TSTP Solution File: LCL049-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL049-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:49:03 EDT 2022
% Result : Unsatisfiable 8.07s 8.25s
% Output : CNFRefutation 8.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 5
% Syntax : Number of clauses : 143 ( 84 unt; 0 nHn; 38 RR)
% Number of literals : 214 ( 0 equ; 72 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 395 ( 70 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_20,negated_conjecture,
~ is_a_theorem(implies(a,implies(implies(a,b),b))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(X_340,X_339),implies(not(X_341),X_339)),X_338))
| ~ is_a_theorem(implies(implies(implies(implies(X_340,X_339),implies(not(X_341),X_339)),X_338),implies(X_341,X_338)))
| is_a_theorem(implies(X_341,X_338)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_340,X_339),implies(not(X_341),X_339)),X_338))),bind(Y,$fot(implies(X_341,X_338)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X_287,implies(implies(X_286,X_285),implies(not(X_287),X_285))))
| is_a_theorem(implies(implies(implies(implies(X_286,X_285),implies(not(X_287),X_285)),Z),implies(X_287,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_287)),bind(Y,$fot(implies(implies(X_286,X_285),implies(not(X_287),X_285))))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(not(X_264),X_263),implies(implies(X_263,Z),implies(not(X_264),Z)))),
inference(subst,[],[cn_1:[bind(X,$fot(not(X_264))),bind(Y,$fot(X_263))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30)))
| ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_29),X_28),X_30))),bind(Y,$fot(implies(X_29,X_30)))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(X_23,implies(not(X_23),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(X_23,implies(not(X_23),Y)))
| is_a_theorem(implies(implies(implies(not(X_23),Y),X_25),implies(X_23,X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_23)),bind(Y,$fot(implies(not(X_23),Y))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(not(X_23),Y),X_25),implies(X_23,X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(X_23,implies(not(X_23),Y))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))),
inference(subst,[],[refute_0_8:[bind(Y,$fot(X_28)),bind(X_23,$fot(X_29)),bind(X_25,$fot(X_30))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(not(X_29),X_28),X_30))
| is_a_theorem(implies(X_29,X_30)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(not(X_264),X_263),implies(implies(X_263,Z),implies(not(X_264),Z))))
| is_a_theorem(implies(X_264,implies(implies(X_263,Z),implies(not(X_264),Z)))) ),
inference(subst,[],[refute_0_10:[bind(X_28,$fot(X_263)),bind(X_29,$fot(X_264)),bind(X_30,$fot(implies(implies(X_263,Z),implies(not(X_264),Z))))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(X_264,implies(implies(X_263,Z),implies(not(X_264),Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_264),X_263),implies(implies(X_263,Z),implies(not(X_264),Z)))) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(X_287,implies(implies(X_286,X_285),implies(not(X_287),X_285)))),
inference(subst,[],[refute_0_12:[bind(Z,$fot(X_285)),bind(X_263,$fot(X_286)),bind(X_264,$fot(X_287))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(implies(X_286,X_285),implies(not(X_287),X_285)),Z),implies(X_287,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_287,implies(implies(X_286,X_285),implies(not(X_287),X_285)))) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(implies(X_340,X_339),implies(not(X_341),X_339)),X_338),implies(X_341,X_338))),
inference(subst,[],[refute_0_14:[bind(Z,$fot(X_338)),bind(X_285,$fot(X_339)),bind(X_286,$fot(X_340)),bind(X_287,$fot(X_341))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_340,X_339),implies(not(X_341),X_339)),X_338))
| is_a_theorem(implies(X_341,X_338)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_340,X_339),implies(not(X_341),X_339)),X_338),implies(X_341,X_338))) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(implies(X_11064,X_11064),implies(not(X_11064),X_11064)),implies(implies(X_11064,X_11065),X_11065)))
| is_a_theorem(implies(X_11064,implies(implies(X_11064,X_11065),X_11065))) ),
inference(subst,[],[refute_0_16:[bind(X_338,$fot(implies(implies(X_11064,X_11065),X_11065))),bind(X_339,$fot(X_11064)),bind(X_340,$fot(X_11064)),bind(X_341,$fot(X_11064))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(X_639,X_641),X_638))
| ~ is_a_theorem(implies(implies(implies(X_639,X_641),X_638),implies(implies(implies(X_640,X_640),X_641),X_638)))
| is_a_theorem(implies(implies(implies(X_640,X_640),X_641),X_638)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_639,X_641),X_638))),bind(Y,$fot(implies(implies(implies(X_640,X_640),X_641),X_638)))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(X_620,X_620),X_621),implies(X_619,X_621)))
| is_a_theorem(implies(implies(implies(X_619,X_621),Z),implies(implies(implies(X_620,X_620),X_621),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(X_620,X_620),X_621))),bind(Y,$fot(implies(X_619,X_621)))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(X_345,implies(not(implies(X_347,X_347)),X_346)))
| is_a_theorem(implies(implies(implies(not(implies(X_347,X_347)),X_346),Z),implies(X_345,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_345)),bind(Y,$fot(implies(not(implies(X_347,X_347)),X_346)))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(not(X_29),X_342),implies(not(implies(X_344,X_344)),X_342)))
| is_a_theorem(implies(X_29,implies(not(implies(X_344,X_344)),X_342))) ),
inference(subst,[],[refute_0_10:[bind(X_28,$fot(X_342)),bind(X_30,$fot(implies(not(implies(X_344,X_344)),X_342)))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(not(implies(X_268,X_268)),X_267))
| is_a_theorem(implies(implies(X_267,Z),implies(not(implies(X_268,X_268)),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(X_268,X_268)))),bind(Y,$fot(X_267))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_24,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_25,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(X_266,X_266))
| is_a_theorem(implies(not(implies(X_266,X_266)),Y)) ),
inference(subst,[],[refute_0_25:[bind(X_6,$fot(implies(X_266,X_266)))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(not(X_265),X_265),X_265)),
inference(subst,[],[cn_2:[bind(X,$fot(X_265))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(not(X_265),X_265),X_265))
| is_a_theorem(implies(X_265,X_265)) ),
inference(subst,[],[refute_0_10:[bind(X_28,$fot(X_265)),bind(X_29,$fot(X_265)),bind(X_30,$fot(X_265))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(X_265,X_265)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_265),X_265),X_265)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(X_266,X_266)),
inference(subst,[],[refute_0_29:[bind(X_265,$fot(X_266))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(not(implies(X_266,X_266)),Y)),
inference(resolve,[$cnf( is_a_theorem(implies(X_266,X_266)) )],[refute_0_30,refute_0_26]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(not(implies(X_268,X_268)),X_267)),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_267)),bind(X_266,$fot(X_268))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(X_267,Z),implies(not(implies(X_268,X_268)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X_268,X_268)),X_267)) )],[refute_0_32,refute_0_22]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(not(X_29),X_342),implies(not(implies(X_344,X_344)),X_342))),
inference(subst,[],[refute_0_33:[bind(Z,$fot(X_342)),bind(X_267,$fot(not(X_29))),bind(X_268,$fot(X_344))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(X_29,implies(not(implies(X_344,X_344)),X_342))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_29),X_342),implies(not(implies(X_344,X_344)),X_342))) )],[refute_0_34,refute_0_21]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(X_345,implies(not(implies(X_347,X_347)),X_346))),
inference(subst,[],[refute_0_35:[bind(X_29,$fot(X_345)),bind(X_342,$fot(X_346)),bind(X_344,$fot(X_347))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(implies(not(implies(X_347,X_347)),X_346),Z),implies(X_345,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_345,implies(not(implies(X_347,X_347)),X_346))) )],[refute_0_36,refute_0_20]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(not(implies(X_347,X_347)),implies(X_347,X_347)),X_618),implies(X_345,X_618))),
inference(subst,[],[refute_0_37:[bind(Z,$fot(X_618)),bind(X_346,$fot(implies(X_347,X_347)))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53)))
| ~ is_a_theorem(implies(implies(implies(not(X_54),X_54),X_55),X_53))
| is_a_theorem(implies(implies(X_54,X_55),X_53)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_54),X_54),X_55),X_53))),bind(Y,$fot(implies(implies(X_54,X_55),X_53)))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27)))
| is_a_theorem(implies(implies(implies(implies(not(X_26),X_26),X_27),Z),implies(implies(X_26,X_27),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X_26,X_27))),bind(Y,$fot(implies(implies(not(X_26),X_26),X_27)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(not(X_24),X_24),X_24)),
inference(subst,[],[cn_2:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(not(X_24),X_24),X_24))
| is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_24),X_24))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_24,X_25),implies(implies(not(X_24),X_24),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_24),X_24),X_24)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))),
inference(subst,[],[refute_0_43:[bind(X_24,$fot(X_26)),bind(X_25,$fot(X_27))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(implies(not(X_26),X_26),X_27),Z),implies(implies(X_26,X_27),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_26,X_27),implies(implies(not(X_26),X_26),X_27))) )],[refute_0_44,refute_0_40]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53))),
inference(subst,[],[refute_0_45:[bind(Z,$fot(X_53)),bind(X_26,$fot(X_54)),bind(X_27,$fot(X_55))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_54),X_54),X_55),X_53))
| is_a_theorem(implies(implies(X_54,X_55),X_53)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_54),X_54),X_55),X_53),implies(implies(X_54,X_55),X_53))) )],[refute_0_46,refute_0_39]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(X_347,X_347)),implies(X_347,X_347)),X_618),implies(X_345,X_618)))
| is_a_theorem(implies(implies(implies(X_347,X_347),X_618),implies(X_345,X_618))) ),
inference(subst,[],[refute_0_47:[bind(X_53,$fot(implies(X_345,X_618))),bind(X_54,$fot(implies(X_347,X_347))),bind(X_55,$fot(X_618))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(X_347,X_347),X_618),implies(X_345,X_618))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(X_347,X_347)),implies(X_347,X_347)),X_618),implies(X_345,X_618))) )],[refute_0_38,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(implies(X_620,X_620),X_621),implies(X_619,X_621))),
inference(subst,[],[refute_0_49:[bind(X_345,$fot(X_619)),bind(X_347,$fot(X_620)),bind(X_618,$fot(X_621))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(implies(X_619,X_621),Z),implies(implies(implies(X_620,X_620),X_621),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_620,X_620),X_621),implies(X_619,X_621))) )],[refute_0_50,refute_0_19]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(implies(X_639,X_641),X_638),implies(implies(implies(X_640,X_640),X_641),X_638))),
inference(subst,[],[refute_0_51:[bind(Z,$fot(X_638)),bind(X_619,$fot(X_639)),bind(X_620,$fot(X_640)),bind(X_621,$fot(X_641))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(implies(X_639,X_641),X_638))
| is_a_theorem(implies(implies(implies(X_640,X_640),X_641),X_638)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_639,X_641),X_638),implies(implies(implies(X_640,X_640),X_641),X_638))) )],[refute_0_52,refute_0_18]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(implies(not(X_10930),implies(not(X_10929),X_10929)),implies(implies(X_10929,X_10930),X_10930)))
| is_a_theorem(implies(implies(implies(X_640,X_640),implies(not(X_10929),X_10929)),implies(implies(X_10929,X_10930),X_10930))) ),
inference(subst,[],[refute_0_53:[bind(X_638,$fot(implies(implies(X_10929,X_10930),X_10930))),bind(X_639,$fot(not(X_10930))),bind(X_641,$fot(implies(not(X_10929),X_10929)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_993)),X_992),X_993),X_993))
| ~ is_a_theorem(implies(implies(not(not(X_993)),X_992),X_993))
| is_a_theorem(X_993) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_993)),X_992),X_993))),bind(Y,$fot(X_993))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(not(X_7),X_7),X_7)),
inference(subst,[],[cn_2:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(implies(not(X_7),X_7),X_7))
| ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_7),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(not(X_7),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_7),X_7),X_7)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)),implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)))
| is_a_theorem(implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)) ),
inference(subst,[],[refute_0_58:[bind(X_7,$fot(implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30)))
| is_a_theorem(implies(implies(implies(X_29,X_30),Z),implies(implies(implies(not(X_29),X_28),X_30),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(not(X_29),X_28),X_30))),bind(Y,$fot(implies(X_29,X_30)))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(implies(X_29,X_30),Z),implies(implies(implies(not(X_29),X_28),X_30),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_29),X_28),X_30),implies(X_29,X_30))) )],[refute_0_9,refute_0_60]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(implies(not(X_617),X_617),X_618),implies(implies(implies(not(not(X_617)),X_28),X_617),X_618))),
inference(subst,[],[refute_0_61:[bind(Z,$fot(X_618)),bind(X_29,$fot(not(X_617))),bind(X_30,$fot(X_617))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_617),X_617),X_618),implies(implies(implies(not(not(X_617)),X_28),X_617),X_618)))
| is_a_theorem(implies(implies(X_617,X_618),implies(implies(implies(not(not(X_617)),X_28),X_617),X_618))) ),
inference(subst,[],[refute_0_47:[bind(X_53,$fot(implies(implies(implies(not(not(X_617)),X_28),X_617),X_618))),bind(X_54,$fot(X_617)),bind(X_55,$fot(X_618))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(X_617,X_618),implies(implies(implies(not(not(X_617)),X_28),X_617),X_618))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_617),X_617),X_618),implies(implies(implies(not(not(X_617)),X_28),X_617),X_618))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(X_896,X_896),implies(implies(implies(not(not(X_896)),X_28),X_896),X_896))),
inference(subst,[],[refute_0_64:[bind(X_617,$fot(X_896)),bind(X_618,$fot(X_896))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(implies(X_620,X_620),X_621))
| ~ is_a_theorem(implies(implies(implies(X_620,X_620),X_621),implies(X_619,X_621)))
| is_a_theorem(implies(X_619,X_621)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_620,X_620),X_621))),bind(Y,$fot(implies(X_619,X_621)))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(X_620,X_620),X_621))
| is_a_theorem(implies(X_619,X_621)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_620,X_620),X_621),implies(X_619,X_621))) )],[refute_0_50,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(X_896,X_896),implies(implies(implies(not(not(X_896)),X_28),X_896),X_896)))
| is_a_theorem(implies(X_895,implies(implies(implies(not(not(X_896)),X_28),X_896),X_896))) ),
inference(subst,[],[refute_0_67:[bind(X_619,$fot(X_895)),bind(X_620,$fot(X_896)),bind(X_621,$fot(implies(implies(implies(not(not(X_896)),X_28),X_896),X_896)))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(X_895,implies(implies(implies(not(not(X_896)),X_28),X_896),X_896))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_896,X_896),implies(implies(implies(not(not(X_896)),X_28),X_896),X_896))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(not(implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)),implies(implies(implies(not(not(X_991)),X_989),X_991),X_991))),
inference(subst,[],[refute_0_69:[bind(X_28,$fot(X_989)),bind(X_895,$fot(not(implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)))),bind(X_896,$fot(X_991))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(not(not(X_991)),X_989),X_991),X_991)),implies(implies(implies(not(not(X_991)),X_989),X_991),X_991))) )],[refute_0_70,refute_0_59]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(implies(not(not(X_993)),X_992),X_993),X_993)),
inference(subst,[],[refute_0_71:[bind(X_989,$fot(X_992)),bind(X_991,$fot(X_993))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(implies(not(not(X_993)),X_992),X_993))
| is_a_theorem(X_993) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_993)),X_992),X_993),X_993)) )],[refute_0_72,refute_0_55]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928)))),X_992),implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928))))
| is_a_theorem(implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928))) ),
inference(subst,[],[refute_0_73:[bind(X_993,$fot(implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928))))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(implies(X_111,X_112),implies(X_110,X_112)),X_113))
| ~ is_a_theorem(implies(implies(implies(implies(X_111,X_112),implies(X_110,X_112)),X_113),implies(implies(X_110,X_111),X_113)))
| is_a_theorem(implies(implies(X_110,X_111),X_113)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_111,X_112),implies(X_110,X_112)),X_113))),bind(Y,$fot(implies(implies(X_110,X_111),X_113)))]]) ).
cnf(refute_0_76,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_25),implies(implies(X,Y),X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_25),implies(implies(X,Y),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_76]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(implies(implies(X_111,X_112),implies(X_110,X_112)),X_113),implies(implies(X_110,X_111),X_113))),
inference(subst,[],[refute_0_77:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(Z,$fot(X_112)),bind(X_25,$fot(X_113))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(implies(implies(implies(X_111,X_112),implies(X_110,X_112)),X_113))
| is_a_theorem(implies(implies(X_110,X_111),X_113)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_111,X_112),implies(X_110,X_112)),X_113),implies(implies(X_110,X_111),X_113))) )],[refute_0_78,refute_0_75]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(implies(implies(X_111,X_3861),implies(X_3860,X_3861)),implies(implies(not(X_3861),X_3860),implies(implies(X_111,X_3861),X_3861))))
| is_a_theorem(implies(implies(X_3860,X_111),implies(implies(not(X_3861),X_3860),implies(implies(X_111,X_3861),X_3861)))) ),
inference(subst,[],[refute_0_79:[bind(X_110,$fot(X_3860)),bind(X_112,$fot(X_3861)),bind(X_113,$fot(implies(implies(not(X_3861),X_3860),implies(implies(X_111,X_3861),X_3861))))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_3180,X_3181),X_3181),implies(X_110,X_3181)),implies(implies(not(X_3181),X_3180),implies(X_110,X_3181))))
| is_a_theorem(implies(implies(X_110,implies(X_3180,X_3181)),implies(implies(not(X_3181),X_3180),implies(X_110,X_3181)))) ),
inference(subst,[],[refute_0_79:[bind(X_111,$fot(implies(X_3180,X_3181))),bind(X_112,$fot(X_3181)),bind(X_113,$fot(implies(implies(not(X_3181),X_3180),implies(X_110,X_3181))))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(implies(not(X_3011),X_3010),implies(implies(X_3010,X_3011),X_3011)))
| is_a_theorem(implies(implies(implies(implies(X_3010,X_3011),X_3011),Z),implies(implies(not(X_3011),X_3010),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(not(X_3011),X_3010))),bind(Y,$fot(implies(implies(X_3010,X_3011),X_3011)))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(implies(implies(X_111,X_2992),implies(not(X_2992),X_2992)),implies(implies(X_111,X_2992),X_2992)))
| is_a_theorem(implies(implies(not(X_2992),X_111),implies(implies(X_111,X_2992),X_2992))) ),
inference(subst,[],[refute_0_79:[bind(X_110,$fot(not(X_2992))),bind(X_112,$fot(X_2992)),bind(X_113,$fot(implies(implies(X_111,X_2992),X_2992)))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1034),X_1034),X_1034)),implies(implies(not(X_1034),X_1034),X_1034)),X_1036),X_1036))
| is_a_theorem(implies(implies(implies(implies(not(X_1034),X_1034),X_1034),X_1036),X_1036)) ),
inference(subst,[],[refute_0_47:[bind(X_53,$fot(X_1036)),bind(X_54,$fot(implies(implies(not(X_1034),X_1034),X_1034))),bind(X_55,$fot(X_1036))]]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(not(implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)),implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)) ),
inference(subst,[],[refute_0_58:[bind(X_7,$fot(implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_804),X_804),X_803),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_804),X_803)))
| is_a_theorem(implies(implies(X_804,X_803),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_804),X_803))) ),
inference(subst,[],[refute_0_47:[bind(X_53,$fot(implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_804),X_803))),bind(X_54,$fot(X_804)),bind(X_55,$fot(X_803))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_335),X_335),X_335)),X_336),X_334),implies(X_337,X_334)))
| is_a_theorem(implies(implies(implies(X_337,X_334),Z),implies(implies(implies(not(implies(implies(not(X_335),X_335),X_335)),X_336),X_334),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(implies(implies(not(implies(implies(not(X_335),X_335),X_335)),X_336),X_334))),bind(Y,$fot(implies(X_337,X_334)))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(X_298,implies(not(implies(implies(not(X_296),X_296),X_296)),X_297)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_296),X_296),X_296)),X_297),Z),implies(X_298,Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_298)),bind(Y,$fot(implies(not(implies(implies(not(X_296),X_296),X_296)),X_297)))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)) ),
inference(subst,[],[refute_0_25:[bind(Y,$fot(X_9)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_9)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_89]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24)),
inference(subst,[],[refute_0_90:[bind(X_9,$fot(X_24))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24))
| is_a_theorem(implies(implies(X_24,X_25),implies(not(implies(implies(not(X),X),X)),X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(X_24,X_25),implies(not(implies(implies(not(X),X),X)),X_25))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_24)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(not(X_264),X_263),implies(not(implies(implies(not(X),X),X)),X_263))),
inference(subst,[],[refute_0_93:[bind(X_24,$fot(not(X_264))),bind(X_25,$fot(X_263))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(implies(not(X_264),X_263),implies(not(implies(implies(not(X),X),X)),X_263)))
| is_a_theorem(implies(X_264,implies(not(implies(implies(not(X),X),X)),X_263))) ),
inference(subst,[],[refute_0_10:[bind(X_28,$fot(X_263)),bind(X_29,$fot(X_264)),bind(X_30,$fot(implies(not(implies(implies(not(X),X),X)),X_263)))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(X_264,implies(not(implies(implies(not(X),X),X)),X_263))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_264),X_263),implies(not(implies(implies(not(X),X),X)),X_263))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(X_298,implies(not(implies(implies(not(X_296),X_296),X_296)),X_297))),
inference(subst,[],[refute_0_96:[bind(X,$fot(X_296)),bind(X_263,$fot(X_297)),bind(X_264,$fot(X_298))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_296),X_296),X_296)),X_297),Z),implies(X_298,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_298,implies(not(implies(implies(not(X_296),X_296),X_296)),X_297))) )],[refute_0_97,refute_0_88]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_335),X_335),X_335)),X_336),X_334),implies(X_337,X_334))),
inference(subst,[],[refute_0_98:[bind(Z,$fot(X_334)),bind(X_296,$fot(X_335)),bind(X_297,$fot(X_336)),bind(X_298,$fot(X_337))]]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(implies(implies(X_337,X_334),Z),implies(implies(implies(not(implies(implies(not(X_335),X_335),X_335)),X_336),X_334),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_335),X_335),X_335)),X_336),X_334),implies(X_337,X_334))) )],[refute_0_99,refute_0_87]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(implies(not(X_804),X_804),X_803),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_804),X_803))),
inference(subst,[],[refute_0_100:[bind(Z,$fot(X_803)),bind(X_334,$fot(X_804)),bind(X_335,$fot(X_805)),bind(X_336,$fot(X_806)),bind(X_337,$fot(not(X_804)))]]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(implies(X_804,X_803),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_804),X_803))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_804),X_804),X_803),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_804),X_803))) )],[refute_0_101,refute_0_86]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(X_896,X_896),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_896),X_896))),
inference(subst,[],[refute_0_102:[bind(X_803,$fot(X_896)),bind(X_804,$fot(X_896))]]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(implies(X_896,X_896),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_896),X_896)))
| is_a_theorem(implies(X_895,implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_896),X_896))) ),
inference(subst,[],[refute_0_67:[bind(X_619,$fot(X_895)),bind(X_620,$fot(X_896)),bind(X_621,$fot(implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_896),X_896)))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(X_895,implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_896),X_896))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_896,X_896),implies(implies(implies(not(implies(implies(not(X_805),X_805),X_805)),X_806),X_896),X_896))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(not(implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)),implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033))),
inference(subst,[],[refute_0_105:[bind(X_805,$fot(X_1030)),bind(X_806,$fot(X_1031)),bind(X_895,$fot(not(implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)))),bind(X_896,$fot(X_1033))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033)),implies(implies(implies(not(implies(implies(not(X_1030),X_1030),X_1030)),X_1031),X_1033),X_1033))) )],[refute_0_106,refute_0_85]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1034),X_1034),X_1034)),implies(implies(not(X_1034),X_1034),X_1034)),X_1036),X_1036)),
inference(subst,[],[refute_0_107:[bind(X_1030,$fot(X_1034)),bind(X_1031,$fot(implies(implies(not(X_1034),X_1034),X_1034))),bind(X_1033,$fot(X_1036))]]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1034),X_1034),X_1034),X_1036),X_1036)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_1034),X_1034),X_1034)),implies(implies(not(X_1034),X_1034),X_1034)),X_1036),X_1036)) )],[refute_0_108,refute_0_84]) ).
cnf(refute_0_110,plain,
is_a_theorem(implies(implies(implies(implies(not(X_2983),X_2983),X_2983),implies(X_2981,X_2983)),implies(X_2981,X_2983))),
inference(subst,[],[refute_0_109:[bind(X_1034,$fot(X_2983)),bind(X_1036,$fot(implies(X_2981,X_2983)))]]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_2983),X_2983),X_2983),implies(X_2981,X_2983)),implies(X_2981,X_2983)))
| is_a_theorem(implies(implies(X_2981,implies(not(X_2983),X_2983)),implies(X_2981,X_2983))) ),
inference(subst,[],[refute_0_79:[bind(X_110,$fot(X_2981)),bind(X_111,$fot(implies(not(X_2983),X_2983))),bind(X_112,$fot(X_2983)),bind(X_113,$fot(implies(X_2981,X_2983)))]]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(X_2981,implies(not(X_2983),X_2983)),implies(X_2981,X_2983))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_2983),X_2983),X_2983),implies(X_2981,X_2983)),implies(X_2981,X_2983))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(implies(X_111,X_2992),implies(not(X_2992),X_2992)),implies(implies(X_111,X_2992),X_2992))),
inference(subst,[],[refute_0_112:[bind(X_2981,$fot(implies(X_111,X_2992))),bind(X_2983,$fot(X_2992))]]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(not(X_2992),X_111),implies(implies(X_111,X_2992),X_2992))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_111,X_2992),implies(not(X_2992),X_2992)),implies(implies(X_111,X_2992),X_2992))) )],[refute_0_113,refute_0_83]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(not(X_3011),X_3010),implies(implies(X_3010,X_3011),X_3011))),
inference(subst,[],[refute_0_114:[bind(X_111,$fot(X_3010)),bind(X_2992,$fot(X_3011))]]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(implies(implies(X_3010,X_3011),X_3011),Z),implies(implies(not(X_3011),X_3010),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_3011),X_3010),implies(implies(X_3010,X_3011),X_3011))) )],[refute_0_115,refute_0_82]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(implies(implies(X_3180,X_3181),X_3181),implies(X_110,X_3181)),implies(implies(not(X_3181),X_3180),implies(X_110,X_3181)))),
inference(subst,[],[refute_0_116:[bind(Z,$fot(implies(X_110,X_3181))),bind(X_3010,$fot(X_3180)),bind(X_3011,$fot(X_3181))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(X_110,implies(X_3180,X_3181)),implies(implies(not(X_3181),X_3180),implies(X_110,X_3181)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_3180,X_3181),X_3181),implies(X_110,X_3181)),implies(implies(not(X_3181),X_3180),implies(X_110,X_3181)))) )],[refute_0_117,refute_0_81]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(implies(X_111,X_3861),implies(X_3860,X_3861)),implies(implies(not(X_3861),X_3860),implies(implies(X_111,X_3861),X_3861)))),
inference(subst,[],[refute_0_118:[bind(X_110,$fot(implies(X_111,X_3861))),bind(X_3180,$fot(X_3860)),bind(X_3181,$fot(X_3861))]]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(implies(X_3860,X_111),implies(implies(not(X_3861),X_3860),implies(implies(X_111,X_3861),X_3861)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_111,X_3861),implies(X_3860,X_3861)),implies(implies(not(X_3861),X_3860),implies(implies(X_111,X_3861),X_3861)))) )],[refute_0_119,refute_0_80]) ).
cnf(refute_0_121,plain,
is_a_theorem(implies(implies(implies(not(X_10904),X_10904),X_10904),implies(implies(not(X_3861),implies(not(X_10904),X_10904)),implies(implies(X_10904,X_3861),X_3861)))),
inference(subst,[],[refute_0_120:[bind(X_111,$fot(X_10904)),bind(X_3860,$fot(implies(not(X_10904),X_10904)))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_622),X_622),X_622),X_624),implies(X_623,X_624)))
| ~ is_a_theorem(implies(implies(implies(not(X_622),X_622),X_622),X_624))
| is_a_theorem(implies(X_623,X_624)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_622),X_622),X_622),X_624))),bind(Y,$fot(implies(X_623,X_624)))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_296),X_296),X_296)),implies(implies(not(X_296),X_296),X_296)),X_618),implies(X_298,X_618))),
inference(subst,[],[refute_0_98:[bind(Z,$fot(X_618)),bind(X_297,$fot(implies(implies(not(X_296),X_296),X_296)))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_296),X_296),X_296)),implies(implies(not(X_296),X_296),X_296)),X_618),implies(X_298,X_618)))
| is_a_theorem(implies(implies(implies(implies(not(X_296),X_296),X_296),X_618),implies(X_298,X_618))) ),
inference(subst,[],[refute_0_47:[bind(X_53,$fot(implies(X_298,X_618))),bind(X_54,$fot(implies(implies(not(X_296),X_296),X_296))),bind(X_55,$fot(X_618))]]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(implies(implies(implies(not(X_296),X_296),X_296),X_618),implies(X_298,X_618))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_296),X_296),X_296)),implies(implies(not(X_296),X_296),X_296)),X_618),implies(X_298,X_618))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(implies(implies(not(X_622),X_622),X_622),X_624),implies(X_623,X_624))),
inference(subst,[],[refute_0_125:[bind(X_296,$fot(X_622)),bind(X_298,$fot(X_623)),bind(X_618,$fot(X_624))]]) ).
cnf(refute_0_127,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_622),X_622),X_622),X_624))
| is_a_theorem(implies(X_623,X_624)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_622),X_622),X_622),X_624),implies(X_623,X_624))) )],[refute_0_126,refute_0_122]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_10904),X_10904),X_10904),implies(implies(not(X_3861),implies(not(X_10904),X_10904)),implies(implies(X_10904,X_3861),X_3861))))
| is_a_theorem(implies(X_10905,implies(implies(not(X_3861),implies(not(X_10904),X_10904)),implies(implies(X_10904,X_3861),X_3861)))) ),
inference(subst,[],[refute_0_127:[bind(X_622,$fot(X_10904)),bind(X_623,$fot(X_10905)),bind(X_624,$fot(implies(implies(not(X_3861),implies(not(X_10904),X_10904)),implies(implies(X_10904,X_3861),X_3861))))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(X_10905,implies(implies(not(X_3861),implies(not(X_10904),X_10904)),implies(implies(X_10904,X_3861),X_3861)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_10904),X_10904),X_10904),implies(implies(not(X_3861),implies(not(X_10904),X_10904)),implies(implies(X_10904,X_3861),X_3861)))) )],[refute_0_121,refute_0_128]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(not(not(implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928)))),X_992),implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928)))),
inference(subst,[],[refute_0_129:[bind(X_10904,$fot(X_10926)),bind(X_10905,$fot(implies(not(not(implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928)))),X_992))),bind(X_3861,$fot(X_10928))]]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928)))),X_992),implies(implies(not(X_10928),implies(not(X_10926),X_10926)),implies(implies(X_10926,X_10928),X_10928)))) )],[refute_0_130,refute_0_74]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(not(X_10930),implies(not(X_10929),X_10929)),implies(implies(X_10929,X_10930),X_10930))),
inference(subst,[],[refute_0_131:[bind(X_10926,$fot(X_10929)),bind(X_10928,$fot(X_10930))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(implies(X_640,X_640),implies(not(X_10929),X_10929)),implies(implies(X_10929,X_10930),X_10930))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_10930),implies(not(X_10929),X_10929)),implies(implies(X_10929,X_10930),X_10930))) )],[refute_0_132,refute_0_54]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(implies(X_11064,X_11064),implies(not(X_11064),X_11064)),implies(implies(X_11064,X_11065),X_11065))),
inference(subst,[],[refute_0_133:[bind(X_10929,$fot(X_11064)),bind(X_10930,$fot(X_11065)),bind(X_640,$fot(X_11064))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(X_11064,implies(implies(X_11064,X_11065),X_11065))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_11064,X_11064),implies(not(X_11064),X_11064)),implies(implies(X_11064,X_11065),X_11065))) )],[refute_0_134,refute_0_17]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(subst,[],[refute_0_135:[bind(X_11064,$fot(a)),bind(X_11065,$fot(b))]]) ).
cnf(refute_0_137,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(implies(a,b),b))) )],[refute_0_136,prove_cn_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL049-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.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 12:45:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.07/8.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.07/8.25
% 8.07/8.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.07/8.27
%------------------------------------------------------------------------------