46),X_43)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_34),X_33),X_35),implies(X_34,X_35)))
| is_a_theorem(implies(implies(implies(X_34,X_35),Z),implies(implies(implies(not(X_34),X_33),X_35),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(X_34),X_33),X_35))),bind(Y,$fot(implies(X_34,X_35)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(X_34,X_35),Z),implies(implies(implies(not(X_34),X_33),X_35),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_34),X_33),X_35),implies(X_34,X_35))) )],[refute_0_6,refute_0_18]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(implies(X_45,X_46),X_43),implies(implies(implies(not(X_45),X_44),X_46),X_43))),
inference(subst,[],[refute_0_19:[bind(Z,$fot(X_43)),bind(X_33,$fot(X_44)),bind(X_34,$fot(X_45)),bind(X_35,$fot(X_46))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(X_45,X_46),X_43))
| is_a_theorem(implies(implies(implies(not(X_45),X_44),X_46),X_43)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_45,X_46),X_43),implies(implies(implies(not(X_45),X_44),X_46),X_43))) )],[refute_0_20,refute_0_17]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(implies(X_1821,implies(not(X_1822),X_1822)),implies(X_1821,X_1822)))
| is_a_theorem(implies(implies(implies(not(X_1821),X_44),implies(not(X_1822),X_1822)),implies(X_1821,X_1822))) ),
inference(subst,[],[refute_0_21:[bind(X_43,$fot(implies(X_1821,X_1822))),bind(X_45,$fot(X_1821)),bind(X_46,$fot(implies(not(X_1822),X_1822)))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_52),X_52),X_53),X_51),implies(implies(X_52,X_53),X_51)))
| ~ is_a_theorem(implies(implies(implies(not(X_52),X_52),X_53),X_51))
| is_a_theorem(implies(implies(X_52,X_53),X_51)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_52),X_52),X_53),X_51))),bind(Y,$fot(implies(implies(X_52,X_53),X_51)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29)))
| is_a_theorem(implies(implies(implies(implies(not(X_28),X_28),X_29),Z),implies(implies(X_28,X_29),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(X_28,X_29))),bind(Y,$fot(implies(implies(not(X_28),X_28),X_29)))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(not(X_26),X_26),X_26)),
inference(subst,[],[cn_2:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(not(X_26),X_26),X_26))
| is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(not(X_26),X_26))),bind(Y,$fot(X_26)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_26),X_26),X_26)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))),
inference(subst,[],[refute_0_27:[bind(X_26,$fot(X_28)),bind(X_27,$fot(X_29))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(implies(implies(implies(not(X_28),X_28),X_29),Z),implies(implies(X_28,X_29),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_28,X_29),implies(implies(not(X_28),X_28),X_29))) )],[refute_0_28,refute_0_24]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(implies(implies(not(X_52),X_52),X_53),X_51),implies(implies(X_52,X_53),X_51))),
inference(subst,[],[refute_0_29:[bind(Z,$fot(X_51)),bind(X_28,$fot(X_52)),bind(X_29,$fot(X_53))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_52),X_52),X_53),X_51))
| is_a_theorem(implies(implies(X_52,X_53),X_51)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_52),X_52),X_53),X_51),implies(implies(X_52,X_53),X_51))) )],[refute_0_30,refute_0_23]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1579),X_1579),X_1579)),implies(implies(not(X_1579),X_1579),X_1579)),X_1578),X_1578))
| is_a_theorem(implies(implies(implies(implies(not(X_1579),X_1579),X_1579),X_1578),X_1578)) ),
inference(subst,[],[refute_0_31:[bind(X_51,$fot(X_1578)),bind(X_52,$fot(implies(implies(not(X_1579),X_1579),X_1579))),bind(X_53,$fot(X_1578))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(X_1284,X_1284),X_1285))
| ~ is_a_theorem(implies(implies(implies(X_1284,X_1284),X_1285),X_1285))
| is_a_theorem(X_1285) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1284,X_1284),X_1285))),bind(Y,$fot(X_1285))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_312)),X_313),X_312),X_312))
| ~ is_a_theorem(implies(implies(not(not(X_312)),X_313),X_312))
| is_a_theorem(X_312) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_312)),X_313),X_312))),bind(Y,$fot(X_312))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(implies(not(X_308),X_308),X_308)),
inference(subst,[],[cn_2:[bind(X,$fot(X_308))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(not(X_308),X_308),X_308))
| is_a_theorem(implies(implies(implies(not(not(X_308)),X_309),X_308),X_308)) ),
inference(subst,[],[refute_0_21:[bind(X_43,$fot(X_308)),bind(X_44,$fot(X_309)),bind(X_45,$fot(not(X_308))),bind(X_46,$fot(X_308))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(implies(not(not(X_308)),X_309),X_308),X_308)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_308),X_308),X_308)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(not(not(X_312)),X_313),X_312),X_312)),
inference(subst,[],[refute_0_37:[bind(X_308,$fot(X_312)),bind(X_309,$fot(X_313))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(not(not(X_312)),X_313),X_312))
| is_a_theorem(X_312) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_312)),X_313),X_312),X_312)) )],[refute_0_38,refute_0_34]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1281,X_1281),X_1282),X_1282))),X_313),implies(implies(implies(X_1281,X_1281),X_1282),X_1282)))
| is_a_theorem(implies(implies(implies(X_1281,X_1281),X_1282),X_1282)) ),
inference(subst,[],[refute_0_39:[bind(X_312,$fot(implies(implies(implies(X_1281,X_1281),X_1282),X_1282)))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1220),X_1220),X_1219),implies(implies(implies(X_1221,X_1221),X_1220),X_1219)))
| is_a_theorem(implies(implies(X_1220,X_1219),implies(implies(implies(X_1221,X_1221),X_1220),X_1219))) ),
inference(subst,[],[refute_0_31:[bind(X_51,$fot(implies(implies(implies(X_1221,X_1221),X_1220),X_1219))),bind(X_52,$fot(X_1220)),bind(X_53,$fot(X_1219))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(X_1006,X_1006),X_1005),implies(X_1007,X_1005)))
| is_a_theorem(implies(implies(implies(X_1007,X_1005),Z),implies(implies(implies(X_1006,X_1006),X_1005),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(X_1006,X_1006),X_1005))),bind(Y,$fot(implies(X_1007,X_1005)))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(X_144,implies(not(implies(X_143,X_143)),X_142)))
| is_a_theorem(implies(implies(implies(not(implies(X_143,X_143)),X_142),Z),implies(X_144,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_144)),bind(Y,$fot(implies(not(implies(X_143,X_143)),X_142)))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(implies(not(X_34),X_122),implies(not(implies(X_124,X_124)),X_122)))
| is_a_theorem(implies(X_34,implies(not(implies(X_124,X_124)),X_122))) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(X_122)),bind(X_35,$fot(implies(not(implies(X_124,X_124)),X_122)))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(not(implies(X_103,X_103)),X_102))
| is_a_theorem(implies(implies(X_102,Z),implies(not(implies(X_103,X_103)),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(X_103,X_103)))),bind(Y,$fot(X_102))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_47,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_48,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(X_101,X_101))
| is_a_theorem(implies(not(implies(X_101,X_101)),Y)) ),
inference(subst,[],[refute_0_48:[bind(X_6,$fot(implies(X_101,X_101)))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(not(X_100),X_100),X_100)),
inference(subst,[],[cn_2:[bind(X,$fot(X_100))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(not(X_100),X_100),X_100))
| is_a_theorem(implies(X_100,X_100)) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(X_100)),bind(X_34,$fot(X_100)),bind(X_35,$fot(X_100))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(X_100,X_100)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_100),X_100),X_100)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_101,X_101)),
inference(subst,[],[refute_0_52:[bind(X_100,$fot(X_101))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(not(implies(X_101,X_101)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_101,X_101)) )],[refute_0_53,refute_0_49]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(not(implies(X_103,X_103)),X_102)),
inference(subst,[],[refute_0_54:[bind(Y,$fot(X_102)),bind(X_101,$fot(X_103))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(X_102,Z),implies(not(implies(X_103,X_103)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_103,X_103)),X_102)) )],[refute_0_55,refute_0_45]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(not(X_34),X_122),implies(not(implies(X_124,X_124)),X_122))),
inference(subst,[],[refute_0_56:[bind(Z,$fot(X_122)),bind(X_102,$fot(not(X_34))),bind(X_103,$fot(X_124))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(X_34,implies(not(implies(X_124,X_124)),X_122))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_34),X_122),implies(not(implies(X_124,X_124)),X_122))) )],[refute_0_57,refute_0_44]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(X_144,implies(not(implies(X_143,X_143)),X_142))),
inference(subst,[],[refute_0_58:[bind(X_122,$fot(X_142)),bind(X_124,$fot(X_143)),bind(X_34,$fot(X_144))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(not(implies(X_143,X_143)),X_142),Z),implies(X_144,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_144,implies(not(implies(X_143,X_143)),X_142))) )],[refute_0_59,refute_0_43]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(not(implies(X_143,X_143)),implies(X_143,X_143)),X_1004),implies(X_144,X_1004))),
inference(subst,[],[refute_0_60:[bind(Z,$fot(X_1004)),bind(X_142,$fot(implies(X_143,X_143)))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_143,X_143)),implies(X_143,X_143)),X_1004),implies(X_144,X_1004)))
| is_a_theorem(implies(implies(implies(X_143,X_143),X_1004),implies(X_144,X_1004))) ),
inference(subst,[],[refute_0_31:[bind(X_51,$fot(implies(X_144,X_1004))),bind(X_52,$fot(implies(X_143,X_143))),bind(X_53,$fot(X_1004))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(implies(X_143,X_143),X_1004),implies(X_144,X_1004))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_143,X_143)),implies(X_143,X_143)),X_1004),implies(X_144,X_1004))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(implies(X_1006,X_1006),X_1005),implies(X_1007,X_1005))),
inference(subst,[],[refute_0_63:[bind(X_1004,$fot(X_1005)),bind(X_143,$fot(X_1006)),bind(X_144,$fot(X_1007))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(implies(X_1007,X_1005),Z),implies(implies(implies(X_1006,X_1006),X_1005),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1006,X_1006),X_1005),implies(X_1007,X_1005))) )],[refute_0_64,refute_0_42]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(not(X_1220),X_1220),X_1219),implies(implies(implies(X_1221,X_1221),X_1220),X_1219))),
inference(subst,[],[refute_0_65:[bind(Z,$fot(X_1219)),bind(X_1005,$fot(X_1220)),bind(X_1006,$fot(X_1221)),bind(X_1007,$fot(not(X_1220)))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(X_1220,X_1219),implies(implies(implies(X_1221,X_1221),X_1220),X_1219))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1220),X_1220),X_1219),implies(implies(implies(X_1221,X_1221),X_1220),X_1219))) )],[refute_0_66,refute_0_41]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(X_1253,X_1253),implies(implies(implies(X_1221,X_1221),X_1253),X_1253))),
inference(subst,[],[refute_0_67:[bind(X_1219,$fot(X_1253)),bind(X_1220,$fot(X_1253))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(implies(X_1006,X_1006),X_1005))
| ~ is_a_theorem(implies(implies(implies(X_1006,X_1006),X_1005),implies(X_1007,X_1005)))
| is_a_theorem(implies(X_1007,X_1005)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1006,X_1006),X_1005))),bind(Y,$fot(implies(X_1007,X_1005)))]]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(implies(implies(X_1006,X_1006),X_1005))
| is_a_theorem(implies(X_1007,X_1005)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1006,X_1006),X_1005),implies(X_1007,X_1005))) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(implies(X_1253,X_1253),implies(implies(implies(X_1221,X_1221),X_1253),X_1253)))
| is_a_theorem(implies(X_1254,implies(implies(implies(X_1221,X_1221),X_1253),X_1253))) ),
inference(subst,[],[refute_0_70:[bind(X_1005,$fot(implies(implies(implies(X_1221,X_1221),X_1253),X_1253))),bind(X_1006,$fot(X_1253)),bind(X_1007,$fot(X_1254))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(X_1254,implies(implies(implies(X_1221,X_1221),X_1253),X_1253))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1253,X_1253),implies(implies(implies(X_1221,X_1221),X_1253),X_1253))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1281,X_1281),X_1282),X_1282))),X_313),implies(implies(implies(X_1281,X_1281),X_1282),X_1282))),
inference(subst,[],[refute_0_72:[bind(X_1221,$fot(X_1281)),bind(X_1253,$fot(X_1282)),bind(X_1254,$fot(implies(not(not(implies(implies(implies(X_1281,X_1281),X_1282),X_1282))),X_313)))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(implies(X_1281,X_1281),X_1282),X_1282)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1281,X_1281),X_1282),X_1282))),X_313),implies(implies(implies(X_1281,X_1281),X_1282),X_1282))) )],[refute_0_73,refute_0_40]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(implies(X_1284,X_1284),X_1285),X_1285)),
inference(subst,[],[refute_0_74:[bind(X_1281,$fot(X_1284)),bind(X_1282,$fot(X_1285))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(X_1284,X_1284),X_1285))
| is_a_theorem(X_1285) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1284,X_1284),X_1285),X_1285)) )],[refute_0_75,refute_0_33]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(X_1570,X_1570),implies(implies(implies(not(implies(implies(not(X_1572),X_1572),X_1572)),X_1573),X_1570),X_1570)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1572),X_1572),X_1572)),X_1573),X_1570),X_1570)) ),
inference(subst,[],[refute_0_76:[bind(X_1284,$fot(X_1570)),bind(X_1285,$fot(implies(implies(implies(not(implies(implies(not(X_1572),X_1572),X_1572)),X_1573),X_1570),X_1570)))]]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1566),X_1566),X_1565),implies(implies(implies(not(implies(implies(not(X_1567),X_1567),X_1567)),X_1568),X_1566),X_1565)))
| is_a_theorem(implies(implies(X_1566,X_1565),implies(implies(implies(not(implies(implies(not(X_1567),X_1567),X_1567)),X_1568),X_1566),X_1565))) ),
inference(subst,[],[refute_0_31:[bind(X_51,$fot(implies(implies(implies(not(implies(implies(not(X_1567),X_1567),X_1567)),X_1568),X_1566),X_1565))),bind(X_52,$fot(X_1566)),bind(X_53,$fot(X_1565))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_146),X_146),X_146)),X_147),X_145),implies(X_148,X_145)))
| is_a_theorem(implies(implies(implies(X_148,X_145),Z),implies(implies(implies(not(implies(implies(not(X_146),X_146),X_146)),X_147),X_145),Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(implies(implies(not(implies(implies(not(X_146),X_146),X_146)),X_147),X_145))),bind(Y,$fot(implies(X_148,X_145)))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(X_137,implies(not(implies(implies(not(X_135),X_135),X_135)),X_136)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_135),X_135),X_135)),X_136),Z),implies(X_137,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_137)),bind(Y,$fot(implies(not(implies(implies(not(X_135),X_135),X_135)),X_136)))]]) ).
cnf(refute_0_81,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_48:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_26)),
inference(subst,[],[refute_0_82:[bind(X_9,$fot(X_26))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_26))
| is_a_theorem(implies(implies(X_26,X_27),implies(not(implies(implies(not(X),X),X)),X_27))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_26)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(X_26,X_27),implies(not(implies(implies(not(X),X),X)),X_27))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_26)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(not(X_99),X_98),implies(not(implies(implies(not(X),X),X)),X_98))),
inference(subst,[],[refute_0_85:[bind(X_26,$fot(not(X_99))),bind(X_27,$fot(X_98))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(not(X_99),X_98),implies(not(implies(implies(not(X),X),X)),X_98)))
| is_a_theorem(implies(X_99,implies(not(implies(implies(not(X),X),X)),X_98))) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(X_98)),bind(X_34,$fot(X_99)),bind(X_35,$fot(implies(not(implies(implies(not(X),X),X)),X_98)))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(X_99,implies(not(implies(implies(not(X),X),X)),X_98))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_99),X_98),implies(not(implies(implies(not(X),X),X)),X_98))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(X_137,implies(not(implies(implies(not(X_135),X_135),X_135)),X_136))),
inference(subst,[],[refute_0_88:[bind(X,$fot(X_135)),bind(X_98,$fot(X_136)),bind(X_99,$fot(X_137))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_135),X_135),X_135)),X_136),Z),implies(X_137,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_137,implies(not(implies(implies(not(X_135),X_135),X_135)),X_136))) )],[refute_0_89,refute_0_80]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_146),X_146),X_146)),X_147),X_145),implies(X_148,X_145))),
inference(subst,[],[refute_0_90:[bind(Z,$fot(X_145)),bind(X_135,$fot(X_146)),bind(X_136,$fot(X_147)),bind(X_137,$fot(X_148))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(implies(X_148,X_145),Z),implies(implies(implies(not(implies(implies(not(X_146),X_146),X_146)),X_147),X_145),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_146),X_146),X_146)),X_147),X_145),implies(X_148,X_145))) )],[refute_0_91,refute_0_79]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(implies(not(X_1566),X_1566),X_1565),implies(implies(implies(not(implies(implies(not(X_1567),X_1567),X_1567)),X_1568),X_1566),X_1565))),
inference(subst,[],[refute_0_92:[bind(Z,$fot(X_1565)),bind(X_145,$fot(X_1566)),bind(X_146,$fot(X_1567)),bind(X_147,$fot(X_1568)),bind(X_148,$fot(not(X_1566)))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(X_1566,X_1565),implies(implies(implies(not(implies(implies(not(X_1567),X_1567),X_1567)),X_1568),X_1566),X_1565))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1566),X_1566),X_1565),implies(implies(implies(not(implies(implies(not(X_1567),X_1567),X_1567)),X_1568),X_1566),X_1565))) )],[refute_0_93,refute_0_78]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(implies(X_1570,X_1570),implies(implies(implies(not(implies(implies(not(X_1572),X_1572),X_1572)),X_1573),X_1570),X_1570))),
inference(subst,[],[refute_0_94:[bind(X_1565,$fot(X_1570)),bind(X_1566,$fot(X_1570)),bind(X_1567,$fot(X_1572)),bind(X_1568,$fot(X_1573))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1572),X_1572),X_1572)),X_1573),X_1570),X_1570)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1570,X_1570),implies(implies(implies(not(implies(implies(not(X_1572),X_1572),X_1572)),X_1573),X_1570),X_1570))) )],[refute_0_95,refute_0_77]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1579),X_1579),X_1579)),implies(implies(not(X_1579),X_1579),X_1579)),X_1578),X_1578)),
inference(subst,[],[refute_0_96:[bind(X_1570,$fot(X_1578)),bind(X_1572,$fot(X_1579)),bind(X_1573,$fot(implies(implies(not(X_1579),X_1579),X_1579)))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1579),X_1579),X_1579),X_1578),X_1578)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1579),X_1579),X_1579)),implies(implies(not(X_1579),X_1579),X_1579)),X_1578),X_1578)) )],[refute_0_97,refute_0_32]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1816),X_1816),X_1816),implies(X_1814,X_1816)),implies(X_1814,X_1816))),
inference(subst,[],[refute_0_98:[bind(X_1578,$fot(implies(X_1814,X_1816))),bind(X_1579,$fot(X_1816))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_1816),X_1816),X_1816),implies(X_1814,X_1816)),implies(X_1814,X_1816)))
| is_a_theorem(implies(implies(X_1814,implies(not(X_1816),X_1816)),implies(X_1814,X_1816))) ),
inference(subst,[],[refute_0_15:[bind(X_82,$fot(X_1814)),bind(X_83,$fot(implies(not(X_1816),X_1816))),bind(X_84,$fot(X_1816)),bind(X_85,$fot(implies(X_1814,X_1816)))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(X_1814,implies(not(X_1816),X_1816)),implies(X_1814,X_1816))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_1816),X_1816),X_1816),implies(X_1814,X_1816)),implies(X_1814,X_1816))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(implies(X_1821,implies(not(X_1822),X_1822)),implies(X_1821,X_1822))),
inference(subst,[],[refute_0_101:[bind(X_1814,$fot(X_1821)),bind(X_1816,$fot(X_1822))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(implies(not(X_1821),X_44),implies(not(X_1822),X_1822)),implies(X_1821,X_1822))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1821,implies(not(X_1822),X_1822)),implies(X_1821,X_1822))) )],[refute_0_102,refute_0_22]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(implies(implies(not(X_1915),X_1916),implies(not(X_1916),X_1916)),implies(X_1915,X_1916))),
inference(subst,[],[refute_0_103:[bind(X_1821,$fot(X_1915)),bind(X_1822,$fot(X_1916)),bind(X_44,$fot(X_1916))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(implies(not(X_1916),not(X_1915)),implies(X_1915,X_1916))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1915),X_1916),implies(not(X_1916),X_1916)),implies(X_1915,X_1916))) )],[refute_0_104,refute_0_16]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(implies(not(X_1927),not(X_1926)),implies(X_1926,X_1927))),
inference(subst,[],[refute_0_105:[bind(X_1915,$fot(X_1926)),bind(X_1916,$fot(X_1927))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(not(X_1927),not(X_1926)))
| is_a_theorem(implies(X_1926,X_1927)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_1927),not(X_1926)),implies(X_1926,X_1927))) )],[refute_0_106,refute_0_10]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(not(not(not(X_1926))),not(X_1926)))
| is_a_theorem(implies(X_1926,not(not(X_1926)))) ),
inference(subst,[],[refute_0_107:[bind(X_1927,$fot(not(not(X_1926))))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(implies(not(not(not(X_5908))),not(not(X_5908))),X_5908))
| is_a_theorem(implies(not(not(X_5908)),X_5908)) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(not(not(X_5908)))),bind(X_34,$fot(not(not(X_5908)))),bind(X_35,$fot(X_5908))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(not(X_1927),not(implies(not(not(not(X_1927))),not(not(X_1927))))))
| is_a_theorem(implies(implies(not(not(not(X_1927))),not(not(X_1927))),X_1927)) ),
inference(subst,[],[refute_0_107:[bind(X_1926,$fot(implies(not(not(not(X_1927))),not(not(X_1927)))))]]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(implies(not(not(implies(not(not(X_1926)),not(X_1926)))),not(X_1926)))
| is_a_theorem(implies(X_1926,not(implies(not(not(X_1926)),not(X_1926))))) ),
inference(subst,[],[refute_0_107:[bind(X_1927,$fot(not(implies(not(not(X_1926)),not(X_1926)))))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(implies(implies(not(not(not(implies(not(X_5903),X_5903)))),not(not(X_5903))),X_5903))
| is_a_theorem(implies(not(not(implies(not(X_5903),X_5903))),X_5903)) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(not(not(X_5903)))),bind(X_34,$fot(not(not(implies(not(X_5903),X_5903))))),bind(X_35,$fot(X_5903))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_5902)),not(not(implies(not(X_5902),X_5902)))),implies(not(not(not(implies(not(X_5902),X_5902)))),not(not(implies(not(X_5902),X_5902))))),X_5902))
| is_a_theorem(implies(implies(not(not(not(implies(not(X_5902),X_5902)))),not(not(X_5902))),X_5902)) ),
inference(subst,[],[refute_0_15:[bind(X_82,$fot(not(not(not(implies(not(X_5902),X_5902)))))),bind(X_83,$fot(not(not(X_5902)))),bind(X_84,$fot(not(not(implies(not(X_5902),X_5902))))),bind(X_85,$fot(X_5902))]]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(implies(not(X_5900),implies(not(not(not(implies(not(X_5900),X_5900)))),not(not(implies(not(X_5900),X_5900))))),X_5900))
| is_a_theorem(implies(implies(implies(not(not(X_5900)),X_44),implies(not(not(not(implies(not(X_5900),X_5900)))),not(not(implies(not(X_5900),X_5900))))),X_5900)) ),
inference(subst,[],[refute_0_21:[bind(X_43,$fot(X_5900)),bind(X_45,$fot(not(X_5900))),bind(X_46,$fot(implies(not(not(not(implies(not(X_5900),X_5900)))),not(not(implies(not(X_5900),X_5900))))))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(implies(X_1821,implies(not(X_1822),X_1822)))
| ~ is_a_theorem(implies(implies(X_1821,implies(not(X_1822),X_1822)),implies(X_1821,X_1822)))
| is_a_theorem(implies(X_1821,X_1822)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1821,implies(not(X_1822),X_1822)))),bind(Y,$fot(implies(X_1821,X_1822)))]]) ).
cnf(refute_0_116,plain,
( ~ is_a_theorem(implies(X_1821,implies(not(X_1822),X_1822)))
| is_a_theorem(implies(X_1821,X_1822)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1821,implies(not(X_1822),X_1822)),implies(X_1821,X_1822))) )],[refute_0_102,refute_0_115]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(implies(not(X_5899),implies(not(not(not(implies(not(X_5899),X_5899)))),not(not(implies(not(X_5899),X_5899))))),implies(not(X_5899),X_5899)))
| is_a_theorem(implies(implies(not(X_5899),implies(not(not(not(implies(not(X_5899),X_5899)))),not(not(implies(not(X_5899),X_5899))))),X_5899)) ),
inference(subst,[],[refute_0_116:[bind(X_1821,$fot(implies(not(X_5899),implies(not(not(not(implies(not(X_5899),X_5899)))),not(not(implies(not(X_5899),X_5899))))))),bind(X_1822,$fot(X_5899))]]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(X_115,implies(implies(not(not(X_115)),not(X_115)),X_114)))
| is_a_theorem(implies(implies(implies(implies(not(not(X_115)),not(X_115)),X_114),Z),implies(X_115,Z))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_115)),bind(Y,$fot(implies(implies(not(not(X_115)),not(X_115)),X_114)))]]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(not(X_99),X_98),implies(implies(not(not(X_99)),not(X_99)),X_98))),
inference(subst,[],[refute_0_27:[bind(X_26,$fot(not(X_99))),bind(X_27,$fot(X_98))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(not(X_99),X_98),implies(implies(not(not(X_99)),not(X_99)),X_98)))
| is_a_theorem(implies(X_99,implies(implies(not(not(X_99)),not(X_99)),X_98))) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(X_98)),bind(X_34,$fot(X_99)),bind(X_35,$fot(implies(implies(not(not(X_99)),not(X_99)),X_98)))]]) ).
cnf(refute_0_121,plain,
is_a_theorem(implies(X_99,implies(implies(not(not(X_99)),not(X_99)),X_98))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_99),X_98),implies(implies(not(not(X_99)),not(X_99)),X_98))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(X_115,implies(implies(not(not(X_115)),not(X_115)),X_114))),
inference(subst,[],[refute_0_121:[bind(X_98,$fot(X_114)),bind(X_99,$fot(X_115))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_115)),not(X_115)),X_114),Z),implies(X_115,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_115,implies(implies(not(not(X_115)),not(X_115)),X_114))) )],[refute_0_122,refute_0_118]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(implies(implies(implies(not(not(X_115)),not(X_115)),X_1816),implies(X_1814,X_1816)),implies(X_115,implies(X_1814,X_1816)))),
inference(subst,[],[refute_0_123:[bind(Z,$fot(implies(X_1814,X_1816))),bind(X_114,$fot(X_1816))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(not(X_115)),not(X_115)),X_1816),implies(X_1814,X_1816)),implies(X_115,implies(X_1814,X_1816))))
| is_a_theorem(implies(implies(X_1814,implies(not(not(X_115)),not(X_115))),implies(X_115,implies(X_1814,X_1816)))) ),
inference(subst,[],[refute_0_15:[bind(X_82,$fot(X_1814)),bind(X_83,$fot(implies(not(not(X_115)),not(X_115)))),bind(X_84,$fot(X_1816)),bind(X_85,$fot(implies(X_115,implies(X_1814,X_1816))))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(X_1814,implies(not(not(X_115)),not(X_115))),implies(X_115,implies(X_1814,X_1816)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(not(X_115)),not(X_115)),X_1816),implies(X_1814,X_1816)),implies(X_115,implies(X_1814,X_1816)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(X_1814,implies(not(not(not(implies(X_1814,X_1816)))),not(not(implies(X_1814,X_1816))))),implies(not(implies(X_1814,X_1816)),implies(X_1814,X_1816)))),
inference(subst,[],[refute_0_126:[bind(X_115,$fot(not(implies(X_1814,X_1816))))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(implies(X_1814,implies(not(not(not(implies(X_1814,X_1816)))),not(not(implies(X_1814,X_1816))))),implies(not(implies(X_1814,X_1816)),implies(X_1814,X_1816))))
| is_a_theorem(implies(implies(X_1814,implies(not(not(not(implies(X_1814,X_1816)))),not(not(implies(X_1814,X_1816))))),implies(X_1814,X_1816))) ),
inference(subst,[],[refute_0_116:[bind(X_1821,$fot(implies(X_1814,implies(not(not(not(implies(X_1814,X_1816)))),not(not(implies(X_1814,X_1816))))))),bind(X_1822,$fot(implies(X_1814,X_1816)))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(X_1814,implies(not(not(not(implies(X_1814,X_1816)))),not(not(implies(X_1814,X_1816))))),implies(X_1814,X_1816))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1814,implies(not(not(not(implies(X_1814,X_1816)))),not(not(implies(X_1814,X_1816))))),implies(not(implies(X_1814,X_1816)),implies(X_1814,X_1816)))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(not(X_5899),implies(not(not(not(implies(not(X_5899),X_5899)))),not(not(implies(not(X_5899),X_5899))))),implies(not(X_5899),X_5899))),
inference(subst,[],[refute_0_129:[bind(X_1814,$fot(not(X_5899))),bind(X_1816,$fot(X_5899))]]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(not(X_5899),implies(not(not(not(implies(not(X_5899),X_5899)))),not(not(implies(not(X_5899),X_5899))))),X_5899)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_5899),implies(not(not(not(implies(not(X_5899),X_5899)))),not(not(implies(not(X_5899),X_5899))))),implies(not(X_5899),X_5899))) )],[refute_0_130,refute_0_117]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(not(X_5900),implies(not(not(not(implies(not(X_5900),X_5900)))),not(not(implies(not(X_5900),X_5900))))),X_5900)),
inference(subst,[],[refute_0_131:[bind(X_5899,$fot(X_5900))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(implies(not(not(X_5900)),X_44),implies(not(not(not(implies(not(X_5900),X_5900)))),not(not(implies(not(X_5900),X_5900))))),X_5900)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_5900),implies(not(not(not(implies(not(X_5900),X_5900)))),not(not(implies(not(X_5900),X_5900))))),X_5900)) )],[refute_0_132,refute_0_114]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(implies(not(not(X_5902)),not(not(implies(not(X_5902),X_5902)))),implies(not(not(not(implies(not(X_5902),X_5902)))),not(not(implies(not(X_5902),X_5902))))),X_5902)),
inference(subst,[],[refute_0_133:[bind(X_44,$fot(not(not(implies(not(X_5902),X_5902))))),bind(X_5900,$fot(X_5902))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(implies(not(not(not(implies(not(X_5902),X_5902)))),not(not(X_5902))),X_5902)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_5902)),not(not(implies(not(X_5902),X_5902)))),implies(not(not(not(implies(not(X_5902),X_5902)))),not(not(implies(not(X_5902),X_5902))))),X_5902)) )],[refute_0_134,refute_0_113]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(implies(not(not(not(implies(not(X_5903),X_5903)))),not(not(X_5903))),X_5903)),
inference(subst,[],[refute_0_135:[bind(X_5902,$fot(X_5903))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(implies(not(not(implies(not(X_5903),X_5903))),X_5903)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(implies(not(X_5903),X_5903)))),not(not(X_5903))),X_5903)) )],[refute_0_136,refute_0_112]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(not(not(implies(not(not(X_1926)),not(X_1926)))),not(X_1926))),
inference(subst,[],[refute_0_137:[bind(X_5903,$fot(not(X_1926)))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(X_1926,not(implies(not(not(X_1926)),not(X_1926))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(implies(not(not(X_1926)),not(X_1926)))),not(X_1926))) )],[refute_0_138,refute_0_111]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(not(X_1927),not(implies(not(not(not(X_1927))),not(not(X_1927)))))),
inference(subst,[],[refute_0_139:[bind(X_1926,$fot(not(X_1927)))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(implies(not(not(not(X_1927))),not(not(X_1927))),X_1927)),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1927),not(implies(not(not(not(X_1927))),not(not(X_1927)))))) )],[refute_0_140,refute_0_110]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(implies(not(not(not(X_5908))),not(not(X_5908))),X_5908)),
inference(subst,[],[refute_0_141:[bind(X_1927,$fot(X_5908))]]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(not(not(X_5908)),X_5908)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(X_5908))),not(not(X_5908))),X_5908)) )],[refute_0_142,refute_0_109]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(not(not(not(X_1926))),not(X_1926))),
inference(subst,[],[refute_0_143:[bind(X_5908,$fot(not(X_1926)))]]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(X_1926,not(not(X_1926)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(X_1926))),not(X_1926))) )],[refute_0_144,refute_0_108]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(X_5910,not(not(X_5910)))),
inference(subst,[],[refute_0_145:[bind(X_1926,$fot(X_5910))]]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(not(not(X_5910)),Z),implies(X_5910,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_5910,not(not(X_5910)))) )],[refute_0_146,refute_0_9]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(not(not(X_6073)),X_6072),implies(X_6073,X_6072))),
inference(subst,[],[refute_0_147:[bind(Z,$fot(X_6072)),bind(X_5910,$fot(X_6073))]]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(not(X_6073),implies(X_6073,X_6072))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(X_6073)),X_6072),implies(X_6073,X_6072))) )],[refute_0_148,refute_0_8]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(not(x),implies(x,y))),
inference(subst,[],[refute_0_149:[bind(X_6072,$fot(y)),bind(X_6073,$fot(x))]]) ).
cnf(refute_0_151,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(not(x),implies(x,y))) )],[refute_0_150,prove_cn_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL378-1 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 11:19:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.36/4.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.36/4.58
% 4.36/4.58 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.43/4.60
%------------------------------------------------------------------------------