TSTP Solution File: SWC013+1 by SnakeForV---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC013+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 : n015.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 18:38:12 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   77 (  11 unt;   0 def)
%            Number of atoms       :  475 ( 147 equ)
%            Maximal formula atoms :   42 (   6 avg)
%            Number of connectives :  654 ( 256   ~; 247   |; 121   &)
%                                         (   8 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  122 (  86   !;  36   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f329,plain,
    $false,
    inference(avatar_sat_refutation,[],[f234,f236,f238,f297,f304,f309,f328]) ).

fof(f328,plain,
    ( spl9_2
    | spl9_6 ),
    inference(avatar_contradiction_clause,[],[f327]) ).

fof(f327,plain,
    ( $false
    | spl9_2
    | spl9_6 ),
    inference(subsumption_resolution,[],[f326,f195]) ).

fof(f195,plain,
    ssList(sK8),
    inference(definition_unfolding,[],[f175,f178]) ).

fof(f178,plain,
    sK6 = sK8,
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ( ssList(sK5)
    & ssList(sK7)
    & ( ( ! [X4] :
            ( sK5 != X4
            | ~ ssList(X4)
            | ! [X5] :
                ( hd(sK6) != X5
                | ~ ssItem(X5)
                | cons(X5,nil) != X4
                | ~ neq(nil,sK6) ) )
        & ! [X6] :
            ( sK7 = X6
            | ! [X7] :
                ( cons(X7,nil) != X6
                | ~ neq(nil,sK8)
                | hd(sK8) != X7
                | ~ ssItem(X7) )
            | ~ ssList(X6) )
        & neq(sK6,nil) )
      | ( ~ neq(sK8,nil)
        & neq(sK6,nil) ) )
    & sK6 = sK8
    & sK5 = sK7
    & ssList(sK8)
    & ssList(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f123,f143,f142,f141,f140]) ).

fof(f140,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ( ( ! [X4] :
                            ( X0 != X4
                            | ~ ssList(X4)
                            | ! [X5] :
                                ( hd(X1) != X5
                                | ~ ssItem(X5)
                                | cons(X5,nil) != X4
                                | ~ neq(nil,X1) ) )
                        & ! [X6] :
                            ( X2 = X6
                            | ! [X7] :
                                ( cons(X7,nil) != X6
                                | ~ neq(nil,X3)
                                | hd(X3) != X7
                                | ~ ssItem(X7) )
                            | ~ ssList(X6) )
                        & neq(X1,nil) )
                      | ( ~ neq(X3,nil)
                        & neq(X1,nil) ) )
                    & X1 = X3
                    & X0 = X2
                    & ssList(X3) ) )
            & ssList(X1) ) )
   => ( ssList(sK5)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( ( ! [X4] :
                          ( sK5 != X4
                          | ~ ssList(X4)
                          | ! [X5] :
                              ( hd(X1) != X5
                              | ~ ssItem(X5)
                              | cons(X5,nil) != X4
                              | ~ neq(nil,X1) ) )
                      & ! [X6] :
                          ( X2 = X6
                          | ! [X7] :
                              ( cons(X7,nil) != X6
                              | ~ neq(nil,X3)
                              | hd(X3) != X7
                              | ~ ssItem(X7) )
                          | ~ ssList(X6) )
                      & neq(X1,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X1 = X3
                  & sK5 = X2
                  & ssList(X3) ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f141,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ( ( ! [X4] :
                        ( sK5 != X4
                        | ~ ssList(X4)
                        | ! [X5] :
                            ( hd(X1) != X5
                            | ~ ssItem(X5)
                            | cons(X5,nil) != X4
                            | ~ neq(nil,X1) ) )
                    & ! [X6] :
                        ( X2 = X6
                        | ! [X7] :
                            ( cons(X7,nil) != X6
                            | ~ neq(nil,X3)
                            | hd(X3) != X7
                            | ~ ssItem(X7) )
                        | ~ ssList(X6) )
                    & neq(X1,nil) )
                  | ( ~ neq(X3,nil)
                    & neq(X1,nil) ) )
                & X1 = X3
                & sK5 = X2
                & ssList(X3) ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ( ( ! [X4] :
                      ( sK5 != X4
                      | ~ ssList(X4)
                      | ! [X5] :
                          ( hd(sK6) != X5
                          | ~ ssItem(X5)
                          | cons(X5,nil) != X4
                          | ~ neq(nil,sK6) ) )
                  & ! [X6] :
                      ( X2 = X6
                      | ! [X7] :
                          ( cons(X7,nil) != X6
                          | ~ neq(nil,X3)
                          | hd(X3) != X7
                          | ~ ssItem(X7) )
                      | ~ ssList(X6) )
                  & neq(sK6,nil) )
                | ( ~ neq(X3,nil)
                  & neq(sK6,nil) ) )
              & sK6 = X3
              & sK5 = X2
              & ssList(X3) ) )
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ( ( ! [X4] :
                    ( sK5 != X4
                    | ~ ssList(X4)
                    | ! [X5] :
                        ( hd(sK6) != X5
                        | ~ ssItem(X5)
                        | cons(X5,nil) != X4
                        | ~ neq(nil,sK6) ) )
                & ! [X6] :
                    ( X2 = X6
                    | ! [X7] :
                        ( cons(X7,nil) != X6
                        | ~ neq(nil,X3)
                        | hd(X3) != X7
                        | ~ ssItem(X7) )
                    | ~ ssList(X6) )
                & neq(sK6,nil) )
              | ( ~ neq(X3,nil)
                & neq(sK6,nil) ) )
            & sK6 = X3
            & sK5 = X2
            & ssList(X3) ) )
   => ( ssList(sK7)
      & ? [X3] :
          ( ( ( ! [X4] :
                  ( sK5 != X4
                  | ~ ssList(X4)
                  | ! [X5] :
                      ( hd(sK6) != X5
                      | ~ ssItem(X5)
                      | cons(X5,nil) != X4
                      | ~ neq(nil,sK6) ) )
              & ! [X6] :
                  ( sK7 = X6
                  | ! [X7] :
                      ( cons(X7,nil) != X6
                      | ~ neq(nil,X3)
                      | hd(X3) != X7
                      | ~ ssItem(X7) )
                  | ~ ssList(X6) )
              & neq(sK6,nil) )
            | ( ~ neq(X3,nil)
              & neq(sK6,nil) ) )
          & sK6 = X3
          & sK5 = sK7
          & ssList(X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ( ? [X3] :
        ( ( ( ! [X4] :
                ( sK5 != X4
                | ~ ssList(X4)
                | ! [X5] :
                    ( hd(sK6) != X5
                    | ~ ssItem(X5)
                    | cons(X5,nil) != X4
                    | ~ neq(nil,sK6) ) )
            & ! [X6] :
                ( sK7 = X6
                | ! [X7] :
                    ( cons(X7,nil) != X6
                    | ~ neq(nil,X3)
                    | hd(X3) != X7
                    | ~ ssItem(X7) )
                | ~ ssList(X6) )
            & neq(sK6,nil) )
          | ( ~ neq(X3,nil)
            & neq(sK6,nil) ) )
        & sK6 = X3
        & sK5 = sK7
        & ssList(X3) )
   => ( ( ( ! [X4] :
              ( sK5 != X4
              | ~ ssList(X4)
              | ! [X5] :
                  ( hd(sK6) != X5
                  | ~ ssItem(X5)
                  | cons(X5,nil) != X4
                  | ~ neq(nil,sK6) ) )
          & ! [X6] :
              ( sK7 = X6
              | ! [X7] :
                  ( cons(X7,nil) != X6
                  | ~ neq(nil,sK8)
                  | hd(sK8) != X7
                  | ~ ssItem(X7) )
              | ~ ssList(X6) )
          & neq(sK6,nil) )
        | ( ~ neq(sK8,nil)
          & neq(sK6,nil) ) )
      & sK6 = sK8
      & sK5 = sK7
      & ssList(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ( ( ! [X4] :
                          ( X0 != X4
                          | ~ ssList(X4)
                          | ! [X5] :
                              ( hd(X1) != X5
                              | ~ ssItem(X5)
                              | cons(X5,nil) != X4
                              | ~ neq(nil,X1) ) )
                      & ! [X6] :
                          ( X2 = X6
                          | ! [X7] :
                              ( cons(X7,nil) != X6
                              | ~ neq(nil,X3)
                              | hd(X3) != X7
                              | ~ ssItem(X7) )
                          | ~ ssList(X6) )
                      & neq(X1,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X1 = X3
                  & X0 = X2
                  & ssList(X3) ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f122]) ).

fof(f122,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( X0 != X4
                          | ~ ssList(X4)
                          | ! [X5] :
                              ( hd(X1) != X5
                              | ~ ssItem(X5)
                              | cons(X5,nil) != X4
                              | ~ neq(nil,X1) ) )
                      & ! [X6] :
                          ( X2 = X6
                          | ! [X7] :
                              ( cons(X7,nil) != X6
                              | ~ neq(nil,X3)
                              | hd(X3) != X7
                              | ~ ssItem(X7) )
                          | ~ ssList(X6) )
                      & neq(X1,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X1 = X3
                  & 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)
                   => ( ( ( ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( hd(X3) = X7
                                  & neq(nil,X3)
                                  & ssItem(X7)
                                  & cons(X7,nil) = X6 )
                              & X2 != X6 )
                          | ? [X4] :
                              ( ? [X5] :
                                  ( neq(nil,X1)
                                  & cons(X5,nil) = X4
                                  & hd(X1) = X5
                                  & ssItem(X5) )
                              & ssList(X4)
                              & X0 = X4 )
                          | ~ neq(X1,nil) )
                        & ( ~ neq(X1,nil)
                          | neq(X3,nil) ) )
                      | X1 != X3
                      | X0 != X2 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f175,plain,
    ssList(sK6),
    inference(cnf_transformation,[],[f144]) ).

fof(f326,plain,
    ( ~ ssList(sK8)
    | spl9_2
    | spl9_6 ),
    inference(subsumption_resolution,[],[f325,f146]) ).

fof(f146,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f325,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK8)
    | spl9_2
    | spl9_6 ),
    inference(subsumption_resolution,[],[f322,f265]) ).

fof(f265,plain,
    ( nil != sK8
    | spl9_6 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f264,plain,
    ( spl9_6
  <=> nil = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).

fof(f322,plain,
    ( nil = sK8
    | ~ ssList(sK8)
    | ~ ssList(nil)
    | spl9_2 ),
    inference(resolution,[],[f154,f220]) ).

fof(f220,plain,
    ( ~ neq(nil,sK8)
    | spl9_2 ),
    inference(avatar_component_clause,[],[f218]) ).

fof(f218,plain,
    ( spl9_2
  <=> neq(nil,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) ) ) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f309,plain,
    ( ~ spl9_4
    | spl9_5 ),
    inference(avatar_contradiction_clause,[],[f308]) ).

fof(f308,plain,
    ( $false
    | ~ spl9_4
    | spl9_5 ),
    inference(subsumption_resolution,[],[f307,f146]) ).

fof(f307,plain,
    ( ~ ssList(nil)
    | ~ spl9_4
    | spl9_5 ),
    inference(subsumption_resolution,[],[f306,f227]) ).

fof(f227,plain,
    ( ssItem(hd(sK8))
    | ~ spl9_4 ),
    inference(avatar_component_clause,[],[f226]) ).

fof(f226,plain,
    ( spl9_4
  <=> ssItem(hd(sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).

fof(f306,plain,
    ( ~ ssItem(hd(sK8))
    | ~ ssList(nil)
    | spl9_5 ),
    inference(resolution,[],[f233,f168]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | ssList(cons(X1,X0)) ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f233,plain,
    ( ~ ssList(cons(hd(sK8),nil))
    | spl9_5 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f231,plain,
    ( spl9_5
  <=> ssList(cons(hd(sK8),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).

fof(f304,plain,
    ( spl9_4
    | spl9_6 ),
    inference(avatar_contradiction_clause,[],[f303]) ).

fof(f303,plain,
    ( $false
    | spl9_4
    | spl9_6 ),
    inference(subsumption_resolution,[],[f302,f265]) ).

fof(f302,plain,
    ( nil = sK8
    | spl9_4 ),
    inference(subsumption_resolution,[],[f301,f195]) ).

fof(f301,plain,
    ( ~ ssList(sK8)
    | nil = sK8
    | spl9_4 ),
    inference(resolution,[],[f228,f174]) ).

fof(f174,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssItem(hd(X0)) ),
    inference(flattening,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f228,plain,
    ( ~ ssItem(hd(sK8))
    | spl9_4 ),
    inference(avatar_component_clause,[],[f226]) ).

fof(f297,plain,
    ( ~ spl9_1
    | ~ spl9_6 ),
    inference(avatar_contradiction_clause,[],[f296]) ).

fof(f296,plain,
    ( $false
    | ~ spl9_1
    | ~ spl9_6 ),
    inference(subsumption_resolution,[],[f294,f146]) ).

fof(f294,plain,
    ( ~ ssList(nil)
    | ~ spl9_1
    | ~ spl9_6 ),
    inference(resolution,[],[f285,f211]) ).

fof(f211,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f196]) ).

fof(f196,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(equality_resolution,[],[f155]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | X0 != X1
      | ~ neq(X0,X1) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f285,plain,
    ( neq(nil,nil)
    | ~ spl9_1
    | ~ spl9_6 ),
    inference(backward_demodulation,[],[f216,f266]) ).

fof(f266,plain,
    ( nil = sK8
    | ~ spl9_6 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f216,plain,
    ( neq(sK8,nil)
    | ~ spl9_1 ),
    inference(avatar_component_clause,[],[f214]) ).

fof(f214,plain,
    ( spl9_1
  <=> neq(sK8,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f238,plain,
    spl9_1,
    inference(avatar_split_clause,[],[f208,f214]) ).

fof(f208,plain,
    neq(sK8,nil),
    inference(duplicate_literal_removal,[],[f194]) ).

fof(f194,plain,
    ( neq(sK8,nil)
    | neq(sK8,nil) ),
    inference(definition_unfolding,[],[f179,f178,f178]) ).

fof(f179,plain,
    ( neq(sK6,nil)
    | neq(sK6,nil) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f236,plain,
    ( ~ spl9_3
    | ~ spl9_4
    | ~ spl9_2
    | ~ spl9_1 ),
    inference(avatar_split_clause,[],[f235,f214,f218,f226,f222]) ).

fof(f222,plain,
    ( spl9_3
  <=> cons(hd(sK8),nil) = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).

fof(f235,plain,
    ( ~ neq(sK8,nil)
    | ~ neq(nil,sK8)
    | ~ ssItem(hd(sK8))
    | cons(hd(sK8),nil) != sK7 ),
    inference(subsumption_resolution,[],[f201,f189]) ).

fof(f189,plain,
    ssList(sK7),
    inference(definition_unfolding,[],[f186,f177]) ).

fof(f177,plain,
    sK5 = sK7,
    inference(cnf_transformation,[],[f144]) ).

fof(f186,plain,
    ssList(sK5),
    inference(cnf_transformation,[],[f144]) ).

fof(f201,plain,
    ( ~ ssList(sK7)
    | ~ neq(nil,sK8)
    | ~ ssItem(hd(sK8))
    | cons(hd(sK8),nil) != sK7
    | ~ neq(sK8,nil) ),
    inference(equality_resolution,[],[f200]) ).

fof(f200,plain,
    ! [X5] :
      ( ~ ssList(sK7)
      | hd(sK8) != X5
      | ~ ssItem(X5)
      | cons(X5,nil) != sK7
      | ~ neq(nil,sK8)
      | ~ neq(sK8,nil) ),
    inference(equality_resolution,[],[f190]) ).

fof(f190,plain,
    ! [X4,X5] :
      ( sK7 != X4
      | ~ ssList(X4)
      | hd(sK8) != X5
      | ~ ssItem(X5)
      | cons(X5,nil) != X4
      | ~ neq(nil,sK8)
      | ~ neq(sK8,nil) ),
    inference(definition_unfolding,[],[f184,f177,f178,f178]) ).

fof(f184,plain,
    ! [X4,X5] :
      ( sK5 != X4
      | ~ ssList(X4)
      | hd(sK6) != X5
      | ~ ssItem(X5)
      | cons(X5,nil) != X4
      | ~ neq(nil,sK6)
      | ~ neq(sK8,nil) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f234,plain,
    ( ~ spl9_1
    | ~ spl9_2
    | ~ spl9_5
    | ~ spl9_4
    | spl9_3 ),
    inference(avatar_split_clause,[],[f205,f222,f226,f231,f218,f214]) ).

fof(f205,plain,
    ( cons(hd(sK8),nil) = sK7
    | ~ ssItem(hd(sK8))
    | ~ ssList(cons(hd(sK8),nil))
    | ~ neq(nil,sK8)
    | ~ neq(sK8,nil) ),
    inference(equality_resolution,[],[f204]) ).

fof(f204,plain,
    ! [X7] :
      ( cons(X7,nil) = sK7
      | ~ neq(nil,sK8)
      | hd(sK8) != X7
      | ~ ssItem(X7)
      | ~ ssList(cons(X7,nil))
      | ~ neq(sK8,nil) ),
    inference(equality_resolution,[],[f182]) ).

fof(f182,plain,
    ! [X6,X7] :
      ( sK7 = X6
      | cons(X7,nil) != X6
      | ~ neq(nil,sK8)
      | hd(sK8) != X7
      | ~ ssItem(X7)
      | ~ ssList(X6)
      | ~ neq(sK8,nil) ),
    inference(cnf_transformation,[],[f144]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWC013+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
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 18:07:51 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (2619)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)
% 0.19/0.50  % (2631)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (2636)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.50  % (2639)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.50  % (2633)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (2626)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.50  % (2645)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.51  % (2622)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)
% 0.19/0.51  % (2619)First to succeed.
% 0.19/0.51  % (2628)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.51  % (2640)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)
% 0.19/0.51  % (2619)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (2619)------------------------------
% 0.19/0.51  % (2619)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (2619)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (2619)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (2619)Memory used [KB]: 6140
% 0.19/0.51  % (2619)Time elapsed: 0.117 s
% 0.19/0.51  % (2619)Instructions burned: 7 (million)
% 0.19/0.51  % (2619)------------------------------
% 0.19/0.51  % (2619)------------------------------
% 0.19/0.51  % (2614)Success in time 0.168 s
%------------------------------------------------------------------------------