TSTP Solution File: LCL087-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL087-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 0.18s 0.40s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of clauses : 68 ( 34 unt; 0 nHn; 18 RR)
% Number of literals : 113 ( 0 equ; 46 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 235 ( 77 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_2,negated_conjecture,
~ is_a_theorem(implies(a,implies(b,a))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(X_116)
| ~ is_a_theorem(implies(X_116,implies(X_116,X_116)))
| is_a_theorem(implies(X_116,X_116)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_116)),bind(Y,$fot(implies(X_116,X_116)))]]) ).
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_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))) ),
inference(subst,[],[refute_0_9:[bind(X_12,$fot(X_33)),bind(X_13,$fot(X_34)),bind(X_14,$fot(X_35)),bind(X_15,$fot(X_36)),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_38))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))) )],[ic_JLukasiewicz_4,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(X_83)
| ~ is_a_theorem(implies(X_83,implies(implies(implies(X_84,X_85),X_84),implies(X_85,X_84))))
| is_a_theorem(implies(implies(implies(X_84,X_85),X_84),implies(X_85,X_84))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_83)),bind(Y,$fot(implies(implies(implies(X_84,X_85),X_84),implies(X_85,X_84))))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(X_81,X_82),implies(X_82,implies(X_81,X_82))))
| is_a_theorem(implies(X_6,implies(implies(implies(X_81,X_82),X_81),implies(X_82,X_81)))) ),
inference(subst,[],[refute_0_5:[bind(X_2,$fot(X_81)),bind(X_3,$fot(X_82)),bind(X_4,$fot(X_82)),bind(X_5,$fot(implies(X_81,X_82)))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(X_64)
| ~ is_a_theorem(implies(X_64,implies(implies(X_62,X_63),implies(X_63,implies(X_62,X_63)))))
| is_a_theorem(implies(implies(X_62,X_63),implies(X_63,implies(X_62,X_63)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_64)),bind(Y,$fot(implies(implies(X_62,X_63),implies(X_63,implies(X_62,X_63)))))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(implies(X_36,X_59),implies(X_35,X_59)),implies(X_59,implies(X_35,X_59))),implies(implies(X_35,X_59),implies(X_59,implies(X_35,X_59))))),
inference(subst,[],[refute_0_11:[bind(X_33,$fot(X_59)),bind(X_34,$fot(implies(X_35,X_59))),bind(X_38,$fot(implies(X_35,X_59)))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)))
| ~ is_a_theorem(implies(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)),implies(X_43,implies(X_39,X_40))))
| is_a_theorem(implies(X_43,implies(X_39,X_40))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)))),bind(Y,$fot(implies(X_43,implies(X_39,X_40))))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)),implies(X_43,implies(X_39,X_40)))),
inference(subst,[],[refute_0_11:[bind(X_33,$fot(X_39)),bind(X_34,$fot(X_40)),bind(X_35,$fot(X_41)),bind(X_36,$fot(X_42)),bind(X_38,$fot(X_43))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)))
| is_a_theorem(implies(X_43,implies(X_39,X_40))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)),implies(X_43,implies(X_39,X_40)))) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_36,X_59),implies(X_35,X_59)),implies(X_59,implies(X_35,X_59))),implies(implies(X_35,X_59),implies(X_59,implies(X_35,X_59)))))
| is_a_theorem(implies(X_61,implies(implies(X_35,X_59),implies(X_59,implies(X_35,X_59))))) ),
inference(subst,[],[refute_0_18:[bind(X_39,$fot(implies(X_35,X_59))),bind(X_40,$fot(implies(X_59,implies(X_35,X_59)))),bind(X_41,$fot(X_59)),bind(X_42,$fot(implies(X_36,X_59))),bind(X_43,$fot(X_61))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(X_61,implies(implies(X_35,X_59),implies(X_59,implies(X_35,X_59))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_36,X_59),implies(X_35,X_59)),implies(X_59,implies(X_35,X_59))),implies(implies(X_35,X_59),implies(X_59,implies(X_35,X_59))))) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_64,implies(implies(X_62,X_63),implies(X_63,implies(X_62,X_63))))),
inference(subst,[],[refute_0_20:[bind(X_35,$fot(X_62)),bind(X_59,$fot(X_63)),bind(X_61,$fot(X_64))]]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(X_64)
| is_a_theorem(implies(implies(X_62,X_63),implies(X_63,implies(X_62,X_63)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_64,implies(implies(X_62,X_63),implies(X_63,implies(X_62,X_63))))) )],[refute_0_21,refute_0_14]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34))))
| is_a_theorem(implies(implies(X_78,X_79),implies(X_79,implies(X_78,X_79)))) ),
inference(subst,[],[refute_0_22:[bind(X_62,$fot(X_78)),bind(X_63,$fot(X_79)),bind(X_64,$fot(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(X_78,X_79),implies(X_79,implies(X_78,X_79)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))) )],[refute_0_11,refute_0_23]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_81,X_82),implies(X_82,implies(X_81,X_82)))),
inference(subst,[],[refute_0_24:[bind(X_78,$fot(X_81)),bind(X_79,$fot(X_82))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(X_6,implies(implies(implies(X_81,X_82),X_81),implies(X_82,X_81)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_81,X_82),implies(X_82,implies(X_81,X_82)))) )],[refute_0_25,refute_0_13]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(X_83,implies(implies(implies(X_84,X_85),X_84),implies(X_85,X_84)))),
inference(subst,[],[refute_0_26:[bind(X_6,$fot(X_83)),bind(X_81,$fot(X_84)),bind(X_82,$fot(X_85))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(X_83)
| is_a_theorem(implies(implies(implies(X_84,X_85),X_84),implies(X_85,X_84))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_83,implies(implies(implies(X_84,X_85),X_84),implies(X_85,X_84)))) )],[refute_0_27,refute_0_12]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34))))
| is_a_theorem(implies(implies(implies(X_104,X_105),X_104),implies(X_105,X_104))) ),
inference(subst,[],[refute_0_28:[bind(X_83,$fot(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34))))),bind(X_84,$fot(X_104)),bind(X_85,$fot(X_105))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(implies(X_104,X_105),X_104),implies(X_105,X_104))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))) )],[refute_0_11,refute_0_29]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(X_115,X_115),X_115),implies(X_115,X_115))),
inference(subst,[],[refute_0_30:[bind(X_104,$fot(X_115)),bind(X_105,$fot(X_115))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(X_106,X_107),X_106))
| ~ is_a_theorem(implies(implies(implies(X_106,X_107),X_106),implies(X_107,X_106)))
| is_a_theorem(implies(X_107,X_106)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_106,X_107),X_106))),bind(Y,$fot(implies(X_107,X_106)))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(implies(X_106,X_107),X_106),implies(X_107,X_106))),
inference(subst,[],[refute_0_30:[bind(X_104,$fot(X_106)),bind(X_105,$fot(X_107))]]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(X_106,X_107),X_106))
| is_a_theorem(implies(X_107,X_106)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_106,X_107),X_106),implies(X_107,X_106))) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(X_115,X_115),X_115),implies(X_115,X_115)))
| is_a_theorem(implies(X_115,implies(X_115,X_115))) ),
inference(subst,[],[refute_0_34:[bind(X_106,$fot(implies(X_115,X_115))),bind(X_107,$fot(X_115))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(X_115,implies(X_115,X_115))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_115,X_115),X_115),implies(X_115,X_115))) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_116,implies(X_116,X_116))),
inference(subst,[],[refute_0_36:[bind(X_115,$fot(X_116))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(X_116)
| is_a_theorem(implies(X_116,X_116)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_116,implies(X_116,X_116))) )],[refute_0_37,refute_0_0]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)))
| is_a_theorem(implies(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)),implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)))) ),
inference(subst,[],[refute_0_38:[bind(X_116,$fot(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166))))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(X_158)
| ~ is_a_theorem(implies(X_158,implies(implies(X_158,X_160),implies(X_159,X_160))))
| is_a_theorem(implies(implies(X_158,X_160),implies(X_159,X_160))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_158)),bind(Y,$fot(implies(implies(X_158,X_160),implies(X_159,X_160))))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(X_68)
| ~ is_a_theorem(implies(X_68,implies(X_65,implies(implies(X_65,X_67),implies(X_66,X_67)))))
| is_a_theorem(implies(X_65,implies(implies(X_65,X_67),implies(X_66,X_67)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_68)),bind(Y,$fot(implies(X_65,implies(implies(X_65,X_67),implies(X_66,X_67)))))]]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(implies(X_60,X_57),implies(X_59,X_57)),implies(X_57,implies(implies(X_57,X_60),implies(X_59,X_60))))),
inference(subst,[],[ic_JLukasiewicz_4:[bind(P,$fot(X_60)),bind(Q,$fot(X_57)),bind(R,$fot(X_59)),bind(S,$fot(X_57)),bind(T,$fot(X_57))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(implies(X_60,X_57),implies(X_59,X_57)),implies(X_57,implies(implies(X_57,X_60),implies(X_59,X_60)))))
| is_a_theorem(implies(X_61,implies(X_57,implies(implies(X_57,X_60),implies(X_59,X_60))))) ),
inference(subst,[],[refute_0_18:[bind(X_39,$fot(X_57)),bind(X_40,$fot(implies(implies(X_57,X_60),implies(X_59,X_60)))),bind(X_41,$fot(X_59)),bind(X_42,$fot(X_60)),bind(X_43,$fot(X_61))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(X_61,implies(X_57,implies(implies(X_57,X_60),implies(X_59,X_60))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_60,X_57),implies(X_59,X_57)),implies(X_57,implies(implies(X_57,X_60),implies(X_59,X_60))))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(X_68,implies(X_65,implies(implies(X_65,X_67),implies(X_66,X_67))))),
inference(subst,[],[refute_0_44:[bind(X_57,$fot(X_65)),bind(X_59,$fot(X_66)),bind(X_60,$fot(X_67)),bind(X_61,$fot(X_68))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(X_68)
| is_a_theorem(implies(X_65,implies(implies(X_65,X_67),implies(X_66,X_67)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_68,implies(X_65,implies(implies(X_65,X_67),implies(X_66,X_67))))) )],[refute_0_45,refute_0_41]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34))))
| is_a_theorem(implies(X_154,implies(implies(X_154,X_156),implies(X_155,X_156)))) ),
inference(subst,[],[refute_0_46:[bind(X_65,$fot(X_154)),bind(X_66,$fot(X_155)),bind(X_67,$fot(X_156)),bind(X_68,$fot(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(X_154,implies(implies(X_154,X_156),implies(X_155,X_156)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))) )],[refute_0_11,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(X_158,implies(implies(X_158,X_160),implies(X_159,X_160)))),
inference(subst,[],[refute_0_48:[bind(X_154,$fot(X_158)),bind(X_155,$fot(X_159)),bind(X_156,$fot(X_160))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(X_158)
| is_a_theorem(implies(implies(X_158,X_160),implies(X_159,X_160))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_158,implies(implies(X_158,X_160),implies(X_159,X_160)))) )],[refute_0_49,refute_0_40]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(X_115,implies(X_115,X_115)))
| is_a_theorem(implies(implies(implies(X_115,implies(X_115,X_115)),X_163),implies(X_162,X_163))) ),
inference(subst,[],[refute_0_50:[bind(X_158,$fot(implies(X_115,implies(X_115,X_115)))),bind(X_159,$fot(X_162)),bind(X_160,$fot(X_163))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(implies(X_115,implies(X_115,X_115)),X_163),implies(X_162,X_163))),
inference(resolve,[$cnf( is_a_theorem(implies(X_115,implies(X_115,X_115))) )],[refute_0_36,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166))),
inference(subst,[],[refute_0_52:[bind(X_115,$fot(X_164)),bind(X_162,$fot(X_165)),bind(X_163,$fot(X_166))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)),implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166))) )],[refute_0_53,refute_0_39]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(X_110)
| ~ is_a_theorem(implies(X_110,implies(X_108,implies(X_109,X_108))))
| is_a_theorem(implies(X_108,implies(X_109,X_108))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_110)),bind(Y,$fot(implies(X_108,implies(X_109,X_108))))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_41,X_107),X_107),implies(X_41,X_107)),implies(X_107,implies(X_41,X_107))))
| is_a_theorem(implies(X_43,implies(X_107,implies(X_41,X_107)))) ),
inference(subst,[],[refute_0_18:[bind(X_39,$fot(X_107)),bind(X_40,$fot(implies(X_41,X_107))),bind(X_42,$fot(implies(X_41,X_107)))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(implies(implies(X_41,X_107),X_107),implies(X_41,X_107)),implies(X_107,implies(X_41,X_107)))),
inference(subst,[],[refute_0_30:[bind(X_104,$fot(implies(X_41,X_107))),bind(X_105,$fot(X_107))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(X_43,implies(X_107,implies(X_41,X_107)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_41,X_107),X_107),implies(X_41,X_107)),implies(X_107,implies(X_41,X_107)))) )],[refute_0_57,refute_0_56]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(X_110,implies(X_108,implies(X_109,X_108)))),
inference(subst,[],[refute_0_58:[bind(X_107,$fot(X_108)),bind(X_41,$fot(X_109)),bind(X_43,$fot(X_110))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(X_110)
| is_a_theorem(implies(X_108,implies(X_109,X_108))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_110,implies(X_108,implies(X_109,X_108)))) )],[refute_0_59,refute_0_55]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)),implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166))))
| is_a_theorem(implies(X_199,implies(X_200,X_199))) ),
inference(subst,[],[refute_0_60:[bind(X_108,$fot(X_199)),bind(X_109,$fot(X_200)),bind(X_110,$fot(implies(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)),implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)))))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(X_199,implies(X_200,X_199))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)),implies(implies(implies(X_164,implies(X_164,X_164)),X_166),implies(X_165,X_166)))) )],[refute_0_54,refute_0_61]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(a,implies(b,a))),
inference(subst,[],[refute_0_62:[bind(X_199,$fot(a)),bind(X_200,$fot(b))]]) ).
cnf(refute_0_64,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(b,a))) )],[refute_0_63,prove_ic_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL087-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 14:54:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.40
% 0.18/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.41
%------------------------------------------------------------------------------