TSTP Solution File: LCL069-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL069-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:49:11 EDT 2022
% Result : Unsatisfiable 4.61s 4.78s
% Output : CNFRefutation 4.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 5
% Syntax : Number of clauses : 138 ( 74 unt; 0 nHn; 45 RR)
% Number of literals : 219 ( 0 equ; 82 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 396 ( 86 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_19,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))) ).
cnf(cn_37,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))) ).
cnf(cn_59,axiom,
is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))) ).
cnf(prove_cn_3,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| ~ is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z)))
| is_a_theorem(implies(Y,Z)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Z))),bind(Y,$fot(implies(Y,Z)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| is_a_theorem(implies(Y,Z)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))) )],[cn_19,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(not(X_3993),implies(implies(X_3992,not(not(X_3992))),X_3993)),not(not(X_3993))))
| is_a_theorem(implies(implies(implies(X_3992,not(not(X_3992))),X_3993),not(not(X_3993)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(X_3993))),bind(Y,$fot(implies(implies(X_3992,not(not(X_3992))),X_3993))),bind(Z,$fot(not(not(X_3993))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(not(not(X_20)),implies(implies(X_21,X_22),implies(implies(X_20,X_21),X_22))))
| ~ is_a_theorem(not(not(X_20)))
| is_a_theorem(implies(implies(X_21,X_22),implies(implies(X_20,X_21),X_22))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(not(not(X_20)))),bind(Y,$fot(implies(implies(X_21,X_22),implies(implies(X_20,X_21),X_22))))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(not(X),X_12),implies(implies(Y,X_12),implies(implies(X,Y),X_12)))),
inference(subst,[],[cn_59:[bind(Z,$fot(X_12))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| ~ is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z)))
| is_a_theorem(implies(not(X),Z)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Z))),bind(Y,$fot(implies(not(X),Z)))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| is_a_theorem(implies(not(X),Z)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))) )],[cn_37,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(not(X),X_12),implies(implies(Y,X_12),implies(implies(X,Y),X_12))))
| is_a_theorem(implies(not(not(X)),implies(implies(Y,X_12),implies(implies(X,Y),X_12)))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(not(X))),bind(Y,$fot(X_12)),bind(Z,$fot(implies(implies(Y,X_12),implies(implies(X,Y),X_12))))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(not(not(X)),implies(implies(Y,X_12),implies(implies(X,Y),X_12)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),X_12),implies(implies(Y,X_12),implies(implies(X,Y),X_12)))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(not(not(X_20)),implies(implies(X_21,X_22),implies(implies(X_20,X_21),X_22)))),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(X_12,$fot(X_22))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(not(not(X_20)))
| is_a_theorem(implies(implies(X_21,X_22),implies(implies(X_20,X_21),X_22))) ),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(X_20)),implies(implies(X_21,X_22),implies(implies(X_20,X_21),X_22)))) )],[refute_0_9,refute_0_3]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(not(not(implies(X_1486,not(not(X_1486))))))
| is_a_theorem(implies(implies(X_21,X_22),implies(implies(implies(X_1486,not(not(X_1486))),X_21),X_22))) ),
inference(subst,[],[refute_0_10:[bind(X_20,$fot(implies(X_1486,not(not(X_1486)))))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(X,not(X_230)),X_232),implies(not(X_230),X_232))),
inference(subst,[],[cn_19:[bind(Y,$fot(not(X_230))),bind(Z,$fot(X_232))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(X_80,implies(not(X_77),X_79)))
| ~ is_a_theorem(implies(implies(X_80,implies(not(X_77),X_79)),implies(implies(implies(X_77,X_78),X_80),implies(not(X_77),X_79))))
| is_a_theorem(implies(implies(implies(X_77,X_78),X_80),implies(not(X_77),X_79))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_80,implies(not(X_77),X_79)))),bind(Y,$fot(implies(implies(implies(X_77,X_78),X_80),implies(not(X_77),X_79))))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(X,Y),X_12),implies(not(X),X_12))),
inference(subst,[],[cn_37:[bind(Z,$fot(X_12))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_12),implies(not(X),X_12)))
| is_a_theorem(implies(not(implies(X,Y)),implies(not(X),X_12))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_12)),bind(Z,$fot(implies(not(X),X_12)))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(not(implies(X,Y)),implies(not(X),X_12))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_12),implies(not(X),X_12))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z))))
| ~ is_a_theorem(implies(not(X),Z))
| is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),Z))),bind(Y,$fot(implies(implies(Y,Z),implies(implies(X,Y),Z))))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(not(X),Z))
| is_a_theorem(implies(implies(Y,Z),implies(implies(X,Y),Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))) )],[cn_59,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(not(implies(X,Y)),implies(not(X),X_12)))
| is_a_theorem(implies(implies(X_69,implies(not(X),X_12)),implies(implies(implies(X,Y),X_69),implies(not(X),X_12)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_69)),bind(Z,$fot(implies(not(X),X_12)))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(X_69,implies(not(X),X_12)),implies(implies(implies(X,Y),X_69),implies(not(X),X_12)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,Y)),implies(not(X),X_12))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(X_80,implies(not(X_77),X_79)),implies(implies(implies(X_77,X_78),X_80),implies(not(X_77),X_79)))),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_77)),bind(Y,$fot(X_78)),bind(X_12,$fot(X_79)),bind(X_69,$fot(X_80))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(X_80,implies(not(X_77),X_79)))
| is_a_theorem(implies(implies(implies(X_77,X_78),X_80),implies(not(X_77),X_79))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_80,implies(not(X_77),X_79)),implies(implies(implies(X_77,X_78),X_80),implies(not(X_77),X_79)))) )],[refute_0_21,refute_0_13]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(X,not(X_230)),X_232),implies(not(X_230),X_232)))
| is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X,not(X_230)),X_232)),implies(not(X_230),X_232))) ),
inference(subst,[],[refute_0_22:[bind(X_77,$fot(X_230)),bind(X_78,$fot(X_231)),bind(X_79,$fot(X_232)),bind(X_80,$fot(implies(implies(X,not(X_230)),X_232)))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X,not(X_230)),X_232)),implies(not(X_230),X_232))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,not(X_230)),X_232),implies(not(X_230),X_232))) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(X_1409)
| ~ is_a_theorem(implies(X_1409,implies(X_1408,not(not(X_1408)))))
| is_a_theorem(implies(X_1408,not(not(X_1408)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1409)),bind(Y,$fot(implies(X_1408,not(not(X_1408)))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(X_504,not(X_502)))
| ~ is_a_theorem(implies(implies(X_504,not(X_502)),implies(X_503,implies(X_502,not(X_504)))))
| is_a_theorem(implies(X_503,implies(X_502,not(X_504)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_504,not(X_502)))),bind(Y,$fot(implies(X_503,implies(X_502,not(X_504)))))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(X_26,implies(X,Y))))
| is_a_theorem(implies(not(X),implies(X_26,implies(X,Y)))) ),
inference(subst,[],[refute_0_6:[bind(Z,$fot(implies(X_26,implies(X,Y))))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(X,Y),X_24),implies(Y,X_24))),
inference(subst,[],[cn_19:[bind(Z,$fot(X_24))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_24),implies(Y,X_24)))
| is_a_theorem(implies(X_24,implies(Y,X_24))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_24)),bind(Z,$fot(implies(Y,X_24)))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(X_24,implies(Y,X_24))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_24),implies(Y,X_24))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(X,Y),implies(X_26,implies(X,Y)))),
inference(subst,[],[refute_0_30:[bind(Y,$fot(X_26)),bind(X_24,$fot(implies(X,Y)))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(not(X),implies(X_26,implies(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(X_26,implies(X,Y)))) )],[refute_0_31,refute_0_27]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(not(X_488),implies(X_489,implies(X_488,not(X_490))))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_488)),bind(Y,$fot(not(X_490))),bind(X_26,$fot(X_489))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(X_185,implies(X_183,implies(X_182,not(X_184)))))
| ~ is_a_theorem(implies(implies(X_185,implies(X_183,implies(X_182,not(X_184)))),implies(implies(X_184,X_185),implies(X_183,implies(X_182,not(X_184))))))
| is_a_theorem(implies(implies(X_184,X_185),implies(X_183,implies(X_182,not(X_184))))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_185,implies(X_183,implies(X_182,not(X_184)))))),bind(Y,$fot(implies(implies(X_184,X_185),implies(X_183,implies(X_182,not(X_184))))))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(X_26,implies(X,Y))))
| is_a_theorem(implies(Y,implies(X_26,implies(X,Y)))) ),
inference(subst,[],[refute_0_1:[bind(Z,$fot(implies(X_26,implies(X,Y))))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(Y,implies(X_26,implies(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(X_26,implies(X,Y)))) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(not(X_68),implies(X_26,implies(X,not(X_68))))),
inference(subst,[],[refute_0_36:[bind(Y,$fot(not(X_68)))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(implies(not(X_68),implies(X_26,implies(X,not(X_68)))))
| is_a_theorem(implies(implies(X_69,implies(X_26,implies(X,not(X_68)))),implies(implies(X_68,X_69),implies(X_26,implies(X,not(X_68)))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_68)),bind(Y,$fot(X_69)),bind(Z,$fot(implies(X_26,implies(X,not(X_68)))))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(X_69,implies(X_26,implies(X,not(X_68)))),implies(implies(X_68,X_69),implies(X_26,implies(X,not(X_68)))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_68),implies(X_26,implies(X,not(X_68))))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(X_185,implies(X_183,implies(X_182,not(X_184)))),implies(implies(X_184,X_185),implies(X_183,implies(X_182,not(X_184)))))),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_182)),bind(X_26,$fot(X_183)),bind(X_68,$fot(X_184)),bind(X_69,$fot(X_185))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(X_185,implies(X_183,implies(X_182,not(X_184)))))
| is_a_theorem(implies(implies(X_184,X_185),implies(X_183,implies(X_182,not(X_184))))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_185,implies(X_183,implies(X_182,not(X_184)))),implies(implies(X_184,X_185),implies(X_183,implies(X_182,not(X_184)))))) )],[refute_0_40,refute_0_34]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(not(X_488),implies(X_489,implies(X_488,not(X_490)))))
| is_a_theorem(implies(implies(X_490,not(X_488)),implies(X_489,implies(X_488,not(X_490))))) ),
inference(subst,[],[refute_0_41:[bind(X_182,$fot(X_488)),bind(X_183,$fot(X_489)),bind(X_184,$fot(X_490)),bind(X_185,$fot(not(X_488)))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_490,not(X_488)),implies(X_489,implies(X_488,not(X_490))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_488),implies(X_489,implies(X_488,not(X_490))))) )],[refute_0_33,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(X_504,not(X_502)),implies(X_503,implies(X_502,not(X_504))))),
inference(subst,[],[refute_0_43:[bind(X_488,$fot(X_502)),bind(X_489,$fot(X_503)),bind(X_490,$fot(X_504))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(X_504,not(X_502)))
| is_a_theorem(implies(X_503,implies(X_502,not(X_504)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_504,not(X_502)),implies(X_503,implies(X_502,not(X_504))))) )],[refute_0_44,refute_0_26]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(not(X_1400),not(X_1400)))
| is_a_theorem(implies(X_503,implies(X_1400,not(not(X_1400))))) ),
inference(subst,[],[refute_0_45:[bind(X_502,$fot(X_1400)),bind(X_504,$fot(not(X_1400)))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(X_27)
| ~ is_a_theorem(implies(X_27,implies(X_26,X_27)))
| is_a_theorem(implies(X_26,X_27)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_27)),bind(Y,$fot(implies(X_26,X_27)))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(X_27,implies(X_26,X_27))),
inference(subst,[],[refute_0_30:[bind(Y,$fot(X_26)),bind(X_24,$fot(X_27))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(X_27)
| is_a_theorem(implies(X_26,X_27)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_27,implies(X_26,X_27))) )],[refute_0_48,refute_0_47]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(implies(X_287,implies(implies(X_285,X_286),not(X_287))),implies(X_286,not(X_287))))
| is_a_theorem(implies(X_26,implies(implies(X_287,implies(implies(X_285,X_286),not(X_287))),implies(X_286,not(X_287))))) ),
inference(subst,[],[refute_0_49:[bind(X_27,$fot(implies(implies(X_287,implies(implies(X_285,X_286),not(X_287))),implies(X_286,not(X_287)))))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(implies(X,X_280),not(X_281)),implies(X_280,not(X_281)))),
inference(subst,[],[cn_19:[bind(Y,$fot(X_280)),bind(Z,$fot(not(X_281)))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(X_73,implies(X_71,not(X_72))))
| ~ is_a_theorem(implies(implies(X_73,implies(X_71,not(X_72))),implies(implies(X_72,X_73),implies(X_71,not(X_72)))))
| is_a_theorem(implies(implies(X_72,X_73),implies(X_71,not(X_72)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_73,implies(X_71,not(X_72))))),bind(Y,$fot(implies(implies(X_72,X_73),implies(X_71,not(X_72)))))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(not(X_68),implies(Y,not(X_68)))),
inference(subst,[],[refute_0_30:[bind(X_24,$fot(not(X_68)))]]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(implies(not(X_68),implies(Y,not(X_68))))
| is_a_theorem(implies(implies(X_69,implies(Y,not(X_68))),implies(implies(X_68,X_69),implies(Y,not(X_68))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_68)),bind(Y,$fot(X_69)),bind(Z,$fot(implies(Y,not(X_68))))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(X_69,implies(Y,not(X_68))),implies(implies(X_68,X_69),implies(Y,not(X_68))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_68),implies(Y,not(X_68)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(X_73,implies(X_71,not(X_72))),implies(implies(X_72,X_73),implies(X_71,not(X_72))))),
inference(subst,[],[refute_0_55:[bind(Y,$fot(X_71)),bind(X_68,$fot(X_72)),bind(X_69,$fot(X_73))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(implies(X_73,implies(X_71,not(X_72))))
| is_a_theorem(implies(implies(X_72,X_73),implies(X_71,not(X_72)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_73,implies(X_71,not(X_72))),implies(implies(X_72,X_73),implies(X_71,not(X_72))))) )],[refute_0_56,refute_0_52]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(implies(X,X_280),not(X_281)),implies(X_280,not(X_281))))
| is_a_theorem(implies(implies(X_281,implies(implies(X,X_280),not(X_281))),implies(X_280,not(X_281)))) ),
inference(subst,[],[refute_0_57:[bind(X_71,$fot(X_280)),bind(X_72,$fot(X_281)),bind(X_73,$fot(implies(implies(X,X_280),not(X_281))))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(implies(X_281,implies(implies(X,X_280),not(X_281))),implies(X_280,not(X_281)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,X_280),not(X_281)),implies(X_280,not(X_281)))) )],[refute_0_51,refute_0_58]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(X_287,implies(implies(X_285,X_286),not(X_287))),implies(X_286,not(X_287)))),
inference(subst,[],[refute_0_59:[bind(X,$fot(X_285)),bind(X_280,$fot(X_286)),bind(X_281,$fot(X_287))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(X_26,implies(implies(X_287,implies(implies(X_285,X_286),not(X_287))),implies(X_286,not(X_287))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_287,implies(implies(X_285,X_286),not(X_287))),implies(X_286,not(X_287)))) )],[refute_0_60,refute_0_50]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(X_1399,implies(implies(X_1399,implies(implies(X_285,implies(X_1399,X_1396)),not(X_1399))),implies(implies(X_1399,X_1396),not(X_1399))))),
inference(subst,[],[refute_0_61:[bind(X_26,$fot(X_1399)),bind(X_286,$fot(implies(X_1399,X_1396))),bind(X_287,$fot(X_1399))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(X_310,implies(implies(X_308,X_309),implies(implies(X_308,X_307),not(X_310)))))
| ~ is_a_theorem(implies(implies(X_310,implies(implies(X_308,X_309),implies(implies(X_308,X_307),not(X_310)))),implies(not(X_308),not(X_310))))
| is_a_theorem(implies(not(X_308),not(X_310))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_310,implies(implies(X_308,X_309),implies(implies(X_308,X_307),not(X_310)))))),bind(Y,$fot(implies(not(X_308),not(X_310))))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(implies(implies(X_230,Y),X_232),implies(not(X_230),X_232))),
inference(subst,[],[cn_37:[bind(X,$fot(X_230)),bind(Z,$fot(X_232))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(implies(implies(implies(X_230,Y),X_232),implies(not(X_230),X_232)))
| is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X_230,Y),X_232)),implies(not(X_230),X_232))) ),
inference(subst,[],[refute_0_22:[bind(X_77,$fot(X_230)),bind(X_78,$fot(X_231)),bind(X_79,$fot(X_232)),bind(X_80,$fot(implies(implies(X_230,Y),X_232)))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X_230,Y),X_232)),implies(not(X_230),X_232))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_230,Y),X_232),implies(not(X_230),X_232))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X_230,Y),not(X_281))),implies(not(X_230),not(X_281)))),
inference(subst,[],[refute_0_66:[bind(X_232,$fot(not(X_281)))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X_230,Y),not(X_281))),implies(not(X_230),not(X_281))))
| is_a_theorem(implies(implies(X_281,implies(implies(X_230,X_231),implies(implies(X_230,Y),not(X_281)))),implies(not(X_230),not(X_281)))) ),
inference(subst,[],[refute_0_57:[bind(X_71,$fot(not(X_230))),bind(X_72,$fot(X_281)),bind(X_73,$fot(implies(implies(X_230,X_231),implies(implies(X_230,Y),not(X_281)))))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(X_281,implies(implies(X_230,X_231),implies(implies(X_230,Y),not(X_281)))),implies(not(X_230),not(X_281)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X_230,Y),not(X_281))),implies(not(X_230),not(X_281)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(X_310,implies(implies(X_308,X_309),implies(implies(X_308,X_307),not(X_310)))),implies(not(X_308),not(X_310)))),
inference(subst,[],[refute_0_69:[bind(Y,$fot(X_307)),bind(X_230,$fot(X_308)),bind(X_231,$fot(X_309)),bind(X_281,$fot(X_310))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(implies(X_310,implies(implies(X_308,X_309),implies(implies(X_308,X_307),not(X_310)))))
| is_a_theorem(implies(not(X_308),not(X_310))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_310,implies(implies(X_308,X_309),implies(implies(X_308,X_307),not(X_310)))),implies(not(X_308),not(X_310)))) )],[refute_0_70,refute_0_63]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(X_1399,implies(implies(X_1399,implies(implies(X_285,implies(X_1399,X_1396)),not(X_1399))),implies(implies(X_1399,X_1396),not(X_1399)))))
| is_a_theorem(implies(not(X_1399),not(X_1399))) ),
inference(subst,[],[refute_0_71:[bind(X_307,$fot(X_1396)),bind(X_308,$fot(X_1399)),bind(X_309,$fot(implies(implies(X_285,implies(X_1399,X_1396)),not(X_1399)))),bind(X_310,$fot(X_1399))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(not(X_1399),not(X_1399))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1399,implies(implies(X_1399,implies(implies(X_285,implies(X_1399,X_1396)),not(X_1399))),implies(implies(X_1399,X_1396),not(X_1399))))) )],[refute_0_62,refute_0_72]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(not(X_1400),not(X_1400))),
inference(subst,[],[refute_0_73:[bind(X_1399,$fot(X_1400))]]) ).
cnf(refute_0_75,plain,
is_a_theorem(implies(X_503,implies(X_1400,not(not(X_1400))))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1400),not(X_1400))) )],[refute_0_74,refute_0_46]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(X_1409,implies(X_1408,not(not(X_1408))))),
inference(subst,[],[refute_0_75:[bind(X_1400,$fot(X_1408)),bind(X_503,$fot(X_1409))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(X_1409)
| is_a_theorem(implies(X_1408,not(not(X_1408)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1409,implies(X_1408,not(not(X_1408))))) )],[refute_0_76,refute_0_25]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X,not(X_230)),X_232)),implies(not(X_230),X_232)))
| is_a_theorem(implies(X_1482,not(not(X_1482)))) ),
inference(subst,[],[refute_0_77:[bind(X_1408,$fot(X_1482)),bind(X_1409,$fot(implies(implies(implies(X_230,X_231),implies(implies(X,not(X_230)),X_232)),implies(not(X_230),X_232))))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(X_1482,not(not(X_1482)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_230,X_231),implies(implies(X,not(X_230)),X_232)),implies(not(X_230),X_232))) )],[refute_0_24,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(X_1484)
| ~ is_a_theorem(implies(X_1484,not(not(X_1484))))
| is_a_theorem(not(not(X_1484))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1484)),bind(Y,$fot(not(not(X_1484))))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(X_1484,not(not(X_1484)))),
inference(subst,[],[refute_0_79:[bind(X_1482,$fot(X_1484))]]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(X_1484)
| is_a_theorem(not(not(X_1484))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1484,not(not(X_1484)))) )],[refute_0_81,refute_0_80]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(X_1482,not(not(X_1482))))
| is_a_theorem(not(not(implies(X_1482,not(not(X_1482)))))) ),
inference(subst,[],[refute_0_82:[bind(X_1484,$fot(implies(X_1482,not(not(X_1482)))))]]) ).
cnf(refute_0_84,plain,
is_a_theorem(not(not(implies(X_1482,not(not(X_1482)))))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1482,not(not(X_1482)))) )],[refute_0_79,refute_0_83]) ).
cnf(refute_0_85,plain,
is_a_theorem(not(not(implies(X_1486,not(not(X_1486)))))),
inference(subst,[],[refute_0_84:[bind(X_1482,$fot(X_1486))]]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(X_21,X_22),implies(implies(implies(X_1486,not(not(X_1486))),X_21),X_22))),
inference(resolve,[$cnf( is_a_theorem(not(not(implies(X_1486,not(not(X_1486)))))) )],[refute_0_85,refute_0_11]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(implies(X_3369,not(implies(X_3369,X_3370))),implies(implies(implies(X_1486,not(not(X_1486))),X_3369),not(implies(X_3369,X_3370))))),
inference(subst,[],[refute_0_86:[bind(X_21,$fot(X_3369)),bind(X_22,$fot(not(implies(X_3369,X_3370))))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(implies(implies(X_1028,X_1031),implies(X_1030,not(implies(X_1028,X_1029)))))
| ~ is_a_theorem(implies(implies(implies(X_1028,X_1031),implies(X_1030,not(implies(X_1028,X_1029)))),implies(not(X_1028),not(X_1030))))
| is_a_theorem(implies(not(X_1028),not(X_1030))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1028,X_1031),implies(X_1030,not(implies(X_1028,X_1029)))))),bind(Y,$fot(implies(not(X_1028),not(X_1030))))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(implies(implies(X_319,not(implies(X_317,X_318))),implies(not(X_317),not(X_319))))
| is_a_theorem(implies(implies(implies(X_317,X_78),implies(X_319,not(implies(X_317,X_318)))),implies(not(X_317),not(X_319)))) ),
inference(subst,[],[refute_0_22:[bind(X_77,$fot(X_317)),bind(X_79,$fot(not(X_319))),bind(X_80,$fot(implies(X_319,not(implies(X_317,X_318)))))]]) ).
cnf(refute_0_90,plain,
is_a_theorem(implies(not(implies(X,Y)),implies(not(X),not(X_281)))),
inference(subst,[],[refute_0_16:[bind(X_12,$fot(not(X_281)))]]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(not(implies(X,Y)),implies(not(X),not(X_281))))
| is_a_theorem(implies(implies(X_281,not(implies(X,Y))),implies(not(X),not(X_281)))) ),
inference(subst,[],[refute_0_57:[bind(X_71,$fot(not(X))),bind(X_72,$fot(X_281)),bind(X_73,$fot(not(implies(X,Y))))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(X_281,not(implies(X,Y))),implies(not(X),not(X_281)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,Y)),implies(not(X),not(X_281)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
is_a_theorem(implies(implies(X_319,not(implies(X_317,X_318))),implies(not(X_317),not(X_319)))),
inference(subst,[],[refute_0_92:[bind(X,$fot(X_317)),bind(Y,$fot(X_318)),bind(X_281,$fot(X_319))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(implies(X_317,X_78),implies(X_319,not(implies(X_317,X_318)))),implies(not(X_317),not(X_319)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_319,not(implies(X_317,X_318))),implies(not(X_317),not(X_319)))) )],[refute_0_93,refute_0_89]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(implies(implies(X_1028,X_1031),implies(X_1030,not(implies(X_1028,X_1029)))),implies(not(X_1028),not(X_1030)))),
inference(subst,[],[refute_0_94:[bind(X_317,$fot(X_1028)),bind(X_318,$fot(X_1029)),bind(X_319,$fot(X_1030)),bind(X_78,$fot(X_1031))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(implies(X_1028,X_1031),implies(X_1030,not(implies(X_1028,X_1029)))))
| is_a_theorem(implies(not(X_1028),not(X_1030))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1028,X_1031),implies(X_1030,not(implies(X_1028,X_1029)))),implies(not(X_1028),not(X_1030)))) )],[refute_0_95,refute_0_88]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(implies(X_3369,not(implies(X_3369,X_3370))),implies(implies(implies(X_1486,not(not(X_1486))),X_3369),not(implies(X_3369,X_3370)))))
| is_a_theorem(implies(not(X_3369),not(implies(implies(X_1486,not(not(X_1486))),X_3369)))) ),
inference(subst,[],[refute_0_96:[bind(X_1028,$fot(X_3369)),bind(X_1029,$fot(X_3370)),bind(X_1030,$fot(implies(implies(X_1486,not(not(X_1486))),X_3369))),bind(X_1031,$fot(not(implies(X_3369,X_3370))))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(not(X_3369),not(implies(implies(X_1486,not(not(X_1486))),X_3369)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_3369,not(implies(X_3369,X_3370))),implies(implies(implies(X_1486,not(not(X_1486))),X_3369),not(implies(X_3369,X_3370))))) )],[refute_0_87,refute_0_97]) ).
cnf(refute_0_99,plain,
( ~ is_a_theorem(implies(X_1443,not(X_1442)))
| ~ is_a_theorem(implies(implies(X_1443,not(X_1442)),implies(implies(X_1443,X_1442),not(X_1443))))
| is_a_theorem(implies(implies(X_1443,X_1442),not(X_1443))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1443,not(X_1442)))),bind(Y,$fot(implies(implies(X_1443,X_1442),not(X_1443))))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(not(X_1417),implies(implies(X_1418,X_1417),not(X_1418))))
| is_a_theorem(implies(implies(X_1418,not(X_1417)),implies(implies(X_1418,X_1417),not(X_1418)))) ),
inference(subst,[],[refute_0_57:[bind(X_71,$fot(implies(X_1418,X_1417))),bind(X_72,$fot(X_1418)),bind(X_73,$fot(not(X_1417)))]]) ).
cnf(refute_0_101,plain,
( ~ is_a_theorem(implies(implies(X_1413,not(X_1414)),implies(implies(X_1414,X_1413),not(X_1414))))
| is_a_theorem(implies(not(X_1413),implies(implies(X_1414,X_1413),not(X_1414)))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_1413)),bind(Y,$fot(not(X_1414))),bind(Z,$fot(implies(implies(X_1414,X_1413),not(X_1414))))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(not(X_1400),not(X_1400)))
| is_a_theorem(implies(implies(Y,not(X_1400)),implies(implies(X_1400,Y),not(X_1400)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_1400)),bind(Z,$fot(not(X_1400)))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(Y,not(X_1400)),implies(implies(X_1400,Y),not(X_1400)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1400),not(X_1400))) )],[refute_0_74,refute_0_102]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(implies(X_1413,not(X_1414)),implies(implies(X_1414,X_1413),not(X_1414)))),
inference(subst,[],[refute_0_103:[bind(Y,$fot(X_1413)),bind(X_1400,$fot(X_1414))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(not(X_1413),implies(implies(X_1414,X_1413),not(X_1414)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1413,not(X_1414)),implies(implies(X_1414,X_1413),not(X_1414)))) )],[refute_0_104,refute_0_101]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(not(X_1417),implies(implies(X_1418,X_1417),not(X_1418)))),
inference(subst,[],[refute_0_105:[bind(X_1413,$fot(X_1417)),bind(X_1414,$fot(X_1418))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(implies(X_1418,not(X_1417)),implies(implies(X_1418,X_1417),not(X_1418)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_1417),implies(implies(X_1418,X_1417),not(X_1418)))) )],[refute_0_106,refute_0_100]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(implies(X_1443,not(X_1442)),implies(implies(X_1443,X_1442),not(X_1443)))),
inference(subst,[],[refute_0_107:[bind(X_1417,$fot(X_1442)),bind(X_1418,$fot(X_1443))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(X_1443,not(X_1442)))
| is_a_theorem(implies(implies(X_1443,X_1442),not(X_1443))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1443,not(X_1442)),implies(implies(X_1443,X_1442),not(X_1443)))) )],[refute_0_108,refute_0_99]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(not(X_3369),not(implies(implies(X_1486,not(not(X_1486))),X_3369))))
| is_a_theorem(implies(implies(not(X_3369),implies(implies(X_1486,not(not(X_1486))),X_3369)),not(not(X_3369)))) ),
inference(subst,[],[refute_0_109:[bind(X_1442,$fot(implies(implies(X_1486,not(not(X_1486))),X_3369))),bind(X_1443,$fot(not(X_3369)))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(implies(not(X_3369),implies(implies(X_1486,not(not(X_1486))),X_3369)),not(not(X_3369)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_3369),not(implies(implies(X_1486,not(not(X_1486))),X_3369)))) )],[refute_0_98,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(implies(not(X_3993),implies(implies(X_3992,not(not(X_3992))),X_3993)),not(not(X_3993)))),
inference(subst,[],[refute_0_111:[bind(X_1486,$fot(X_3992)),bind(X_3369,$fot(X_3993))]]) ).
cnf(refute_0_113,plain,
is_a_theorem(implies(implies(implies(X_3992,not(not(X_3992))),X_3993),not(not(X_3993)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_3993),implies(implies(X_3992,not(not(X_3992))),X_3993)),not(not(X_3993)))) )],[refute_0_112,refute_0_2]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(implies(X_3992,not(not(X_3992))),X_8212),not(not(X_8212)))),
inference(subst,[],[refute_0_113:[bind(X_3993,$fot(X_8212))]]) ).
cnf(refute_0_115,plain,
( ~ is_a_theorem(implies(implies(X_7268,X_7269),not(X_7266)))
| ~ is_a_theorem(implies(implies(implies(X_7268,X_7269),not(X_7266)),implies(X_7269,implies(X_7266,X_7267))))
| is_a_theorem(implies(X_7269,implies(X_7266,X_7267))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_7268,X_7269),not(X_7266)))),bind(Y,$fot(implies(X_7269,implies(X_7266,X_7267))))]]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(not(X),implies(X_7259,implies(X,Y)))),
inference(subst,[],[refute_0_32:[bind(X_26,$fot(X_7259))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(implies(X_124,implies(X_122,X_123)))
| ~ is_a_theorem(implies(implies(X_124,implies(X_122,X_123)),implies(implies(implies(X_121,X_122),X_124),implies(X_122,X_123))))
| is_a_theorem(implies(implies(implies(X_121,X_122),X_124),implies(X_122,X_123))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_124,implies(X_122,X_123)))),bind(Y,$fot(implies(implies(implies(X_121,X_122),X_124),implies(X_122,X_123))))]]) ).
cnf(refute_0_118,plain,
is_a_theorem(implies(implies(implies(X,Y),X_12),implies(Y,X_12))),
inference(subst,[],[cn_19:[bind(Z,$fot(X_12))]]) ).
cnf(refute_0_119,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_12),implies(Y,X_12)))
| is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_12))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_12)),bind(Z,$fot(implies(Y,X_12)))]]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_12))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_12),implies(Y,X_12))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_12)))
| is_a_theorem(implies(implies(X_69,implies(Y,X_12)),implies(implies(implies(X,Y),X_69),implies(Y,X_12)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_69)),bind(Z,$fot(implies(Y,X_12)))]]) ).
cnf(refute_0_122,plain,
is_a_theorem(implies(implies(X_69,implies(Y,X_12)),implies(implies(implies(X,Y),X_69),implies(Y,X_12)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(implies(X,Y)),implies(Y,X_12))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(X_124,implies(X_122,X_123)),implies(implies(implies(X_121,X_122),X_124),implies(X_122,X_123)))),
inference(subst,[],[refute_0_122:[bind(X,$fot(X_121)),bind(Y,$fot(X_122)),bind(X_12,$fot(X_123)),bind(X_69,$fot(X_124))]]) ).
cnf(refute_0_124,plain,
( ~ is_a_theorem(implies(X_124,implies(X_122,X_123)))
| is_a_theorem(implies(implies(implies(X_121,X_122),X_124),implies(X_122,X_123))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_124,implies(X_122,X_123)),implies(implies(implies(X_121,X_122),X_124),implies(X_122,X_123)))) )],[refute_0_123,refute_0_117]) ).
cnf(refute_0_125,plain,
( ~ is_a_theorem(implies(not(X),implies(X_7259,implies(X,Y))))
| is_a_theorem(implies(implies(implies(X_7258,X_7259),not(X)),implies(X_7259,implies(X,Y)))) ),
inference(subst,[],[refute_0_124:[bind(X_121,$fot(X_7258)),bind(X_122,$fot(X_7259)),bind(X_123,$fot(implies(X,Y))),bind(X_124,$fot(not(X)))]]) ).
cnf(refute_0_126,plain,
is_a_theorem(implies(implies(implies(X_7258,X_7259),not(X)),implies(X_7259,implies(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X),implies(X_7259,implies(X,Y)))) )],[refute_0_116,refute_0_125]) ).
cnf(refute_0_127,plain,
is_a_theorem(implies(implies(implies(X_7268,X_7269),not(X_7266)),implies(X_7269,implies(X_7266,X_7267)))),
inference(subst,[],[refute_0_126:[bind(X,$fot(X_7266)),bind(Y,$fot(X_7267)),bind(X_7258,$fot(X_7268)),bind(X_7259,$fot(X_7269))]]) ).
cnf(refute_0_128,plain,
( ~ is_a_theorem(implies(implies(X_7268,X_7269),not(X_7266)))
| is_a_theorem(implies(X_7269,implies(X_7266,X_7267))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_7268,X_7269),not(X_7266)),implies(X_7269,implies(X_7266,X_7267)))) )],[refute_0_127,refute_0_115]) ).
cnf(refute_0_129,plain,
( ~ is_a_theorem(implies(implies(implies(X_3992,not(not(X_3992))),X_8212),not(not(X_8212))))
| is_a_theorem(implies(X_8212,implies(not(X_8212),X_8210))) ),
inference(subst,[],[refute_0_128:[bind(X_7266,$fot(not(X_8212))),bind(X_7267,$fot(X_8210)),bind(X_7268,$fot(implies(X_3992,not(not(X_3992))))),bind(X_7269,$fot(X_8212))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(X_8212,implies(not(X_8212),X_8210))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_3992,not(not(X_3992))),X_8212),not(not(X_8212)))) )],[refute_0_114,refute_0_129]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(a,implies(not(a),b))),
inference(subst,[],[refute_0_130:[bind(X_8210,$fot(b)),bind(X_8212,$fot(a))]]) ).
cnf(refute_0_132,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(not(a),b))) )],[refute_0_131,prove_cn_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL069-1 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 23:27:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.61/4.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.61/4.78
% 4.61/4.78 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.61/4.79
%------------------------------------------------------------------------------