TSTP Solution File: LCL113-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL113-1 : 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 12:49:39 EDT 2022
% Result : Unsatisfiable 223.45s 223.60s
% Output : CNFRefutation 223.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 6
% Syntax : Number of clauses : 204 ( 115 unt; 0 nHn; 64 RR)
% Number of literals : 313 ( 0 equ; 110 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 : 563 ( 92 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(mv_1,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(mv_2,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(mv_3,axiom,
is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) ).
cnf(mv_5,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
cnf(prove_mv_33,negated_conjecture,
~ is_a_theorem(implies(implies(not(a),b),implies(not(b),a))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),X_39),X_39))
| ~ is_a_theorem(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),X_39))
| is_a_theorem(X_39) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),X_39))),bind(Y,$fot(X_39))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(X_9,implies(Y,X_9))),
inference(subst,[],[mv_1:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(X_9)
| ~ is_a_theorem(implies(X_9,implies(Y,X_9)))
| is_a_theorem(implies(Y,X_9)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_9)),bind(Y,$fot(implies(Y,X_9)))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X_9)
| is_a_theorem(implies(Y,X_9)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_9,implies(Y,X_9))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(X_11,implies(implies(not(X),not(Y)),implies(Y,X)))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(X_11,implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[mv_5,refute_0_4]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(X_29,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(subst,[],[refute_0_5:[bind(X_11,$fot(implies(X_29,implies(implies(not(X),not(Y)),implies(Y,X)))))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(X,Y),Y))
| ~ is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))
| is_a_theorem(implies(implies(Y,X),X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Y))),bind(Y,$fot(implies(implies(Y,X),X)))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(X,Y),Y))
| is_a_theorem(implies(implies(Y,X),X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) )],[mv_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(X_29,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X))))
| is_a_theorem(implies(implies(implies(implies(not(X),not(Y)),implies(Y,X)),X_29),X_29)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_29)),bind(Y,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(implies(not(X),not(Y)),implies(Y,X)),X_29),X_29)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_29,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X)))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),X_39),X_39)),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(X_29,$fot(X_39))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),X_39))
| is_a_theorem(X_39) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),X_39),X_39)) )],[refute_0_11,refute_0_0]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_37),not(not(X_125990))),implies(not(X_125990),X_37)),implies(implies(not(X_37),X_125990),implies(not(X_125990),X_37))))
| is_a_theorem(implies(implies(not(X_37),X_125990),implies(not(X_125990),X_37))) ),
inference(subst,[],[refute_0_12:[bind(X_38,$fot(not(X_125990))),bind(X_39,$fot(implies(implies(not(X_37),X_125990),implies(not(X_125990),X_37))))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(implies(X_124,X_125),implies(implies(X_125,X_126),implies(X_124,X_126))),X_127))
| ~ is_a_theorem(implies(implies(implies(implies(X_124,X_125),implies(implies(X_125,X_126),implies(X_124,X_126))),X_127),X_127))
| is_a_theorem(X_127) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_124,X_125),implies(implies(X_125,X_126),implies(X_124,X_126))),X_127))),bind(Y,$fot(X_127))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(X_11,implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_11,implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[mv_2,refute_0_15]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(X_29,implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))),
inference(subst,[],[refute_0_16:[bind(X_11,$fot(implies(X_29,implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(X_29,implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))))
| is_a_theorem(implies(implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),X_29),X_29)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_29)),bind(Y,$fot(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),X_29),X_29)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_29,implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(implies(implies(X_124,X_125),implies(implies(X_125,X_126),implies(X_124,X_126))),X_127),X_127)),
inference(subst,[],[refute_0_19:[bind(X,$fot(X_124)),bind(Y,$fot(X_125)),bind(Z,$fot(X_126)),bind(X_29,$fot(X_127))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(implies(X_124,X_125),implies(implies(X_125,X_126),implies(X_124,X_126))),X_127))
| is_a_theorem(X_127) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_124,X_125),implies(implies(X_125,X_126),implies(X_124,X_126))),X_127),X_127)) )],[refute_0_20,refute_0_14]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_125448,X_125449),implies(X_125448,not(not(X_125449)))),implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126))),implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126))))
| is_a_theorem(implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126))) ),
inference(subst,[],[refute_0_21:[bind(X_124,$fot(implies(X_125448,X_125449))),bind(X_125,$fot(implies(X_125448,not(not(X_125449))))),bind(X_127,$fot(implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126))))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(not(X_3445),not(implies(not(not(X_3445)),X_3445))),not(not(X_3445))))
| ~ is_a_theorem(implies(not(X_3445),not(implies(not(not(X_3445)),X_3445))))
| is_a_theorem(not(not(X_3445))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_3445),not(implies(not(not(X_3445)),X_3445))))),bind(Y,$fot(not(not(X_3445))))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(implies(X_72,X_71),X_71),X_73))
| ~ is_a_theorem(implies(implies(implies(implies(X_72,X_71),X_71),X_73),implies(implies(implies(X_71,X_72),X_72),X_73)))
| is_a_theorem(implies(implies(implies(X_71,X_72),X_72),X_73)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_72,X_71),X_71),X_73))),bind(Y,$fot(implies(implies(implies(X_71,X_72),X_72),X_73)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[mv_2,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))
| is_a_theorem(implies(implies(implies(implies(Y,X),X),X_42),implies(implies(implies(X,Y),Y),X_42))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(implies(implies(X,Y),Y))),bind(Y,$fot(implies(implies(Y,X),X))),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(implies(Y,X),X),X_42),implies(implies(implies(X,Y),Y),X_42))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) )],[mv_3,refute_0_27]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(implies(implies(implies(X_72,X_71),X_71),X_73),implies(implies(implies(X_71,X_72),X_72),X_73))),
inference(subst,[],[refute_0_28:[bind(X,$fot(X_71)),bind(Y,$fot(X_72)),bind(X_42,$fot(X_73))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(X_72,X_71),X_71),X_73))
| is_a_theorem(implies(implies(implies(X_71,X_72),X_72),X_73)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_72,X_71),X_71),X_73),implies(implies(implies(X_71,X_72),X_72),X_73))) )],[refute_0_29,refute_0_24]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(X_2079,not(not(X_2079))),not(not(X_2079))),not(not(X_2079))))
| is_a_theorem(implies(implies(implies(not(not(X_2079)),X_2079),X_2079),not(not(X_2079)))) ),
inference(subst,[],[refute_0_30:[bind(X_71,$fot(not(not(X_2079)))),bind(X_72,$fot(X_2079)),bind(X_73,$fot(not(not(X_2079))))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(X,implies(X_1835,not(not(X_1835)))),implies(X_1835,not(not(X_1835)))))
| is_a_theorem(implies(implies(implies(X_1835,not(not(X_1835))),X),X)) ),
inference(subst,[],[refute_0_8:[bind(Y,$fot(implies(X_1835,not(not(X_1835)))))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(not(X_95),not(X_96)),implies(X_97,implies(X_96,X_95))))
| ~ is_a_theorem(implies(not(X_95),not(X_96)))
| is_a_theorem(implies(X_97,implies(X_96,X_95))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X_95),not(X_96)))),bind(Y,$fot(implies(X_97,implies(X_96,X_95))))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(implies(implies(Y,X),X_42),implies(implies(not(X),not(Y)),X_42))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X))),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(implies(implies(Y,X),X_42),implies(implies(not(X),not(Y)),X_42))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[mv_5,refute_0_34]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(implies(Y,X),implies(X_90,implies(Y,X))),implies(implies(not(X),not(Y)),implies(X_90,implies(Y,X))))),
inference(subst,[],[refute_0_35:[bind(X_42,$fot(implies(X_90,implies(Y,X))))]]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(X_31,implies(X_32,X_31)),X_33))
| ~ is_a_theorem(implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33))
| is_a_theorem(X_33) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_31,implies(X_32,X_31)),X_33))),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(X,implies(Y,X)))
| is_a_theorem(implies(X_11,implies(X,implies(Y,X)))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(X,implies(Y,X))))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(X_11,implies(X,implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(X,implies(Y,X))) )],[mv_1,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(X_29,implies(X,implies(Y,X))),implies(X,implies(Y,X)))),
inference(subst,[],[refute_0_39:[bind(X_11,$fot(implies(X_29,implies(X,implies(Y,X)))))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(implies(X_29,implies(X,implies(Y,X))),implies(X,implies(Y,X))))
| is_a_theorem(implies(implies(implies(X,implies(Y,X)),X_29),X_29)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_29)),bind(Y,$fot(implies(X,implies(Y,X))))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(implies(X,implies(Y,X)),X_29),X_29)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_29,implies(X,implies(Y,X))),implies(X,implies(Y,X)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(X_29,$fot(X_33))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(implies(X_31,implies(X_32,X_31)),X_33))
| is_a_theorem(X_33) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33)) )],[refute_0_43,refute_0_37]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(implies(implies(Y,X),implies(X_90,implies(Y,X))),implies(implies(not(X),not(Y)),implies(X_90,implies(Y,X)))))
| is_a_theorem(implies(implies(not(X),not(Y)),implies(X_90,implies(Y,X)))) ),
inference(subst,[],[refute_0_44:[bind(X_31,$fot(implies(Y,X))),bind(X_32,$fot(X_90)),bind(X_33,$fot(implies(implies(not(X),not(Y)),implies(X_90,implies(Y,X)))))]]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(not(X),not(Y)),implies(X_90,implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(Y,X),implies(X_90,implies(Y,X))),implies(implies(not(X),not(Y)),implies(X_90,implies(Y,X))))) )],[refute_0_36,refute_0_45]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(not(X_95),not(X_96)),implies(X_97,implies(X_96,X_95)))),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_95)),bind(Y,$fot(X_96)),bind(X_90,$fot(X_97))]]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(implies(not(X_95),not(X_96)))
| is_a_theorem(implies(X_97,implies(X_96,X_95))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_95),not(X_96)),implies(X_97,implies(X_96,X_95)))) )],[refute_0_47,refute_0_33]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(not(not(not(X_96))),not(X_96)))
| is_a_theorem(implies(X_97,implies(X_96,not(not(X_96))))) ),
inference(subst,[],[refute_0_48:[bind(X_95,$fot(not(not(X_96))))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(implies(X_251,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),X_248))
| ~ is_a_theorem(implies(implies(implies(X_251,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),X_248),X_248))
| is_a_theorem(X_248) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_251,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),X_248))),bind(Y,$fot(X_248))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(X,implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103)))),implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103)))))
| is_a_theorem(implies(implies(implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103))),X),X)) ),
inference(subst,[],[refute_0_8:[bind(Y,$fot(implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103)))))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(X_24,implies(implies(not(X_22),not(X_23)),implies(X_23,X_22))))
| is_a_theorem(implies(Y,implies(X_24,implies(implies(not(X_22),not(X_23)),implies(X_23,X_22))))) ),
inference(subst,[],[refute_0_3:[bind(X_9,$fot(implies(X_24,implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)))))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(X_24,implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)))),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(X_11,$fot(X_24))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(Y,implies(X_24,implies(implies(not(X_22),not(X_23)),implies(X_23,X_22))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_24,implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)))) )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(X,implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103)))),implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103))))),
inference(subst,[],[refute_0_54:[bind(Y,$fot(implies(X,implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103)))))),bind(X_22,$fot(X_103)),bind(X_23,$fot(X_104)),bind(X_24,$fot(X_105))]]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103))),X),X)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103)))),implies(X_105,implies(implies(not(X_103),not(X_104)),implies(X_104,X_103))))) )],[refute_0_55,refute_0_51]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(implies(X_251,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),X_248),X_248)),
inference(subst,[],[refute_0_56:[bind(X,$fot(X_248)),bind(X_103,$fot(X_249)),bind(X_104,$fot(X_250)),bind(X_105,$fot(X_251))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(X_251,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),X_248))
| is_a_theorem(X_248) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_251,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),X_248),X_248)) )],[refute_0_57,refute_0_50]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(implies(implies(X_1830,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),implies(not(not(X_1830)),X_1830)))
| is_a_theorem(implies(not(not(X_1830)),X_1830)) ),
inference(subst,[],[refute_0_58:[bind(X_248,$fot(implies(not(not(X_1830)),X_1830))),bind(X_251,$fot(implies(X_1830,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249)))))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(not(not(X_140)),implies(X_141,X_140)))
| is_a_theorem(implies(implies(implies(X_141,X_140),Z),implies(not(not(X_140)),Z))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(not(not(X_140)))),bind(Y,$fot(implies(X_141,X_140)))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),implies(not(not(X_37)),implies(X_38,X_37))))
| is_a_theorem(implies(not(not(X_37)),implies(X_38,X_37))) ),
inference(subst,[],[refute_0_12:[bind(X_39,$fot(implies(not(not(X_37)),implies(X_38,X_37))))]]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(not(X_132),implies(X_132,X_131)))
| is_a_theorem(implies(implies(implies(X_132,X_131),Z),implies(not(X_132),Z))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(not(X_132))),bind(Y,$fot(implies(X_132,X_131)))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(X_40,implies(Y,X_40))),
inference(subst,[],[mv_1:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(X_40,implies(Y,X_40)))
| is_a_theorem(implies(implies(implies(Y,X_40),X_42),implies(X_40,X_42))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_40)),bind(Y,$fot(implies(Y,X_40))),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(implies(Y,X_40),X_42),implies(X_40,X_42))),
inference(resolve,[$cnf( is_a_theorem(implies(X_40,implies(Y,X_40))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(not(X_128),not(X_129)),implies(X_129,X_128)),implies(not(X_129),implies(X_129,X_128)))),
inference(subst,[],[refute_0_65:[bind(Y,$fot(not(X_128))),bind(X_40,$fot(not(X_129))),bind(X_42,$fot(implies(X_129,X_128)))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_128),not(X_129)),implies(X_129,X_128)),implies(not(X_129),implies(X_129,X_128))))
| is_a_theorem(implies(not(X_129),implies(X_129,X_128))) ),
inference(subst,[],[refute_0_12:[bind(X_37,$fot(X_128)),bind(X_38,$fot(X_129)),bind(X_39,$fot(implies(not(X_129),implies(X_129,X_128))))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(not(X_129),implies(X_129,X_128))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_128),not(X_129)),implies(X_129,X_128)),implies(not(X_129),implies(X_129,X_128)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(not(X_132),implies(X_132,X_131))),
inference(subst,[],[refute_0_68:[bind(X_128,$fot(X_131)),bind(X_129,$fot(X_132))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(X_132,X_131),Z),implies(not(X_132),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_132),implies(X_132,X_131))) )],[refute_0_69,refute_0_62]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),implies(not(not(X_37)),implies(X_38,X_37)))),
inference(subst,[],[refute_0_70:[bind(Z,$fot(implies(X_38,X_37))),bind(X_131,$fot(not(X_38))),bind(X_132,$fot(not(X_37)))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(not(not(X_37)),implies(X_38,X_37))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_37),not(X_38)),implies(X_38,X_37)),implies(not(not(X_37)),implies(X_38,X_37)))) )],[refute_0_71,refute_0_61]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(not(not(X_140)),implies(X_141,X_140))),
inference(subst,[],[refute_0_72:[bind(X_37,$fot(X_140)),bind(X_38,$fot(X_141))]]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(implies(X_141,X_140),Z),implies(not(not(X_140)),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_140)),implies(X_141,X_140))) )],[refute_0_73,refute_0_60]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(implies(implies(X_1828,X_1827),X_1827),implies(not(not(X_1827)),X_1827))),
inference(subst,[],[refute_0_74:[bind(Z,$fot(X_1827)),bind(X_140,$fot(X_1827)),bind(X_141,$fot(X_1828))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(implies(X_1828,X_1827),X_1827),implies(not(not(X_1827)),X_1827)))
| is_a_theorem(implies(implies(implies(X_1827,X_1828),X_1828),implies(not(not(X_1827)),X_1827))) ),
inference(subst,[],[refute_0_30:[bind(X_71,$fot(X_1827)),bind(X_72,$fot(X_1828)),bind(X_73,$fot(implies(not(not(X_1827)),X_1827)))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(implies(X_1827,X_1828),X_1828),implies(not(not(X_1827)),X_1827))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1828,X_1827),X_1827),implies(not(not(X_1827)),X_1827))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(implies(implies(X_1830,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),implies(not(not(X_1830)),X_1830))),
inference(subst,[],[refute_0_77:[bind(X_1827,$fot(X_1830)),bind(X_1828,$fot(implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(not(not(X_1830)),X_1830)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1830,implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),implies(implies(not(X_249),not(X_250)),implies(X_250,X_249))),implies(not(not(X_1830)),X_1830))) )],[refute_0_78,refute_0_59]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(not(not(not(X_96))),not(X_96))),
inference(subst,[],[refute_0_79:[bind(X_1830,$fot(not(X_96)))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(X_97,implies(X_96,not(not(X_96))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(X_96))),not(X_96))) )],[refute_0_80,refute_0_49]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(X,implies(X_1835,not(not(X_1835)))),implies(X_1835,not(not(X_1835))))),
inference(subst,[],[refute_0_81:[bind(X_96,$fot(X_1835)),bind(X_97,$fot(implies(X,implies(X_1835,not(not(X_1835))))))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(implies(X_1835,not(not(X_1835))),X),X)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X_1835,not(not(X_1835)))),implies(X_1835,not(not(X_1835))))) )],[refute_0_82,refute_0_32]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(implies(implies(X_2079,not(not(X_2079))),not(not(X_2079))),not(not(X_2079)))),
inference(subst,[],[refute_0_83:[bind(X,$fot(not(not(X_2079)))),bind(X_1835,$fot(X_2079))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(implies(not(not(X_2079)),X_2079),X_2079),not(not(X_2079)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_2079,not(not(X_2079))),not(not(X_2079))),not(not(X_2079)))) )],[refute_0_84,refute_0_31]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(implies(not(not(X_3438)),X_3438),X_3438),not(not(X_3438)))),
inference(subst,[],[refute_0_85:[bind(X_2079,$fot(X_3438))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(X_75,X_74),X_76))
| ~ is_a_theorem(implies(implies(implies(X_75,X_74),X_76),implies(implies(not(X_74),not(X_75)),X_76)))
| is_a_theorem(implies(implies(not(X_74),not(X_75)),X_76)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_75,X_74),X_76))),bind(Y,$fot(implies(implies(not(X_74),not(X_75)),X_76)))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(implies(implies(X_75,X_74),X_76),implies(implies(not(X_74),not(X_75)),X_76))),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_74)),bind(Y,$fot(X_75)),bind(X_42,$fot(X_76))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(implies(implies(X_75,X_74),X_76))
| is_a_theorem(implies(implies(not(X_74),not(X_75)),X_76)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_75,X_74),X_76),implies(implies(not(X_74),not(X_75)),X_76))) )],[refute_0_88,refute_0_87]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_3438)),X_3438),X_3438),not(not(X_3438))))
| is_a_theorem(implies(implies(not(X_3438),not(implies(not(not(X_3438)),X_3438))),not(not(X_3438)))) ),
inference(subst,[],[refute_0_89:[bind(X_74,$fot(X_3438)),bind(X_75,$fot(implies(not(not(X_3438)),X_3438))),bind(X_76,$fot(not(not(X_3438))))]]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(implies(not(X_3438),not(implies(not(not(X_3438)),X_3438))),not(not(X_3438)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_3438)),X_3438),X_3438),not(not(X_3438)))) )],[refute_0_86,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(not(X_3445),not(implies(not(not(X_3445)),X_3445))),not(not(X_3445)))),
inference(subst,[],[refute_0_91:[bind(X_3438,$fot(X_3445))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(not(X_3445),not(implies(not(not(X_3445)),X_3445))))
| is_a_theorem(not(not(X_3445))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_3445),not(implies(not(not(X_3445)),X_3445))),not(not(X_3445)))) )],[refute_0_92,refute_0_23]) ).
cnf(refute_0_94,plain,
( ~ is_a_theorem(implies(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))),not(implies(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))),implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))))
| is_a_theorem(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))) ),
inference(subst,[],[refute_0_93:[bind(X_3445,$fot(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(X_1864)
| ~ is_a_theorem(implies(X_1864,implies(not(X_1864),X_1863)))
| is_a_theorem(implies(not(X_1864),X_1863)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1864)),bind(Y,$fot(implies(not(X_1864),X_1863)))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(implies(X_47,X_48),X_49))
| ~ is_a_theorem(implies(implies(implies(X_47,X_48),X_49),implies(X_48,X_49)))
| is_a_theorem(implies(X_48,X_49)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_47,X_48),X_49))),bind(Y,$fot(implies(X_48,X_49)))]]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(implies(X_47,X_48),X_49),implies(X_48,X_49))),
inference(subst,[],[refute_0_65:[bind(Y,$fot(X_47)),bind(X_40,$fot(X_48)),bind(X_42,$fot(X_49))]]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(implies(X_47,X_48),X_49))
| is_a_theorem(implies(X_48,X_49)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_47,X_48),X_49),implies(X_48,X_49))) )],[refute_0_97,refute_0_96]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(implies(implies(X_1861,X_1862),X_1862),implies(not(X_1862),X_1861)))
| is_a_theorem(implies(X_1862,implies(not(X_1862),X_1861))) ),
inference(subst,[],[refute_0_98:[bind(X_47,$fot(implies(X_1861,X_1862))),bind(X_48,$fot(X_1862)),bind(X_49,$fot(implies(not(X_1862),X_1861)))]]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(implies(implies(X_1828,X_1827),X_1827),implies(not(X_1828),X_1827))),
inference(subst,[],[refute_0_70:[bind(Z,$fot(X_1827)),bind(X_131,$fot(X_1827)),bind(X_132,$fot(X_1828))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(implies(implies(X_1828,X_1827),X_1827),implies(not(X_1828),X_1827)))
| is_a_theorem(implies(implies(implies(X_1827,X_1828),X_1828),implies(not(X_1828),X_1827))) ),
inference(subst,[],[refute_0_30:[bind(X_71,$fot(X_1827)),bind(X_72,$fot(X_1828)),bind(X_73,$fot(implies(not(X_1828),X_1827)))]]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(implies(implies(X_1827,X_1828),X_1828),implies(not(X_1828),X_1827))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1828,X_1827),X_1827),implies(not(X_1828),X_1827))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(implies(X_1861,X_1862),X_1862),implies(not(X_1862),X_1861))),
inference(subst,[],[refute_0_102:[bind(X_1827,$fot(X_1861)),bind(X_1828,$fot(X_1862))]]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(X_1862,implies(not(X_1862),X_1861))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1861,X_1862),X_1862),implies(not(X_1862),X_1861))) )],[refute_0_103,refute_0_99]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(X_1864,implies(not(X_1864),X_1863))),
inference(subst,[],[refute_0_104:[bind(X_1861,$fot(X_1863)),bind(X_1862,$fot(X_1864))]]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(X_1864)
| is_a_theorem(implies(not(X_1864),X_1863)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1864,implies(not(X_1864),X_1863))) )],[refute_0_105,refute_0_95]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(implies(X_14683,X_14684),implies(X_14683,not(not(X_14684)))))
| is_a_theorem(implies(not(implies(implies(X_14683,X_14684),implies(X_14683,not(not(X_14684))))),X_1863)) ),
inference(subst,[],[refute_0_106:[bind(X_1864,$fot(implies(implies(X_14683,X_14684),implies(X_14683,not(not(X_14684))))))]]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(implies(X_10071,X_10072),implies(implies(X_10070,X_10071),implies(X_10070,X_10072))))
| is_a_theorem(implies(implies(not(X_10072),not(X_10071)),implies(implies(X_10070,X_10071),implies(X_10070,X_10072)))) ),
inference(subst,[],[refute_0_89:[bind(X_74,$fot(X_10072)),bind(X_75,$fot(X_10071)),bind(X_76,$fot(implies(implies(X_10070,X_10071),implies(X_10070,X_10072))))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_10064,X_10066),implies(X_10065,X_10066)),implies(X_10065,X_10066)),implies(implies(X_10064,X_10065),implies(X_10064,X_10066))))
| is_a_theorem(implies(implies(X_10065,X_10066),implies(implies(X_10064,X_10065),implies(X_10064,X_10066)))) ),
inference(subst,[],[refute_0_98:[bind(X_47,$fot(implies(implies(X_10064,X_10066),implies(X_10065,X_10066)))),bind(X_48,$fot(implies(X_10065,X_10066))),bind(X_49,$fot(implies(implies(X_10064,X_10065),implies(X_10064,X_10066))))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_42),implies(implies(X,Y),X_42))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_42),implies(implies(X,Y),X_42))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[mv_2,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(subst,[],[refute_0_111:[bind(X_42,$fot(implies(X,Z)))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X,Z)),implies(implies(X,Y),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(X,Z),implies(Y,Z)),implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))) ),
inference(subst,[],[refute_0_30:[bind(X_71,$fot(implies(X,Z))),bind(X_72,$fot(implies(Y,Z))),bind(X_73,$fot(implies(implies(X,Y),implies(X,Z))))]]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(implies(implies(X,Z),implies(Y,Z)),implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),implies(X,Z)),implies(implies(X,Y),implies(X,Z)))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(implies(implies(implies(X_10064,X_10066),implies(X_10065,X_10066)),implies(X_10065,X_10066)),implies(implies(X_10064,X_10065),implies(X_10064,X_10066)))),
inference(subst,[],[refute_0_114:[bind(X,$fot(X_10064)),bind(Y,$fot(X_10065)),bind(Z,$fot(X_10066))]]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(implies(X_10065,X_10066),implies(implies(X_10064,X_10065),implies(X_10064,X_10066)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_10064,X_10066),implies(X_10065,X_10066)),implies(X_10065,X_10066)),implies(implies(X_10064,X_10065),implies(X_10064,X_10066)))) )],[refute_0_115,refute_0_109]) ).
cnf(refute_0_117,plain,
is_a_theorem(implies(implies(X_10071,X_10072),implies(implies(X_10070,X_10071),implies(X_10070,X_10072)))),
inference(subst,[],[refute_0_116:[bind(X_10064,$fot(X_10070)),bind(X_10065,$fot(X_10071)),bind(X_10066,$fot(X_10072))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(not(X_10072),not(X_10071)),implies(implies(X_10070,X_10071),implies(X_10070,X_10072)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_10071,X_10072),implies(implies(X_10070,X_10071),implies(X_10070,X_10072)))) )],[refute_0_117,refute_0_108]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(not(not(not(X_10071))),not(X_10071)),implies(implies(X_10070,X_10071),implies(X_10070,not(not(X_10071)))))),
inference(subst,[],[refute_0_118:[bind(X_10072,$fot(not(not(X_10071))))]]) ).
cnf(refute_0_120,plain,
( ~ is_a_theorem(implies(implies(implies(not(not(X_1844)),X_1844),X_1845),X_1845))
| ~ is_a_theorem(implies(implies(not(not(X_1844)),X_1844),X_1845))
| is_a_theorem(X_1845) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(not(not(X_1844)),X_1844),X_1845))),bind(Y,$fot(X_1845))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(X_280)
| ~ is_a_theorem(implies(X_280,implies(implies(X_280,X_279),X_279)))
| is_a_theorem(implies(implies(X_280,X_279),X_279)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_280)),bind(Y,$fot(implies(implies(X_280,X_279),X_279)))]]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(implies(implies(X,X_270),X_270),implies(implies(X_270,X),X))),
inference(subst,[],[mv_3:[bind(Y,$fot(X_270))]]) ).
cnf(refute_0_123,plain,
( ~ is_a_theorem(implies(implies(implies(X,X_270),X_270),implies(implies(X_270,X),X)))
| is_a_theorem(implies(X_270,implies(implies(X_270,X),X))) ),
inference(subst,[],[refute_0_98:[bind(X_47,$fot(implies(X,X_270))),bind(X_48,$fot(X_270)),bind(X_49,$fot(implies(implies(X_270,X),X)))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(X_270,implies(implies(X_270,X),X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,X_270),X_270),implies(implies(X_270,X),X))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(X_280,implies(implies(X_280,X_279),X_279))),
inference(subst,[],[refute_0_124:[bind(X,$fot(X_279)),bind(X_270,$fot(X_280))]]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(X_280)
| is_a_theorem(implies(implies(X_280,X_279),X_279)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_280,implies(implies(X_280,X_279),X_279))) )],[refute_0_125,refute_0_121]) ).
cnf(refute_0_127,plain,
( ~ is_a_theorem(implies(not(not(X_1832)),X_1832))
| is_a_theorem(implies(implies(implies(not(not(X_1832)),X_1832),X_279),X_279)) ),
inference(subst,[],[refute_0_126:[bind(X_280,$fot(implies(not(not(X_1832)),X_1832)))]]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(not(not(X_1832)),X_1832)),
inference(subst,[],[refute_0_79:[bind(X_1830,$fot(X_1832))]]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(implies(not(not(X_1832)),X_1832),X_279),X_279)),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_1832)),X_1832)) )],[refute_0_128,refute_0_127]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(implies(implies(not(not(X_1844)),X_1844),X_1845),X_1845)),
inference(subst,[],[refute_0_129:[bind(X_1832,$fot(X_1844)),bind(X_279,$fot(X_1845))]]) ).
cnf(refute_0_131,plain,
( ~ is_a_theorem(implies(implies(not(not(X_1844)),X_1844),X_1845))
| is_a_theorem(X_1845) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(not(X_1844)),X_1844),X_1845),X_1845)) )],[refute_0_130,refute_0_120]) ).
cnf(refute_0_132,plain,
( ~ is_a_theorem(implies(implies(not(not(not(X_10071))),not(X_10071)),implies(implies(X_10070,X_10071),implies(X_10070,not(not(X_10071))))))
| is_a_theorem(implies(implies(X_10070,X_10071),implies(X_10070,not(not(X_10071))))) ),
inference(subst,[],[refute_0_131:[bind(X_1844,$fot(not(X_10071))),bind(X_1845,$fot(implies(implies(X_10070,X_10071),implies(X_10070,not(not(X_10071))))))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(X_10070,X_10071),implies(X_10070,not(not(X_10071))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(not(X_10071))),not(X_10071)),implies(implies(X_10070,X_10071),implies(X_10070,not(not(X_10071)))))) )],[refute_0_119,refute_0_132]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(X_14683,X_14684),implies(X_14683,not(not(X_14684))))),
inference(subst,[],[refute_0_133:[bind(X_10070,$fot(X_14683)),bind(X_10071,$fot(X_14684))]]) ).
cnf(refute_0_135,plain,
is_a_theorem(implies(not(implies(implies(X_14683,X_14684),implies(X_14683,not(not(X_14684))))),X_1863)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_14683,X_14684),implies(X_14683,not(not(X_14684))))) )],[refute_0_134,refute_0_107]) ).
cnf(refute_0_136,plain,
is_a_theorem(implies(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))),not(implies(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))),implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))))),
inference(subst,[],[refute_0_135:[bind(X_14683,$fot(X_21556)),bind(X_14684,$fot(X_21557)),bind(X_1863,$fot(not(implies(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))),implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))))]]) ).
cnf(refute_0_137,plain,
is_a_theorem(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))),not(implies(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))),implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))))) )],[refute_0_136,refute_0_94]) ).
cnf(refute_0_138,plain,
( ~ is_a_theorem(implies(not(not(X_412)),implies(X_411,implies(X_413,X_412))))
| ~ is_a_theorem(not(not(X_412)))
| is_a_theorem(implies(X_411,implies(X_413,X_412))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(not(not(X_412)))),bind(Y,$fot(implies(X_411,implies(X_413,X_412))))]]) ).
cnf(refute_0_139,plain,
( ~ is_a_theorem(implies(implies(implies(X_410,X_409),implies(X_32,implies(X_410,X_409))),implies(not(not(X_409)),implies(X_32,implies(X_410,X_409)))))
| is_a_theorem(implies(not(not(X_409)),implies(X_32,implies(X_410,X_409)))) ),
inference(subst,[],[refute_0_44:[bind(X_31,$fot(implies(X_410,X_409))),bind(X_33,$fot(implies(not(not(X_409)),implies(X_32,implies(X_410,X_409)))))]]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(implies(implies(X_410,X_409),implies(X_32,implies(X_410,X_409))),implies(not(not(X_409)),implies(X_32,implies(X_410,X_409))))),
inference(subst,[],[refute_0_74:[bind(Z,$fot(implies(X_32,implies(X_410,X_409)))),bind(X_140,$fot(X_409)),bind(X_141,$fot(X_410))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(not(not(X_409)),implies(X_32,implies(X_410,X_409)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_410,X_409),implies(X_32,implies(X_410,X_409))),implies(not(not(X_409)),implies(X_32,implies(X_410,X_409))))) )],[refute_0_140,refute_0_139]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(not(not(X_412)),implies(X_411,implies(X_413,X_412)))),
inference(subst,[],[refute_0_141:[bind(X_32,$fot(X_411)),bind(X_409,$fot(X_412)),bind(X_410,$fot(X_413))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(not(not(X_412)))
| is_a_theorem(implies(X_411,implies(X_413,X_412))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_412)),implies(X_411,implies(X_413,X_412)))) )],[refute_0_142,refute_0_138]) ).
cnf(refute_0_144,plain,
( ~ is_a_theorem(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))))
| is_a_theorem(implies(X_39790,implies(X_39792,implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))) ),
inference(subst,[],[refute_0_143:[bind(X_411,$fot(X_39790)),bind(X_412,$fot(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))),bind(X_413,$fot(X_39792))]]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(X_39790,implies(X_39792,implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))) )],[refute_0_137,refute_0_144]) ).
cnf(refute_0_146,plain,
is_a_theorem(implies(implies(X_125367,X_125367),implies(implies(X_125368,implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))),implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))),
inference(subst,[],[refute_0_145:[bind(X_39790,$fot(implies(X_125367,X_125367))),bind(X_39792,$fot(implies(X_125368,implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))))]]) ).
cnf(refute_0_147,plain,
( ~ is_a_theorem(implies(implies(X_1130,X_1130),implies(implies(X_1131,X_1132),X_1132)))
| ~ is_a_theorem(implies(implies(implies(X_1130,X_1130),implies(implies(X_1131,X_1132),X_1132)),implies(implies(X_1132,X_1131),X_1131)))
| is_a_theorem(implies(implies(X_1132,X_1131),X_1131)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1130,X_1130),implies(implies(X_1131,X_1132),X_1132)))),bind(Y,$fot(implies(implies(X_1132,X_1131),X_1131)))]]) ).
cnf(refute_0_148,plain,
( ~ is_a_theorem(implies(implies(implies(X_276,X_276),X_275),X_275))
| is_a_theorem(implies(implies(X_275,Z),implies(implies(implies(X_276,X_276),X_275),Z))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(implies(implies(X_276,X_276),X_275))),bind(Y,$fot(X_275))]]) ).
cnf(refute_0_149,plain,
( ~ is_a_theorem(implies(implies(X,implies(X_274,X_274)),implies(X_274,X_274)))
| is_a_theorem(implies(implies(implies(X_274,X_274),X),X)) ),
inference(subst,[],[refute_0_8:[bind(Y,$fot(implies(X_274,X_274)))]]) ).
cnf(refute_0_150,plain,
( ~ is_a_theorem(implies(X_272,X_272))
| is_a_theorem(implies(Y,implies(X_272,X_272))) ),
inference(subst,[],[refute_0_3:[bind(X_9,$fot(implies(X_272,X_272)))]]) ).
cnf(refute_0_151,plain,
( ~ is_a_theorem(implies(implies(X,implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84)),implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84)))
| is_a_theorem(implies(implies(implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84),X),X)) ),
inference(subst,[],[refute_0_8:[bind(Y,$fot(implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84)))]]) ).
cnf(refute_0_152,plain,
( ~ is_a_theorem(implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33))
| is_a_theorem(implies(Y,implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33))) ),
inference(subst,[],[refute_0_3:[bind(X_9,$fot(implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33)))]]) ).
cnf(refute_0_153,plain,
is_a_theorem(implies(Y,implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_31,implies(X_32,X_31)),X_33),X_33)) )],[refute_0_43,refute_0_152]) ).
cnf(refute_0_154,plain,
is_a_theorem(implies(implies(X,implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84)),implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84))),
inference(subst,[],[refute_0_153:[bind(Y,$fot(implies(X,implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84)))),bind(X_31,$fot(X_82)),bind(X_32,$fot(X_83)),bind(X_33,$fot(X_84))]]) ).
cnf(refute_0_155,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84),X),X)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84)),implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84))) )],[refute_0_154,refute_0_151]) ).
cnf(refute_0_156,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84),X_271),X_271)),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_271))]]) ).
cnf(refute_0_157,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84),X_271),X_271))
| is_a_theorem(implies(X_271,X_271)) ),
inference(subst,[],[refute_0_98:[bind(X_47,$fot(implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84))),bind(X_48,$fot(X_271)),bind(X_49,$fot(X_271))]]) ).
cnf(refute_0_158,plain,
is_a_theorem(implies(X_271,X_271)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_82,implies(X_83,X_82)),X_84),X_84),X_271),X_271)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
is_a_theorem(implies(X_272,X_272)),
inference(subst,[],[refute_0_158:[bind(X_271,$fot(X_272))]]) ).
cnf(refute_0_160,plain,
is_a_theorem(implies(Y,implies(X_272,X_272))),
inference(resolve,[$cnf( is_a_theorem(implies(X_272,X_272)) )],[refute_0_159,refute_0_150]) ).
cnf(refute_0_161,plain,
is_a_theorem(implies(implies(X,implies(X_274,X_274)),implies(X_274,X_274))),
inference(subst,[],[refute_0_160:[bind(Y,$fot(implies(X,implies(X_274,X_274)))),bind(X_272,$fot(X_274))]]) ).
cnf(refute_0_162,plain,
is_a_theorem(implies(implies(implies(X_274,X_274),X),X)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X_274,X_274)),implies(X_274,X_274))) )],[refute_0_161,refute_0_149]) ).
cnf(refute_0_163,plain,
is_a_theorem(implies(implies(implies(X_276,X_276),X_275),X_275)),
inference(subst,[],[refute_0_162:[bind(X,$fot(X_275)),bind(X_274,$fot(X_276))]]) ).
cnf(refute_0_164,plain,
is_a_theorem(implies(implies(X_275,Z),implies(implies(implies(X_276,X_276),X_275),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_276,X_276),X_275),X_275)) )],[refute_0_163,refute_0_148]) ).
cnf(refute_0_165,plain,
is_a_theorem(implies(implies(implies(implies(X_703,X_704),X_704),implies(implies(X_704,X_703),X_703)),implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703)))),
inference(subst,[],[refute_0_164:[bind(Z,$fot(implies(implies(X_704,X_703),X_703))),bind(X_275,$fot(implies(implies(X_703,X_704),X_704)))]]) ).
cnf(refute_0_166,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_50,X_51),X_51),implies(implies(X_51,X_50),X_50)),X_53))
| ~ is_a_theorem(implies(implies(implies(implies(implies(X_50,X_51),X_51),implies(implies(X_51,X_50),X_50)),X_53),implies(X_52,X_53)))
| is_a_theorem(implies(X_52,X_53)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_50,X_51),X_51),implies(implies(X_51,X_50),X_50)),X_53))),bind(Y,$fot(implies(X_52,X_53)))]]) ).
cnf(refute_0_167,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))
| is_a_theorem(implies(X_11,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))))]]) ).
cnf(refute_0_168,plain,
is_a_theorem(implies(X_11,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) )],[mv_3,refute_0_167]) ).
cnf(refute_0_169,plain,
is_a_theorem(implies(X_40,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))),
inference(subst,[],[refute_0_168:[bind(X_11,$fot(X_40))]]) ).
cnf(refute_0_170,plain,
( ~ is_a_theorem(implies(X_40,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))))
| is_a_theorem(implies(implies(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)),X_42),implies(X_40,X_42))) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_40)),bind(Y,$fot(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_171,plain,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)),X_42),implies(X_40,X_42))),
inference(resolve,[$cnf( is_a_theorem(implies(X_40,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_50,X_51),X_51),implies(implies(X_51,X_50),X_50)),X_53),implies(X_52,X_53))),
inference(subst,[],[refute_0_171:[bind(X,$fot(X_50)),bind(Y,$fot(X_51)),bind(X_40,$fot(X_52)),bind(X_42,$fot(X_53))]]) ).
cnf(refute_0_173,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_50,X_51),X_51),implies(implies(X_51,X_50),X_50)),X_53))
| is_a_theorem(implies(X_52,X_53)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_50,X_51),X_51),implies(implies(X_51,X_50),X_50)),X_53),implies(X_52,X_53))) )],[refute_0_172,refute_0_166]) ).
cnf(refute_0_174,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_703,X_704),X_704),implies(implies(X_704,X_703),X_703)),implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703))))
| is_a_theorem(implies(X_705,implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703)))) ),
inference(subst,[],[refute_0_173:[bind(X_50,$fot(X_703)),bind(X_51,$fot(X_704)),bind(X_52,$fot(X_705)),bind(X_53,$fot(implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703))))]]) ).
cnf(refute_0_175,plain,
is_a_theorem(implies(X_705,implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_703,X_704),X_704),implies(implies(X_704,X_703),X_703)),implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703)))) )],[refute_0_165,refute_0_174]) ).
cnf(refute_0_176,plain,
is_a_theorem(implies(implies(X_1118,implies(X_1116,implies(X_1117,X_1116))),implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703)))),
inference(subst,[],[refute_0_175:[bind(X_705,$fot(implies(X_1118,implies(X_1116,implies(X_1117,X_1116)))))]]) ).
cnf(refute_0_177,plain,
( ~ is_a_theorem(implies(implies(X_56,implies(X_54,implies(X_55,X_54))),X_57))
| ~ is_a_theorem(implies(implies(implies(X_56,implies(X_54,implies(X_55,X_54))),X_57),X_57))
| is_a_theorem(X_57) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_56,implies(X_54,implies(X_55,X_54))),X_57))),bind(Y,$fot(X_57))]]) ).
cnf(refute_0_178,plain,
( ~ is_a_theorem(implies(X_15,implies(X_13,implies(X_14,X_13))))
| is_a_theorem(implies(Y,implies(X_15,implies(X_13,implies(X_14,X_13))))) ),
inference(subst,[],[refute_0_3:[bind(X_9,$fot(implies(X_15,implies(X_13,implies(X_14,X_13)))))]]) ).
cnf(refute_0_179,plain,
is_a_theorem(implies(X_15,implies(X_13,implies(X_14,X_13)))),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_13)),bind(Y,$fot(X_14)),bind(X_11,$fot(X_15))]]) ).
cnf(refute_0_180,plain,
is_a_theorem(implies(Y,implies(X_15,implies(X_13,implies(X_14,X_13))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_15,implies(X_13,implies(X_14,X_13)))) )],[refute_0_179,refute_0_178]) ).
cnf(refute_0_181,plain,
is_a_theorem(implies(implies(X_29,implies(X_15,implies(X_13,implies(X_14,X_13)))),implies(X_15,implies(X_13,implies(X_14,X_13))))),
inference(subst,[],[refute_0_180:[bind(Y,$fot(implies(X_29,implies(X_15,implies(X_13,implies(X_14,X_13))))))]]) ).
cnf(refute_0_182,plain,
( ~ is_a_theorem(implies(implies(X_29,implies(X_15,implies(X_13,implies(X_14,X_13)))),implies(X_15,implies(X_13,implies(X_14,X_13)))))
| is_a_theorem(implies(implies(implies(X_15,implies(X_13,implies(X_14,X_13))),X_29),X_29)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_29)),bind(Y,$fot(implies(X_15,implies(X_13,implies(X_14,X_13)))))]]) ).
cnf(refute_0_183,plain,
is_a_theorem(implies(implies(implies(X_15,implies(X_13,implies(X_14,X_13))),X_29),X_29)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_29,implies(X_15,implies(X_13,implies(X_14,X_13)))),implies(X_15,implies(X_13,implies(X_14,X_13))))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
is_a_theorem(implies(implies(implies(X_56,implies(X_54,implies(X_55,X_54))),X_57),X_57)),
inference(subst,[],[refute_0_183:[bind(X_13,$fot(X_54)),bind(X_14,$fot(X_55)),bind(X_15,$fot(X_56)),bind(X_29,$fot(X_57))]]) ).
cnf(refute_0_185,plain,
( ~ is_a_theorem(implies(implies(X_56,implies(X_54,implies(X_55,X_54))),X_57))
| is_a_theorem(X_57) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_56,implies(X_54,implies(X_55,X_54))),X_57),X_57)) )],[refute_0_184,refute_0_177]) ).
cnf(refute_0_186,plain,
( ~ is_a_theorem(implies(implies(X_1118,implies(X_1116,implies(X_1117,X_1116))),implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703))))
| is_a_theorem(implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703))) ),
inference(subst,[],[refute_0_185:[bind(X_54,$fot(X_1116)),bind(X_55,$fot(X_1117)),bind(X_56,$fot(X_1118)),bind(X_57,$fot(implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703))))]]) ).
cnf(refute_0_187,plain,
is_a_theorem(implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1118,implies(X_1116,implies(X_1117,X_1116))),implies(implies(implies(X_276,X_276),implies(implies(X_703,X_704),X_704)),implies(implies(X_704,X_703),X_703)))) )],[refute_0_176,refute_0_186]) ).
cnf(refute_0_188,plain,
is_a_theorem(implies(implies(implies(X_1130,X_1130),implies(implies(X_1131,X_1132),X_1132)),implies(implies(X_1132,X_1131),X_1131))),
inference(subst,[],[refute_0_187:[bind(X_276,$fot(X_1130)),bind(X_703,$fot(X_1131)),bind(X_704,$fot(X_1132))]]) ).
cnf(refute_0_189,plain,
( ~ is_a_theorem(implies(implies(X_1130,X_1130),implies(implies(X_1131,X_1132),X_1132)))
| is_a_theorem(implies(implies(X_1132,X_1131),X_1131)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1130,X_1130),implies(implies(X_1131,X_1132),X_1132)),implies(implies(X_1132,X_1131),X_1131))) )],[refute_0_188,refute_0_147]) ).
cnf(refute_0_190,plain,
( ~ is_a_theorem(implies(implies(X_125367,X_125367),implies(implies(X_125368,implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))),implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))))))
| is_a_theorem(implies(implies(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))),X_125368),X_125368)) ),
inference(subst,[],[refute_0_189:[bind(X_1130,$fot(X_125367)),bind(X_1131,$fot(X_125368)),bind(X_1132,$fot(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))]]) ).
cnf(refute_0_191,plain,
is_a_theorem(implies(implies(implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557)))),X_125368),X_125368)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_125367,X_125367),implies(implies(X_125368,implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))),implies(implies(X_21556,X_21557),implies(X_21556,not(not(X_21557))))))) )],[refute_0_146,refute_0_190]) ).
cnf(refute_0_192,plain,
is_a_theorem(implies(implies(implies(implies(X_125448,X_125449),implies(X_125448,not(not(X_125449)))),implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126))),implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126)))),
inference(subst,[],[refute_0_191:[bind(X_125368,$fot(implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126)))),bind(X_21556,$fot(X_125448)),bind(X_21557,$fot(X_125449))]]) ).
cnf(refute_0_193,plain,
is_a_theorem(implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_125448,X_125449),implies(X_125448,not(not(X_125449)))),implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126))),implies(implies(implies(X_125448,not(not(X_125449))),X_126),implies(implies(X_125448,X_125449),X_126)))) )],[refute_0_192,refute_0_22]) ).
cnf(refute_0_194,plain,
is_a_theorem(implies(implies(implies(not(X_37),not(not(X_125990))),implies(not(X_125990),X_37)),implies(implies(not(X_37),X_125990),implies(not(X_125990),X_37)))),
inference(subst,[],[refute_0_193:[bind(X_125448,$fot(not(X_37))),bind(X_125449,$fot(X_125990)),bind(X_126,$fot(implies(not(X_125990),X_37)))]]) ).
cnf(refute_0_195,plain,
is_a_theorem(implies(implies(not(X_37),X_125990),implies(not(X_125990),X_37))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_37),not(not(X_125990))),implies(not(X_125990),X_37)),implies(implies(not(X_37),X_125990),implies(not(X_125990),X_37)))) )],[refute_0_194,refute_0_13]) ).
cnf(refute_0_196,plain,
is_a_theorem(implies(implies(not(a),b),implies(not(b),a))),
inference(subst,[],[refute_0_195:[bind(X_125990,$fot(b)),bind(X_37,$fot(a))]]) ).
cnf(refute_0_197,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(a),b),implies(not(b),a))) )],[refute_0_196,prove_mv_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL113-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % 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 : Mon Jul 4 14:37:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 223.45/223.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 223.45/223.60
% 223.45/223.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 223.45/223.62
%------------------------------------------------------------------------------