TSTP Solution File: LCL081-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL081-1 : 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 12:49:17 EDT 2022
% Result : Unsatisfiable 0.41s 0.57s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 3
% Syntax : Number of clauses : 89 ( 47 unt; 0 nHn; 20 RR)
% Number of literals : 142 ( 0 equ; 54 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 : 303 ( 105 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(ic_JLukasiewicz,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))) ).
cnf(prove_ic_1,negated_conjecture,
~ is_a_theorem(implies(a,a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| ~ is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X))))
| is_a_theorem(implies(implies(Z,X),implies(U,X))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Z))),bind(Y,$fot(implies(implies(Z,X),implies(U,X))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(implies(X,Y),Z))
| is_a_theorem(implies(implies(Z,X),implies(U,X))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))) )],[ic_JLukasiewicz,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(X_296,X_297),implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297))))
| is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_296)),bind(Y,$fot(X_297)),bind(Z,$fot(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(X_51,X_52))
| ~ is_a_theorem(implies(implies(X_51,X_52),implies(X_52,implies(X_51,X_52))))
| is_a_theorem(implies(X_52,implies(X_51,X_52))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_51,X_52))),bind(Y,$fot(implies(X_52,implies(X_51,X_52))))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26)))))
| is_a_theorem(implies(implies(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))),X),implies(U,X))) ),
inference(subst,[],[refute_0_1:[bind(Z,$fot(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26)))))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)),implies(X_13,implies(X_11,X_12))))
| is_a_theorem(implies(implies(implies(X_13,implies(X_11,X_12)),implies(implies(X_14,X_11),implies(X_10,X_11))),implies(U,implies(implies(X_14,X_11),implies(X_10,X_11))))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(implies(implies(X_14,X_11),implies(X_10,X_11)))),bind(Y,$fot(implies(X_11,X_12))),bind(Z,$fot(implies(X_13,implies(X_11,X_12))))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(X,Y),X_8),implies(implies(X_8,X),implies(U,X)))),
inference(subst,[],[ic_JLukasiewicz:[bind(Z,$fot(X_8))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X_8),implies(implies(X_8,X),implies(U,X))))
| is_a_theorem(implies(implies(implies(implies(X_8,X),implies(U,X)),implies(X,Y)),implies(X_6,implies(X,Y)))) ),
inference(subst,[],[refute_0_1:[bind(U,$fot(X_6)),bind(X,$fot(implies(X,Y))),bind(Y,$fot(X_8)),bind(Z,$fot(implies(implies(X_8,X),implies(U,X))))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(implies(X_8,X),implies(U,X)),implies(X,Y)),implies(X_6,implies(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X_8),implies(implies(X_8,X),implies(U,X)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)),implies(X_13,implies(X_11,X_12)))),
inference(subst,[],[refute_0_8:[bind(U,$fot(X_10)),bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(X_6,$fot(X_13)),bind(X_8,$fot(X_14))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(X_13,implies(X_11,X_12)),implies(implies(X_14,X_11),implies(X_10,X_11))),implies(U,implies(implies(X_14,X_11),implies(X_10,X_11))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)),implies(X_13,implies(X_11,X_12)))) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(X_25,implies(X_12,X_12)),implies(implies(X_14,X_12),implies(X_12,X_12))),implies(implies(X_12,X_12),implies(implies(X_14,X_12),implies(X_12,X_12))))),
inference(subst,[],[refute_0_10:[bind(U,$fot(implies(X_12,X_12))),bind(X_10,$fot(X_12)),bind(X_11,$fot(X_12)),bind(X_13,$fot(X_25))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)))
| ~ is_a_theorem(implies(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)),implies(X_13,implies(X_11,X_12))))
| is_a_theorem(implies(X_13,implies(X_11,X_12))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)))),bind(Y,$fot(implies(X_13,implies(X_11,X_12))))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)))
| is_a_theorem(implies(X_13,implies(X_11,X_12))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_14,X_11),implies(X_10,X_11)),implies(X_11,X_12)),implies(X_13,implies(X_11,X_12)))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(implies(X_25,implies(X_12,X_12)),implies(implies(X_14,X_12),implies(X_12,X_12))),implies(implies(X_12,X_12),implies(implies(X_14,X_12),implies(X_12,X_12)))))
| is_a_theorem(implies(X_24,implies(implies(X_12,X_12),implies(implies(X_14,X_12),implies(X_12,X_12))))) ),
inference(subst,[],[refute_0_13:[bind(X_10,$fot(implies(X_14,X_12))),bind(X_11,$fot(implies(X_12,X_12))),bind(X_12,$fot(implies(implies(X_14,X_12),implies(X_12,X_12)))),bind(X_13,$fot(X_24)),bind(X_14,$fot(X_25))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(X_24,implies(implies(X_12,X_12),implies(implies(X_14,X_12),implies(X_12,X_12))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_25,implies(X_12,X_12)),implies(implies(X_14,X_12),implies(X_12,X_12))),implies(implies(X_12,X_12),implies(implies(X_14,X_12),implies(X_12,X_12))))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(X,Y),implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))))),
inference(subst,[],[refute_0_15:[bind(X_12,$fot(X_26)),bind(X_14,$fot(X_27)),bind(X_24,$fot(implies(X,Y)))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))),X),implies(U,X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))))) )],[refute_0_16,refute_0_4]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X_31)
| ~ is_a_theorem(implies(X_31,implies(implies(X_29,X_30),implies(X_30,implies(X_29,X_30)))))
| is_a_theorem(implies(implies(X_29,X_30),implies(X_30,implies(X_29,X_30)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_31)),bind(Y,$fot(implies(implies(X_29,X_30),implies(X_30,implies(X_29,X_30)))))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(implies(X_8,X_21),implies(U,X_21)),implies(X_21,implies(U,X_21))),implies(implies(U,X_21),implies(X_21,implies(U,X_21))))),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_21)),bind(Y,$fot(implies(U,X_21))),bind(X_6,$fot(implies(U,X_21)))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_8,X_21),implies(U,X_21)),implies(X_21,implies(U,X_21))),implies(implies(U,X_21),implies(X_21,implies(U,X_21)))))
| is_a_theorem(implies(X_24,implies(implies(U,X_21),implies(X_21,implies(U,X_21))))) ),
inference(subst,[],[refute_0_13:[bind(X_10,$fot(X_21)),bind(X_11,$fot(implies(U,X_21))),bind(X_12,$fot(implies(X_21,implies(U,X_21)))),bind(X_13,$fot(X_24)),bind(X_14,$fot(implies(X_8,X_21)))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_24,implies(implies(U,X_21),implies(X_21,implies(U,X_21))))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_8,X_21),implies(U,X_21)),implies(X_21,implies(U,X_21))),implies(implies(U,X_21),implies(X_21,implies(U,X_21))))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(X_31,implies(implies(X_29,X_30),implies(X_30,implies(X_29,X_30))))),
inference(subst,[],[refute_0_21:[bind(U,$fot(X_29)),bind(X_21,$fot(X_30)),bind(X_24,$fot(X_31))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(X_31)
| is_a_theorem(implies(implies(X_29,X_30),implies(X_30,implies(X_29,X_30)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_31,implies(implies(X_29,X_30),implies(X_30,implies(X_29,X_30))))) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))),X),implies(U,X)))
| is_a_theorem(implies(implies(X_48,X_49),implies(X_49,implies(X_48,X_49)))) ),
inference(subst,[],[refute_0_23:[bind(X_29,$fot(X_48)),bind(X_30,$fot(X_49)),bind(X_31,$fot(implies(implies(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))),X),implies(U,X))))]]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(X_48,X_49),implies(X_49,implies(X_48,X_49)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))),X),implies(U,X))) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(X_51,X_52),implies(X_52,implies(X_51,X_52)))),
inference(subst,[],[refute_0_25:[bind(X_48,$fot(X_51)),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(implies(X_51,X_52))
| is_a_theorem(implies(X_52,implies(X_51,X_52))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_51,X_52),implies(X_52,implies(X_51,X_52)))) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(X_294,X_295),implies(X_295,X_295)),X_295),implies(X_293,X_295)),X_293),implies(X_292,X_293)))
| is_a_theorem(implies(implies(X_292,X_293),implies(implies(implies(implies(implies(implies(X_294,X_295),implies(X_295,X_295)),X_295),implies(X_293,X_295)),X_293),implies(X_292,X_293)))) ),
inference(subst,[],[refute_0_27:[bind(X_51,$fot(implies(implies(implies(implies(implies(X_294,X_295),implies(X_295,X_295)),X_295),implies(X_293,X_295)),X_293))),bind(X_52,$fot(implies(X_292,X_293)))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(X_106,X_108),implies(implies(implies(implies(X_107,X_108),implies(X_108,X_108)),X_108),implies(X_106,X_108))))
| is_a_theorem(implies(implies(implies(implies(implies(implies(X_107,X_108),implies(X_108,X_108)),X_108),implies(X_106,X_108)),X_106),implies(U,X_106))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_106)),bind(Y,$fot(X_108)),bind(Z,$fot(implies(implies(implies(implies(X_107,X_108),implies(X_108,X_108)),X_108),implies(X_106,X_108))))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_102,X_103),implies(X_103,X_103)),X_103),implies(X_101,X_103)))
| is_a_theorem(implies(implies(X_101,X_103),implies(implies(implies(implies(X_102,X_103),implies(X_103,X_103)),X_103),implies(X_101,X_103)))) ),
inference(subst,[],[refute_0_27:[bind(X_51,$fot(implies(implies(implies(X_102,X_103),implies(X_103,X_103)),X_103))),bind(X_52,$fot(implies(X_101,X_103)))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(X_99,X_99),implies(implies(X_100,X_99),implies(X_99,X_99))))
| is_a_theorem(implies(implies(implies(implies(X_100,X_99),implies(X_99,X_99)),X_99),implies(U,X_99))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_99)),bind(Y,$fot(X_99)),bind(Z,$fot(implies(implies(X_100,X_99),implies(X_99,X_99))))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(implies(implies(X_62,X_63),implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63))))
| is_a_theorem(implies(implies(implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63)),X_62),implies(U,X_62))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_62)),bind(Y,$fot(X_63)),bind(Z,$fot(implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63))))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(X_51,X_52),implies(X_52,implies(X_51,X_52))))
| is_a_theorem(implies(implies(implies(X_52,implies(X_51,X_52)),X_51),implies(U,X_51))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(implies(X_52,implies(X_51,X_52))))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(implies(X_52,implies(X_51,X_52)),X_51),implies(U,X_51))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_51,X_52),implies(X_52,implies(X_51,X_52)))) )],[refute_0_26,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(X_52,implies(X_51,X_52)),X_51),implies(U,X_51)))
| is_a_theorem(implies(implies(U,X_51),implies(implies(implies(X_52,implies(X_51,X_52)),X_51),implies(U,X_51)))) ),
inference(subst,[],[refute_0_27:[bind(X_51,$fot(implies(implies(X_52,implies(X_51,X_52)),X_51))),bind(X_52,$fot(implies(U,X_51)))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(implies(U,X_51),implies(implies(implies(X_52,implies(X_51,X_52)),X_51),implies(U,X_51)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_52,implies(X_51,X_52)),X_51),implies(U,X_51))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(implies(X_62,X_63),implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63)))),
inference(subst,[],[refute_0_36:[bind(U,$fot(X_62)),bind(X_51,$fot(X_63)),bind(X_52,$fot(X_64))]]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63)),X_62),implies(U,X_62))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_62,X_63),implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63)))) )],[refute_0_37,refute_0_32]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(X_28)
| ~ is_a_theorem(implies(X_28,implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26)))))
| is_a_theorem(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_28)),bind(Y,$fot(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26)))))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(X_28,implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))))),
inference(subst,[],[refute_0_15:[bind(X_12,$fot(X_26)),bind(X_14,$fot(X_27)),bind(X_24,$fot(X_28))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(X_28)
| is_a_theorem(implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_28,implies(implies(X_26,X_26),implies(implies(X_27,X_26),implies(X_26,X_26))))) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63)),X_62),implies(U,X_62)))
| is_a_theorem(implies(implies(X_96,X_96),implies(implies(X_97,X_96),implies(X_96,X_96)))) ),
inference(subst,[],[refute_0_41:[bind(X_26,$fot(X_96)),bind(X_27,$fot(X_97)),bind(X_28,$fot(implies(implies(implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63)),X_62),implies(U,X_62))))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(implies(implies(X_96,X_96),implies(implies(X_97,X_96),implies(X_96,X_96)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_64,implies(X_63,X_64)),X_63),implies(X_62,X_63)),X_62),implies(U,X_62))) )],[refute_0_38,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(implies(implies(X_99,X_99),implies(implies(X_100,X_99),implies(X_99,X_99)))),
inference(subst,[],[refute_0_43:[bind(X_96,$fot(X_99)),bind(X_97,$fot(X_100))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(implies(X_100,X_99),implies(X_99,X_99)),X_99),implies(U,X_99))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_99,X_99),implies(implies(X_100,X_99),implies(X_99,X_99)))) )],[refute_0_44,refute_0_31]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(implies(implies(implies(X_102,X_103),implies(X_103,X_103)),X_103),implies(X_101,X_103))),
inference(subst,[],[refute_0_45:[bind(U,$fot(X_101)),bind(X_100,$fot(X_102)),bind(X_99,$fot(X_103))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(implies(X_101,X_103),implies(implies(implies(implies(X_102,X_103),implies(X_103,X_103)),X_103),implies(X_101,X_103)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_102,X_103),implies(X_103,X_103)),X_103),implies(X_101,X_103))) )],[refute_0_46,refute_0_30]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(X_106,X_108),implies(implies(implies(implies(X_107,X_108),implies(X_108,X_108)),X_108),implies(X_106,X_108)))),
inference(subst,[],[refute_0_47:[bind(X_101,$fot(X_106)),bind(X_102,$fot(X_107)),bind(X_103,$fot(X_108))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_107,X_108),implies(X_108,X_108)),X_108),implies(X_106,X_108)),X_106),implies(U,X_106))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_106,X_108),implies(implies(implies(implies(X_107,X_108),implies(X_108,X_108)),X_108),implies(X_106,X_108)))) )],[refute_0_48,refute_0_29]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X_294,X_295),implies(X_295,X_295)),X_295),implies(X_293,X_295)),X_293),implies(X_292,X_293))),
inference(subst,[],[refute_0_49:[bind(U,$fot(X_292)),bind(X_106,$fot(X_293)),bind(X_107,$fot(X_294)),bind(X_108,$fot(X_295))]]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(X_292,X_293),implies(implies(implies(implies(implies(implies(X_294,X_295),implies(X_295,X_295)),X_295),implies(X_293,X_295)),X_293),implies(X_292,X_293)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(X_294,X_295),implies(X_295,X_295)),X_295),implies(X_293,X_295)),X_293),implies(X_292,X_293))) )],[refute_0_50,refute_0_28]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(implies(X_296,X_297),implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)))),
inference(subst,[],[refute_0_51:[bind(X_292,$fot(X_296)),bind(X_293,$fot(X_297)),bind(X_294,$fot(X_298)),bind(X_295,$fot(X_299))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_296,X_297),implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)))) )],[refute_0_52,refute_0_2]) ).
cnf(refute_0_54,plain,
( ~ is_a_theorem(X_734)
| ~ is_a_theorem(implies(X_734,implies(X_733,X_733)))
| is_a_theorem(implies(X_733,X_733)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_734)),bind(Y,$fot(implies(X_733,X_733)))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(implies(X_677,X_678),implies(X_677,X_678)))
| is_a_theorem(implies(implies(implies(X_677,X_678),X_677),implies(U,X_677))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_677)),bind(Y,$fot(X_678)),bind(Z,$fot(implies(X_677,X_678)))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(X_658,X_657))
| ~ is_a_theorem(implies(implies(X_658,X_657),implies(X_657,X_657)))
| is_a_theorem(implies(X_657,X_657)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X_658,X_657))),bind(Y,$fot(implies(X_657,X_657)))]]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(X_647)
| ~ is_a_theorem(implies(X_647,implies(implies(X_649,X_648),implies(X_648,X_648))))
| is_a_theorem(implies(implies(X_649,X_648),implies(X_648,X_648))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_647)),bind(Y,$fot(implies(implies(X_649,X_648),implies(X_648,X_648))))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(implies(X_642,X_642),X_297)),implies(X_642,X_642)),implies(implies(X_646,X_642),implies(X_642,X_642)))),
inference(subst,[],[refute_0_53:[bind(U,$fot(implies(X_646,X_642))),bind(X_296,$fot(implies(X_642,X_642)))]]) ).
cnf(refute_0_59,plain,
( ~ is_a_theorem(implies(implies(X_19,implies(X_17,X_18)),implies(implies(X_20,X_17),implies(X_16,X_17))))
| ~ is_a_theorem(implies(implies(implies(X_19,implies(X_17,X_18)),implies(implies(X_20,X_17),implies(X_16,X_17))),implies(X_15,implies(implies(X_20,X_17),implies(X_16,X_17)))))
| is_a_theorem(implies(X_15,implies(implies(X_20,X_17),implies(X_16,X_17)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_19,implies(X_17,X_18)),implies(implies(X_20,X_17),implies(X_16,X_17))))),bind(Y,$fot(implies(X_15,implies(implies(X_20,X_17),implies(X_16,X_17)))))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(implies(X_19,implies(X_17,X_18)),implies(implies(X_20,X_17),implies(X_16,X_17))),implies(X_15,implies(implies(X_20,X_17),implies(X_16,X_17))))),
inference(subst,[],[refute_0_10:[bind(U,$fot(X_15)),bind(X_10,$fot(X_16)),bind(X_11,$fot(X_17)),bind(X_12,$fot(X_18)),bind(X_13,$fot(X_19)),bind(X_14,$fot(X_20))]]) ).
cnf(refute_0_61,plain,
( ~ is_a_theorem(implies(implies(X_19,implies(X_17,X_18)),implies(implies(X_20,X_17),implies(X_16,X_17))))
| is_a_theorem(implies(X_15,implies(implies(X_20,X_17),implies(X_16,X_17)))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_19,implies(X_17,X_18)),implies(implies(X_20,X_17),implies(X_16,X_17))),implies(X_15,implies(implies(X_20,X_17),implies(X_16,X_17))))) )],[refute_0_60,refute_0_59]) ).
cnf(refute_0_62,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(implies(X_642,X_642),X_297)),implies(X_642,X_642)),implies(implies(X_646,X_642),implies(X_642,X_642))))
| is_a_theorem(implies(X_641,implies(implies(X_646,X_642),implies(X_642,X_642)))) ),
inference(subst,[],[refute_0_61:[bind(X_15,$fot(X_641)),bind(X_16,$fot(X_642)),bind(X_17,$fot(X_642)),bind(X_18,$fot(X_642)),bind(X_19,$fot(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(implies(X_642,X_642),X_297)))),bind(X_20,$fot(X_646))]]) ).
cnf(refute_0_63,plain,
is_a_theorem(implies(X_641,implies(implies(X_646,X_642),implies(X_642,X_642)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(implies(X_642,X_642),X_297)),implies(X_642,X_642)),implies(implies(X_646,X_642),implies(X_642,X_642)))) )],[refute_0_58,refute_0_62]) ).
cnf(refute_0_64,plain,
is_a_theorem(implies(X_647,implies(implies(X_649,X_648),implies(X_648,X_648)))),
inference(subst,[],[refute_0_63:[bind(X_641,$fot(X_647)),bind(X_642,$fot(X_648)),bind(X_646,$fot(X_649))]]) ).
cnf(refute_0_65,plain,
( ~ is_a_theorem(X_647)
| is_a_theorem(implies(implies(X_649,X_648),implies(X_648,X_648))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_647,implies(implies(X_649,X_648),implies(X_648,X_648)))) )],[refute_0_64,refute_0_57]) ).
cnf(refute_0_66,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296)))
| is_a_theorem(implies(implies(X_656,X_655),implies(X_655,X_655))) ),
inference(subst,[],[refute_0_65:[bind(X_647,$fot(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296)))),bind(X_648,$fot(X_655)),bind(X_649,$fot(X_656))]]) ).
cnf(refute_0_67,plain,
is_a_theorem(implies(implies(X_656,X_655),implies(X_655,X_655))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296))) )],[refute_0_53,refute_0_66]) ).
cnf(refute_0_68,plain,
is_a_theorem(implies(implies(X_658,X_657),implies(X_657,X_657))),
inference(subst,[],[refute_0_67:[bind(X_655,$fot(X_657)),bind(X_656,$fot(X_658))]]) ).
cnf(refute_0_69,plain,
( ~ is_a_theorem(implies(X_658,X_657))
| is_a_theorem(implies(X_657,X_657)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_658,X_657),implies(X_657,X_657))) )],[refute_0_68,refute_0_56]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296)))
| is_a_theorem(implies(implies(U,X_296),implies(U,X_296))) ),
inference(subst,[],[refute_0_69:[bind(X_657,$fot(implies(U,X_296))),bind(X_658,$fot(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296)))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(implies(U,X_296),implies(U,X_296))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296))) )],[refute_0_53,refute_0_70]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(implies(X_677,X_678),implies(X_677,X_678))),
inference(subst,[],[refute_0_71:[bind(U,$fot(X_677)),bind(X_296,$fot(X_678))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(implies(implies(X_677,X_678),X_677),implies(U,X_677))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_677,X_678),implies(X_677,X_678))) )],[refute_0_72,refute_0_55]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(implies(implies(X_678,X_678),X_678),implies(X_678,X_678))),
inference(subst,[],[refute_0_73:[bind(U,$fot(X_678)),bind(X_677,$fot(X_678))]]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(X_680,X_681),X_680))
| ~ is_a_theorem(implies(implies(implies(X_680,X_681),X_680),implies(X_679,X_680)))
| is_a_theorem(implies(X_679,X_680)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_680,X_681),X_680))),bind(Y,$fot(implies(X_679,X_680)))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(implies(X_680,X_681),X_680),implies(X_679,X_680))),
inference(subst,[],[refute_0_73:[bind(U,$fot(X_679)),bind(X_677,$fot(X_680)),bind(X_678,$fot(X_681))]]) ).
cnf(refute_0_77,plain,
( ~ is_a_theorem(implies(implies(X_680,X_681),X_680))
| is_a_theorem(implies(X_679,X_680)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_680,X_681),X_680),implies(X_679,X_680))) )],[refute_0_76,refute_0_75]) ).
cnf(refute_0_78,plain,
( ~ is_a_theorem(implies(implies(implies(X_678,X_678),X_678),implies(X_678,X_678)))
| is_a_theorem(implies(X_730,implies(X_678,X_678))) ),
inference(subst,[],[refute_0_77:[bind(X_679,$fot(X_730)),bind(X_680,$fot(implies(X_678,X_678))),bind(X_681,$fot(X_678))]]) ).
cnf(refute_0_79,plain,
is_a_theorem(implies(X_730,implies(X_678,X_678))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_678,X_678),X_678),implies(X_678,X_678))) )],[refute_0_74,refute_0_78]) ).
cnf(refute_0_80,plain,
is_a_theorem(implies(X_734,implies(X_733,X_733))),
inference(subst,[],[refute_0_79:[bind(X_678,$fot(X_733)),bind(X_730,$fot(X_734))]]) ).
cnf(refute_0_81,plain,
( ~ is_a_theorem(X_734)
| is_a_theorem(implies(X_733,X_733)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_734,implies(X_733,X_733))) )],[refute_0_80,refute_0_54]) ).
cnf(refute_0_82,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296)))
| is_a_theorem(implies(X_735,X_735)) ),
inference(subst,[],[refute_0_81:[bind(X_733,$fot(X_735)),bind(X_734,$fot(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296))))]]) ).
cnf(refute_0_83,plain,
is_a_theorem(implies(X_735,X_735)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(X_298,X_299),implies(X_299,X_299)),X_299),implies(X_297,X_299)),X_297),implies(X_296,X_297)),X_296),implies(U,X_296))) )],[refute_0_53,refute_0_82]) ).
cnf(refute_0_84,plain,
is_a_theorem(implies(a,a)),
inference(subst,[],[refute_0_83:[bind(X_735,$fot(a))]]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,a)) )],[refute_0_84,prove_ic_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL081-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 10:08:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.57
% 0.41/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.41/0.58
%------------------------------------------------------------------------------