TSTP Solution File: LCL094-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL094-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:49:26 EDT 2022
% Result : Unsatisfiable 0.73s 0.93s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 3
% Syntax : Number of clauses : 156 ( 82 unt; 0 nHn; 32 RR)
% Number of literals : 250 ( 0 equ; 95 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 613 ( 213 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(ic_JLukasiewicz_4,axiom,
is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))) ).
cnf(prove_ic_5,negated_conjecture,
~ is_a_theorem(implies(a,implies(implies(a,b),b))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(X_1376,X_1376),X_1375))
| ~ is_a_theorem(implies(implies(implies(X_1376,X_1376),X_1375),X_1375))
| is_a_theorem(X_1375) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1376,X_1376),X_1375))),bind(Y,$fot(X_1375))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(X_1208,X_1209),X_1208))
| ~ is_a_theorem(implies(implies(implies(X_1208,X_1209),X_1208),X_1208))
| is_a_theorem(X_1208) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1208,X_1209),X_1208))),bind(Y,$fot(X_1208))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(X_159)
| ~ is_a_theorem(implies(X_159,implies(implies(X_159,X_161),implies(X_160,X_161))))
| is_a_theorem(implies(implies(X_159,X_161),implies(X_160,X_161))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_159)),bind(Y,$fot(implies(implies(X_159,X_161),implies(X_160,X_161))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X_16)
| ~ is_a_theorem(implies(X_16,implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13)))))
| is_a_theorem(implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_16)),bind(Y,$fot(implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13)))))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(X_9,implies(implies(S,P),implies(R,P))))),
inference(subst,[],[ic_JLukasiewicz_4:[bind(T,$fot(X_9))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_4,X_5)))
| ~ is_a_theorem(implies(implies(implies(X_2,X_3),implies(X_4,X_5)),implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2)))))
| is_a_theorem(implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_2,X_3),implies(X_4,X_5)))),bind(Y,$fot(implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2)))))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(X_2,X_3),implies(X_4,X_5)),implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2))))),
inference(subst,[],[ic_JLukasiewicz_4:[bind(P,$fot(X_2)),bind(Q,$fot(X_3)),bind(R,$fot(X_4)),bind(S,$fot(X_5)),bind(T,$fot(X_6))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_4,X_5)))
| is_a_theorem(implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_2,X_3),implies(X_4,X_5)),implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2))))) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(X_9,implies(implies(S,P),implies(R,P)))))
| is_a_theorem(implies(X_11,implies(implies(implies(implies(S,P),implies(R,P)),implies(P,Q)),implies(X_9,implies(P,Q))))) ),
inference(subst,[],[refute_0_7:[bind(X_2,$fot(implies(P,Q))),bind(X_3,$fot(implies(R,S))),bind(X_4,$fot(X_9)),bind(X_5,$fot(implies(implies(S,P),implies(R,P)))),bind(X_6,$fot(X_11))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(X_11,implies(implies(implies(implies(S,P),implies(R,P)),implies(P,Q)),implies(X_9,implies(P,Q))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(X_9,implies(implies(S,P),implies(R,P))))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(X_16,implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13))))),
inference(subst,[],[refute_0_9:[bind(P,$fot(X_12)),bind(Q,$fot(X_13)),bind(R,$fot(X_14)),bind(S,$fot(X_15)),bind(X_11,$fot(X_16)),bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(X_16)
| is_a_theorem(implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_16,implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13))))) )],[refute_0_10,refute_0_3]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P)))))
| is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))) ),
inference(subst,[],[refute_0_11:[bind(X_12,$fot(X_25)),bind(X_13,$fot(X_26)),bind(X_14,$fot(X_27)),bind(X_15,$fot(X_28)),bind(X_16,$fot(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P)))))),bind(X_17,$fot(X_30))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))) )],[ic_JLukasiewicz_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(X_60)
| ~ is_a_theorem(implies(X_60,implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59)))))
| is_a_theorem(implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_60)),bind(Y,$fot(implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59)))))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(X_52,X_49),implies(X_51,X_49)),implies(X_49,implies(implies(X_49,X_52),implies(X_51,X_52))))),
inference(subst,[],[ic_JLukasiewicz_4:[bind(P,$fot(X_52)),bind(Q,$fot(X_49)),bind(R,$fot(X_51)),bind(S,$fot(X_49)),bind(T,$fot(X_49))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_34,X_31),implies(X_33,X_31)),implies(X_31,X_32)))
| ~ is_a_theorem(implies(implies(implies(implies(X_34,X_31),implies(X_33,X_31)),implies(X_31,X_32)),implies(X_35,implies(X_31,X_32))))
| is_a_theorem(implies(X_35,implies(X_31,X_32))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_34,X_31),implies(X_33,X_31)),implies(X_31,X_32)))),bind(Y,$fot(implies(X_35,implies(X_31,X_32))))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(implies(X_34,X_31),implies(X_33,X_31)),implies(X_31,X_32)),implies(X_35,implies(X_31,X_32)))),
inference(subst,[],[refute_0_13:[bind(X_25,$fot(X_31)),bind(X_26,$fot(X_32)),bind(X_27,$fot(X_33)),bind(X_28,$fot(X_34)),bind(X_30,$fot(X_35))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(implies(X_34,X_31),implies(X_33,X_31)),implies(X_31,X_32)))
| is_a_theorem(implies(X_35,implies(X_31,X_32))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_34,X_31),implies(X_33,X_31)),implies(X_31,X_32)),implies(X_35,implies(X_31,X_32)))) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(X_52,X_49),implies(X_51,X_49)),implies(X_49,implies(implies(X_49,X_52),implies(X_51,X_52)))))
| is_a_theorem(implies(X_53,implies(X_49,implies(implies(X_49,X_52),implies(X_51,X_52))))) ),
inference(subst,[],[refute_0_18:[bind(X_31,$fot(X_49)),bind(X_32,$fot(implies(implies(X_49,X_52),implies(X_51,X_52)))),bind(X_33,$fot(X_51)),bind(X_34,$fot(X_52)),bind(X_35,$fot(X_53))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(X_53,implies(X_49,implies(implies(X_49,X_52),implies(X_51,X_52))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_52,X_49),implies(X_51,X_49)),implies(X_49,implies(implies(X_49,X_52),implies(X_51,X_52))))) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_60,implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59))))),
inference(subst,[],[refute_0_20:[bind(X_49,$fot(X_57)),bind(X_51,$fot(X_58)),bind(X_52,$fot(X_59)),bind(X_53,$fot(X_60))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(X_60)
| is_a_theorem(implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_60,implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59))))) )],[refute_0_21,refute_0_14]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26))))
| is_a_theorem(implies(X_155,implies(implies(X_155,X_157),implies(X_156,X_157)))) ),
inference(subst,[],[refute_0_22:[bind(X_57,$fot(X_155)),bind(X_58,$fot(X_156)),bind(X_59,$fot(X_157)),bind(X_60,$fot(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(X_155,implies(implies(X_155,X_157),implies(X_156,X_157)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))) )],[refute_0_13,refute_0_23]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(X_159,implies(implies(X_159,X_161),implies(X_160,X_161)))),
inference(subst,[],[refute_0_24:[bind(X_155,$fot(X_159)),bind(X_156,$fot(X_160)),bind(X_157,$fot(X_161))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(X_159)
| is_a_theorem(implies(implies(X_159,X_161),implies(X_160,X_161))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_159,implies(implies(X_159,X_161),implies(X_160,X_161)))) )],[refute_0_25,refute_0_2]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)))
| is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))) ),
inference(subst,[],[refute_0_26:[bind(X_159,$fot(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173))))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(X_75)
| ~ is_a_theorem(implies(X_75,implies(implies(implies(X_76,X_77),X_76),implies(X_77,X_76))))
| is_a_theorem(implies(implies(implies(X_76,X_77),X_76),implies(X_77,X_76))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_75)),bind(Y,$fot(implies(implies(implies(X_76,X_77),X_76),implies(X_77,X_76))))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(X_73,X_74),implies(X_74,implies(X_73,X_74))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73)))) ),
inference(subst,[],[refute_0_7:[bind(X_2,$fot(X_73)),bind(X_3,$fot(X_74)),bind(X_4,$fot(X_74)),bind(X_5,$fot(implies(X_73,X_74)))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(X_56)
| ~ is_a_theorem(implies(X_56,implies(implies(X_54,X_55),implies(X_55,implies(X_54,X_55)))))
| is_a_theorem(implies(implies(X_54,X_55),implies(X_55,implies(X_54,X_55)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_56)),bind(Y,$fot(implies(implies(X_54,X_55),implies(X_55,implies(X_54,X_55)))))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(implies(X_28,X_51),implies(X_27,X_51)),implies(X_51,implies(X_27,X_51))),implies(implies(X_27,X_51),implies(X_51,implies(X_27,X_51))))),
inference(subst,[],[refute_0_13:[bind(X_25,$fot(X_51)),bind(X_26,$fot(implies(X_27,X_51))),bind(X_30,$fot(implies(X_27,X_51)))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_51),implies(X_27,X_51)),implies(X_51,implies(X_27,X_51))),implies(implies(X_27,X_51),implies(X_51,implies(X_27,X_51)))))
| is_a_theorem(implies(X_53,implies(implies(X_27,X_51),implies(X_51,implies(X_27,X_51))))) ),
inference(subst,[],[refute_0_18:[bind(X_31,$fot(implies(X_27,X_51))),bind(X_32,$fot(implies(X_51,implies(X_27,X_51)))),bind(X_33,$fot(X_51)),bind(X_34,$fot(implies(X_28,X_51))),bind(X_35,$fot(X_53))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(X_53,implies(implies(X_27,X_51),implies(X_51,implies(X_27,X_51))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28,X_51),implies(X_27,X_51)),implies(X_51,implies(X_27,X_51))),implies(implies(X_27,X_51),implies(X_51,implies(X_27,X_51))))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(X_56,implies(implies(X_54,X_55),implies(X_55,implies(X_54,X_55))))),
inference(subst,[],[refute_0_33:[bind(X_27,$fot(X_54)),bind(X_51,$fot(X_55)),bind(X_53,$fot(X_56))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(X_56)
| is_a_theorem(implies(implies(X_54,X_55),implies(X_55,implies(X_54,X_55)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_56,implies(implies(X_54,X_55),implies(X_55,implies(X_54,X_55))))) )],[refute_0_34,refute_0_30]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26))))
| is_a_theorem(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71)))) ),
inference(subst,[],[refute_0_35:[bind(X_54,$fot(X_70)),bind(X_55,$fot(X_71)),bind(X_56,$fot(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))) )],[refute_0_13,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(X_73,X_74),implies(X_74,implies(X_73,X_74)))),
inference(subst,[],[refute_0_37:[bind(X_70,$fot(X_73)),bind(X_71,$fot(X_74))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_73,X_74),implies(X_74,implies(X_73,X_74)))) )],[refute_0_38,refute_0_29]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(X_75,implies(implies(implies(X_76,X_77),X_76),implies(X_77,X_76)))),
inference(subst,[],[refute_0_39:[bind(X_6,$fot(X_75)),bind(X_73,$fot(X_76)),bind(X_74,$fot(X_77))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(X_75)
| is_a_theorem(implies(implies(implies(X_76,X_77),X_76),implies(X_77,X_76))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_75,implies(implies(implies(X_76,X_77),X_76),implies(X_77,X_76)))) )],[refute_0_40,refute_0_28]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26))))
| is_a_theorem(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113))) ),
inference(subst,[],[refute_0_41:[bind(X_75,$fot(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26))))),bind(X_76,$fot(X_113)),bind(X_77,$fot(X_114))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))) )],[refute_0_13,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113)))
| is_a_theorem(implies(implies(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113)),X_169),implies(X_168,X_169))) ),
inference(subst,[],[refute_0_26:[bind(X_159,$fot(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113)))),bind(X_160,$fot(X_168)),bind(X_161,$fot(X_169))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113)),X_169),implies(X_168,X_169))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173))),
inference(subst,[],[refute_0_45:[bind(X_113,$fot(X_170)),bind(X_114,$fot(X_171)),bind(X_168,$fot(X_172)),bind(X_169,$fot(X_173))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173))) )],[refute_0_46,refute_0_27]) ).
cnf(refute_0_48,plain,
( ~ is_a_theorem(X_1127)
| ~ is_a_theorem(implies(X_1127,implies(implies(implies(X_1125,X_1126),X_1125),X_1125)))
| is_a_theorem(implies(implies(implies(X_1125,X_1126),X_1125),X_1125)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1127)),bind(Y,$fot(implies(implies(implies(X_1125,X_1126),X_1125),X_1125)))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(implies(X_220,X_221),X_220))
| ~ is_a_theorem(implies(implies(implies(X_220,X_221),X_220),implies(X_219,X_220)))
| is_a_theorem(implies(X_219,X_220)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_220,X_221),X_220))),bind(Y,$fot(implies(X_219,X_220)))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(X_142)
| ~ is_a_theorem(implies(X_142,implies(implies(implies(X_140,X_141),X_140),implies(X_139,X_140))))
| is_a_theorem(implies(implies(implies(X_140,X_141),X_140),implies(X_139,X_140))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_142)),bind(Y,$fot(implies(implies(implies(X_140,X_141),X_140),implies(X_139,X_140))))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_134,implies(X_2,X_3))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_2,X_3),X_2),implies(X_134,X_2)))) ),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(X_134)),bind(X_5,$fot(implies(X_2,X_3)))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(X_119)
| ~ is_a_theorem(implies(X_119,implies(X_117,implies(X_118,X_117))))
| is_a_theorem(implies(X_117,implies(X_118,X_117))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_119)),bind(Y,$fot(implies(X_117,implies(X_118,X_117))))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_33,X_116),X_116),implies(X_33,X_116)),implies(X_116,implies(X_33,X_116))))
| is_a_theorem(implies(X_35,implies(X_116,implies(X_33,X_116)))) ),
inference(subst,[],[refute_0_18:[bind(X_31,$fot(X_116)),bind(X_32,$fot(implies(X_33,X_116))),bind(X_34,$fot(implies(X_33,X_116)))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(implies(X_33,X_116),X_116),implies(X_33,X_116)),implies(X_116,implies(X_33,X_116)))),
inference(subst,[],[refute_0_43:[bind(X_113,$fot(implies(X_33,X_116))),bind(X_114,$fot(X_116))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(X_35,implies(X_116,implies(X_33,X_116)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_33,X_116),X_116),implies(X_33,X_116)),implies(X_116,implies(X_33,X_116)))) )],[refute_0_54,refute_0_53]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(X_119,implies(X_117,implies(X_118,X_117)))),
inference(subst,[],[refute_0_55:[bind(X_116,$fot(X_117)),bind(X_33,$fot(X_118)),bind(X_35,$fot(X_119))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(X_119)
| is_a_theorem(implies(X_117,implies(X_118,X_117))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_119,implies(X_117,implies(X_118,X_117)))) )],[refute_0_56,refute_0_52]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26))))
| is_a_theorem(implies(X_130,implies(X_131,X_130))) ),
inference(subst,[],[refute_0_57:[bind(X_117,$fot(X_130)),bind(X_118,$fot(X_131)),bind(X_119,$fot(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(X_130,implies(X_131,X_130))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))) )],[refute_0_13,refute_0_58]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(X_134,implies(X_2,X_3)))),
inference(subst,[],[refute_0_59:[bind(X_130,$fot(implies(X_2,X_3))),bind(X_131,$fot(X_134))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_2,X_3),X_2),implies(X_134,X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(X_134,implies(X_2,X_3)))) )],[refute_0_60,refute_0_51]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(X_142,implies(implies(implies(X_140,X_141),X_140),implies(X_139,X_140)))),
inference(subst,[],[refute_0_61:[bind(X_134,$fot(X_139)),bind(X_2,$fot(X_140)),bind(X_3,$fot(X_141)),bind(X_6,$fot(X_142))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(X_142)
| is_a_theorem(implies(implies(implies(X_140,X_141),X_140),implies(X_139,X_140))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_142,implies(implies(implies(X_140,X_141),X_140),implies(X_139,X_140)))) )],[refute_0_62,refute_0_50]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113)),X_169),implies(X_168,X_169)))
| is_a_theorem(implies(implies(implies(X_216,X_217),X_216),implies(X_215,X_216))) ),
inference(subst,[],[refute_0_63:[bind(X_139,$fot(X_215)),bind(X_140,$fot(X_216)),bind(X_141,$fot(X_217)),bind(X_142,$fot(implies(implies(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113)),X_169),implies(X_168,X_169))))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(implies(X_216,X_217),X_216),implies(X_215,X_216))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_113,X_114),X_113),implies(X_114,X_113)),X_169),implies(X_168,X_169))) )],[refute_0_45,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(X_220,X_221),X_220),implies(X_219,X_220))),
inference(subst,[],[refute_0_65:[bind(X_215,$fot(X_219)),bind(X_216,$fot(X_220)),bind(X_217,$fot(X_221))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(X_220,X_221),X_220))
| is_a_theorem(implies(X_219,X_220)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_220,X_221),X_220),implies(X_219,X_220))) )],[refute_0_66,refute_0_49]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_1123,X_1124),X_1123),X_1123),X_1123),implies(implies(implies(X_1123,X_1124),X_1123),X_1123)))
| is_a_theorem(implies(X_219,implies(implies(implies(X_1123,X_1124),X_1123),X_1123))) ),
inference(subst,[],[refute_0_67:[bind(X_220,$fot(implies(implies(implies(X_1123,X_1124),X_1123),X_1123))),bind(X_221,$fot(X_1123))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(X_166)
| ~ is_a_theorem(implies(X_166,implies(implies(implies(X_162,X_163),X_164),implies(implies(implies(X_164,X_165),X_163),X_164))))
| is_a_theorem(implies(implies(implies(X_162,X_163),X_164),implies(implies(implies(X_164,X_165),X_163),X_164))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_166)),bind(Y,$fot(implies(implies(implies(X_162,X_163),X_164),implies(implies(implies(X_164,X_165),X_163),X_164))))]]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_2,X_3),X_161),implies(X_160,X_161))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_160,X_161),X_2),implies(implies(implies(X_2,X_3),X_161),X_2)))) ),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(implies(implies(X_2,X_3),X_161))),bind(X_5,$fot(implies(X_160,X_161)))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_2,X_3),X_161),implies(X_160,X_161)))),
inference(subst,[],[refute_0_24:[bind(X_155,$fot(implies(X_2,X_3))),bind(X_156,$fot(X_160)),bind(X_157,$fot(X_161))]]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_160,X_161),X_2),implies(implies(implies(X_2,X_3),X_161),X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_2,X_3),X_161),implies(X_160,X_161)))) )],[refute_0_71,refute_0_70]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(X_166,implies(implies(implies(X_162,X_163),X_164),implies(implies(implies(X_164,X_165),X_163),X_164)))),
inference(subst,[],[refute_0_72:[bind(X_160,$fot(X_162)),bind(X_161,$fot(X_163)),bind(X_2,$fot(X_164)),bind(X_3,$fot(X_165)),bind(X_6,$fot(X_166))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(X_166)
| is_a_theorem(implies(implies(implies(X_162,X_163),X_164),implies(implies(implies(X_164,X_165),X_163),X_164))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_166,implies(implies(implies(X_162,X_163),X_164),implies(implies(implies(X_164,X_165),X_163),X_164)))) )],[refute_0_73,refute_0_69]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161)))
| is_a_theorem(implies(implies(implies(X_1116,X_1117),X_1118),implies(implies(implies(X_1118,X_1119),X_1117),X_1118))) ),
inference(subst,[],[refute_0_74:[bind(X_162,$fot(X_1116)),bind(X_163,$fot(X_1117)),bind(X_164,$fot(X_1118)),bind(X_165,$fot(X_1119)),bind(X_166,$fot(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(implies(X_1116,X_1117),X_1118),implies(implies(implies(X_1118,X_1119),X_1117),X_1118))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))) )],[refute_0_47,refute_0_75]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_1123,X_1124),X_1123),X_1123),X_1123),implies(implies(implies(X_1123,X_1124),X_1123),X_1123))),
inference(subst,[],[refute_0_76:[bind(X_1116,$fot(implies(implies(X_1123,X_1124),X_1123))),bind(X_1117,$fot(X_1123)),bind(X_1118,$fot(X_1123)),bind(X_1119,$fot(X_1124))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(X_219,implies(implies(implies(X_1123,X_1124),X_1123),X_1123))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_1123,X_1124),X_1123),X_1123),X_1123),implies(implies(implies(X_1123,X_1124),X_1123),X_1123))) )],[refute_0_77,refute_0_68]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(X_1127,implies(implies(implies(X_1125,X_1126),X_1125),X_1125))),
inference(subst,[],[refute_0_78:[bind(X_1123,$fot(X_1125)),bind(X_1124,$fot(X_1126)),bind(X_219,$fot(X_1127))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(X_1127)
| is_a_theorem(implies(implies(implies(X_1125,X_1126),X_1125),X_1125)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1127,implies(implies(implies(X_1125,X_1126),X_1125),X_1125))) )],[refute_0_79,refute_0_48]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161)))
| is_a_theorem(implies(implies(implies(X_1205,X_1206),X_1205),X_1205)) ),
inference(subst,[],[refute_0_80:[bind(X_1125,$fot(X_1205)),bind(X_1126,$fot(X_1206)),bind(X_1127,$fot(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(implies(X_1205,X_1206),X_1205),X_1205)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))) )],[refute_0_47,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(implies(X_1208,X_1209),X_1208),X_1208)),
inference(subst,[],[refute_0_82:[bind(X_1205,$fot(X_1208)),bind(X_1206,$fot(X_1209))]]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(X_1208,X_1209),X_1208))
| is_a_theorem(X_1208) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1208,X_1209),X_1208),X_1208)) )],[refute_0_83,refute_0_1]) ).
cnf(refute_0_85,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_1373,X_1373),X_1371),X_1371),X_1371),implies(implies(implies(X_1373,X_1373),X_1371),X_1371)))
| is_a_theorem(implies(implies(implies(X_1373,X_1373),X_1371),X_1371)) ),
inference(subst,[],[refute_0_84:[bind(X_1208,$fot(implies(implies(implies(X_1373,X_1373),X_1371),X_1371))),bind(X_1209,$fot(X_1371))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_370,X_370),X_369),implies(X_371,X_369))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)))) ),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(implies(implies(X_370,X_370),X_369))),bind(X_5,$fot(implies(X_371,X_369)))]]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_357,implies(X_356,X_356))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_356,X_356),X_2),implies(X_357,X_2)))) ),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(X_357)),bind(X_5,$fot(implies(X_356,X_356)))]]) ).
cnf(refute_0_88,plain,
( ~ is_a_theorem(X_133)
| ~ is_a_theorem(implies(X_133,implies(X_134,X_133)))
| is_a_theorem(implies(X_134,X_133)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_133)),bind(Y,$fot(implies(X_134,X_133)))]]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(X_133,implies(X_134,X_133))),
inference(subst,[],[refute_0_59:[bind(X_130,$fot(X_133)),bind(X_131,$fot(X_134))]]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(X_133)
| is_a_theorem(implies(X_134,X_133)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_133,implies(X_134,X_133))) )],[refute_0_89,refute_0_88]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(X_351,implies(X_350,X_350)))
| is_a_theorem(implies(X_134,implies(X_351,implies(X_350,X_350)))) ),
inference(subst,[],[refute_0_90:[bind(X_133,$fot(implies(X_351,implies(X_350,X_350))))]]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(implies(implies(X_217,X_217),X_217),implies(X_217,X_217))),
inference(subst,[],[refute_0_65:[bind(X_215,$fot(X_217)),bind(X_216,$fot(X_217))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(implies(implies(X_217,X_217),X_217),implies(X_217,X_217)))
| is_a_theorem(implies(X_347,implies(X_217,X_217))) ),
inference(subst,[],[refute_0_67:[bind(X_219,$fot(X_347)),bind(X_220,$fot(implies(X_217,X_217))),bind(X_221,$fot(X_217))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(X_347,implies(X_217,X_217))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_217,X_217),X_217),implies(X_217,X_217))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(X_351,implies(X_350,X_350))),
inference(subst,[],[refute_0_94:[bind(X_217,$fot(X_350)),bind(X_347,$fot(X_351))]]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(X_134,implies(X_351,implies(X_350,X_350)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_351,implies(X_350,X_350))) )],[refute_0_95,refute_0_91]) ).
cnf(refute_0_97,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(X_357,implies(X_356,X_356)))),
inference(subst,[],[refute_0_96:[bind(X_134,$fot(implies(X_2,X_3))),bind(X_350,$fot(X_356)),bind(X_351,$fot(X_357))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_356,X_356),X_2),implies(X_357,X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(X_357,implies(X_356,X_356)))) )],[refute_0_97,refute_0_87]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_370,X_370),X_369),implies(X_371,X_369)))),
inference(subst,[],[refute_0_98:[bind(X_2,$fot(X_369)),bind(X_356,$fot(X_370)),bind(X_357,$fot(X_371)),bind(X_6,$fot(implies(X_2,X_3)))]]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_370,X_370),X_369),implies(X_371,X_369)))) )],[refute_0_99,refute_0_86]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)),X_1211),implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)))),
inference(subst,[],[refute_0_100:[bind(X_6,$fot(implies(implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)),X_1211)))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)),X_1211),implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2))))
| is_a_theorem(implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2))) ),
inference(subst,[],[refute_0_84:[bind(X_1208,$fot(implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)))),bind(X_1209,$fot(X_1211))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)),X_1211),implies(implies(implies(X_371,X_369),X_2),implies(implies(implies(X_370,X_370),X_369),X_2)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_1373,X_1373),X_1371),X_1371),X_1371),implies(implies(implies(X_1373,X_1373),X_1371),X_1371))),
inference(subst,[],[refute_0_103:[bind(X_2,$fot(X_1371)),bind(X_369,$fot(X_1371)),bind(X_370,$fot(X_1373)),bind(X_371,$fot(implies(implies(X_1373,X_1373),X_1371)))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(implies(implies(X_1373,X_1373),X_1371),X_1371)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_1373,X_1373),X_1371),X_1371),X_1371),implies(implies(implies(X_1373,X_1373),X_1371),X_1371))) )],[refute_0_104,refute_0_85]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(implies(implies(X_1376,X_1376),X_1375),X_1375)),
inference(subst,[],[refute_0_105:[bind(X_1371,$fot(X_1375)),bind(X_1373,$fot(X_1376))]]) ).
cnf(refute_0_107,plain,
( ~ is_a_theorem(implies(implies(X_1376,X_1376),X_1375))
| is_a_theorem(X_1375) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1376,X_1376),X_1375),X_1375)) )],[refute_0_106,refute_0_0]) ).
cnf(refute_0_108,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_1685,X_1684),X_1684),implies(implies(X_1685,X_1684),X_1684)),implies(X_1685,implies(implies(X_1685,X_1684),X_1684))))
| is_a_theorem(implies(X_1685,implies(implies(X_1685,X_1684),X_1684))) ),
inference(subst,[],[refute_0_107:[bind(X_1375,$fot(implies(X_1685,implies(implies(X_1685,X_1684),X_1684)))),bind(X_1376,$fot(implies(implies(X_1685,X_1684),X_1684)))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_1162,X_1160),X_1161),X_1160),implies(X_1162,X_1160)))
| is_a_theorem(implies(X_6,implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))))) ),
inference(subst,[],[refute_0_7:[bind(X_2,$fot(implies(implies(X_1162,X_1160),X_1161))),bind(X_3,$fot(X_1160)),bind(X_4,$fot(X_1162)),bind(X_5,$fot(X_1160))]]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(X_1142)
| ~ is_a_theorem(implies(X_1142,implies(implies(implies(implies(X_1145,X_1143),X_1144),X_1143),implies(X_1145,X_1143))))
| is_a_theorem(implies(implies(implies(implies(X_1145,X_1143),X_1144),X_1143),implies(X_1145,X_1143))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1142)),bind(Y,$fot(implies(implies(implies(implies(X_1145,X_1143),X_1144),X_1143),implies(X_1145,X_1143))))]]) ).
cnf(refute_0_111,plain,
( ~ is_a_theorem(implies(implies(implies(X_614,X_616),implies(X_615,X_616)),X_613))
| ~ is_a_theorem(implies(implies(implies(implies(X_614,X_616),implies(X_615,X_616)),X_613),implies(X_614,X_613)))
| is_a_theorem(implies(X_614,X_613)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_614,X_616),implies(X_615,X_616)),X_613))),bind(Y,$fot(implies(X_614,X_613)))]]) ).
cnf(refute_0_112,plain,
( ~ is_a_theorem(X_69)
| ~ is_a_theorem(implies(X_69,implies(implies(implies(implies(X_66,X_68),implies(X_67,X_68)),X_65),implies(X_66,X_65))))
| is_a_theorem(implies(implies(implies(implies(X_66,X_68),implies(X_67,X_68)),X_65),implies(X_66,X_65))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_69)),bind(Y,$fot(implies(implies(implies(implies(X_66,X_68),implies(X_67,X_68)),X_65),implies(X_66,X_65))))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59)))))
| is_a_theorem(implies(X_6,implies(implies(implies(implies(X_57,X_59),implies(X_58,X_59)),X_2),implies(X_57,X_2)))) ),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(X_57)),bind(X_5,$fot(implies(implies(X_57,X_59),implies(X_58,X_59))))]]) ).
cnf(refute_0_114,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59))))),
inference(subst,[],[refute_0_20:[bind(X_49,$fot(X_57)),bind(X_51,$fot(X_58)),bind(X_52,$fot(X_59)),bind(X_53,$fot(implies(X_2,X_3)))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(X_6,implies(implies(implies(implies(X_57,X_59),implies(X_58,X_59)),X_2),implies(X_57,X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59))))) )],[refute_0_114,refute_0_113]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(X_69,implies(implies(implies(implies(X_66,X_68),implies(X_67,X_68)),X_65),implies(X_66,X_65)))),
inference(subst,[],[refute_0_115:[bind(X_2,$fot(X_65)),bind(X_57,$fot(X_66)),bind(X_58,$fot(X_67)),bind(X_59,$fot(X_68)),bind(X_6,$fot(X_69))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(X_69)
| is_a_theorem(implies(implies(implies(implies(X_66,X_68),implies(X_67,X_68)),X_65),implies(X_66,X_65))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_69,implies(implies(implies(implies(X_66,X_68),implies(X_67,X_68)),X_65),implies(X_66,X_65)))) )],[refute_0_116,refute_0_112]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161)))
| is_a_theorem(implies(implies(implies(implies(X_609,X_611),implies(X_610,X_611)),X_608),implies(X_609,X_608))) ),
inference(subst,[],[refute_0_117:[bind(X_65,$fot(X_608)),bind(X_66,$fot(X_609)),bind(X_67,$fot(X_610)),bind(X_68,$fot(X_611)),bind(X_69,$fot(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))))]]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(implies(implies(implies(X_609,X_611),implies(X_610,X_611)),X_608),implies(X_609,X_608))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))) )],[refute_0_47,refute_0_118]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(implies(implies(implies(X_614,X_616),implies(X_615,X_616)),X_613),implies(X_614,X_613))),
inference(subst,[],[refute_0_119:[bind(X_608,$fot(X_613)),bind(X_609,$fot(X_614)),bind(X_610,$fot(X_615)),bind(X_611,$fot(X_616))]]) ).
cnf(refute_0_121,plain,
( ~ is_a_theorem(implies(implies(implies(X_614,X_616),implies(X_615,X_616)),X_613))
| is_a_theorem(implies(X_614,X_613)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_614,X_616),implies(X_615,X_616)),X_613),implies(X_614,X_613))) )],[refute_0_120,refute_0_111]) ).
cnf(refute_0_122,plain,
( ~ is_a_theorem(implies(implies(implies(X_1121,X_1122),implies(X_615,X_1122)),implies(implies(implies(implies(X_615,X_1122),X_1124),X_1122),implies(X_615,X_1122))))
| is_a_theorem(implies(X_1121,implies(implies(implies(implies(X_615,X_1122),X_1124),X_1122),implies(X_615,X_1122)))) ),
inference(subst,[],[refute_0_121:[bind(X_613,$fot(implies(implies(implies(implies(X_615,X_1122),X_1124),X_1122),implies(X_615,X_1122)))),bind(X_614,$fot(X_1121)),bind(X_616,$fot(X_1122))]]) ).
cnf(refute_0_123,plain,
is_a_theorem(implies(implies(implies(X_1121,X_1122),implies(X_615,X_1122)),implies(implies(implies(implies(X_615,X_1122),X_1124),X_1122),implies(X_615,X_1122)))),
inference(subst,[],[refute_0_76:[bind(X_1116,$fot(X_1121)),bind(X_1117,$fot(X_1122)),bind(X_1118,$fot(implies(X_615,X_1122))),bind(X_1119,$fot(X_1124))]]) ).
cnf(refute_0_124,plain,
is_a_theorem(implies(X_1121,implies(implies(implies(implies(X_615,X_1122),X_1124),X_1122),implies(X_615,X_1122)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1121,X_1122),implies(X_615,X_1122)),implies(implies(implies(implies(X_615,X_1122),X_1124),X_1122),implies(X_615,X_1122)))) )],[refute_0_123,refute_0_122]) ).
cnf(refute_0_125,plain,
is_a_theorem(implies(X_1142,implies(implies(implies(implies(X_1145,X_1143),X_1144),X_1143),implies(X_1145,X_1143)))),
inference(subst,[],[refute_0_124:[bind(X_1121,$fot(X_1142)),bind(X_1122,$fot(X_1143)),bind(X_1124,$fot(X_1144)),bind(X_615,$fot(X_1145))]]) ).
cnf(refute_0_126,plain,
( ~ is_a_theorem(X_1142)
| is_a_theorem(implies(implies(implies(implies(X_1145,X_1143),X_1144),X_1143),implies(X_1145,X_1143))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1142,implies(implies(implies(implies(X_1145,X_1143),X_1144),X_1143),implies(X_1145,X_1143)))) )],[refute_0_125,refute_0_110]) ).
cnf(refute_0_127,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161)))
| is_a_theorem(implies(implies(implies(implies(X_1159,X_1157),X_1158),X_1157),implies(X_1159,X_1157))) ),
inference(subst,[],[refute_0_126:[bind(X_1142,$fot(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161)))),bind(X_1143,$fot(X_1157)),bind(X_1144,$fot(X_1158)),bind(X_1145,$fot(X_1159))]]) ).
cnf(refute_0_128,plain,
is_a_theorem(implies(implies(implies(implies(X_1159,X_1157),X_1158),X_1157),implies(X_1159,X_1157))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_170,X_171),X_170),implies(X_171,X_170)),X_173),implies(X_172,X_173)),X_161),implies(X_160,X_161))) )],[refute_0_47,refute_0_127]) ).
cnf(refute_0_129,plain,
is_a_theorem(implies(implies(implies(implies(X_1162,X_1160),X_1161),X_1160),implies(X_1162,X_1160))),
inference(subst,[],[refute_0_128:[bind(X_1157,$fot(X_1160)),bind(X_1158,$fot(X_1161)),bind(X_1159,$fot(X_1162))]]) ).
cnf(refute_0_130,plain,
is_a_theorem(implies(X_6,implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_1162,X_1160),X_1161),X_1160),implies(X_1162,X_1160))) )],[refute_0_129,refute_0_109]) ).
cnf(refute_0_131,plain,
is_a_theorem(implies(implies(implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))),X_1211),implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))))),
inference(subst,[],[refute_0_130:[bind(X_6,$fot(implies(implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))),X_1211)))]]) ).
cnf(refute_0_132,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))),X_1211),implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161)))))
| is_a_theorem(implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161)))) ),
inference(subst,[],[refute_0_84:[bind(X_1208,$fot(implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))))),bind(X_1209,$fot(X_1211))]]) ).
cnf(refute_0_133,plain,
is_a_theorem(implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))),X_1211),implies(implies(X_1160,implies(implies(X_1162,X_1160),X_1161)),implies(X_1162,implies(implies(X_1162,X_1160),X_1161))))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
is_a_theorem(implies(implies(X_1677,implies(implies(X_1162,X_1677),X_1161)),implies(X_1162,implies(implies(X_1162,X_1677),X_1161)))),
inference(subst,[],[refute_0_133:[bind(X_1160,$fot(X_1677))]]) ).
cnf(refute_0_135,plain,
( ~ is_a_theorem(implies(implies(X_1431,X_1433),X_1434))
| ~ is_a_theorem(implies(implies(implies(X_1431,X_1433),X_1434),implies(implies(implies(X_1432,X_1431),X_1433),X_1434)))
| is_a_theorem(implies(implies(implies(X_1432,X_1431),X_1433),X_1434)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_1431,X_1433),X_1434))),bind(Y,$fot(implies(implies(implies(X_1432,X_1431),X_1433),X_1434)))]]) ).
cnf(refute_0_136,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_152,X_151),X_153),implies(X_151,X_153))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)))) ),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(implies(implies(X_152,X_151),X_153))),bind(X_5,$fot(implies(X_151,X_153)))]]) ).
cnf(refute_0_137,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_117,implies(X_118,X_117))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_118,X_117),X_2),implies(X_117,X_2)))) ),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(X_117)),bind(X_5,$fot(implies(X_118,X_117)))]]) ).
cnf(refute_0_138,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(X_117,implies(X_118,X_117)))),
inference(subst,[],[refute_0_55:[bind(X_116,$fot(X_117)),bind(X_33,$fot(X_118)),bind(X_35,$fot(implies(X_2,X_3)))]]) ).
cnf(refute_0_139,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_118,X_117),X_2),implies(X_117,X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(X_117,implies(X_118,X_117)))) )],[refute_0_138,refute_0_137]) ).
cnf(refute_0_140,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_152,X_151),X_153),implies(X_151,X_153)))),
inference(subst,[],[refute_0_139:[bind(X_117,$fot(X_151)),bind(X_118,$fot(X_152)),bind(X_2,$fot(X_153)),bind(X_6,$fot(implies(X_2,X_3)))]]) ).
cnf(refute_0_141,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_152,X_151),X_153),implies(X_151,X_153)))) )],[refute_0_140,refute_0_136]) ).
cnf(refute_0_142,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)),X_1211),implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)))),
inference(subst,[],[refute_0_141:[bind(X_6,$fot(implies(implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)),X_1211)))]]) ).
cnf(refute_0_143,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)),X_1211),implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2))))
| is_a_theorem(implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2))) ),
inference(subst,[],[refute_0_84:[bind(X_1208,$fot(implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)))),bind(X_1209,$fot(X_1211))]]) ).
cnf(refute_0_144,plain,
is_a_theorem(implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)),X_1211),implies(implies(implies(X_151,X_153),X_2),implies(implies(implies(X_152,X_151),X_153),X_2)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
is_a_theorem(implies(implies(implies(X_1431,X_1433),X_1434),implies(implies(implies(X_1432,X_1431),X_1433),X_1434))),
inference(subst,[],[refute_0_144:[bind(X_151,$fot(X_1431)),bind(X_152,$fot(X_1432)),bind(X_153,$fot(X_1433)),bind(X_2,$fot(X_1434))]]) ).
cnf(refute_0_146,plain,
( ~ is_a_theorem(implies(implies(X_1431,X_1433),X_1434))
| is_a_theorem(implies(implies(implies(X_1432,X_1431),X_1433),X_1434)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_1431,X_1433),X_1434),implies(implies(implies(X_1432,X_1431),X_1433),X_1434))) )],[refute_0_145,refute_0_135]) ).
cnf(refute_0_147,plain,
( ~ is_a_theorem(implies(implies(X_1677,implies(implies(X_1162,X_1677),X_1161)),implies(X_1162,implies(implies(X_1162,X_1677),X_1161))))
| is_a_theorem(implies(implies(implies(X_1678,X_1677),implies(implies(X_1162,X_1677),X_1161)),implies(X_1162,implies(implies(X_1162,X_1677),X_1161)))) ),
inference(subst,[],[refute_0_146:[bind(X_1431,$fot(X_1677)),bind(X_1432,$fot(X_1678)),bind(X_1433,$fot(implies(implies(X_1162,X_1677),X_1161))),bind(X_1434,$fot(implies(X_1162,implies(implies(X_1162,X_1677),X_1161))))]]) ).
cnf(refute_0_148,plain,
is_a_theorem(implies(implies(implies(X_1678,X_1677),implies(implies(X_1162,X_1677),X_1161)),implies(X_1162,implies(implies(X_1162,X_1677),X_1161)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1677,implies(implies(X_1162,X_1677),X_1161)),implies(X_1162,implies(implies(X_1162,X_1677),X_1161)))) )],[refute_0_134,refute_0_147]) ).
cnf(refute_0_149,plain,
is_a_theorem(implies(implies(implies(implies(X_1685,X_1684),X_1684),implies(implies(X_1685,X_1684),X_1684)),implies(X_1685,implies(implies(X_1685,X_1684),X_1684)))),
inference(subst,[],[refute_0_148:[bind(X_1161,$fot(X_1684)),bind(X_1162,$fot(X_1685)),bind(X_1677,$fot(X_1684)),bind(X_1678,$fot(implies(X_1685,X_1684)))]]) ).
cnf(refute_0_150,plain,
is_a_theorem(implies(X_1685,implies(implies(X_1685,X_1684),X_1684))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_1685,X_1684),X_1684),implies(implies(X_1685,X_1684),X_1684)),implies(X_1685,implies(implies(X_1685,X_1684),X_1684)))) )],[refute_0_149,refute_0_108]) ).
cnf(refute_0_151,plain,
is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(subst,[],[refute_0_150:[bind(X_1684,$fot(b)),bind(X_1685,$fot(a))]]) ).
cnf(refute_0_152,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(implies(a,b),b))) )],[refute_0_151,prove_ic_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL094-1 : TPTP v8.1.0. Released v1.0.0.
% 0.14/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 3 14:52:16 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.73/0.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.73/0.93
% 0.73/0.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.80/0.95
%------------------------------------------------------------------------------