TSTP Solution File: LCL405-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL405-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:52:01 EDT 2022
% Result : Unsatisfiable 11.48s 11.66s
% Output : CNFRefutation 11.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of clauses : 165 ( 94 unt; 0 nHn; 47 RR)
% Number of literals : 252 ( 0 equ; 88 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 : 447 ( 80 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_71,negated_conjecture,
~ is_a_theorem(not(implies(implies(x,x),not(implies(y,y))))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(X_10226,not(X_10227)),X_10227))
| ~ is_a_theorem(implies(implies(implies(X_10226,not(X_10227)),X_10227),X_10227))
| is_a_theorem(X_10227) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_10226,not(X_10227)),X_10227))),bind(Y,$fot(X_10227))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(not(X_2729),X_2730),implies(implies(X_2730,X_2729),X_2729)))
| ~ is_a_theorem(implies(not(X_2729),X_2730))
| is_a_theorem(implies(implies(X_2730,X_2729),X_2729)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_2729),X_2730))),bind(Y,$fot(implies(implies(X_2730,X_2729),X_2729)))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(implies(X_38,X_39),implies(X_37,X_39)),X_40))
| ~ is_a_theorem(implies(implies(implies(implies(X_38,X_39),implies(X_37,X_39)),X_40),implies(implies(X_37,X_38),X_40)))
| is_a_theorem(implies(implies(X_37,X_38),X_40)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_38,X_39),implies(X_37,X_39)),X_40))),bind(Y,$fot(implies(implies(X_37,X_38),X_40)))]]) ).
cnf(refute_0_3,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_4,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_21),implies(implies(X,Y),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[cn_1,refute_0_5]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(implies(implies(X_38,X_39),implies(X_37,X_39)),X_40),implies(implies(X_37,X_38),X_40))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(X_39)),bind(X_21,$fot(X_40))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(X_38,X_39),implies(X_37,X_39)),X_40))
| is_a_theorem(implies(implies(X_37,X_38),X_40)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_38,X_39),implies(X_37,X_39)),X_40),implies(implies(X_37,X_38),X_40))) )],[refute_0_7,refute_0_2]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(X_38,X_2726),implies(not(X_2726),X_2726)),implies(implies(X_38,X_2726),X_2726)))
| is_a_theorem(implies(implies(not(X_2726),X_38),implies(implies(X_38,X_2726),X_2726))) ),
inference(subst,[],[refute_0_8:[bind(X_37,$fot(not(X_2726))),bind(X_39,$fot(X_2726)),bind(X_40,$fot(implies(implies(X_38,X_2726),X_2726)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_597)),X_596),X_597),X_597))
| ~ is_a_theorem(implies(implies(not(not(X_597)),X_596),X_597))
| is_a_theorem(X_597) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_597)),X_596),X_597))),bind(Y,$fot(X_597))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(X_595,implies(implies(not(X_594),X_594),X_594)))
| ~ is_a_theorem(implies(implies(X_595,implies(implies(not(X_594),X_594),X_594)),implies(implies(implies(not(not(X_594)),X_593),X_594),X_594)))
| is_a_theorem(implies(implies(implies(not(not(X_594)),X_593),X_594),X_594)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_595,implies(implies(not(X_594),X_594),X_594)))),bind(Y,$fot(implies(implies(implies(not(not(X_594)),X_593),X_594),X_594)))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26)))
| is_a_theorem(implies(implies(implies(X_25,X_26),Z),implies(implies(implies(not(X_25),X_24),X_26),Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(implies(not(X_25),X_24),X_26))),bind(Y,$fot(implies(X_25,X_26)))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(X_19,implies(not(X_19),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(X_19,implies(not(X_19),Y)))
| is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_19)),bind(Y,$fot(implies(not(X_19),Y))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(X_19,implies(not(X_19),Y))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26))),
inference(subst,[],[refute_0_15:[bind(Y,$fot(X_24)),bind(X_19,$fot(X_25)),bind(X_21,$fot(X_26))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(X_25,X_26),Z),implies(implies(implies(not(X_25),X_24),X_26),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26))) )],[refute_0_16,refute_0_12]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(X_22,X_23))
| ~ is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23)))
| is_a_theorem(implies(implies(not(X_22),X_22),X_23)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_22,X_23))),bind(Y,$fot(implies(implies(not(X_22),X_22),X_23)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(not(X_20),X_20),X_20)),
inference(subst,[],[cn_2:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(not(X_20),X_20),X_20))
| is_a_theorem(implies(implies(X_20,X_21),implies(implies(not(X_20),X_20),X_21))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(not(X_20),X_20))),bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_20,X_21),implies(implies(not(X_20),X_20),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_20),X_20),X_20)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))),
inference(subst,[],[refute_0_21:[bind(X_20,$fot(X_22)),bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(X_22,X_23))
| is_a_theorem(implies(implies(not(X_22),X_22),X_23)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(implies(X_25,X_26),Z),implies(implies(implies(not(X_25),X_24),X_26),Z)))
| is_a_theorem(implies(implies(not(implies(implies(X_25,X_26),Z)),implies(implies(X_25,X_26),Z)),implies(implies(implies(not(X_25),X_24),X_26),Z))) ),
inference(subst,[],[refute_0_23:[bind(X_22,$fot(implies(implies(X_25,X_26),Z))),bind(X_23,$fot(implies(implies(implies(not(X_25),X_24),X_26),Z)))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(not(implies(implies(X_25,X_26),Z)),implies(implies(X_25,X_26),Z)),implies(implies(implies(not(X_25),X_24),X_26),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_25,X_26),Z),implies(implies(implies(not(X_25),X_24),X_26),Z))) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(implies(implies(not(not(X_581)),X_24),X_581),X_581))),
inference(subst,[],[refute_0_25:[bind(Z,$fot(X_581)),bind(X_25,$fot(not(X_581))),bind(X_26,$fot(X_581))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_181),X_178),implies(implies(X_180,X_181),X_178)))
| ~ is_a_theorem(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_181),X_178))
| is_a_theorem(implies(implies(X_180,X_181),X_178)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_181),X_178))),bind(Y,$fot(implies(implies(X_180,X_181),X_178)))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(X_31,X_32),implies(not(implies(implies(not(X_30),X_30),X_30)),X_32)))
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X_30),X_30),X_30)),X_32),Z),implies(implies(X_31,X_32),Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(X_31,X_32))),bind(Y,$fot(implies(not(implies(implies(not(X_30),X_30),X_30)),X_32)))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(X_6,implies(not(X_6),Y))),
inference(subst,[],[cn_3:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(implies(X_6,implies(not(X_6),Y)))
| is_a_theorem(implies(not(X_6),Y)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(implies(not(X_6),Y)))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(implies(not(X_6),Y)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_6,implies(not(X_6),Y))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(not(X),X),X))
| is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_8)) ),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_8)),bind(X_6,$fot(implies(implies(not(X),X),X)))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_8)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X),X)) )],[cn_2,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20)),
inference(subst,[],[refute_0_33:[bind(X_8,$fot(X_20))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20))
| is_a_theorem(implies(implies(X_20,X_21),implies(not(implies(implies(not(X),X),X)),X_21))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(not(implies(implies(not(X),X),X)))),bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(X_20,X_21),implies(not(implies(implies(not(X),X),X)),X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(not(X),X),X)),X_20)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(X_31,X_32),implies(not(implies(implies(not(X_30),X_30),X_30)),X_32))),
inference(subst,[],[refute_0_36:[bind(X,$fot(X_30)),bind(X_20,$fot(X_31)),bind(X_21,$fot(X_32))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_30),X_30),X_30)),X_32),Z),implies(implies(X_31,X_32),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_31,X_32),implies(not(implies(implies(not(X_30),X_30),X_30)),X_32))) )],[refute_0_37,refute_0_28]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_181),X_178),implies(implies(X_180,X_181),X_178))),
inference(subst,[],[refute_0_38:[bind(Z,$fot(X_178)),bind(X_30,$fot(X_179)),bind(X_31,$fot(X_180)),bind(X_32,$fot(X_181))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_181),X_178))
| is_a_theorem(implies(implies(X_180,X_181),X_178)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(implies(implies(not(X_179),X_179),X_179)),X_181),X_178),implies(implies(X_180,X_181),X_178))) )],[refute_0_39,refute_0_27]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(implies(implies(not(not(X_581)),X_24),X_581),X_581)))
| is_a_theorem(implies(implies(X_582,implies(implies(not(X_581),X_581),X_581)),implies(implies(implies(not(not(X_581)),X_24),X_581),X_581))) ),
inference(subst,[],[refute_0_40:[bind(X_178,$fot(implies(implies(implies(not(not(X_581)),X_24),X_581),X_581))),bind(X_179,$fot(X_581)),bind(X_180,$fot(X_582)),bind(X_181,$fot(implies(implies(not(X_581),X_581),X_581)))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(X_582,implies(implies(not(X_581),X_581),X_581)),implies(implies(implies(not(not(X_581)),X_24),X_581),X_581))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(implies(implies(not(not(X_581)),X_24),X_581),X_581))) )],[refute_0_26,refute_0_41]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_595,implies(implies(not(X_594),X_594),X_594)),implies(implies(implies(not(not(X_594)),X_593),X_594),X_594))),
inference(subst,[],[refute_0_42:[bind(X_24,$fot(X_593)),bind(X_581,$fot(X_594)),bind(X_582,$fot(X_595))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(X_595,implies(implies(not(X_594),X_594),X_594)))
| is_a_theorem(implies(implies(implies(not(not(X_594)),X_593),X_594),X_594)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_595,implies(implies(not(X_594),X_594),X_594)),implies(implies(implies(not(not(X_594)),X_593),X_594),X_594))) )],[refute_0_43,refute_0_11]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26)))
| ~ is_a_theorem(implies(implies(not(X_25),X_24),X_26))
| is_a_theorem(implies(X_25,X_26)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(X_25),X_24),X_26))),bind(Y,$fot(implies(X_25,X_26)))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(not(X_25),X_24),X_26))
| is_a_theorem(implies(X_25,X_26)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_25),X_24),X_26),implies(X_25,X_26))) )],[refute_0_16,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(not(X_25),implies(implies(not(X_584),X_584),X_584)),implies(implies(not(X_584),X_584),X_584)))
| is_a_theorem(implies(X_25,implies(implies(not(X_584),X_584),X_584))) ),
inference(subst,[],[refute_0_46:[bind(X_24,$fot(implies(implies(not(X_584),X_584),X_584))),bind(X_26,$fot(implies(implies(not(X_584),X_584),X_584)))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581))),
inference(subst,[],[cn_2:[bind(X,$fot(implies(implies(not(X_581),X_581),X_581)))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)))
| is_a_theorem(implies(implies(X_582,implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581))) ),
inference(subst,[],[refute_0_40:[bind(X_178,$fot(implies(implies(not(X_581),X_581),X_581))),bind(X_179,$fot(X_581)),bind(X_180,$fot(X_582)),bind(X_181,$fot(implies(implies(not(X_581),X_581),X_581)))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(X_582,implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(not(X_25),implies(implies(not(X_584),X_584),X_584)),implies(implies(not(X_584),X_584),X_584))),
inference(subst,[],[refute_0_50:[bind(X_581,$fot(X_584)),bind(X_582,$fot(not(X_25)))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(X_25,implies(implies(not(X_584),X_584),X_584))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_25),implies(implies(not(X_584),X_584),X_584)),implies(implies(not(X_584),X_584),X_584))) )],[refute_0_51,refute_0_47]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_595,implies(implies(not(X_594),X_594),X_594))),
inference(subst,[],[refute_0_52:[bind(X_25,$fot(X_595)),bind(X_584,$fot(X_594))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(not(not(X_594)),X_593),X_594),X_594)),
inference(resolve,[$cnf( is_a_theorem(implies(X_595,implies(implies(not(X_594),X_594),X_594))) )],[refute_0_53,refute_0_44]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(not(not(X_597)),X_596),X_597),X_597)),
inference(subst,[],[refute_0_54:[bind(X_593,$fot(X_596)),bind(X_594,$fot(X_597))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(not(not(X_597)),X_596),X_597))
| is_a_theorem(X_597) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_597)),X_596),X_597),X_597)) )],[refute_0_55,refute_0_10]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676))),X_596),implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676)))
| is_a_theorem(implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676)) ),
inference(subst,[],[refute_0_56:[bind(X_597,$fot(implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676)))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(X_614,X_614),X_612))
| ~ is_a_theorem(implies(implies(implies(X_614,X_614),X_612),implies(X_613,X_612)))
| is_a_theorem(implies(X_613,X_612)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_614,X_614),X_612))),bind(Y,$fot(implies(X_613,X_612)))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(X_607,implies(X_608,X_608)))
| is_a_theorem(implies(implies(implies(X_608,X_608),Z),implies(X_607,Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_607)),bind(Y,$fot(implies(X_608,X_608)))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(implies(not(X_25),implies(implies(not(X_605),X_605),X_605)),implies(X_605,X_605)))
| is_a_theorem(implies(X_25,implies(X_605,X_605))) ),
inference(subst,[],[refute_0_46:[bind(X_24,$fot(implies(implies(not(X_605),X_605),X_605))),bind(X_26,$fot(implies(X_605,X_605)))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21)))
| is_a_theorem(implies(implies(not(implies(implies(not(X_19),Y),X_21)),implies(implies(not(X_19),Y),X_21)),implies(X_19,X_21))) ),
inference(subst,[],[refute_0_23:[bind(X_22,$fot(implies(implies(not(X_19),Y),X_21))),bind(X_23,$fot(implies(X_19,X_21)))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(not(implies(implies(not(X_19),Y),X_21)),implies(implies(not(X_19),Y),X_21)),implies(X_19,X_21))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_19),Y),X_21),implies(X_19,X_21))) )],[refute_0_15,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(X_581,X_581))),
inference(subst,[],[refute_0_62:[bind(Y,$fot(X_581)),bind(X_19,$fot(X_581)),bind(X_21,$fot(X_581))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(X_581,X_581)))
| is_a_theorem(implies(implies(X_582,implies(implies(not(X_581),X_581),X_581)),implies(X_581,X_581))) ),
inference(subst,[],[refute_0_40:[bind(X_178,$fot(implies(X_581,X_581))),bind(X_179,$fot(X_581)),bind(X_180,$fot(X_582)),bind(X_181,$fot(implies(implies(not(X_581),X_581),X_581)))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(X_582,implies(implies(not(X_581),X_581),X_581)),implies(X_581,X_581))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(not(X_581),X_581),X_581)),implies(implies(not(X_581),X_581),X_581)),implies(X_581,X_581))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(not(X_25),implies(implies(not(X_605),X_605),X_605)),implies(X_605,X_605))),
inference(subst,[],[refute_0_65:[bind(X_581,$fot(X_605)),bind(X_582,$fot(not(X_25)))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(X_25,implies(X_605,X_605))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_25),implies(implies(not(X_605),X_605),X_605)),implies(X_605,X_605))) )],[refute_0_66,refute_0_60]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(X_607,implies(X_608,X_608))),
inference(subst,[],[refute_0_67:[bind(X_25,$fot(X_607)),bind(X_605,$fot(X_608))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(implies(X_608,X_608),Z),implies(X_607,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_607,implies(X_608,X_608))) )],[refute_0_68,refute_0_59]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(X_614,X_614),X_612),implies(X_613,X_612))),
inference(subst,[],[refute_0_69:[bind(Z,$fot(X_612)),bind(X_607,$fot(X_613)),bind(X_608,$fot(X_614))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(implies(X_614,X_614),X_612))
| is_a_theorem(implies(X_613,X_612)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_614,X_614),X_612),implies(X_613,X_612))) )],[refute_0_70,refute_0_58]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(X_1619,X_1619),implies(implies(implies(implies(not(X_1620),X_1620),X_1620),X_1619),X_1619)))
| is_a_theorem(implies(X_613,implies(implies(implies(implies(not(X_1620),X_1620),X_1620),X_1619),X_1619))) ),
inference(subst,[],[refute_0_71:[bind(X_612,$fot(implies(implies(implies(implies(not(X_1620),X_1620),X_1620),X_1619),X_1619))),bind(X_614,$fot(X_1619))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_590),X_590),X_590),X_588),implies(X_589,X_588)))
| is_a_theorem(implies(implies(implies(X_589,X_588),Z),implies(implies(implies(implies(not(X_590),X_590),X_590),X_588),Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(implies(implies(not(X_590),X_590),X_590),X_588))),bind(Y,$fot(implies(X_589,X_588)))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(X_586,implies(implies(not(X_587),X_587),X_587)))
| is_a_theorem(implies(implies(implies(implies(not(X_587),X_587),X_587),Z),implies(X_586,Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_586)),bind(Y,$fot(implies(implies(not(X_587),X_587),X_587)))]]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(X_586,implies(implies(not(X_587),X_587),X_587))),
inference(subst,[],[refute_0_52:[bind(X_25,$fot(X_586)),bind(X_584,$fot(X_587))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(implies(implies(not(X_587),X_587),X_587),Z),implies(X_586,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_586,implies(implies(not(X_587),X_587),X_587))) )],[refute_0_75,refute_0_74]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(implies(implies(not(X_590),X_590),X_590),X_588),implies(X_589,X_588))),
inference(subst,[],[refute_0_76:[bind(Z,$fot(X_588)),bind(X_586,$fot(X_589)),bind(X_587,$fot(X_590))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(implies(X_589,X_588),Z),implies(implies(implies(implies(not(X_590),X_590),X_590),X_588),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_590),X_590),X_590),X_588),implies(X_589,X_588))) )],[refute_0_77,refute_0_73]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(implies(implies(not(X_590),X_590),X_590),X_1582),X_1583))),
inference(subst,[],[refute_0_78:[bind(Z,$fot(X_1583)),bind(X_588,$fot(X_1582)),bind(X_589,$fot(not(X_1582)))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_56),X_56),X_57),X_55),implies(implies(X_56,X_57),X_55)))
| ~ is_a_theorem(implies(implies(implies(not(X_56),X_56),X_57),X_55))
| is_a_theorem(implies(implies(X_56,X_57),X_55)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_56),X_56),X_57),X_55))),bind(Y,$fot(implies(implies(X_56,X_57),X_55)))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23)))
| is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_23),Z),implies(implies(X_22,X_23),Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(X_22,X_23))),bind(Y,$fot(implies(implies(not(X_22),X_22),X_23)))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(implies(implies(not(X_22),X_22),X_23),Z),implies(implies(X_22,X_23),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_22,X_23),implies(implies(not(X_22),X_22),X_23))) )],[refute_0_22,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(implies(implies(not(X_56),X_56),X_57),X_55),implies(implies(X_56,X_57),X_55))),
inference(subst,[],[refute_0_82:[bind(Z,$fot(X_55)),bind(X_22,$fot(X_56)),bind(X_23,$fot(X_57))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_56),X_56),X_57),X_55))
| is_a_theorem(implies(implies(X_56,X_57),X_55)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_56),X_56),X_57),X_55),implies(implies(X_56,X_57),X_55))) )],[refute_0_83,refute_0_80]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(implies(implies(not(X_590),X_590),X_590),X_1582),X_1583)))
| is_a_theorem(implies(implies(X_1582,X_1583),implies(implies(implies(implies(not(X_590),X_590),X_590),X_1582),X_1583))) ),
inference(subst,[],[refute_0_84:[bind(X_55,$fot(implies(implies(implies(implies(not(X_590),X_590),X_590),X_1582),X_1583))),bind(X_56,$fot(X_1582)),bind(X_57,$fot(X_1583))]]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(X_1582,X_1583),implies(implies(implies(implies(not(X_590),X_590),X_590),X_1582),X_1583))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(implies(implies(not(X_590),X_590),X_590),X_1582),X_1583))) )],[refute_0_79,refute_0_85]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(implies(X_1619,X_1619),implies(implies(implies(implies(not(X_1620),X_1620),X_1620),X_1619),X_1619))),
inference(subst,[],[refute_0_86:[bind(X_1582,$fot(X_1619)),bind(X_1583,$fot(X_1619)),bind(X_590,$fot(X_1620))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(X_613,implies(implies(implies(implies(not(X_1620),X_1620),X_1620),X_1619),X_1619))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1619,X_1619),implies(implies(implies(implies(not(X_1620),X_1620),X_1620),X_1619),X_1619))) )],[refute_0_87,refute_0_72]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676))),X_596),implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676))),
inference(subst,[],[refute_0_88:[bind(X_1619,$fot(X_1676)),bind(X_1620,$fot(X_1677)),bind(X_613,$fot(implies(not(not(implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676))),X_596)))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676))),X_596),implies(implies(implies(implies(not(X_1677),X_1677),X_1677),X_1676),X_1676))) )],[refute_0_89,refute_0_57]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(implies(implies(not(X_2696),X_2696),X_2696),implies(X_2694,X_2696)),implies(X_2694,X_2696))),
inference(subst,[],[refute_0_90:[bind(X_1676,$fot(implies(X_2694,X_2696))),bind(X_1677,$fot(X_2696))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_2696),X_2696),X_2696),implies(X_2694,X_2696)),implies(X_2694,X_2696)))
| is_a_theorem(implies(implies(X_2694,implies(not(X_2696),X_2696)),implies(X_2694,X_2696))) ),
inference(subst,[],[refute_0_8:[bind(X_37,$fot(X_2694)),bind(X_38,$fot(implies(not(X_2696),X_2696))),bind(X_39,$fot(X_2696)),bind(X_40,$fot(implies(X_2694,X_2696)))]]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(X_2694,implies(not(X_2696),X_2696)),implies(X_2694,X_2696))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_2696),X_2696),X_2696),implies(X_2694,X_2696)),implies(X_2694,X_2696))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(implies(X_38,X_2726),implies(not(X_2726),X_2726)),implies(implies(X_38,X_2726),X_2726))),
inference(subst,[],[refute_0_93:[bind(X_2694,$fot(implies(X_38,X_2726))),bind(X_2696,$fot(X_2726))]]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(implies(not(X_2726),X_38),implies(implies(X_38,X_2726),X_2726))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_38,X_2726),implies(not(X_2726),X_2726)),implies(implies(X_38,X_2726),X_2726))) )],[refute_0_94,refute_0_9]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(implies(not(X_2729),X_2730),implies(implies(X_2730,X_2729),X_2729))),
inference(subst,[],[refute_0_95:[bind(X_2726,$fot(X_2729)),bind(X_38,$fot(X_2730))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(not(X_2729),X_2730))
| is_a_theorem(implies(implies(X_2730,X_2729),X_2729)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_2729),X_2730),implies(implies(X_2730,X_2729),X_2729))) )],[refute_0_96,refute_0_1]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(not(X_2729),implies(X_10216,not(X_2729))))
| is_a_theorem(implies(implies(implies(X_10216,not(X_2729)),X_2729),X_2729)) ),
inference(subst,[],[refute_0_97:[bind(X_2730,$fot(implies(X_10216,not(X_2729))))]]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(implies(implies(X_334,X_333),implies(not(X_335),X_333)),X_332))
| ~ is_a_theorem(implies(implies(implies(implies(X_334,X_333),implies(not(X_335),X_333)),X_332),implies(X_335,X_332)))
| is_a_theorem(implies(X_335,X_332)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_334,X_333),implies(not(X_335),X_333)),X_332))),bind(Y,$fot(implies(X_335,X_332)))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(X_265,implies(implies(X_264,X_263),implies(not(X_265),X_263))))
| is_a_theorem(implies(implies(implies(implies(X_264,X_263),implies(not(X_265),X_263)),Z),implies(X_265,Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_265)),bind(Y,$fot(implies(implies(X_264,X_263),implies(not(X_265),X_263))))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(not(X_255),X_254),implies(implies(X_254,Z),implies(not(X_255),Z)))),
inference(subst,[],[cn_1:[bind(X,$fot(not(X_255))),bind(Y,$fot(X_254))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(implies(not(X_255),X_254),implies(implies(X_254,Z),implies(not(X_255),Z))))
| is_a_theorem(implies(X_255,implies(implies(X_254,Z),implies(not(X_255),Z)))) ),
inference(subst,[],[refute_0_46:[bind(X_24,$fot(X_254)),bind(X_25,$fot(X_255)),bind(X_26,$fot(implies(implies(X_254,Z),implies(not(X_255),Z))))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(X_255,implies(implies(X_254,Z),implies(not(X_255),Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_255),X_254),implies(implies(X_254,Z),implies(not(X_255),Z)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(X_265,implies(implies(X_264,X_263),implies(not(X_265),X_263)))),
inference(subst,[],[refute_0_103:[bind(Z,$fot(X_263)),bind(X_254,$fot(X_264)),bind(X_255,$fot(X_265))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(implies(implies(implies(X_264,X_263),implies(not(X_265),X_263)),Z),implies(X_265,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_265,implies(implies(X_264,X_263),implies(not(X_265),X_263)))) )],[refute_0_104,refute_0_100]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(implies(implies(implies(X_334,X_333),implies(not(X_335),X_333)),X_332),implies(X_335,X_332))),
inference(subst,[],[refute_0_105:[bind(Z,$fot(X_332)),bind(X_263,$fot(X_333)),bind(X_264,$fot(X_334)),bind(X_265,$fot(X_335))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(implies(implies(X_334,X_333),implies(not(X_335),X_333)),X_332))
| is_a_theorem(implies(X_335,X_332)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_334,X_333),implies(not(X_335),X_333)),X_332),implies(X_335,X_332))) )],[refute_0_106,refute_0_99]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_10214),X_10215),implies(not(X_10215),X_10215)),implies(X_10214,X_10215)))
| is_a_theorem(implies(X_10215,implies(X_10214,X_10215))) ),
inference(subst,[],[refute_0_107:[bind(X_332,$fot(implies(X_10214,X_10215))),bind(X_333,$fot(X_10215)),bind(X_334,$fot(not(X_10214))),bind(X_335,$fot(X_10215))]]) ).
cnf(refute_0_109,plain,
is_a_theorem(implies(implies(X_10151,implies(not(X_2696),X_2696)),implies(X_10151,X_2696))),
inference(subst,[],[refute_0_93:[bind(X_2694,$fot(X_10151))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(implies(X_49,X_50),X_47))
| ~ is_a_theorem(implies(implies(implies(X_49,X_50),X_47),implies(implies(implies(not(X_49),X_48),X_50),X_47)))
| is_a_theorem(implies(implies(implies(not(X_49),X_48),X_50),X_47)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_49,X_50),X_47))),bind(Y,$fot(implies(implies(implies(not(X_49),X_48),X_50),X_47)))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(implies(X_49,X_50),X_47),implies(implies(implies(not(X_49),X_48),X_50),X_47))),
inference(subst,[],[refute_0_17:[bind(Z,$fot(X_47)),bind(X_24,$fot(X_48)),bind(X_25,$fot(X_49)),bind(X_26,$fot(X_50))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(implies(implies(X_49,X_50),X_47))
| is_a_theorem(implies(implies(implies(not(X_49),X_48),X_50),X_47)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_49,X_50),X_47),implies(implies(implies(not(X_49),X_48),X_50),X_47))) )],[refute_0_111,refute_0_110]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(implies(X_10151,implies(not(X_2696),X_2696)),implies(X_10151,X_2696)))
| is_a_theorem(implies(implies(implies(not(X_10151),X_10150),implies(not(X_2696),X_2696)),implies(X_10151,X_2696))) ),
inference(subst,[],[refute_0_112:[bind(X_47,$fot(implies(X_10151,X_2696))),bind(X_48,$fot(X_10150)),bind(X_49,$fot(X_10151)),bind(X_50,$fot(implies(not(X_2696),X_2696)))]]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(implies(not(X_10151),X_10150),implies(not(X_2696),X_2696)),implies(X_10151,X_2696))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_10151,implies(not(X_2696),X_2696)),implies(X_10151,X_2696))) )],[refute_0_109,refute_0_113]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(implies(not(X_10214),X_10215),implies(not(X_10215),X_10215)),implies(X_10214,X_10215))),
inference(subst,[],[refute_0_114:[bind(X_10150,$fot(X_10215)),bind(X_10151,$fot(X_10214)),bind(X_2696,$fot(X_10215))]]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(X_10215,implies(X_10214,X_10215))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_10214),X_10215),implies(not(X_10215),X_10215)),implies(X_10214,X_10215))) )],[refute_0_115,refute_0_108]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(not(X_2729),implies(X_10216,not(X_2729)))),
inference(subst,[],[refute_0_116:[bind(X_10214,$fot(X_10216)),bind(X_10215,$fot(not(X_2729)))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(implies(X_10216,not(X_2729)),X_2729),X_2729)),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_2729),implies(X_10216,not(X_2729)))) )],[refute_0_117,refute_0_98]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(implies(X_10226,not(X_10227)),X_10227),X_10227)),
inference(subst,[],[refute_0_118:[bind(X_10216,$fot(X_10226)),bind(X_2729,$fot(X_10227))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(X_10226,not(X_10227)),X_10227))
| is_a_theorem(X_10227) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_10226,not(X_10227)),X_10227),X_10227)) )],[refute_0_119,refute_0_0]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(implies(implies(X_16426,X_16426),not(not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427)))))),not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427))))))
| is_a_theorem(not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427))))) ),
inference(subst,[],[refute_0_120:[bind(X_10226,$fot(implies(X_16426,X_16426))),bind(X_10227,$fot(not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427))))))]]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130))))),not(implies(X_13130,X_13130))),implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130)))),X_13127))
| is_a_theorem(implies(implies(implies(X_13129,X_13129),not(not(implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130)))))),X_13127)) ),
inference(subst,[],[refute_0_8:[bind(X_37,$fot(implies(X_13129,X_13129))),bind(X_38,$fot(not(not(implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130))))))),bind(X_39,$fot(not(implies(X_13130,X_13130)))),bind(X_40,$fot(X_13127))]]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(implies(not(X_25),X_1639),implies(implies(not(implies(implies(X_1640,X_1640),not(X_25))),implies(implies(X_1640,X_1640),not(X_25))),X_1639)))
| is_a_theorem(implies(X_25,implies(implies(not(implies(implies(X_1640,X_1640),not(X_25))),implies(implies(X_1640,X_1640),not(X_25))),X_1639))) ),
inference(subst,[],[refute_0_46:[bind(X_24,$fot(X_1639)),bind(X_26,$fot(implies(implies(not(implies(implies(X_1640,X_1640),not(X_25))),implies(implies(X_1640,X_1640),not(X_25))),X_1639)))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(X_928,X_928),X_926)),implies(implies(X_928,X_928),X_926)),implies(X_927,X_926)))
| is_a_theorem(implies(implies(implies(X_927,X_926),Z),implies(implies(not(implies(implies(X_928,X_928),X_926)),implies(implies(X_928,X_928),X_926)),Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(not(implies(implies(X_928,X_928),X_926)),implies(implies(X_928,X_928),X_926)))),bind(Y,$fot(implies(X_927,X_926)))]]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(implies(implies(X_614,X_614),X_612),implies(X_613,X_612)))
| is_a_theorem(implies(implies(not(implies(implies(X_614,X_614),X_612)),implies(implies(X_614,X_614),X_612)),implies(X_613,X_612))) ),
inference(subst,[],[refute_0_23:[bind(X_22,$fot(implies(implies(X_614,X_614),X_612))),bind(X_23,$fot(implies(X_613,X_612)))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(not(implies(implies(X_614,X_614),X_612)),implies(implies(X_614,X_614),X_612)),implies(X_613,X_612))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_614,X_614),X_612),implies(X_613,X_612))) )],[refute_0_70,refute_0_125]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(not(implies(implies(X_928,X_928),X_926)),implies(implies(X_928,X_928),X_926)),implies(X_927,X_926))),
inference(subst,[],[refute_0_126:[bind(X_612,$fot(X_926)),bind(X_613,$fot(X_927)),bind(X_614,$fot(X_928))]]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(implies(X_927,X_926),Z),implies(implies(not(implies(implies(X_928,X_928),X_926)),implies(implies(X_928,X_928),X_926)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(X_928,X_928),X_926)),implies(implies(X_928,X_928),X_926)),implies(X_927,X_926))) )],[refute_0_127,refute_0_124]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(not(implies(implies(X_928,X_928),X_1582)),implies(implies(X_928,X_928),X_1582)),X_1583))),
inference(subst,[],[refute_0_128:[bind(Z,$fot(X_1583)),bind(X_926,$fot(X_1582)),bind(X_927,$fot(not(X_1582)))]]) ).
cnf(refute_0_130,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(not(implies(implies(X_928,X_928),X_1582)),implies(implies(X_928,X_928),X_1582)),X_1583)))
| is_a_theorem(implies(implies(X_1582,X_1583),implies(implies(not(implies(implies(X_928,X_928),X_1582)),implies(implies(X_928,X_928),X_1582)),X_1583))) ),
inference(subst,[],[refute_0_84:[bind(X_55,$fot(implies(implies(not(implies(implies(X_928,X_928),X_1582)),implies(implies(X_928,X_928),X_1582)),X_1583))),bind(X_56,$fot(X_1582)),bind(X_57,$fot(X_1583))]]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(X_1582,X_1583),implies(implies(not(implies(implies(X_928,X_928),X_1582)),implies(implies(X_928,X_928),X_1582)),X_1583))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(not(implies(implies(X_928,X_928),X_1582)),implies(implies(X_928,X_928),X_1582)),X_1583))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
is_a_theorem(implies(implies(not(X_25),X_1639),implies(implies(not(implies(implies(X_1640,X_1640),not(X_25))),implies(implies(X_1640,X_1640),not(X_25))),X_1639))),
inference(subst,[],[refute_0_131:[bind(X_1582,$fot(not(X_25))),bind(X_1583,$fot(X_1639)),bind(X_928,$fot(X_1640))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(X_25,implies(implies(not(implies(implies(X_1640,X_1640),not(X_25))),implies(implies(X_1640,X_1640),not(X_25))),X_1639))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_25),X_1639),implies(implies(not(implies(implies(X_1640,X_1640),not(X_25))),implies(implies(X_1640,X_1640),not(X_25))),X_1639))) )],[refute_0_132,refute_0_123]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(X_1911,X_1911),implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_1639))),
inference(subst,[],[refute_0_133:[bind(X_25,$fot(implies(X_1911,X_1911)))]]) ).
cnf(refute_0_135,plain,
( ~ is_a_theorem(implies(implies(X_1591,X_1591),X_1590))
| ~ is_a_theorem(implies(implies(implies(X_1591,X_1591),X_1590),X_1590))
| is_a_theorem(X_1590) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1591,X_1591),X_1590))),bind(Y,$fot(X_1590))]]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1588,X_1588),X_1587),X_1587))),X_596),implies(implies(implies(X_1588,X_1588),X_1587),X_1587)))
| is_a_theorem(implies(implies(implies(X_1588,X_1588),X_1587),X_1587)) ),
inference(subst,[],[refute_0_56:[bind(X_597,$fot(implies(implies(implies(X_1588,X_1588),X_1587),X_1587)))]]) ).
cnf(refute_0_137,plain,
( ~ is_a_theorem(implies(implies(X_1585,X_1585),implies(implies(implies(X_1586,X_1586),X_1585),X_1585)))
| is_a_theorem(implies(X_613,implies(implies(implies(X_1586,X_1586),X_1585),X_1585))) ),
inference(subst,[],[refute_0_71:[bind(X_612,$fot(implies(implies(implies(X_1586,X_1586),X_1585),X_1585))),bind(X_614,$fot(X_1585))]]) ).
cnf(refute_0_138,plain,
( ~ is_a_theorem(implies(implies(implies(X_614,X_614),X_612),implies(X_613,X_612)))
| is_a_theorem(implies(implies(implies(X_613,X_612),Z),implies(implies(implies(X_614,X_614),X_612),Z))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(implies(implies(X_614,X_614),X_612))),bind(Y,$fot(implies(X_613,X_612)))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(implies(implies(X_613,X_612),Z),implies(implies(implies(X_614,X_614),X_612),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_614,X_614),X_612),implies(X_613,X_612))) )],[refute_0_70,refute_0_138]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(implies(X_614,X_614),X_1582),X_1583))),
inference(subst,[],[refute_0_139:[bind(Z,$fot(X_1583)),bind(X_612,$fot(X_1582)),bind(X_613,$fot(not(X_1582)))]]) ).
cnf(refute_0_141,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(implies(X_614,X_614),X_1582),X_1583)))
| is_a_theorem(implies(implies(X_1582,X_1583),implies(implies(implies(X_614,X_614),X_1582),X_1583))) ),
inference(subst,[],[refute_0_84:[bind(X_55,$fot(implies(implies(implies(X_614,X_614),X_1582),X_1583))),bind(X_56,$fot(X_1582)),bind(X_57,$fot(X_1583))]]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(implies(X_1582,X_1583),implies(implies(implies(X_614,X_614),X_1582),X_1583))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_1582),X_1582),X_1583),implies(implies(implies(X_614,X_614),X_1582),X_1583))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
is_a_theorem(implies(implies(X_1585,X_1585),implies(implies(implies(X_1586,X_1586),X_1585),X_1585))),
inference(subst,[],[refute_0_142:[bind(X_1582,$fot(X_1585)),bind(X_1583,$fot(X_1585)),bind(X_614,$fot(X_1586))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(X_613,implies(implies(implies(X_1586,X_1586),X_1585),X_1585))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1585,X_1585),implies(implies(implies(X_1586,X_1586),X_1585),X_1585))) )],[refute_0_143,refute_0_137]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1588,X_1588),X_1587),X_1587))),X_596),implies(implies(implies(X_1588,X_1588),X_1587),X_1587))),
inference(subst,[],[refute_0_144:[bind(X_1585,$fot(X_1587)),bind(X_1586,$fot(X_1588)),bind(X_613,$fot(implies(not(not(implies(implies(implies(X_1588,X_1588),X_1587),X_1587))),X_596)))]]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(implies(X_1588,X_1588),X_1587),X_1587)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(implies(implies(X_1588,X_1588),X_1587),X_1587))),X_596),implies(implies(implies(X_1588,X_1588),X_1587),X_1587))) )],[refute_0_145,refute_0_136]) ).
cnf(refute_0_147,plain,
is_a_theorem(implies(implies(implies(X_1591,X_1591),X_1590),X_1590)),
inference(subst,[],[refute_0_146:[bind(X_1587,$fot(X_1590)),bind(X_1588,$fot(X_1591))]]) ).
cnf(refute_0_148,plain,
( ~ is_a_theorem(implies(implies(X_1591,X_1591),X_1590))
| is_a_theorem(X_1590) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1591,X_1591),X_1590),X_1590)) )],[refute_0_147,refute_0_135]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(implies(X_1911,X_1911),implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_1639)))
| is_a_theorem(implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_1639)) ),
inference(subst,[],[refute_0_148:[bind(X_1590,$fot(implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_1639))),bind(X_1591,$fot(X_1911))]]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_1639)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1911,X_1911),implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_1639))) )],[refute_0_134,refute_0_149]) ).
cnf(refute_0_151,plain,
is_a_theorem(implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_10149)),
inference(subst,[],[refute_0_150:[bind(X_1639,$fot(X_10149))]]) ).
cnf(refute_0_152,plain,
( ~ is_a_theorem(implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_10149))
| is_a_theorem(implies(implies(implies(not(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911))))),X_10150),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_10149)) ),
inference(subst,[],[refute_0_112:[bind(X_47,$fot(X_10149)),bind(X_48,$fot(X_10150)),bind(X_49,$fot(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))))),bind(X_50,$fot(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))))]]) ).
cnf(refute_0_153,plain,
is_a_theorem(implies(implies(implies(not(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911))))),X_10150),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_10149)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),implies(implies(X_1640,X_1640),not(implies(X_1911,X_1911)))),X_10149)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
is_a_theorem(implies(implies(implies(not(not(implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130))))),not(implies(X_13130,X_13130))),implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130)))),X_13127)),
inference(subst,[],[refute_0_153:[bind(X_10149,$fot(X_13127)),bind(X_10150,$fot(not(implies(X_13130,X_13130)))),bind(X_1640,$fot(X_13129)),bind(X_1911,$fot(X_13130))]]) ).
cnf(refute_0_155,plain,
is_a_theorem(implies(implies(implies(X_13129,X_13129),not(not(implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130)))))),X_13127)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130))))),not(implies(X_13130,X_13130))),implies(implies(X_13129,X_13129),not(implies(X_13130,X_13130)))),X_13127)) )],[refute_0_154,refute_0_122]) ).
cnf(refute_0_156,plain,
is_a_theorem(implies(implies(implies(X_16426,X_16426),not(not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427)))))),not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427)))))),
inference(subst,[],[refute_0_155:[bind(X_13127,$fot(not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427)))))),bind(X_13129,$fot(X_16426)),bind(X_13130,$fot(X_16427))]]) ).
cnf(refute_0_157,plain,
is_a_theorem(not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_16426,X_16426),not(not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427)))))),not(implies(implies(X_16426,X_16426),not(implies(X_16427,X_16427)))))) )],[refute_0_156,refute_0_121]) ).
cnf(refute_0_158,plain,
is_a_theorem(not(implies(implies(x,x),not(implies(y,y))))),
inference(subst,[],[refute_0_157:[bind(X_16426,$fot(x)),bind(X_16427,$fot(y))]]) ).
cnf(refute_0_159,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(not(implies(implies(x,x),not(implies(y,y))))) )],[refute_0_158,prove_cn_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL405-1 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 17:05:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 11.48/11.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.48/11.66
% 11.48/11.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.48/11.68
%------------------------------------------------------------------------------