TSTP Solution File: LCL112-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL112-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:49:38 EDT 2022
% Result : Unsatisfiable 1.07s 1.24s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of clauses : 82 ( 45 unt; 0 nHn; 31 RR)
% Number of literals : 129 ( 0 equ; 48 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; 1 con; 0-2 aty)
% Number of variables : 195 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(mv_1,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(mv_2,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(mv_3,axiom,
is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) ).
cnf(mv_5,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).
cnf(prove_mv_29,negated_conjecture,
~ is_a_theorem(implies(a,not(not(a)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(implies(not(X),not(Y)))
| is_a_theorem(implies(Y,X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[mv_5,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(not(not(not(Y))),not(Y)))
| is_a_theorem(implies(Y,not(not(Y)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X_79,X_80),X_81))
| ~ is_a_theorem(implies(implies(implies(X_79,X_80),X_81),implies(X_80,X_81)))
| is_a_theorem(implies(X_80,X_81)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_79,X_80),X_81))),bind(Y,$fot(implies(X_80,X_81)))]]) ).
cnf(refute_0_4,plain,
is_a_theorem(implies(X_65,implies(Y,X_65))),
inference(subst,[],[mv_1:[bind(X,$fot(X_65))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[mv_2,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(X_65,implies(Y,X_65)))
| is_a_theorem(implies(implies(implies(Y,X_65),X_67),implies(X_65,X_67))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_65)),bind(Y,$fot(implies(Y,X_65))),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(Y,X_65),X_67),implies(X_65,X_67))),
inference(resolve,[$cnf( is_a_theorem(implies(X_65,implies(Y,X_65))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(implies(X_79,X_80),X_81),implies(X_80,X_81))),
inference(subst,[],[refute_0_8:[bind(Y,$fot(X_79)),bind(X_65,$fot(X_80)),bind(X_67,$fot(X_81))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(implies(implies(X_79,X_80),X_81))
| is_a_theorem(implies(X_80,X_81)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_79,X_80),X_81),implies(X_80,X_81))) )],[refute_0_9,refute_0_3]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(X_2496,X_2496))),not(not(X_2495))),X_2495))
| is_a_theorem(implies(not(not(X_2495)),X_2495)) ),
inference(subst,[],[refute_0_10:[bind(X_79,$fot(not(not(implies(X_2496,X_2496))))),bind(X_80,$fot(not(not(X_2495)))),bind(X_81,$fot(X_2495))]]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(implies(implies(X_338,X_338),X_337))
| ~ is_a_theorem(implies(implies(implies(X_338,X_338),X_337),X_337))
| is_a_theorem(X_337) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_338,X_338),X_337))),bind(Y,$fot(X_337))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(implies(implies(X,Y),Y))
| ~ is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))
| is_a_theorem(implies(implies(Y,X),X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X,Y),Y))),bind(Y,$fot(implies(implies(Y,X),X)))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(implies(X,Y),Y))
| is_a_theorem(implies(implies(Y,X),X)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) )],[mv_3,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(X,implies(X_333,X_333)),implies(X_333,X_333)))
| is_a_theorem(implies(implies(implies(X_333,X_333),X),X)) ),
inference(subst,[],[refute_0_14:[bind(Y,$fot(implies(X_333,X_333)))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(X_9,implies(Y,X_9))),
inference(subst,[],[mv_1:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(X_9)
| ~ is_a_theorem(implies(X_9,implies(Y,X_9)))
| is_a_theorem(implies(Y,X_9)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_9)),bind(Y,$fot(implies(Y,X_9)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(X_9)
| is_a_theorem(implies(Y,X_9)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_9,implies(Y,X_9))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(implies(X_331,X_331))
| is_a_theorem(implies(Y,implies(X_331,X_331))) ),
inference(subst,[],[refute_0_18:[bind(X_9,$fot(implies(X_331,X_331)))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))
| is_a_theorem(implies(X_11,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(X_11,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))) )],[mv_3,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(X_37,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))),implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))),
inference(subst,[],[refute_0_21:[bind(X_11,$fot(implies(X_37,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(X_37,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))),implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))))
| is_a_theorem(implies(implies(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)),X_37),X_37)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_37)),bind(Y,$fot(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))))]]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)),X_37),X_37)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_37,implies(implies(implies(X,Y),Y),implies(implies(Y,X),X))),implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)),X_330),X_330)),
inference(subst,[],[refute_0_24:[bind(X_37,$fot(X_330))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)),X_330),X_330))
| is_a_theorem(implies(X_330,X_330)) ),
inference(subst,[],[refute_0_10:[bind(X_79,$fot(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))),bind(X_80,$fot(X_330)),bind(X_81,$fot(X_330))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(X_330,X_330)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)),X_330),X_330)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(X_331,X_331)),
inference(subst,[],[refute_0_27:[bind(X_330,$fot(X_331))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(Y,implies(X_331,X_331))),
inference(resolve,[$cnf( is_a_theorem(implies(X_331,X_331)) )],[refute_0_28,refute_0_19]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(implies(X,implies(X_333,X_333)),implies(X_333,X_333))),
inference(subst,[],[refute_0_29:[bind(Y,$fot(implies(X,implies(X_333,X_333)))),bind(X_331,$fot(X_333))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(implies(implies(X_333,X_333),X),X)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,implies(X_333,X_333)),implies(X_333,X_333))) )],[refute_0_30,refute_0_15]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(X_338,X_338),X_337),X_337)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_337)),bind(X_333,$fot(X_338))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(X_338,X_338),X_337))
| is_a_theorem(X_337) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_338,X_338),X_337),X_337)) )],[refute_0_32,refute_0_12]) ).
cnf(refute_0_34,plain,
( ~ is_a_theorem(implies(implies(X_338,X_338),implies(implies(not(X_947),not(implies(X_338,X_338))),X_947)))
| is_a_theorem(implies(implies(not(X_947),not(implies(X_338,X_338))),X_947)) ),
inference(subst,[],[refute_0_33:[bind(X_337,$fot(implies(implies(not(X_947),not(implies(X_338,X_338))),X_947)))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_46),not(X_47)),implies(X_47,X_46)),X_48),X_48))
| ~ is_a_theorem(implies(implies(implies(not(X_46),not(X_47)),implies(X_47,X_46)),X_48))
| is_a_theorem(X_48) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_46),not(X_47)),implies(X_47,X_46)),X_48))),bind(Y,$fot(X_48))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(X_11,implies(implies(not(X),not(Y)),implies(Y,X)))) ),
inference(subst,[],[refute_0_18:[bind(Y,$fot(X_11)),bind(X_9,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_11,implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[mv_5,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(X_37,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X)))),
inference(subst,[],[refute_0_37:[bind(X_11,$fot(implies(X_37,implies(implies(not(X),not(Y)),implies(Y,X)))))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(implies(implies(X_37,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X))))
| is_a_theorem(implies(implies(implies(implies(not(X),not(Y)),implies(Y,X)),X_37),X_37)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(X_37)),bind(Y,$fot(implies(implies(not(X),not(Y)),implies(Y,X))))]]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(implies(implies(not(X),not(Y)),implies(Y,X)),X_37),X_37)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_37,implies(implies(not(X),not(Y)),implies(Y,X))),implies(implies(not(X),not(Y)),implies(Y,X)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(implies(implies(not(X_46),not(X_47)),implies(X_47,X_46)),X_48),X_48)),
inference(subst,[],[refute_0_40:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(X_37,$fot(X_48))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_46),not(X_47)),implies(X_47,X_46)),X_48))
| is_a_theorem(X_48) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_46),not(X_47)),implies(X_47,X_46)),X_48),X_48)) )],[refute_0_41,refute_0_35]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_945),not(X_943)),implies(X_943,X_945)),implies(X_943,implies(implies(not(X_945),not(X_943)),X_945))))
| is_a_theorem(implies(X_943,implies(implies(not(X_945),not(X_943)),X_945))) ),
inference(subst,[],[refute_0_42:[bind(X_46,$fot(X_945)),bind(X_47,$fot(X_943)),bind(X_48,$fot(implies(X_943,implies(implies(not(X_945),not(X_943)),X_945))))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(X_340,implies(implies(X_340,X_339),X_339)))
| is_a_theorem(implies(implies(implies(implies(X_340,X_339),X_339),Z),implies(X_340,Z))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_340)),bind(Y,$fot(implies(implies(X_340,X_339),X_339)))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(implies(implies(X,X_329),X_329),implies(implies(X_329,X),X))),
inference(subst,[],[mv_3:[bind(Y,$fot(X_329))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(implies(implies(implies(X,X_329),X_329),implies(implies(X_329,X),X)))
| is_a_theorem(implies(X_329,implies(implies(X_329,X),X))) ),
inference(subst,[],[refute_0_10:[bind(X_79,$fot(implies(X,X_329))),bind(X_80,$fot(X_329)),bind(X_81,$fot(implies(implies(X_329,X),X)))]]) ).
cnf(refute_0_47,plain,
is_a_theorem(implies(X_329,implies(implies(X_329,X),X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,X_329),X_329),implies(implies(X_329,X),X))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(X_340,implies(implies(X_340,X_339),X_339))),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_339)),bind(X_329,$fot(X_340))]]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(implies(X_340,X_339),X_339),Z),implies(X_340,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_340,implies(implies(X_340,X_339),X_339))) )],[refute_0_48,refute_0_44]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(implies(implies(X_340,X_908),X_908),implies(X_906,X_908)),implies(X_340,implies(X_906,X_908)))),
inference(subst,[],[refute_0_49:[bind(Z,$fot(implies(X_906,X_908))),bind(X_339,$fot(X_908))]]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(implies(X_87,X_88),implies(X_86,X_88)),X_89))
| ~ is_a_theorem(implies(implies(implies(implies(X_87,X_88),implies(X_86,X_88)),X_89),implies(implies(X_86,X_87),X_89)))
| is_a_theorem(implies(implies(X_86,X_87),X_89)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_87,X_88),implies(X_86,X_88)),X_89))),bind(Y,$fot(implies(implies(X_86,X_87),X_89)))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_67),implies(implies(X,Y),X_67))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_67),implies(implies(X,Y),X_67))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[mv_2,refute_0_52]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(implies(X_87,X_88),implies(X_86,X_88)),X_89),implies(implies(X_86,X_87),X_89))),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_86)),bind(Y,$fot(X_87)),bind(Z,$fot(X_88)),bind(X_67,$fot(X_89))]]) ).
cnf(refute_0_55,plain,
( ~ is_a_theorem(implies(implies(implies(X_87,X_88),implies(X_86,X_88)),X_89))
| is_a_theorem(implies(implies(X_86,X_87),X_89)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_87,X_88),implies(X_86,X_88)),X_89),implies(implies(X_86,X_87),X_89))) )],[refute_0_54,refute_0_51]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_340,X_908),X_908),implies(X_906,X_908)),implies(X_340,implies(X_906,X_908))))
| is_a_theorem(implies(implies(X_906,implies(X_340,X_908)),implies(X_340,implies(X_906,X_908)))) ),
inference(subst,[],[refute_0_55:[bind(X_86,$fot(X_906)),bind(X_87,$fot(implies(X_340,X_908))),bind(X_88,$fot(X_908)),bind(X_89,$fot(implies(X_340,implies(X_906,X_908))))]]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(X_906,implies(X_340,X_908)),implies(X_340,implies(X_906,X_908)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_340,X_908),X_908),implies(X_906,X_908)),implies(X_340,implies(X_906,X_908)))) )],[refute_0_50,refute_0_56]) ).
cnf(refute_0_58,plain,
is_a_theorem(implies(implies(implies(not(X_945),not(X_943)),implies(X_943,X_945)),implies(X_943,implies(implies(not(X_945),not(X_943)),X_945)))),
inference(subst,[],[refute_0_57:[bind(X_340,$fot(X_943)),bind(X_906,$fot(implies(not(X_945),not(X_943)))),bind(X_908,$fot(X_945))]]) ).
cnf(refute_0_59,plain,
is_a_theorem(implies(X_943,implies(implies(not(X_945),not(X_943)),X_945))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_945),not(X_943)),implies(X_943,X_945)),implies(X_943,implies(implies(not(X_945),not(X_943)),X_945)))) )],[refute_0_58,refute_0_43]) ).
cnf(refute_0_60,plain,
is_a_theorem(implies(implies(X_338,X_338),implies(implies(not(X_947),not(implies(X_338,X_338))),X_947))),
inference(subst,[],[refute_0_59:[bind(X_943,$fot(implies(X_338,X_338))),bind(X_945,$fot(X_947))]]) ).
cnf(refute_0_61,plain,
is_a_theorem(implies(implies(not(X_947),not(implies(X_338,X_338))),X_947)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_338,X_338),implies(implies(not(X_947),not(implies(X_338,X_338))),X_947))) )],[refute_0_60,refute_0_34]) ).
cnf(refute_0_62,plain,
is_a_theorem(implies(implies(not(X_2450),not(implies(X_338,X_338))),X_2450)),
inference(subst,[],[refute_0_61:[bind(X_947,$fot(X_2450))]]) ).
cnf(refute_0_63,plain,
( ~ is_a_theorem(implies(implies(X_77,X_76),X_78))
| ~ is_a_theorem(implies(implies(implies(X_77,X_76),X_78),implies(implies(not(X_76),not(X_77)),X_78)))
| is_a_theorem(implies(implies(not(X_76),not(X_77)),X_78)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_77,X_76),X_78))),bind(Y,$fot(implies(implies(not(X_76),not(X_77)),X_78)))]]) ).
cnf(refute_0_64,plain,
( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
| is_a_theorem(implies(implies(implies(Y,X),X_67),implies(implies(not(X),not(Y)),X_67))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X))),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_65,plain,
is_a_theorem(implies(implies(implies(Y,X),X_67),implies(implies(not(X),not(Y)),X_67))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[mv_5,refute_0_64]) ).
cnf(refute_0_66,plain,
is_a_theorem(implies(implies(implies(X_77,X_76),X_78),implies(implies(not(X_76),not(X_77)),X_78))),
inference(subst,[],[refute_0_65:[bind(X,$fot(X_76)),bind(Y,$fot(X_77)),bind(X_67,$fot(X_78))]]) ).
cnf(refute_0_67,plain,
( ~ is_a_theorem(implies(implies(X_77,X_76),X_78))
| is_a_theorem(implies(implies(not(X_76),not(X_77)),X_78)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_77,X_76),X_78),implies(implies(not(X_76),not(X_77)),X_78))) )],[refute_0_66,refute_0_63]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(not(X_2450),not(implies(X_338,X_338))),X_2450))
| is_a_theorem(implies(implies(not(not(implies(X_338,X_338))),not(not(X_2450))),X_2450)) ),
inference(subst,[],[refute_0_67:[bind(X_76,$fot(not(implies(X_338,X_338)))),bind(X_77,$fot(not(X_2450))),bind(X_78,$fot(X_2450))]]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(not(not(implies(X_338,X_338))),not(not(X_2450))),X_2450)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X_2450),not(implies(X_338,X_338))),X_2450)) )],[refute_0_62,refute_0_68]) ).
cnf(refute_0_70,plain,
is_a_theorem(implies(implies(not(not(implies(X_2496,X_2496))),not(not(X_2495))),X_2495)),
inference(subst,[],[refute_0_69:[bind(X_2450,$fot(X_2495)),bind(X_338,$fot(X_2496))]]) ).
cnf(refute_0_71,plain,
is_a_theorem(implies(not(not(X_2495)),X_2495)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(not(not(implies(X_2496,X_2496))),not(not(X_2495))),X_2495)) )],[refute_0_70,refute_0_11]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(not(not(not(Y))),not(Y))),
inference(subst,[],[refute_0_71:[bind(X_2495,$fot(not(Y)))]]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(Y,not(not(Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(Y))),not(Y))) )],[refute_0_72,refute_0_2]) ).
cnf(refute_0_74,plain,
is_a_theorem(implies(a,not(not(a)))),
inference(subst,[],[refute_0_73:[bind(Y,$fot(a))]]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,not(not(a)))) )],[refute_0_74,prove_mv_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL112-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 17:18:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.07/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/1.24
% 1.07/1.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.07/1.25
%------------------------------------------------------------------------------