TSTP Solution File: LCL086-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL086-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 12:49:21 EDT 2022
% Result : Unsatisfiable 0.78s 0.95s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 3
% Syntax : Number of clauses : 125 ( 63 unt; 0 nHn; 25 RR)
% Number of literals : 205 ( 0 equ; 81 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 546 ( 183 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_1,negated_conjecture,
~ is_a_theorem(implies(a,a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(X_61)
| ~ is_a_theorem(implies(X_61,implies(implies(X_61,X_63),implies(X_62,X_63))))
| is_a_theorem(implies(implies(X_61,X_63),implies(X_62,X_63))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_61)),bind(Y,$fot(implies(implies(X_61,X_63),implies(X_62,X_63))))]]) ).
cnf(refute_0_1,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_2,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,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_4,X_5)))
| ~ is_a_theorem(implies(implies(implies(X_2,X_3),implies(X_4,X_5)),implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2)))))
| is_a_theorem(implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_2,X_3),implies(X_4,X_5)))),bind(Y,$fot(implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2)))))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(implies(implies(X_2,X_3),implies(X_4,X_5)),implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2))))),
inference(subst,[],[ic_JLukasiewicz_4:[bind(P,$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_5,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,[$cnf( is_a_theorem(implies(implies(implies(X_2,X_3),implies(X_4,X_5)),implies(X_6,implies(implies(X_5,X_2),implies(X_4,X_2))))) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(X_9,implies(implies(S,P),implies(R,P)))))
| is_a_theorem(implies(X_11,implies(implies(implies(implies(S,P),implies(R,P)),implies(P,Q)),implies(X_9,implies(P,Q))))) ),
inference(subst,[],[refute_0_5:[bind(X_2,$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_7,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,[$cnf( is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(X_9,implies(implies(S,P),implies(R,P))))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(X_16,implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13))))),
inference(subst,[],[refute_0_7:[bind(P,$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,$fot(X_17))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(X_16)
| is_a_theorem(implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13)))) ),
inference(resolve,[$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_8,refute_0_1]) ).
cnf(refute_0_10,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_9:[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_11,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,[$cnf( is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))) )],[ic_JLukasiewicz_4,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(X_51)
| ~ is_a_theorem(implies(X_51,implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50)))))
| is_a_theorem(implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_51)),bind(Y,$fot(implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50)))))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(X_39,X_36),implies(X_38,X_36)),implies(X_36,implies(implies(X_36,X_39),implies(X_38,X_39))))),
inference(subst,[],[ic_JLukasiewicz_4:[bind(P,$fot(X_39)),bind(Q,$fot(X_36)),bind(R,$fot(X_38)),bind(S,$fot(X_36)),bind(T,$fot(X_36))]]) ).
cnf(refute_0_14,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_15,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_11:[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,$fot(X_35))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_34,X_31),implies(X_33,X_31)),implies(X_31,X_32)))
| is_a_theorem(implies(X_35,implies(X_31,X_32))) ),
inference(resolve,[$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_15,refute_0_14]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(implies(X_39,X_36),implies(X_38,X_36)),implies(X_36,implies(implies(X_36,X_39),implies(X_38,X_39)))))
| is_a_theorem(implies(X_40,implies(X_36,implies(implies(X_36,X_39),implies(X_38,X_39))))) ),
inference(subst,[],[refute_0_16:[bind(X_31,$fot(X_36)),bind(X_32,$fot(implies(implies(X_36,X_39),implies(X_38,X_39)))),bind(X_33,$fot(X_38)),bind(X_34,$fot(X_39)),bind(X_35,$fot(X_40))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(X_40,implies(X_36,implies(implies(X_36,X_39),implies(X_38,X_39))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_39,X_36),implies(X_38,X_36)),implies(X_36,implies(implies(X_36,X_39),implies(X_38,X_39))))) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(X_51,implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50))))),
inference(subst,[],[refute_0_18:[bind(X_36,$fot(X_48)),bind(X_38,$fot(X_49)),bind(X_39,$fot(X_50)),bind(X_40,$fot(X_51))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(X_51)
| is_a_theorem(implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_51,implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50))))) )],[refute_0_19,refute_0_12]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26))))
| is_a_theorem(implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59)))) ),
inference(subst,[],[refute_0_20:[bind(X_48,$fot(X_57)),bind(X_49,$fot(X_58)),bind(X_50,$fot(X_59)),bind(X_51,$fot(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(X_57,implies(implies(X_57,X_59),implies(X_58,X_59)))),
inference(resolve,[$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_11,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(X_61,implies(implies(X_61,X_63),implies(X_62,X_63)))),
inference(subst,[],[refute_0_22:[bind(X_57,$fot(X_61)),bind(X_58,$fot(X_62)),bind(X_59,$fot(X_63))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(X_61)
| is_a_theorem(implies(implies(X_61,X_63),implies(X_62,X_63))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_61,implies(implies(X_61,X_63),implies(X_62,X_63)))) )],[refute_0_23,refute_0_0]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)))
| is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63))) ),
inference(subst,[],[refute_0_24:[bind(X_61,$fot(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593)))
| is_a_theorem(implies(implies(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593)),X_63),implies(X_62,X_63))) ),
inference(subst,[],[refute_0_24:[bind(X_61,$fot(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593))))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)))
| is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))) ),
inference(subst,[],[refute_0_24:[bind(X_61,$fot(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87))))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71))))
| is_a_theorem(implies(implies(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71))),X_63),implies(X_62,X_63))) ),
inference(subst,[],[refute_0_24:[bind(X_61,$fot(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71)))))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(X_43)
| ~ is_a_theorem(implies(X_43,implies(implies(X_41,X_42),implies(X_42,implies(X_41,X_42)))))
| is_a_theorem(implies(implies(X_41,X_42),implies(X_42,implies(X_41,X_42)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_43)),bind(Y,$fot(implies(implies(X_41,X_42),implies(X_42,implies(X_41,X_42)))))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(implies(implies(X_28,X_38),implies(X_27,X_38)),implies(X_38,implies(X_27,X_38))),implies(implies(X_27,X_38),implies(X_38,implies(X_27,X_38))))),
inference(subst,[],[refute_0_11:[bind(X_25,$fot(X_38)),bind(X_26,$fot(implies(X_27,X_38))),bind(X_30,$fot(implies(X_27,X_38)))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_38),implies(X_27,X_38)),implies(X_38,implies(X_27,X_38))),implies(implies(X_27,X_38),implies(X_38,implies(X_27,X_38)))))
| is_a_theorem(implies(X_40,implies(implies(X_27,X_38),implies(X_38,implies(X_27,X_38))))) ),
inference(subst,[],[refute_0_16:[bind(X_31,$fot(implies(X_27,X_38))),bind(X_32,$fot(implies(X_38,implies(X_27,X_38)))),bind(X_33,$fot(X_38)),bind(X_34,$fot(implies(X_28,X_38))),bind(X_35,$fot(X_40))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(X_40,implies(implies(X_27,X_38),implies(X_38,implies(X_27,X_38))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28,X_38),implies(X_27,X_38)),implies(X_38,implies(X_27,X_38))),implies(implies(X_27,X_38),implies(X_38,implies(X_27,X_38))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(X_43,implies(implies(X_41,X_42),implies(X_42,implies(X_41,X_42))))),
inference(subst,[],[refute_0_32:[bind(X_27,$fot(X_41)),bind(X_38,$fot(X_42)),bind(X_40,$fot(X_43))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(X_43)
| is_a_theorem(implies(implies(X_41,X_42),implies(X_42,implies(X_41,X_42)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_43,implies(implies(X_41,X_42),implies(X_42,implies(X_41,X_42))))) )],[refute_0_33,refute_0_29]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26))))
| is_a_theorem(implies(implies(X_67,X_68),implies(X_68,implies(X_67,X_68)))) ),
inference(subst,[],[refute_0_34:[bind(X_41,$fot(X_67)),bind(X_42,$fot(X_68)),bind(X_43,$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_36,plain,
is_a_theorem(implies(implies(X_67,X_68),implies(X_68,implies(X_67,X_68)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_28,X_25),implies(X_27,X_25)),implies(X_25,X_26)),implies(X_30,implies(X_25,X_26)))) )],[refute_0_11,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71)))),
inference(subst,[],[refute_0_36:[bind(X_67,$fot(X_70)),bind(X_68,$fot(X_71))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71))),X_63),implies(X_62,X_63))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71)))) )],[refute_0_37,refute_0_28]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87))),
inference(subst,[],[refute_0_38:[bind(X_62,$fot(X_86)),bind(X_63,$fot(X_87)),bind(X_70,$fot(X_88)),bind(X_71,$fot(X_89))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87))) )],[refute_0_39,refute_0_27]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(X_56)
| ~ is_a_theorem(implies(X_56,implies(implies(implies(implies(X_53,X_55),implies(X_54,X_55)),X_52),implies(X_53,X_52))))
| is_a_theorem(implies(implies(implies(implies(X_53,X_55),implies(X_54,X_55)),X_52),implies(X_53,X_52))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_56)),bind(Y,$fot(implies(implies(implies(implies(X_53,X_55),implies(X_54,X_55)),X_52),implies(X_53,X_52))))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50)))))
| is_a_theorem(implies(X_6,implies(implies(implies(implies(X_48,X_50),implies(X_49,X_50)),X_2),implies(X_48,X_2)))) ),
inference(subst,[],[refute_0_5:[bind(X_4,$fot(X_48)),bind(X_5,$fot(implies(implies(X_48,X_50),implies(X_49,X_50))))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50))))),
inference(subst,[],[refute_0_18:[bind(X_36,$fot(X_48)),bind(X_38,$fot(X_49)),bind(X_39,$fot(X_50)),bind(X_40,$fot(implies(X_2,X_3)))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(X_6,implies(implies(implies(implies(X_48,X_50),implies(X_49,X_50)),X_2),implies(X_48,X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(X_48,implies(implies(X_48,X_50),implies(X_49,X_50))))) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(X_56,implies(implies(implies(implies(X_53,X_55),implies(X_54,X_55)),X_52),implies(X_53,X_52)))),
inference(subst,[],[refute_0_44:[bind(X_2,$fot(X_52)),bind(X_48,$fot(X_53)),bind(X_49,$fot(X_54)),bind(X_50,$fot(X_55)),bind(X_6,$fot(X_56))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(X_56)
| is_a_theorem(implies(implies(implies(implies(X_53,X_55),implies(X_54,X_55)),X_52),implies(X_53,X_52))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_56,implies(implies(implies(implies(X_53,X_55),implies(X_54,X_55)),X_52),implies(X_53,X_52)))) )],[refute_0_45,refute_0_41]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63)))
| is_a_theorem(implies(implies(implies(implies(X_589,X_591),implies(X_590,X_591)),X_588),implies(X_589,X_588))) ),
inference(subst,[],[refute_0_46:[bind(X_52,$fot(X_588)),bind(X_53,$fot(X_589)),bind(X_54,$fot(X_590)),bind(X_55,$fot(X_591)),bind(X_56,$fot(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(implies(implies(X_589,X_591),implies(X_590,X_591)),X_588),implies(X_589,X_588))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))) )],[refute_0_40,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593))),
inference(subst,[],[refute_0_48:[bind(X_588,$fot(X_593)),bind(X_589,$fot(X_594)),bind(X_590,$fot(X_595)),bind(X_591,$fot(X_596))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593)),X_63),implies(X_62,X_63))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593))) )],[refute_0_49,refute_0_26]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602))),
inference(subst,[],[refute_0_50:[bind(X_593,$fot(X_597)),bind(X_594,$fot(X_598)),bind(X_595,$fot(X_599)),bind(X_596,$fot(X_600)),bind(X_62,$fot(X_601)),bind(X_63,$fot(X_602))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602))) )],[refute_0_51,refute_0_25]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(X_1800)
| ~ is_a_theorem(implies(X_1800,implies(X_1799,X_1799)))
| is_a_theorem(implies(X_1799,X_1799)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1800)),bind(Y,$fot(implies(X_1799,X_1799)))]]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(X_1786)
| ~ is_a_theorem(implies(X_1786,implies(X_1787,implies(X_1785,X_1785))))
| is_a_theorem(implies(X_1787,implies(X_1785,X_1785))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1786)),bind(Y,$fot(implies(X_1787,implies(X_1785,X_1785))))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(X_1182)
| ~ is_a_theorem(implies(X_1182,implies(X_1180,implies(X_1179,implies(X_1181,X_1180)))))
| is_a_theorem(implies(X_1180,implies(X_1179,implies(X_1181,X_1180)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_1182)),bind(Y,$fot(implies(X_1180,implies(X_1179,implies(X_1181,X_1180)))))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_1178,implies(X_1176,implies(X_33,X_1178))),X_1178),implies(X_33,X_1178)),implies(X_1178,implies(X_1176,implies(X_33,X_1178)))))
| is_a_theorem(implies(X_35,implies(X_1178,implies(X_1176,implies(X_33,X_1178))))) ),
inference(subst,[],[refute_0_16:[bind(X_31,$fot(X_1178)),bind(X_32,$fot(implies(X_1176,implies(X_33,X_1178)))),bind(X_34,$fot(implies(X_1178,implies(X_1176,implies(X_33,X_1178)))))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(X_178)
| ~ is_a_theorem(implies(X_178,implies(X_176,implies(X_177,X_176))))
| is_a_theorem(implies(X_176,implies(X_177,X_176))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_178)),bind(Y,$fot(implies(X_176,implies(X_177,X_176))))]]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_33,X_175),X_175),implies(X_33,X_175)),implies(X_175,implies(X_33,X_175))))
| is_a_theorem(implies(X_35,implies(X_175,implies(X_33,X_175)))) ),
inference(subst,[],[refute_0_16:[bind(X_31,$fot(X_175)),bind(X_32,$fot(implies(X_33,X_175))),bind(X_34,$fot(implies(X_33,X_175)))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(X_72)
| ~ is_a_theorem(implies(X_72,implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73))))
| is_a_theorem(implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_72)),bind(Y,$fot(implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73))))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_70,X_71),X_70),implies(X_71,X_70)))) ),
inference(subst,[],[refute_0_5:[bind(X_2,$fot(X_70)),bind(X_3,$fot(X_71)),bind(X_4,$fot(X_71)),bind(X_5,$fot(implies(X_70,X_71)))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_70,X_71),X_70),implies(X_71,X_70)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_70,X_71),implies(X_71,implies(X_70,X_71)))) )],[refute_0_37,refute_0_60]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(X_72,implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73)))),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(X_72)),bind(X_70,$fot(X_73)),bind(X_71,$fot(X_74))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(X_72)
| is_a_theorem(implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_72,implies(implies(implies(X_73,X_74),X_73),implies(X_74,X_73)))) )],[refute_0_62,refute_0_59]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63)))
| is_a_theorem(implies(implies(implies(X_172,X_173),X_172),implies(X_173,X_172))) ),
inference(subst,[],[refute_0_63:[bind(X_72,$fot(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63)))),bind(X_73,$fot(X_172)),bind(X_74,$fot(X_173))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(implies(X_172,X_173),X_172),implies(X_173,X_172))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))) )],[refute_0_40,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(implies(X_33,X_175),X_175),implies(X_33,X_175)),implies(X_175,implies(X_33,X_175)))),
inference(subst,[],[refute_0_65:[bind(X_172,$fot(implies(X_33,X_175))),bind(X_173,$fot(X_175))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(X_35,implies(X_175,implies(X_33,X_175)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_33,X_175),X_175),implies(X_33,X_175)),implies(X_175,implies(X_33,X_175)))) )],[refute_0_66,refute_0_58]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(X_178,implies(X_176,implies(X_177,X_176)))),
inference(subst,[],[refute_0_67:[bind(X_175,$fot(X_176)),bind(X_33,$fot(X_177)),bind(X_35,$fot(X_178))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(X_178)
| is_a_theorem(implies(X_176,implies(X_177,X_176))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_178,implies(X_176,implies(X_177,X_176)))) )],[refute_0_68,refute_0_57]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63)))
| is_a_theorem(implies(X_211,implies(X_212,X_211))) ),
inference(subst,[],[refute_0_69:[bind(X_176,$fot(X_211)),bind(X_177,$fot(X_212)),bind(X_178,$fot(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(X_211,implies(X_212,X_211))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))) )],[refute_0_40,refute_0_70]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(X_1167,X_1168),implies(X_212,implies(X_1167,X_1168)))),
inference(subst,[],[refute_0_71:[bind(X_211,$fot(implies(X_1167,X_1168)))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(implies(X_535,X_536),X_533))
| ~ is_a_theorem(implies(implies(implies(X_535,X_536),X_533),implies(implies(implies(X_533,X_534),X_536),X_533)))
| is_a_theorem(implies(implies(implies(X_533,X_534),X_536),X_533)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_535,X_536),X_533))),bind(Y,$fot(implies(implies(implies(X_533,X_534),X_536),X_533)))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(X_83)
| ~ is_a_theorem(implies(X_83,implies(implies(implies(X_84,X_85),X_81),implies(implies(implies(X_81,X_82),X_85),X_81))))
| is_a_theorem(implies(implies(implies(X_84,X_85),X_81),implies(implies(implies(X_81,X_82),X_85),X_81))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_83)),bind(Y,$fot(implies(implies(implies(X_84,X_85),X_81),implies(implies(implies(X_81,X_82),X_85),X_81))))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_2,X_3),X_63),implies(X_62,X_63))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_62,X_63),X_2),implies(implies(implies(X_2,X_3),X_63),X_2)))) ),
inference(subst,[],[refute_0_5:[bind(X_4,$fot(implies(implies(X_2,X_3),X_63))),bind(X_5,$fot(implies(X_62,X_63)))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_2,X_3),X_63),implies(X_62,X_63)))),
inference(subst,[],[refute_0_22:[bind(X_57,$fot(implies(X_2,X_3))),bind(X_58,$fot(X_62)),bind(X_59,$fot(X_63))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_62,X_63),X_2),implies(implies(implies(X_2,X_3),X_63),X_2)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_2,X_3),implies(implies(implies(X_2,X_3),X_63),implies(X_62,X_63)))) )],[refute_0_76,refute_0_75]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(X_83,implies(implies(implies(X_84,X_85),X_81),implies(implies(implies(X_81,X_82),X_85),X_81)))),
inference(subst,[],[refute_0_77:[bind(X_2,$fot(X_81)),bind(X_3,$fot(X_82)),bind(X_6,$fot(X_83)),bind(X_62,$fot(X_84)),bind(X_63,$fot(X_85))]]) ).
cnf(refute_0_79,plain,
( ~ is_a_theorem(X_83)
| is_a_theorem(implies(implies(implies(X_84,X_85),X_81),implies(implies(implies(X_81,X_82),X_85),X_81))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_83,implies(implies(implies(X_84,X_85),X_81),implies(implies(implies(X_81,X_82),X_85),X_81)))) )],[refute_0_78,refute_0_74]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63)))
| is_a_theorem(implies(implies(implies(X_531,X_532),X_528),implies(implies(implies(X_528,X_529),X_532),X_528))) ),
inference(subst,[],[refute_0_79:[bind(X_81,$fot(X_528)),bind(X_82,$fot(X_529)),bind(X_83,$fot(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63)))),bind(X_84,$fot(X_531)),bind(X_85,$fot(X_532))]]) ).
cnf(refute_0_81,plain,
is_a_theorem(implies(implies(implies(X_531,X_532),X_528),implies(implies(implies(X_528,X_529),X_532),X_528))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_88,X_89),implies(X_89,implies(X_88,X_89))),X_87),implies(X_86,X_87)),X_63),implies(X_62,X_63))) )],[refute_0_40,refute_0_80]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(implies(implies(X_535,X_536),X_533),implies(implies(implies(X_533,X_534),X_536),X_533))),
inference(subst,[],[refute_0_81:[bind(X_528,$fot(X_533)),bind(X_529,$fot(X_534)),bind(X_531,$fot(X_535)),bind(X_532,$fot(X_536))]]) ).
cnf(refute_0_83,plain,
( ~ is_a_theorem(implies(implies(X_535,X_536),X_533))
| is_a_theorem(implies(implies(implies(X_533,X_534),X_536),X_533)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_535,X_536),X_533),implies(implies(implies(X_533,X_534),X_536),X_533))) )],[refute_0_82,refute_0_73]) ).
cnf(refute_0_84,plain,
( ~ is_a_theorem(implies(implies(X_1167,X_1168),implies(X_212,implies(X_1167,X_1168))))
| is_a_theorem(implies(implies(implies(implies(X_212,implies(X_1167,X_1168)),X_1166),X_1168),implies(X_212,implies(X_1167,X_1168)))) ),
inference(subst,[],[refute_0_83:[bind(X_533,$fot(implies(X_212,implies(X_1167,X_1168)))),bind(X_534,$fot(X_1166)),bind(X_535,$fot(X_1167)),bind(X_536,$fot(X_1168))]]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(implies(implies(implies(X_212,implies(X_1167,X_1168)),X_1166),X_1168),implies(X_212,implies(X_1167,X_1168)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1167,X_1168),implies(X_212,implies(X_1167,X_1168)))) )],[refute_0_72,refute_0_84]) ).
cnf(refute_0_86,plain,
is_a_theorem(implies(implies(implies(implies(X_1178,implies(X_1176,implies(X_33,X_1178))),X_1178),implies(X_33,X_1178)),implies(X_1178,implies(X_1176,implies(X_33,X_1178))))),
inference(subst,[],[refute_0_85:[bind(X_1166,$fot(X_1178)),bind(X_1167,$fot(X_1176)),bind(X_1168,$fot(implies(X_33,X_1178))),bind(X_212,$fot(X_1178))]]) ).
cnf(refute_0_87,plain,
is_a_theorem(implies(X_35,implies(X_1178,implies(X_1176,implies(X_33,X_1178))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_1178,implies(X_1176,implies(X_33,X_1178))),X_1178),implies(X_33,X_1178)),implies(X_1178,implies(X_1176,implies(X_33,X_1178))))) )],[refute_0_86,refute_0_56]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(X_1182,implies(X_1180,implies(X_1179,implies(X_1181,X_1180))))),
inference(subst,[],[refute_0_87:[bind(X_1176,$fot(X_1179)),bind(X_1178,$fot(X_1180)),bind(X_33,$fot(X_1181)),bind(X_35,$fot(X_1182))]]) ).
cnf(refute_0_89,plain,
( ~ is_a_theorem(X_1182)
| is_a_theorem(implies(X_1180,implies(X_1179,implies(X_1181,X_1180)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1182,implies(X_1180,implies(X_1179,implies(X_1181,X_1180))))) )],[refute_0_88,refute_0_55]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63)))
| is_a_theorem(implies(X_1190,implies(X_1189,implies(X_1191,X_1190)))) ),
inference(subst,[],[refute_0_89:[bind(X_1179,$fot(X_1189)),bind(X_1180,$fot(X_1190)),bind(X_1181,$fot(X_1191)),bind(X_1182,$fot(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63))))]]) ).
cnf(refute_0_91,plain,
is_a_theorem(implies(X_1190,implies(X_1189,implies(X_1191,X_1190)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63))) )],[refute_0_52,refute_0_90]) ).
cnf(refute_0_92,plain,
is_a_theorem(implies(X_1781,implies(X_1784,implies(X_1781,X_1781)))),
inference(subst,[],[refute_0_91:[bind(X_1189,$fot(X_1784)),bind(X_1190,$fot(X_1781)),bind(X_1191,$fot(X_1781))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(X_1313,implies(X_1315,implies(X_1313,X_1312))))
| ~ is_a_theorem(implies(implies(X_1313,implies(X_1315,implies(X_1313,X_1312))),implies(X_1314,implies(X_1315,implies(X_1313,X_1312)))))
| is_a_theorem(implies(X_1314,implies(X_1315,implies(X_1313,X_1312)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_1313,implies(X_1315,implies(X_1313,X_1312))))),bind(Y,$fot(implies(X_1314,implies(X_1315,implies(X_1313,X_1312)))))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593)),implies(X_605,implies(X_594,X_593))),implies(X_62,implies(X_605,implies(X_594,X_593))))),
inference(subst,[],[refute_0_50:[bind(X_63,$fot(implies(X_605,implies(X_594,X_593))))]]) ).
cnf(refute_0_95,plain,
( ~ is_a_theorem(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593))
| ~ is_a_theorem(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593)))
| is_a_theorem(implies(X_594,X_593)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593))),bind(Y,$fot(implies(X_594,X_593)))]]) ).
cnf(refute_0_96,plain,
( ~ is_a_theorem(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593))
| is_a_theorem(implies(X_594,X_593)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593))) )],[refute_0_49,refute_0_95]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593)),implies(X_605,implies(X_594,X_593))),implies(X_62,implies(X_605,implies(X_594,X_593)))))
| is_a_theorem(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_62,implies(X_605,implies(X_594,X_593))))) ),
inference(subst,[],[refute_0_96:[bind(X_593,$fot(implies(X_62,implies(X_605,implies(X_594,X_593))))),bind(X_594,$fot(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593))),bind(X_595,$fot(X_605)),bind(X_596,$fot(implies(X_594,X_593)))]]) ).
cnf(refute_0_98,plain,
is_a_theorem(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_62,implies(X_605,implies(X_594,X_593))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_594,X_596),implies(X_595,X_596)),X_593),implies(X_594,X_593)),implies(X_605,implies(X_594,X_593))),implies(X_62,implies(X_605,implies(X_594,X_593))))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(implies(implies(X_594,implies(X_605,implies(X_594,X_1259))),implies(X_595,implies(X_605,implies(X_594,X_1259)))),X_1259),implies(X_595,implies(X_605,implies(X_594,X_1259))))),
inference(subst,[],[refute_0_98:[bind(X_593,$fot(X_1259)),bind(X_596,$fot(implies(X_605,implies(X_594,X_1259)))),bind(X_62,$fot(X_595))]]) ).
cnf(refute_0_100,plain,
( ~ is_a_theorem(implies(implies(implies(X_1171,X_1170),X_1169),X_1170))
| ~ is_a_theorem(implies(implies(implies(implies(X_1171,X_1170),X_1169),X_1170),implies(X_1171,X_1170)))
| is_a_theorem(implies(X_1171,X_1170)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_1171,X_1170),X_1169),X_1170))),bind(Y,$fot(implies(X_1171,X_1170)))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_1168),implies(X_62,X_1168))),
inference(subst,[],[refute_0_52:[bind(X_63,$fot(X_1168))]]) ).
cnf(refute_0_102,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_1168),implies(X_62,X_1168)))
| is_a_theorem(implies(implies(implies(implies(X_62,X_1168),X_1166),X_1168),implies(X_62,X_1168))) ),
inference(subst,[],[refute_0_83:[bind(X_533,$fot(implies(X_62,X_1168))),bind(X_534,$fot(X_1166)),bind(X_535,$fot(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)))),bind(X_536,$fot(X_1168))]]) ).
cnf(refute_0_103,plain,
is_a_theorem(implies(implies(implies(implies(X_62,X_1168),X_1166),X_1168),implies(X_62,X_1168))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_1168),implies(X_62,X_1168))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
is_a_theorem(implies(implies(implies(implies(X_1171,X_1170),X_1169),X_1170),implies(X_1171,X_1170))),
inference(subst,[],[refute_0_103:[bind(X_1166,$fot(X_1169)),bind(X_1168,$fot(X_1170)),bind(X_62,$fot(X_1171))]]) ).
cnf(refute_0_105,plain,
( ~ is_a_theorem(implies(implies(implies(X_1171,X_1170),X_1169),X_1170))
| is_a_theorem(implies(X_1171,X_1170)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_1171,X_1170),X_1169),X_1170),implies(X_1171,X_1170))) )],[refute_0_104,refute_0_100]) ).
cnf(refute_0_106,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_594,implies(X_605,implies(X_594,X_1259))),implies(X_595,implies(X_605,implies(X_594,X_1259)))),X_1259),implies(X_595,implies(X_605,implies(X_594,X_1259)))))
| is_a_theorem(implies(implies(X_594,implies(X_605,implies(X_594,X_1259))),implies(X_595,implies(X_605,implies(X_594,X_1259))))) ),
inference(subst,[],[refute_0_105:[bind(X_1169,$fot(X_1259)),bind(X_1170,$fot(implies(X_595,implies(X_605,implies(X_594,X_1259))))),bind(X_1171,$fot(implies(X_594,implies(X_605,implies(X_594,X_1259)))))]]) ).
cnf(refute_0_107,plain,
is_a_theorem(implies(implies(X_594,implies(X_605,implies(X_594,X_1259))),implies(X_595,implies(X_605,implies(X_594,X_1259))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_594,implies(X_605,implies(X_594,X_1259))),implies(X_595,implies(X_605,implies(X_594,X_1259)))),X_1259),implies(X_595,implies(X_605,implies(X_594,X_1259))))) )],[refute_0_99,refute_0_106]) ).
cnf(refute_0_108,plain,
is_a_theorem(implies(implies(X_1313,implies(X_1315,implies(X_1313,X_1312))),implies(X_1314,implies(X_1315,implies(X_1313,X_1312))))),
inference(subst,[],[refute_0_107:[bind(X_1259,$fot(X_1312)),bind(X_594,$fot(X_1313)),bind(X_595,$fot(X_1314)),bind(X_605,$fot(X_1315))]]) ).
cnf(refute_0_109,plain,
( ~ is_a_theorem(implies(X_1313,implies(X_1315,implies(X_1313,X_1312))))
| is_a_theorem(implies(X_1314,implies(X_1315,implies(X_1313,X_1312)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1313,implies(X_1315,implies(X_1313,X_1312))),implies(X_1314,implies(X_1315,implies(X_1313,X_1312))))) )],[refute_0_108,refute_0_93]) ).
cnf(refute_0_110,plain,
( ~ is_a_theorem(implies(X_1781,implies(X_1784,implies(X_1781,X_1781))))
| is_a_theorem(implies(X_1783,implies(X_1784,implies(X_1781,X_1781)))) ),
inference(subst,[],[refute_0_109:[bind(X_1312,$fot(X_1781)),bind(X_1313,$fot(X_1781)),bind(X_1314,$fot(X_1783)),bind(X_1315,$fot(X_1784))]]) ).
cnf(refute_0_111,plain,
is_a_theorem(implies(X_1783,implies(X_1784,implies(X_1781,X_1781)))),
inference(resolve,[$cnf( is_a_theorem(implies(X_1781,implies(X_1784,implies(X_1781,X_1781)))) )],[refute_0_92,refute_0_110]) ).
cnf(refute_0_112,plain,
is_a_theorem(implies(X_1786,implies(X_1787,implies(X_1785,X_1785)))),
inference(subst,[],[refute_0_111:[bind(X_1781,$fot(X_1785)),bind(X_1783,$fot(X_1786)),bind(X_1784,$fot(X_1787))]]) ).
cnf(refute_0_113,plain,
( ~ is_a_theorem(X_1786)
| is_a_theorem(implies(X_1787,implies(X_1785,X_1785))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1786,implies(X_1787,implies(X_1785,X_1785)))) )],[refute_0_112,refute_0_54]) ).
cnf(refute_0_114,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63)))
| is_a_theorem(implies(X_1798,implies(X_1796,X_1796))) ),
inference(subst,[],[refute_0_113:[bind(X_1785,$fot(X_1796)),bind(X_1786,$fot(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63)))),bind(X_1787,$fot(X_1798))]]) ).
cnf(refute_0_115,plain,
is_a_theorem(implies(X_1798,implies(X_1796,X_1796))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63))) )],[refute_0_52,refute_0_114]) ).
cnf(refute_0_116,plain,
is_a_theorem(implies(X_1800,implies(X_1799,X_1799))),
inference(subst,[],[refute_0_115:[bind(X_1796,$fot(X_1799)),bind(X_1798,$fot(X_1800))]]) ).
cnf(refute_0_117,plain,
( ~ is_a_theorem(X_1800)
| is_a_theorem(implies(X_1799,X_1799)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_1800,implies(X_1799,X_1799))) )],[refute_0_116,refute_0_53]) ).
cnf(refute_0_118,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63)))
| is_a_theorem(implies(X_1801,X_1801)) ),
inference(subst,[],[refute_0_117:[bind(X_1799,$fot(X_1801)),bind(X_1800,$fot(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63))))]]) ).
cnf(refute_0_119,plain,
is_a_theorem(implies(X_1801,X_1801)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_598,X_600),implies(X_599,X_600)),X_597),implies(X_598,X_597)),X_602),implies(X_601,X_602)),X_63),implies(X_62,X_63))) )],[refute_0_52,refute_0_118]) ).
cnf(refute_0_120,plain,
is_a_theorem(implies(a,a)),
inference(subst,[],[refute_0_119:[bind(X_1801,$fot(a))]]) ).
cnf(refute_0_121,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,a)) )],[refute_0_120,prove_ic_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL086-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 20:28:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.78/0.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.95
% 0.78/0.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.78/0.96
%------------------------------------------------------------------------------