TSTP Solution File: LCL088-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL088-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 12:49:22 EDT 2022
% Result : Unsatisfiable 0.88s 1.05s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 3
% Syntax : Number of clauses : 111 ( 57 unt; 0 nHn; 18 RR)
% Number of literals : 180 ( 0 equ; 70 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 516 ( 188 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_3,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(X_71)
| ~ is_a_theorem(implies(X_71,implies(implies(X_71,X_73),implies(X_72,X_73))))
| is_a_theorem(implies(implies(X_71,X_73),implies(X_72,X_73))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_71)),bind(Y,$fot(implies(implies(X_71,X_73),implies(X_72,X_73))))]]) ).
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,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(R,S)))
| ~ is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P)))))
| is_a_theorem(implies(T,implies(implies(S,P),implies(R,P)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(P,Q),implies(R,S)))),bind(Y,$fot(implies(T,implies(implies(S,P),implies(R,P)))))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(R,S)))
| is_a_theorem(implies(T,implies(implies(S,P),implies(R,P)))) ),
inference(resolve,[$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_3]) ).
cnf(refute_0_5,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_4:[bind(P,$fot(implies(P,Q))),bind(Q,$fot(implies(R,S))),bind(R,$fot(X_9)),bind(S,$fot(implies(implies(S,P),implies(R,P)))),bind(T,$fot(X_11))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(X_11,implies(implies(implies(implies(S,P),implies(R,P)),implies(P,Q)),implies(X_9,implies(P,Q))))),
inference(resolve,[$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_5]) ).
cnf(refute_0_7,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_6:[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_8,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,[$cnf( is_a_theorem(implies(X_16,implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13))))) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P)))))
| is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))) ),
inference(subst,[],[refute_0_8:[bind(X_12,$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,$fot(X_38))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))),
inference(resolve,[$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_9]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(X_58)
| ~ is_a_theorem(implies(X_58,implies(X_55,implies(implies(X_55,X_57),implies(X_56,X_57)))))
| is_a_theorem(implies(X_55,implies(implies(X_55,X_57),implies(X_56,X_57)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_58)),bind(Y,$fot(implies(X_55,implies(implies(X_55,X_57),implies(X_56,X_57)))))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(X_53,X_50),implies(X_52,X_50)),implies(X_50,implies(implies(X_50,X_53),implies(X_52,X_53))))),
inference(subst,[],[ic_JLukasiewicz_4:[bind(P,$fot(X_53)),bind(Q,$fot(X_50)),bind(R,$fot(X_52)),bind(S,$fot(X_50)),bind(T,$fot(X_50))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)))
| ~ is_a_theorem(implies(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)),implies(X_43,implies(X_39,X_40))))
| is_a_theorem(implies(X_43,implies(X_39,X_40))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)))),bind(Y,$fot(implies(X_43,implies(X_39,X_40))))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)),implies(X_43,implies(X_39,X_40)))),
inference(subst,[],[refute_0_10:[bind(X_33,$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_15,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,[$cnf( is_a_theorem(implies(implies(implies(implies(X_42,X_39),implies(X_41,X_39)),implies(X_39,X_40)),implies(X_43,implies(X_39,X_40)))) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(implies(implies(implies(X_53,X_50),implies(X_52,X_50)),implies(X_50,implies(implies(X_50,X_53),implies(X_52,X_53)))))
| is_a_theorem(implies(X_54,implies(X_50,implies(implies(X_50,X_53),implies(X_52,X_53))))) ),
inference(subst,[],[refute_0_15:[bind(X_39,$fot(X_50)),bind(X_40,$fot(implies(implies(X_50,X_53),implies(X_52,X_53)))),bind(X_41,$fot(X_52)),bind(X_42,$fot(X_53)),bind(X_43,$fot(X_54))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(X_54,implies(X_50,implies(implies(X_50,X_53),implies(X_52,X_53))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_53,X_50),implies(X_52,X_50)),implies(X_50,implies(implies(X_50,X_53),implies(X_52,X_53))))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(X_58,implies(X_55,implies(implies(X_55,X_57),implies(X_56,X_57))))),
inference(subst,[],[refute_0_17:[bind(X_50,$fot(X_55)),bind(X_52,$fot(X_56)),bind(X_53,$fot(X_57)),bind(X_54,$fot(X_58))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(X_58)
| is_a_theorem(implies(X_55,implies(implies(X_55,X_57),implies(X_56,X_57)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_58,implies(X_55,implies(implies(X_55,X_57),implies(X_56,X_57))))) )],[refute_0_18,refute_0_11]) ).
cnf(refute_0_20,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_67,implies(implies(X_67,X_69),implies(X_68,X_69)))) ),
inference(subst,[],[refute_0_19:[bind(X_55,$fot(X_67)),bind(X_56,$fot(X_68)),bind(X_57,$fot(X_69)),bind(X_58,$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_21,plain,
is_a_theorem(implies(X_67,implies(implies(X_67,X_69),implies(X_68,X_69)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))) )],[refute_0_10,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(X_71,implies(implies(X_71,X_73),implies(X_72,X_73)))),
inference(subst,[],[refute_0_21:[bind(X_67,$fot(X_71)),bind(X_68,$fot(X_72)),bind(X_69,$fot(X_73))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(X_71)
| is_a_theorem(implies(implies(X_71,X_73),implies(X_72,X_73))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_71,implies(implies(X_71,X_73),implies(X_72,X_73)))) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)))
| is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73))) ),
inference(subst,[],[refute_0_23:[bind(X_71,$fot(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992))))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)))
| is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73))) ),
inference(subst,[],[refute_0_23:[bind(X_71,$fot(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(X_141,X_142),X_141),implies(X_142,X_141)))
| is_a_theorem(implies(implies(implies(implies(implies(X_141,X_142),X_141),implies(X_142,X_141)),X_73),implies(X_72,X_73))) ),
inference(subst,[],[refute_0_23:[bind(X_71,$fot(implies(implies(implies(X_141,X_142),X_141),implies(X_142,X_141))))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)))
| is_a_theorem(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73))) ),
inference(subst,[],[refute_0_23:[bind(X_71,$fot(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104))))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(X_80)
| ~ is_a_theorem(implies(X_80,implies(implies(implies(X_82,implies(X_81,X_82)),X_79),implies(implies(X_81,X_82),X_79))))
| is_a_theorem(implies(implies(implies(X_82,implies(X_81,X_82)),X_79),implies(implies(X_81,X_82),X_79))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_80)),bind(Y,$fot(implies(implies(implies(X_82,implies(X_81,X_82)),X_79),implies(implies(X_81,X_82),X_79))))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60)))))
| is_a_theorem(implies(T,implies(implies(implies(X_60,implies(X_59,X_60)),P),implies(implies(X_59,X_60),P)))) ),
inference(subst,[],[refute_0_4:[bind(R,$fot(implies(X_59,X_60))),bind(S,$fot(implies(X_60,implies(X_59,X_60))))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(implies(implies(X_36,X_52),implies(X_35,X_52)),implies(X_52,implies(X_35,X_52))),implies(implies(X_35,X_52),implies(X_52,implies(X_35,X_52))))),
inference(subst,[],[refute_0_10:[bind(X_33,$fot(X_52)),bind(X_34,$fot(implies(X_35,X_52))),bind(X_38,$fot(implies(X_35,X_52)))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_36,X_52),implies(X_35,X_52)),implies(X_52,implies(X_35,X_52))),implies(implies(X_35,X_52),implies(X_52,implies(X_35,X_52)))))
| is_a_theorem(implies(X_54,implies(implies(X_35,X_52),implies(X_52,implies(X_35,X_52))))) ),
inference(subst,[],[refute_0_15:[bind(X_39,$fot(implies(X_35,X_52))),bind(X_40,$fot(implies(X_52,implies(X_35,X_52)))),bind(X_41,$fot(X_52)),bind(X_42,$fot(implies(X_36,X_52))),bind(X_43,$fot(X_54))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(X_54,implies(implies(X_35,X_52),implies(X_52,implies(X_35,X_52))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_36,X_52),implies(X_35,X_52)),implies(X_52,implies(X_35,X_52))),implies(implies(X_35,X_52),implies(X_52,implies(X_35,X_52))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(P,Q),implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60))))),
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_59)),bind(X_52,$fot(X_60)),bind(X_54,$fot(implies(P,Q)))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(T,implies(implies(implies(X_60,implies(X_59,X_60)),P),implies(implies(X_59,X_60),P)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60))))) )],[refute_0_33,refute_0_29]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(X_80,implies(implies(implies(X_82,implies(X_81,X_82)),X_79),implies(implies(X_81,X_82),X_79)))),
inference(subst,[],[refute_0_34:[bind(P,$fot(X_79)),bind(T,$fot(X_80)),bind(X_59,$fot(X_81)),bind(X_60,$fot(X_82))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(X_80)
| is_a_theorem(implies(implies(implies(X_82,implies(X_81,X_82)),X_79),implies(implies(X_81,X_82),X_79))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_80,implies(implies(implies(X_82,implies(X_81,X_82)),X_79),implies(implies(X_81,X_82),X_79)))) )],[refute_0_35,refute_0_28]) ).
cnf(refute_0_37,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34))))
| is_a_theorem(implies(implies(implies(X_103,implies(X_102,X_103)),X_100),implies(implies(X_102,X_103),X_100))) ),
inference(subst,[],[refute_0_36:[bind(X_79,$fot(X_100)),bind(X_80,$fot(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34))))),bind(X_81,$fot(X_102)),bind(X_82,$fot(X_103))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(X_103,implies(X_102,X_103)),X_100),implies(implies(X_102,X_103),X_100))),
inference(resolve,[$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_10,refute_0_37]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104))),
inference(subst,[],[refute_0_38:[bind(X_100,$fot(X_104)),bind(X_102,$fot(X_105)),bind(X_103,$fot(X_106))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104))) )],[refute_0_39,refute_0_27]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(X_88)
| ~ is_a_theorem(implies(X_88,implies(implies(implies(X_89,X_90),X_89),implies(X_90,X_89))))
| is_a_theorem(implies(implies(implies(X_89,X_90),X_89),implies(X_90,X_89))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_88)),bind(Y,$fot(implies(implies(implies(X_89,X_90),X_89),implies(X_90,X_89))))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(X_86,X_87),implies(X_87,implies(X_86,X_87))))
| is_a_theorem(implies(T,implies(implies(implies(X_86,X_87),X_86),implies(X_87,X_86)))) ),
inference(subst,[],[refute_0_4:[bind(P,$fot(X_86)),bind(Q,$fot(X_87)),bind(R,$fot(X_87)),bind(S,$fot(implies(X_86,X_87)))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(X_61)
| ~ is_a_theorem(implies(X_61,implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60)))))
| is_a_theorem(implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_61)),bind(Y,$fot(implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60)))))]]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(X_61,implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60))))),
inference(subst,[],[refute_0_32:[bind(X_35,$fot(X_59)),bind(X_52,$fot(X_60)),bind(X_54,$fot(X_61))]]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(X_61)
| is_a_theorem(implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_61,implies(implies(X_59,X_60),implies(X_60,implies(X_59,X_60))))) )],[refute_0_44,refute_0_43]) ).
cnf(refute_0_46,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_83,X_84),implies(X_84,implies(X_83,X_84)))) ),
inference(subst,[],[refute_0_45:[bind(X_59,$fot(X_83)),bind(X_60,$fot(X_84)),bind(X_61,$fot(implies(implies(implies(implies(X_36,X_33),implies(X_35,X_33)),implies(X_33,X_34)),implies(X_38,implies(X_33,X_34)))))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(X_83,X_84),implies(X_84,implies(X_83,X_84)))),
inference(resolve,[$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_10,refute_0_46]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(X_86,X_87),implies(X_87,implies(X_86,X_87)))),
inference(subst,[],[refute_0_47:[bind(X_83,$fot(X_86)),bind(X_84,$fot(X_87))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(T,implies(implies(implies(X_86,X_87),X_86),implies(X_87,X_86)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_86,X_87),implies(X_87,implies(X_86,X_87)))) )],[refute_0_48,refute_0_42]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(X_88,implies(implies(implies(X_89,X_90),X_89),implies(X_90,X_89)))),
inference(subst,[],[refute_0_49:[bind(T,$fot(X_88)),bind(X_86,$fot(X_89)),bind(X_87,$fot(X_90))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(X_88)
| is_a_theorem(implies(implies(implies(X_89,X_90),X_89),implies(X_90,X_89))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_88,implies(implies(implies(X_89,X_90),X_89),implies(X_90,X_89)))) )],[refute_0_50,refute_0_41]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73)))
| is_a_theorem(implies(implies(implies(X_139,X_140),X_139),implies(X_140,X_139))) ),
inference(subst,[],[refute_0_51:[bind(X_88,$fot(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73)))),bind(X_89,$fot(X_139)),bind(X_90,$fot(X_140))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(X_139,X_140),X_139),implies(X_140,X_139))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73))) )],[refute_0_40,refute_0_52]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(X_141,X_142),X_141),implies(X_142,X_141))),
inference(subst,[],[refute_0_53:[bind(X_139,$fot(X_141)),bind(X_140,$fot(X_142))]]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_141,X_142),X_141),implies(X_142,X_141)),X_73),implies(X_72,X_73))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_141,X_142),X_141),implies(X_142,X_141))) )],[refute_0_54,refute_0_26]) ).
cnf(refute_0_56,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156))),
inference(subst,[],[refute_0_55:[bind(X_141,$fot(X_153)),bind(X_142,$fot(X_154)),bind(X_72,$fot(X_155)),bind(X_73,$fot(X_156))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156))) )],[refute_0_56,refute_0_25]) ).
cnf(refute_0_58,plain,
( ~ is_a_theorem(X_26)
| ~ is_a_theorem(implies(X_26,implies(implies(implies(implies(implies(implies(X_31,X_28),implies(X_30,X_28)),implies(X_28,X_29)),X_27),X_25),implies(implies(implies(X_32,implies(X_28,X_29)),X_27),X_25))))
| is_a_theorem(implies(implies(implies(implies(implies(implies(X_31,X_28),implies(X_30,X_28)),implies(X_28,X_29)),X_27),X_25),implies(implies(implies(X_32,implies(X_28,X_29)),X_27),X_25))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_26)),bind(Y,$fot(implies(implies(implies(implies(implies(implies(X_31,X_28),implies(X_30,X_28)),implies(X_28,X_29)),X_27),X_25),implies(implies(implies(X_32,implies(X_28,X_29)),X_27),X_25))))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(implies(implies(X_24,implies(X_20,X_21)),X_18),implies(implies(implies(implies(X_23,X_20),implies(X_22,X_20)),implies(X_20,X_21)),X_18))))
| is_a_theorem(implies(T,implies(implies(implies(implies(implies(implies(X_23,X_20),implies(X_22,X_20)),implies(X_20,X_21)),X_18),P),implies(implies(implies(X_24,implies(X_20,X_21)),X_18),P)))) ),
inference(subst,[],[refute_0_4:[bind(R,$fot(implies(implies(X_24,implies(X_20,X_21)),X_18))),bind(S,$fot(implies(implies(implies(implies(X_23,X_20),implies(X_22,X_20)),implies(X_20,X_21)),X_18)))]]) ).
cnf(refute_0_60,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13)))))
| is_a_theorem(implies(T,implies(implies(implies(X_17,implies(X_12,X_13)),P),implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),P)))) ),
inference(subst,[],[refute_0_4:[bind(R,$fot(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)))),bind(S,$fot(implies(X_17,implies(X_12,X_13))))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(P,Q),implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_17,implies(X_12,X_13))))),
inference(subst,[],[refute_0_6:[bind(P,$fot(X_12)),bind(Q,$fot(X_13)),bind(R,$fot(X_14)),bind(S,$fot(X_15)),bind(X_11,$fot(implies(P,Q))),bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(T,implies(implies(implies(X_17,implies(X_12,X_13)),P),implies(implies(implies(implies(X_15,X_12),implies(X_14,X_12)),implies(X_12,X_13)),P)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),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_61,refute_0_60]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(implies(P,Q),implies(implies(implies(X_24,implies(X_20,X_21)),X_18),implies(implies(implies(implies(X_23,X_20),implies(X_22,X_20)),implies(X_20,X_21)),X_18)))),
inference(subst,[],[refute_0_62:[bind(P,$fot(X_18)),bind(T,$fot(implies(P,Q))),bind(X_12,$fot(X_20)),bind(X_13,$fot(X_21)),bind(X_14,$fot(X_22)),bind(X_15,$fot(X_23)),bind(X_17,$fot(X_24))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(T,implies(implies(implies(implies(implies(implies(X_23,X_20),implies(X_22,X_20)),implies(X_20,X_21)),X_18),P),implies(implies(implies(X_24,implies(X_20,X_21)),X_18),P)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(implies(implies(X_24,implies(X_20,X_21)),X_18),implies(implies(implies(implies(X_23,X_20),implies(X_22,X_20)),implies(X_20,X_21)),X_18)))) )],[refute_0_63,refute_0_59]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(X_26,implies(implies(implies(implies(implies(implies(X_31,X_28),implies(X_30,X_28)),implies(X_28,X_29)),X_27),X_25),implies(implies(implies(X_32,implies(X_28,X_29)),X_27),X_25)))),
inference(subst,[],[refute_0_64:[bind(P,$fot(X_25)),bind(T,$fot(X_26)),bind(X_18,$fot(X_27)),bind(X_20,$fot(X_28)),bind(X_21,$fot(X_29)),bind(X_22,$fot(X_30)),bind(X_23,$fot(X_31)),bind(X_24,$fot(X_32))]]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(X_26)
| is_a_theorem(implies(implies(implies(implies(implies(implies(X_31,X_28),implies(X_30,X_28)),implies(X_28,X_29)),X_27),X_25),implies(implies(implies(X_32,implies(X_28,X_29)),X_27),X_25))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_26,implies(implies(implies(implies(implies(implies(X_31,X_28),implies(X_30,X_28)),implies(X_28,X_29)),X_27),X_25),implies(implies(implies(X_32,implies(X_28,X_29)),X_27),X_25)))) )],[refute_0_65,refute_0_58]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73)))
| is_a_theorem(implies(implies(implies(implies(implies(implies(X_990,X_987),implies(X_989,X_987)),implies(X_987,X_988)),X_986),X_984),implies(implies(implies(X_991,implies(X_987,X_988)),X_986),X_984))) ),
inference(subst,[],[refute_0_66:[bind(X_25,$fot(X_984)),bind(X_26,$fot(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73)))),bind(X_27,$fot(X_986)),bind(X_28,$fot(X_987)),bind(X_29,$fot(X_988)),bind(X_30,$fot(X_989)),bind(X_31,$fot(X_990)),bind(X_32,$fot(X_991))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_990,X_987),implies(X_989,X_987)),implies(X_987,X_988)),X_986),X_984),implies(implies(implies(X_991,implies(X_987,X_988)),X_986),X_984))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73))) )],[refute_0_57,refute_0_67]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992))),
inference(subst,[],[refute_0_68:[bind(X_984,$fot(X_992)),bind(X_986,$fot(X_993)),bind(X_987,$fot(X_994)),bind(X_988,$fot(X_995)),bind(X_989,$fot(X_996)),bind(X_990,$fot(X_997)),bind(X_991,$fot(X_998))]]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992))) )],[refute_0_69,refute_0_24]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(X_2226)
| ~ is_a_theorem(implies(X_2226,implies(implies(implies(X_2224,X_2225),X_2224),X_2224)))
| is_a_theorem(implies(implies(implies(X_2224,X_2225),X_2224),X_2224)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_2226)),bind(Y,$fot(implies(implies(implies(X_2224,X_2225),X_2224),X_2224)))]]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(implies(implies(X_319,X_320),X_319))
| ~ is_a_theorem(implies(implies(implies(X_319,X_320),X_319),implies(X_321,X_319)))
| is_a_theorem(implies(X_321,X_319)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_319,X_320),X_319))),bind(Y,$fot(implies(X_321,X_319)))]]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(X_188)
| ~ is_a_theorem(implies(X_188,implies(implies(implies(X_186,X_187),X_186),implies(X_189,X_186))))
| is_a_theorem(implies(implies(implies(X_186,X_187),X_186),implies(X_189,X_186))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_188)),bind(Y,$fot(implies(implies(implies(X_186,X_187),X_186),implies(X_189,X_186))))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(X_177,implies(P,Q))))
| is_a_theorem(implies(T,implies(implies(implies(P,Q),P),implies(X_177,P)))) ),
inference(subst,[],[refute_0_4:[bind(R,$fot(X_177)),bind(S,$fot(implies(P,Q)))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(X_148)
| ~ is_a_theorem(implies(X_148,implies(X_146,implies(X_147,X_146))))
| is_a_theorem(implies(X_146,implies(X_147,X_146))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_148)),bind(Y,$fot(implies(X_146,implies(X_147,X_146))))]]) ).
cnf(refute_0_76,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_41,X_142),X_142),implies(X_41,X_142)),implies(X_142,implies(X_41,X_142))))
| is_a_theorem(implies(X_43,implies(X_142,implies(X_41,X_142)))) ),
inference(subst,[],[refute_0_15:[bind(X_39,$fot(X_142)),bind(X_40,$fot(implies(X_41,X_142))),bind(X_42,$fot(implies(X_41,X_142)))]]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(implies(implies(X_41,X_142),X_142),implies(X_41,X_142)),implies(X_142,implies(X_41,X_142)))),
inference(subst,[],[refute_0_53:[bind(X_139,$fot(implies(X_41,X_142))),bind(X_140,$fot(X_142))]]) ).
cnf(refute_0_78,plain,
is_a_theorem(implies(X_43,implies(X_142,implies(X_41,X_142)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_41,X_142),X_142),implies(X_41,X_142)),implies(X_142,implies(X_41,X_142)))) )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(X_148,implies(X_146,implies(X_147,X_146)))),
inference(subst,[],[refute_0_78:[bind(X_142,$fot(X_146)),bind(X_41,$fot(X_147)),bind(X_43,$fot(X_148))]]) ).
cnf(refute_0_80,plain,
( ~ is_a_theorem(X_148)
| is_a_theorem(implies(X_146,implies(X_147,X_146))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_148,implies(X_146,implies(X_147,X_146)))) )],[refute_0_79,refute_0_75]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73)))
| is_a_theorem(implies(X_173,implies(X_174,X_173))) ),
inference(subst,[],[refute_0_80:[bind(X_146,$fot(X_173)),bind(X_147,$fot(X_174)),bind(X_148,$fot(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73))))]]) ).
cnf(refute_0_82,plain,
is_a_theorem(implies(X_173,implies(X_174,X_173))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_106,implies(X_105,X_106)),X_104),implies(implies(X_105,X_106),X_104)),X_73),implies(X_72,X_73))) )],[refute_0_40,refute_0_81]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(implies(P,Q),implies(X_177,implies(P,Q)))),
inference(subst,[],[refute_0_82:[bind(X_173,$fot(implies(P,Q))),bind(X_174,$fot(X_177))]]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(T,implies(implies(implies(P,Q),P),implies(X_177,P)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(X_177,implies(P,Q)))) )],[refute_0_83,refute_0_74]) ).
cnf(refute_0_85,plain,
is_a_theorem(implies(X_188,implies(implies(implies(X_186,X_187),X_186),implies(X_189,X_186)))),
inference(subst,[],[refute_0_84:[bind(P,$fot(X_186)),bind(Q,$fot(X_187)),bind(T,$fot(X_188)),bind(X_177,$fot(X_189))]]) ).
cnf(refute_0_86,plain,
( ~ is_a_theorem(X_188)
| is_a_theorem(implies(implies(implies(X_186,X_187),X_186),implies(X_189,X_186))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_188,implies(implies(implies(X_186,X_187),X_186),implies(X_189,X_186)))) )],[refute_0_85,refute_0_73]) ).
cnf(refute_0_87,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73)))
| is_a_theorem(implies(implies(implies(X_315,X_316),X_315),implies(X_318,X_315))) ),
inference(subst,[],[refute_0_86:[bind(X_186,$fot(X_315)),bind(X_187,$fot(X_316)),bind(X_188,$fot(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73)))),bind(X_189,$fot(X_318))]]) ).
cnf(refute_0_88,plain,
is_a_theorem(implies(implies(implies(X_315,X_316),X_315),implies(X_318,X_315))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X_153,X_154),X_153),implies(X_154,X_153)),X_156),implies(X_155,X_156)),X_73),implies(X_72,X_73))) )],[refute_0_57,refute_0_87]) ).
cnf(refute_0_89,plain,
is_a_theorem(implies(implies(implies(X_319,X_320),X_319),implies(X_321,X_319))),
inference(subst,[],[refute_0_88:[bind(X_315,$fot(X_319)),bind(X_316,$fot(X_320)),bind(X_318,$fot(X_321))]]) ).
cnf(refute_0_90,plain,
( ~ is_a_theorem(implies(implies(X_319,X_320),X_319))
| is_a_theorem(implies(X_321,X_319)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_319,X_320),X_319),implies(X_321,X_319))) )],[refute_0_89,refute_0_72]) ).
cnf(refute_0_91,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_2220,X_2221),X_2220),X_2220),X_2220),implies(implies(implies(X_2220,X_2221),X_2220),X_2220)))
| is_a_theorem(implies(X_321,implies(implies(implies(X_2220,X_2221),X_2220),X_2220))) ),
inference(subst,[],[refute_0_90:[bind(X_319,$fot(implies(implies(implies(X_2220,X_2221),X_2220),X_2220))),bind(X_320,$fot(X_2220))]]) ).
cnf(refute_0_92,plain,
( ~ is_a_theorem(X_76)
| ~ is_a_theorem(implies(X_76,implies(implies(implies(X_77,X_78),X_74),implies(implies(implies(X_74,X_75),X_78),X_74))))
| is_a_theorem(implies(implies(implies(X_77,X_78),X_74),implies(implies(implies(X_74,X_75),X_78),X_74))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_76)),bind(Y,$fot(implies(implies(implies(X_77,X_78),X_74),implies(implies(implies(X_74,X_75),X_78),X_74))))]]) ).
cnf(refute_0_93,plain,
( ~ is_a_theorem(implies(implies(P,Q),implies(implies(implies(P,Q),X_73),implies(X_72,X_73))))
| is_a_theorem(implies(T,implies(implies(implies(X_72,X_73),P),implies(implies(implies(P,Q),X_73),P)))) ),
inference(subst,[],[refute_0_4:[bind(R,$fot(implies(implies(P,Q),X_73))),bind(S,$fot(implies(X_72,X_73)))]]) ).
cnf(refute_0_94,plain,
is_a_theorem(implies(implies(P,Q),implies(implies(implies(P,Q),X_73),implies(X_72,X_73)))),
inference(subst,[],[refute_0_21:[bind(X_67,$fot(implies(P,Q))),bind(X_68,$fot(X_72)),bind(X_69,$fot(X_73))]]) ).
cnf(refute_0_95,plain,
is_a_theorem(implies(T,implies(implies(implies(X_72,X_73),P),implies(implies(implies(P,Q),X_73),P)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(P,Q),implies(implies(implies(P,Q),X_73),implies(X_72,X_73)))) )],[refute_0_94,refute_0_93]) ).
cnf(refute_0_96,plain,
is_a_theorem(implies(X_76,implies(implies(implies(X_77,X_78),X_74),implies(implies(implies(X_74,X_75),X_78),X_74)))),
inference(subst,[],[refute_0_95:[bind(P,$fot(X_74)),bind(Q,$fot(X_75)),bind(T,$fot(X_76)),bind(X_72,$fot(X_77)),bind(X_73,$fot(X_78))]]) ).
cnf(refute_0_97,plain,
( ~ is_a_theorem(X_76)
| is_a_theorem(implies(implies(implies(X_77,X_78),X_74),implies(implies(implies(X_74,X_75),X_78),X_74))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_76,implies(implies(implies(X_77,X_78),X_74),implies(implies(implies(X_74,X_75),X_78),X_74)))) )],[refute_0_96,refute_0_92]) ).
cnf(refute_0_98,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73)))
| is_a_theorem(implies(implies(implies(X_2218,X_2219),X_2215),implies(implies(implies(X_2215,X_2216),X_2219),X_2215))) ),
inference(subst,[],[refute_0_97:[bind(X_74,$fot(X_2215)),bind(X_75,$fot(X_2216)),bind(X_76,$fot(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73)))),bind(X_77,$fot(X_2218)),bind(X_78,$fot(X_2219))]]) ).
cnf(refute_0_99,plain,
is_a_theorem(implies(implies(implies(X_2218,X_2219),X_2215),implies(implies(implies(X_2215,X_2216),X_2219),X_2215))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73))) )],[refute_0_70,refute_0_98]) ).
cnf(refute_0_100,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_2220,X_2221),X_2220),X_2220),X_2220),implies(implies(implies(X_2220,X_2221),X_2220),X_2220))),
inference(subst,[],[refute_0_99:[bind(X_2215,$fot(X_2220)),bind(X_2216,$fot(X_2221)),bind(X_2218,$fot(implies(implies(X_2220,X_2221),X_2220))),bind(X_2219,$fot(X_2220))]]) ).
cnf(refute_0_101,plain,
is_a_theorem(implies(X_321,implies(implies(implies(X_2220,X_2221),X_2220),X_2220))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_2220,X_2221),X_2220),X_2220),X_2220),implies(implies(implies(X_2220,X_2221),X_2220),X_2220))) )],[refute_0_100,refute_0_91]) ).
cnf(refute_0_102,plain,
is_a_theorem(implies(X_2226,implies(implies(implies(X_2224,X_2225),X_2224),X_2224))),
inference(subst,[],[refute_0_101:[bind(X_2220,$fot(X_2224)),bind(X_2221,$fot(X_2225)),bind(X_321,$fot(X_2226))]]) ).
cnf(refute_0_103,plain,
( ~ is_a_theorem(X_2226)
| is_a_theorem(implies(implies(implies(X_2224,X_2225),X_2224),X_2224)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_2226,implies(implies(implies(X_2224,X_2225),X_2224),X_2224))) )],[refute_0_102,refute_0_71]) ).
cnf(refute_0_104,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73)))
| is_a_theorem(implies(implies(implies(X_2294,X_2295),X_2294),X_2294)) ),
inference(subst,[],[refute_0_103:[bind(X_2224,$fot(X_2294)),bind(X_2225,$fot(X_2295)),bind(X_2226,$fot(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73))))]]) ).
cnf(refute_0_105,plain,
is_a_theorem(implies(implies(implies(X_2294,X_2295),X_2294),X_2294)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_997,X_994),implies(X_996,X_994)),implies(X_994,X_995)),X_993),X_992),implies(implies(implies(X_998,implies(X_994,X_995)),X_993),X_992)),X_73),implies(X_72,X_73))) )],[refute_0_70,refute_0_104]) ).
cnf(refute_0_106,plain,
is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(subst,[],[refute_0_105:[bind(X_2294,$fot(a)),bind(X_2295,$fot(b))]]) ).
cnf(refute_0_107,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(a,b),a),a)) )],[refute_0_106,prove_ic_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL088-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 12:05:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.88/1.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.88/1.05
% 0.88/1.05 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.88/1.07
%------------------------------------------------------------------------------