TSTP Solution File: SWC219+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC219+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n020.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  : 300s
% DateTime : Wed Aug 31 18:39:41 EDT 2022

% Result   : Theorem 1.45s 0.55s
% Output   : Refutation 1.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   62 (  10 unt;   0 def)
%            Number of atoms       :  531 ( 155 equ)
%            Maximal formula atoms :   50 (   8 avg)
%            Number of connectives :  710 ( 241   ~; 221   |; 218   &)
%                                         (   3 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :  168 ( 104   !;  64   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f302,plain,
    $false,
    inference(avatar_sat_refutation,[],[f238,f248,f261,f301]) ).

fof(f301,plain,
    ( ~ spl12_2
    | ~ spl12_3 ),
    inference(avatar_contradiction_clause,[],[f300]) ).

fof(f300,plain,
    ( $false
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f299,f292]) ).

fof(f292,plain,
    ( ssItem(sK10(sK11,nil,nil))
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f291,f166]) ).

fof(f166,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f291,plain,
    ( ~ ssList(nil)
    | ssItem(sK10(sK11,nil,nil))
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(trivial_inequality_removal,[],[f290]) ).

fof(f290,plain,
    ( sK8 != sK8
    | ~ ssList(nil)
    | ssItem(sK10(sK11,nil,nil))
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(superposition,[],[f287,f275]) ).

fof(f275,plain,
    app(sK8,nil) = sK8,
    inference(resolution,[],[f163,f202]) ).

fof(f202,plain,
    ssList(sK8),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ( ssList(sK8)
    & sK9 = sK7
    & nil != sK6
    & sK6 = sK8
    & ! [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( app(app(X5,cons(X4,nil)),X6) != sK6
                | ~ ssList(X6)
                | ( leq(X4,sK10(X4,X5,X6))
                  & ssItem(sK10(X4,X5,X6))
                  & memberP(X6,sK10(X4,X5,X6))
                  & ~ leq(sK10(X4,X5,X6),X4)
                  & memberP(X5,sK10(X4,X5,X6)) ) )
            | ~ ssList(X5) )
        | ~ ssItem(X4) )
    & ssList(sK9)
    & ( ( ssItem(sK11)
        & ! [X9] :
            ( sK11 = X9
            | ~ memberP(sK9,X9)
            | ~ ssItem(X9)
            | ~ leq(X9,sK11) )
        & cons(sK11,nil) = sK8
        & memberP(sK9,sK11) )
      | ( nil = sK9
        & nil = sK8 ) )
    & ssList(sK7)
    & ssList(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11])],[f141,f147,f146,f145,f144,f143,f142]) ).

fof(f142,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X1 = X3
                    & nil != X0
                    & X0 = X2
                    & ! [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( app(app(X5,cons(X4,nil)),X6) != X0
                                | ~ ssList(X6)
                                | ? [X7] :
                                    ( leq(X4,X7)
                                    & ssItem(X7)
                                    & memberP(X6,X7)
                                    & ~ leq(X7,X4)
                                    & memberP(X5,X7) ) )
                            | ~ ssList(X5) )
                        | ~ ssItem(X4) )
                    & ssList(X3)
                    & ( ? [X8] :
                          ( ssItem(X8)
                          & ! [X9] :
                              ( X8 = X9
                              | ~ memberP(X3,X9)
                              | ~ ssItem(X9)
                              | ~ leq(X9,X8) )
                          & cons(X8,nil) = X2
                          & memberP(X3,X8) )
                      | ( nil = X3
                        & nil = X2 ) ) ) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & nil != sK6
                  & sK6 = X2
                  & ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( app(app(X5,cons(X4,nil)),X6) != sK6
                              | ~ ssList(X6)
                              | ? [X7] :
                                  ( leq(X4,X7)
                                  & ssItem(X7)
                                  & memberP(X6,X7)
                                  & ~ leq(X7,X4)
                                  & memberP(X5,X7) ) )
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & ssList(X3)
                  & ( ? [X8] :
                        ( ssItem(X8)
                        & ! [X9] :
                            ( X8 = X9
                            | ~ memberP(X3,X9)
                            | ~ ssItem(X9)
                            | ~ leq(X9,X8) )
                        & cons(X8,nil) = X2
                        & memberP(X3,X8) )
                    | ( nil = X3
                      & nil = X2 ) ) ) )
          & ssList(X1) )
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( X1 = X3
                & nil != sK6
                & sK6 = X2
                & ! [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( app(app(X5,cons(X4,nil)),X6) != sK6
                            | ~ ssList(X6)
                            | ? [X7] :
                                ( leq(X4,X7)
                                & ssItem(X7)
                                & memberP(X6,X7)
                                & ~ leq(X7,X4)
                                & memberP(X5,X7) ) )
                        | ~ ssList(X5) )
                    | ~ ssItem(X4) )
                & ssList(X3)
                & ( ? [X8] :
                      ( ssItem(X8)
                      & ! [X9] :
                          ( X8 = X9
                          | ~ memberP(X3,X9)
                          | ~ ssItem(X9)
                          | ~ leq(X9,X8) )
                      & cons(X8,nil) = X2
                      & memberP(X3,X8) )
                  | ( nil = X3
                    & nil = X2 ) ) ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK7 = X3
              & nil != sK6
              & sK6 = X2
              & ! [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( app(app(X5,cons(X4,nil)),X6) != sK6
                          | ~ ssList(X6)
                          | ? [X7] :
                              ( leq(X4,X7)
                              & ssItem(X7)
                              & memberP(X6,X7)
                              & ~ leq(X7,X4)
                              & memberP(X5,X7) ) )
                      | ~ ssList(X5) )
                  | ~ ssItem(X4) )
              & ssList(X3)
              & ( ? [X8] :
                    ( ssItem(X8)
                    & ! [X9] :
                        ( X8 = X9
                        | ~ memberP(X3,X9)
                        | ~ ssItem(X9)
                        | ~ leq(X9,X8) )
                    & cons(X8,nil) = X2
                    & memberP(X3,X8) )
                | ( nil = X3
                  & nil = X2 ) ) ) )
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK7 = X3
            & nil != sK6
            & sK6 = X2
            & ! [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( app(app(X5,cons(X4,nil)),X6) != sK6
                        | ~ ssList(X6)
                        | ? [X7] :
                            ( leq(X4,X7)
                            & ssItem(X7)
                            & memberP(X6,X7)
                            & ~ leq(X7,X4)
                            & memberP(X5,X7) ) )
                    | ~ ssList(X5) )
                | ~ ssItem(X4) )
            & ssList(X3)
            & ( ? [X8] :
                  ( ssItem(X8)
                  & ! [X9] :
                      ( X8 = X9
                      | ~ memberP(X3,X9)
                      | ~ ssItem(X9)
                      | ~ leq(X9,X8) )
                  & cons(X8,nil) = X2
                  & memberP(X3,X8) )
              | ( nil = X3
                & nil = X2 ) ) ) )
   => ( ssList(sK8)
      & ? [X3] :
          ( sK7 = X3
          & nil != sK6
          & sK6 = sK8
          & ! [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( app(app(X5,cons(X4,nil)),X6) != sK6
                      | ~ ssList(X6)
                      | ? [X7] :
                          ( leq(X4,X7)
                          & ssItem(X7)
                          & memberP(X6,X7)
                          & ~ leq(X7,X4)
                          & memberP(X5,X7) ) )
                  | ~ ssList(X5) )
              | ~ ssItem(X4) )
          & ssList(X3)
          & ( ? [X8] :
                ( ssItem(X8)
                & ! [X9] :
                    ( X8 = X9
                    | ~ memberP(X3,X9)
                    | ~ ssItem(X9)
                    | ~ leq(X9,X8) )
                & cons(X8,nil) = sK8
                & memberP(X3,X8) )
            | ( nil = X3
              & nil = sK8 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ( ? [X3] :
        ( sK7 = X3
        & nil != sK6
        & sK6 = sK8
        & ! [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( app(app(X5,cons(X4,nil)),X6) != sK6
                    | ~ ssList(X6)
                    | ? [X7] :
                        ( leq(X4,X7)
                        & ssItem(X7)
                        & memberP(X6,X7)
                        & ~ leq(X7,X4)
                        & memberP(X5,X7) ) )
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ssList(X3)
        & ( ? [X8] :
              ( ssItem(X8)
              & ! [X9] :
                  ( X8 = X9
                  | ~ memberP(X3,X9)
                  | ~ ssItem(X9)
                  | ~ leq(X9,X8) )
              & cons(X8,nil) = sK8
              & memberP(X3,X8) )
          | ( nil = X3
            & nil = sK8 ) ) )
   => ( sK9 = sK7
      & nil != sK6
      & sK6 = sK8
      & ! [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( app(app(X5,cons(X4,nil)),X6) != sK6
                  | ~ ssList(X6)
                  | ? [X7] :
                      ( leq(X4,X7)
                      & ssItem(X7)
                      & memberP(X6,X7)
                      & ~ leq(X7,X4)
                      & memberP(X5,X7) ) )
              | ~ ssList(X5) )
          | ~ ssItem(X4) )
      & ssList(sK9)
      & ( ? [X8] :
            ( ssItem(X8)
            & ! [X9] :
                ( X8 = X9
                | ~ memberP(sK9,X9)
                | ~ ssItem(X9)
                | ~ leq(X9,X8) )
            & cons(X8,nil) = sK8
            & memberP(sK9,X8) )
        | ( nil = sK9
          & nil = sK8 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ! [X4,X5,X6] :
      ( ? [X7] :
          ( leq(X4,X7)
          & ssItem(X7)
          & memberP(X6,X7)
          & ~ leq(X7,X4)
          & memberP(X5,X7) )
     => ( leq(X4,sK10(X4,X5,X6))
        & ssItem(sK10(X4,X5,X6))
        & memberP(X6,sK10(X4,X5,X6))
        & ~ leq(sK10(X4,X5,X6),X4)
        & memberP(X5,sK10(X4,X5,X6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ( ? [X8] :
        ( ssItem(X8)
        & ! [X9] :
            ( X8 = X9
            | ~ memberP(sK9,X9)
            | ~ ssItem(X9)
            | ~ leq(X9,X8) )
        & cons(X8,nil) = sK8
        & memberP(sK9,X8) )
   => ( ssItem(sK11)
      & ! [X9] :
          ( sK11 = X9
          | ~ memberP(sK9,X9)
          | ~ ssItem(X9)
          | ~ leq(X9,sK11) )
      & cons(sK11,nil) = sK8
      & memberP(sK9,sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f141,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & nil != X0
                  & X0 = X2
                  & ! [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( app(app(X5,cons(X4,nil)),X6) != X0
                              | ~ ssList(X6)
                              | ? [X7] :
                                  ( leq(X4,X7)
                                  & ssItem(X7)
                                  & memberP(X6,X7)
                                  & ~ leq(X7,X4)
                                  & memberP(X5,X7) ) )
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & ssList(X3)
                  & ( ? [X8] :
                        ( ssItem(X8)
                        & ! [X9] :
                            ( X8 = X9
                            | ~ memberP(X3,X9)
                            | ~ ssItem(X9)
                            | ~ leq(X9,X8) )
                        & cons(X8,nil) = X2
                        & memberP(X3,X8) )
                    | ( nil = X3
                      & nil = X2 ) ) ) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(rectify,[],[f107]) ).

fof(f107,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & nil != X0
                  & X0 = X2
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( app(app(X7,cons(X6,nil)),X8) != X0
                              | ~ ssList(X8)
                              | ? [X9] :
                                  ( leq(X6,X9)
                                  & ssItem(X9)
                                  & memberP(X8,X9)
                                  & ~ leq(X9,X6)
                                  & memberP(X7,X9) ) )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & ssList(X3)
                  & ( ? [X4] :
                        ( ssItem(X4)
                        & ! [X5] :
                            ( X4 = X5
                            | ~ memberP(X3,X5)
                            | ~ ssItem(X5)
                            | ~ leq(X5,X4) )
                        & cons(X4,nil) = X2
                        & memberP(X3,X4) )
                    | ( nil = X3
                      & nil = X2 ) ) ) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f106]) ).

fof(f106,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & ( ? [X4] :
                        ( ! [X5] :
                            ( X4 = X5
                            | ~ memberP(X3,X5)
                            | ~ ssItem(X5)
                            | ~ leq(X5,X4) )
                        & memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) )
                    | ( nil = X3
                      & nil = X2 ) )
                  & nil != X0
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ! [X7] :
                          ( ! [X8] :
                              ( app(app(X7,cons(X6,nil)),X8) != X0
                              | ? [X9] :
                                  ( leq(X6,X9)
                                  & ~ leq(X9,X6)
                                  & memberP(X8,X9)
                                  & memberP(X7,X9)
                                  & ssItem(X9) )
                              | ~ ssList(X8) )
                          | ~ ssList(X7) ) )
                  & X0 = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X1 != X3
                      | ( ! [X4] :
                            ( ssItem(X4)
                           => ( ? [X5] :
                                  ( leq(X5,X4)
                                  & ssItem(X5)
                                  & memberP(X3,X5)
                                  & X4 != X5 )
                              | ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) )
                        & ( nil != X3
                          | nil != X2 ) )
                      | nil = X0
                      | ? [X6] :
                          ( ssItem(X6)
                          & ? [X7] :
                              ( ? [X8] :
                                  ( app(app(X7,cons(X6,nil)),X8) = X0
                                  & ! [X9] :
                                      ( ssItem(X9)
                                     => ( ~ leq(X6,X9)
                                        | leq(X9,X6)
                                        | ~ memberP(X8,X9)
                                        | ~ memberP(X7,X9) ) )
                                  & ssList(X8) )
                              & ssList(X7) ) )
                      | X0 != X2 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ! [X8] :
                            ( ssItem(X8)
                           => ( cons(X8,nil) != X2
                              | ~ memberP(X3,X8)
                              | ? [X9] :
                                  ( X8 != X9
                                  & leq(X9,X8)
                                  & ssItem(X9)
                                  & memberP(X3,X9) ) ) )
                        & ( nil != X3
                          | nil != X2 ) )
                      | X1 != X3
                      | X0 != X2
                      | ? [X4] :
                          ( ssItem(X4)
                          & ? [X5] :
                              ( ssList(X5)
                              & ? [X6] :
                                  ( app(app(X5,cons(X4,nil)),X6) = X0
                                  & ! [X7] :
                                      ( ssItem(X7)
                                     => ( ~ memberP(X5,X7)
                                        | ~ memberP(X6,X7)
                                        | ~ leq(X4,X7)
                                        | leq(X7,X4) ) )
                                  & ssList(X6) ) ) )
                      | nil = X0 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ! [X8] :
                          ( ssItem(X8)
                         => ( cons(X8,nil) != X2
                            | ~ memberP(X3,X8)
                            | ? [X9] :
                                ( X8 != X9
                                & leq(X9,X8)
                                & ssItem(X9)
                                & memberP(X3,X9) ) ) )
                      & ( nil != X3
                        | nil != X2 ) )
                    | X1 != X3
                    | X0 != X2
                    | ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( app(app(X5,cons(X4,nil)),X6) = X0
                                & ! [X7] :
                                    ( ssItem(X7)
                                   => ( ~ memberP(X5,X7)
                                      | ~ memberP(X6,X7)
                                      | ~ leq(X4,X7)
                                      | leq(X7,X4) ) )
                                & ssList(X6) ) ) )
                    | nil = X0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f163,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

fof(f287,plain,
    ( ! [X4] :
        ( app(sK8,X4) != sK8
        | ~ ssList(X4)
        | ssItem(sK10(sK11,nil,X4)) )
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f284,f166]) ).

fof(f284,plain,
    ( ! [X4] :
        ( ~ ssList(X4)
        | ~ ssList(nil)
        | ssItem(sK10(sK11,nil,X4))
        | app(sK8,X4) != sK8 )
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(superposition,[],[f263,f278]) ).

fof(f278,plain,
    app(nil,sK8) = sK8,
    inference(resolution,[],[f175,f202]) ).

fof(f175,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f263,plain,
    ( ! [X0,X1] :
        ( sK8 != app(app(X0,sK8),X1)
        | ssItem(sK10(sK11,X0,X1))
        | ~ ssList(X1)
        | ~ ssList(X0) )
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f262,f237]) ).

fof(f237,plain,
    ( ssItem(sK11)
    | ~ spl12_2 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f235,plain,
    ( spl12_2
  <=> ssItem(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f262,plain,
    ( ! [X0,X1] :
        ( sK8 != app(app(X0,sK8),X1)
        | ~ ssList(X1)
        | ssItem(sK10(sK11,X0,X1))
        | ~ ssList(X0)
        | ~ ssItem(sK11) )
    | ~ spl12_3 ),
    inference(superposition,[],[f212,f242]) ).

fof(f242,plain,
    ( cons(sK11,nil) = sK8
    | ~ spl12_3 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f240,plain,
    ( spl12_3
  <=> cons(sK11,nil) = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).

fof(f212,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK8
      | ssItem(sK10(X4,X5,X6))
      | ~ ssList(X5)
      | ~ ssList(X6)
      | ~ ssItem(X4) ),
    inference(definition_unfolding,[],[f197,f199]) ).

fof(f199,plain,
    sK6 = sK8,
    inference(cnf_transformation,[],[f148]) ).

fof(f197,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK6
      | ~ ssList(X6)
      | ssItem(sK10(X4,X5,X6))
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f299,plain,
    ( ~ ssItem(sK10(sK11,nil,nil))
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(resolution,[],[f298,f160]) ).

fof(f160,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f298,plain,
    ( memberP(nil,sK10(sK11,nil,nil))
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f297,f166]) ).

fof(f297,plain,
    ( memberP(nil,sK10(sK11,nil,nil))
    | ~ ssList(nil)
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(trivial_inequality_removal,[],[f296]) ).

fof(f296,plain,
    ( memberP(nil,sK10(sK11,nil,nil))
    | sK8 != sK8
    | ~ ssList(nil)
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(superposition,[],[f286,f275]) ).

fof(f286,plain,
    ( ! [X2] :
        ( app(sK8,X2) != sK8
        | ~ ssList(X2)
        | memberP(X2,sK10(sK11,nil,X2)) )
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f282,f166]) ).

fof(f282,plain,
    ( ! [X2] :
        ( ~ ssList(nil)
        | ~ ssList(X2)
        | app(sK8,X2) != sK8
        | memberP(X2,sK10(sK11,nil,X2)) )
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(superposition,[],[f267,f278]) ).

fof(f267,plain,
    ( ! [X0,X1] :
        ( sK8 != app(app(X0,sK8),X1)
        | ~ ssList(X1)
        | memberP(X1,sK10(sK11,X0,X1))
        | ~ ssList(X0) )
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f266,f237]) ).

fof(f266,plain,
    ( ! [X0,X1] :
        ( ~ ssItem(sK11)
        | sK8 != app(app(X0,sK8),X1)
        | ~ ssList(X1)
        | memberP(X1,sK10(sK11,X0,X1))
        | ~ ssList(X0) )
    | ~ spl12_3 ),
    inference(superposition,[],[f213,f242]) ).

fof(f213,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK8
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ ssList(X6)
      | memberP(X6,sK10(X4,X5,X6)) ),
    inference(definition_unfolding,[],[f196,f199]) ).

fof(f196,plain,
    ! [X6,X4,X5] :
      ( app(app(X5,cons(X4,nil)),X6) != sK6
      | ~ ssList(X6)
      | memberP(X6,sK10(X4,X5,X6))
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f261,plain,
    ( spl12_1
    | spl12_3 ),
    inference(avatar_split_clause,[],[f187,f240,f231]) ).

fof(f231,plain,
    ( spl12_1
  <=> nil = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f187,plain,
    ( cons(sK11,nil) = sK8
    | nil = sK8 ),
    inference(cnf_transformation,[],[f148]) ).

fof(f248,plain,
    ~ spl12_1,
    inference(avatar_split_clause,[],[f210,f231]) ).

fof(f210,plain,
    nil != sK8,
    inference(definition_unfolding,[],[f200,f199]) ).

fof(f200,plain,
    nil != sK6,
    inference(cnf_transformation,[],[f148]) ).

fof(f238,plain,
    ( spl12_1
    | spl12_2 ),
    inference(avatar_split_clause,[],[f191,f235,f231]) ).

fof(f191,plain,
    ( ssItem(sK11)
    | nil = sK8 ),
    inference(cnf_transformation,[],[f148]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWC219+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 18:37:15 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.51  % (31416)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.51  % (31400)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.52  % (31400)Instruction limit reached!
% 0.21/0.52  % (31400)------------------------------
% 0.21/0.52  % (31400)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (31399)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.53  % (31404)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.21/0.53  % (31408)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53  % (31412)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.53  % (31412)Instruction limit reached!
% 0.21/0.53  % (31412)------------------------------
% 0.21/0.53  % (31412)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (31412)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (31412)Termination reason: Unknown
% 0.21/0.53  % (31412)Termination phase: Naming
% 0.21/0.53  
% 0.21/0.53  % (31412)Memory used [KB]: 1663
% 0.21/0.53  % (31412)Time elapsed: 0.004 s
% 0.21/0.53  % (31412)Instructions burned: 3 (million)
% 0.21/0.53  % (31412)------------------------------
% 0.21/0.53  % (31412)------------------------------
% 0.21/0.53  % (31422)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.21/0.54  % (31420)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.21/0.54  % (31400)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (31400)Termination reason: Unknown
% 0.21/0.54  % (31400)Termination phase: Saturation
% 0.21/0.54  
% 0.21/0.54  % (31400)Memory used [KB]: 1663
% 0.21/0.54  % (31400)Time elapsed: 0.104 s
% 0.21/0.54  % (31400)Instructions burned: 15 (million)
% 0.21/0.54  % (31400)------------------------------
% 0.21/0.54  % (31400)------------------------------
% 0.21/0.54  % (31424)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.21/0.54  % (31419)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.54  % (31395)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.54  % (31398)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.54  % (31402)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.45/0.55  % (31399)First to succeed.
% 1.45/0.55  % (31411)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.45/0.55  % (31399)Refutation found. Thanks to Tanya!
% 1.45/0.55  % SZS status Theorem for theBenchmark
% 1.45/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.45/0.55  % (31399)------------------------------
% 1.45/0.55  % (31399)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.45/0.55  % (31399)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.45/0.55  % (31399)Termination reason: Refutation
% 1.45/0.55  
% 1.45/0.55  % (31399)Memory used [KB]: 6140
% 1.45/0.55  % (31399)Time elapsed: 0.134 s
% 1.45/0.55  % (31399)Instructions burned: 7 (million)
% 1.45/0.55  % (31399)------------------------------
% 1.45/0.55  % (31399)------------------------------
% 1.45/0.55  % (31394)Success in time 0.189 s
%------------------------------------------------------------------------------