TSTP Solution File: SWC046+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC046+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 : n018.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 18:38:24 EDT 2022

% Result   : Theorem 1.41s 0.54s
% Output   : Refutation 1.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   67 (  10 unt;   0 def)
%            Number of atoms       :  394 (  94 equ)
%            Maximal formula atoms :   34 (   5 avg)
%            Number of connectives :  481 ( 154   ~; 151   |; 144   &)
%                                         (   5 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  126 (  75   !;  51   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f386,plain,
    $false,
    inference(avatar_sat_refutation,[],[f338,f342,f355,f385]) ).

fof(f385,plain,
    ( ~ spl13_1
    | ~ spl13_3 ),
    inference(avatar_contradiction_clause,[],[f384]) ).

fof(f384,plain,
    ( $false
    | ~ spl13_1
    | ~ spl13_3 ),
    inference(subsumption_resolution,[],[f383,f328]) ).

fof(f328,plain,
    ( ssItem(sK3(sK10))
    | ~ spl13_1 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f327,plain,
    ( spl13_1
  <=> ssItem(sK3(sK10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f383,plain,
    ( ~ ssItem(sK3(sK10))
    | ~ spl13_1
    | ~ spl13_3 ),
    inference(resolution,[],[f361,f240]) ).

fof(f240,plain,
    ! [X0] :
      ( ~ memberP(sK9,X0)
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f218,f207]) ).

fof(f207,plain,
    nil = sK9,
    inference(cnf_transformation,[],[f161]) ).

fof(f161,plain,
    ( ssList(sK8)
    & ssList(sK9)
    & nil != sK8
    & ssList(sK11)
    & ! [X4] :
        ( ( ( ( memberP(sK11,X4)
              & ! [X5] :
                  ( ~ ssList(X5)
                  | ~ segmentP(sK11,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
            | ~ memberP(sK10,X4) )
          & ( ~ memberP(sK11,X4)
            | ( ssList(sK12(X4))
              & segmentP(sK11,app(app(cons(X4,nil),sK12(X4)),cons(X4,nil))) )
            | memberP(sK10,X4) ) )
        | ~ ssItem(X4) )
    & nil = sK9
    & sK11 = sK9
    & sK8 = sK10
    & ssList(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f122,f160,f159,f158,f157,f156]) ).

fof(f156,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( nil != X0
                    & ssList(X3)
                    & ! [X4] :
                        ( ( ( ( memberP(X3,X4)
                              & ! [X5] :
                                  ( ~ ssList(X5)
                                  | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                            | ~ memberP(X2,X4) )
                          & ( ~ memberP(X3,X4)
                            | ? [X6] :
                                ( ssList(X6)
                                & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                            | memberP(X2,X4) ) )
                        | ~ ssItem(X4) )
                    & nil = X1
                    & X1 = X3
                    & X0 = X2 )
                & ssList(X2) ) ) )
   => ( ssList(sK8)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( nil != sK8
                  & ssList(X3)
                  & ! [X4] :
                      ( ( ( ( memberP(X3,X4)
                            & ! [X5] :
                                ( ~ ssList(X5)
                                | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                          | ~ memberP(X2,X4) )
                        & ( ~ memberP(X3,X4)
                          | ? [X6] :
                              ( ssList(X6)
                              & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                          | memberP(X2,X4) ) )
                      | ~ ssItem(X4) )
                  & nil = X1
                  & X1 = X3
                  & sK8 = X2 )
              & ssList(X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( nil != sK8
                & ssList(X3)
                & ! [X4] :
                    ( ( ( ( memberP(X3,X4)
                          & ! [X5] :
                              ( ~ ssList(X5)
                              | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                        | ~ memberP(X2,X4) )
                      & ( ~ memberP(X3,X4)
                        | ? [X6] :
                            ( ssList(X6)
                            & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                        | memberP(X2,X4) ) )
                    | ~ ssItem(X4) )
                & nil = X1
                & X1 = X3
                & sK8 = X2 )
            & ssList(X2) ) )
   => ( ssList(sK9)
      & ? [X2] :
          ( ? [X3] :
              ( nil != sK8
              & ssList(X3)
              & ! [X4] :
                  ( ( ( ( memberP(X3,X4)
                        & ! [X5] :
                            ( ~ ssList(X5)
                            | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                      | ~ memberP(X2,X4) )
                    & ( ~ memberP(X3,X4)
                      | ? [X6] :
                          ( ssList(X6)
                          & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                      | memberP(X2,X4) ) )
                  | ~ ssItem(X4) )
              & nil = sK9
              & sK9 = X3
              & sK8 = X2 )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( nil != sK8
            & ssList(X3)
            & ! [X4] :
                ( ( ( ( memberP(X3,X4)
                      & ! [X5] :
                          ( ~ ssList(X5)
                          | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                    | ~ memberP(X2,X4) )
                  & ( ~ memberP(X3,X4)
                    | ? [X6] :
                        ( ssList(X6)
                        & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                    | memberP(X2,X4) ) )
                | ~ ssItem(X4) )
            & nil = sK9
            & sK9 = X3
            & sK8 = X2 )
        & ssList(X2) )
   => ( ? [X3] :
          ( nil != sK8
          & ssList(X3)
          & ! [X4] :
              ( ( ( ( memberP(X3,X4)
                    & ! [X5] :
                        ( ~ ssList(X5)
                        | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                  | ~ memberP(sK10,X4) )
                & ( ~ memberP(X3,X4)
                  | ? [X6] :
                      ( ssList(X6)
                      & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                  | memberP(sK10,X4) ) )
              | ~ ssItem(X4) )
          & nil = sK9
          & sK9 = X3
          & sK8 = sK10 )
      & ssList(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ( ? [X3] :
        ( nil != sK8
        & ssList(X3)
        & ! [X4] :
            ( ( ( ( memberP(X3,X4)
                  & ! [X5] :
                      ( ~ ssList(X5)
                      | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                | ~ memberP(sK10,X4) )
              & ( ~ memberP(X3,X4)
                | ? [X6] :
                    ( ssList(X6)
                    & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                | memberP(sK10,X4) ) )
            | ~ ssItem(X4) )
        & nil = sK9
        & sK9 = X3
        & sK8 = sK10 )
   => ( nil != sK8
      & ssList(sK11)
      & ! [X4] :
          ( ( ( ( memberP(sK11,X4)
                & ! [X5] :
                    ( ~ ssList(X5)
                    | ~ segmentP(sK11,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
              | ~ memberP(sK10,X4) )
            & ( ~ memberP(sK11,X4)
              | ? [X6] :
                  ( ssList(X6)
                  & segmentP(sK11,app(app(cons(X4,nil),X6),cons(X4,nil))) )
              | memberP(sK10,X4) ) )
          | ~ ssItem(X4) )
      & nil = sK9
      & sK11 = sK9
      & sK8 = sK10 ) ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ! [X4] :
      ( ? [X6] :
          ( ssList(X6)
          & segmentP(sK11,app(app(cons(X4,nil),X6),cons(X4,nil))) )
     => ( ssList(sK12(X4))
        & segmentP(sK11,app(app(cons(X4,nil),sK12(X4)),cons(X4,nil))) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( nil != X0
                  & ssList(X3)
                  & ! [X4] :
                      ( ( ( ( memberP(X3,X4)
                            & ! [X5] :
                                ( ~ ssList(X5)
                                | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                          | ~ memberP(X2,X4) )
                        & ( ~ memberP(X3,X4)
                          | ? [X6] :
                              ( ssList(X6)
                              & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                          | memberP(X2,X4) ) )
                      | ~ ssItem(X4) )
                  & nil = X1
                  & X1 = X3
                  & X0 = X2 )
              & ssList(X2) ) ) ),
    inference(flattening,[],[f121]) ).

fof(f121,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( nil != X0
                  & X0 = X2
                  & X1 = X3
                  & ! [X4] :
                      ( ( ( ( memberP(X3,X4)
                            & ! [X5] :
                                ( ~ ssList(X5)
                                | ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
                          | ~ memberP(X2,X4) )
                        & ( ~ memberP(X3,X4)
                          | ? [X6] :
                              ( ssList(X6)
                              & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                          | memberP(X2,X4) ) )
                      | ~ ssItem(X4) )
                  & nil = X1
                  & 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)
                   => ( nil = X0
                      | X0 != X2
                      | X1 != X3
                      | ? [X4] :
                          ( ssItem(X4)
                          & ( ( memberP(X2,X4)
                              & ( ~ memberP(X3,X4)
                                | ? [X5] :
                                    ( ssList(X5)
                                    & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) ) )
                            | ( ! [X6] :
                                  ( ssList(X6)
                                 => ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                              & memberP(X3,X4)
                              & ~ memberP(X2,X4) ) ) )
                      | nil != X1 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f218,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f361,plain,
    ( memberP(sK9,sK3(sK10))
    | ~ spl13_1
    | ~ spl13_3 ),
    inference(subsumption_resolution,[],[f360,f328]) ).

fof(f360,plain,
    ( ~ ssItem(sK3(sK10))
    | memberP(sK9,sK3(sK10))
    | ~ spl13_3 ),
    inference(resolution,[],[f337,f236]) ).

fof(f236,plain,
    ! [X4] :
      ( ~ memberP(sK10,X4)
      | memberP(sK9,X4)
      | ~ ssItem(X4) ),
    inference(definition_unfolding,[],[f211,f206]) ).

fof(f206,plain,
    sK11 = sK9,
    inference(cnf_transformation,[],[f161]) ).

fof(f211,plain,
    ! [X4] :
      ( memberP(sK11,X4)
      | ~ memberP(sK10,X4)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f161]) ).

fof(f337,plain,
    ( memberP(sK10,sK3(sK10))
    | ~ spl13_3 ),
    inference(avatar_component_clause,[],[f335]) ).

fof(f335,plain,
    ( spl13_3
  <=> memberP(sK10,sK3(sK10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f355,plain,
    spl13_2,
    inference(avatar_contradiction_clause,[],[f354]) ).

fof(f354,plain,
    ( $false
    | spl13_2 ),
    inference(subsumption_resolution,[],[f353,f234]) ).

fof(f234,plain,
    sK9 != sK10,
    inference(definition_unfolding,[],[f213,f207,f205]) ).

fof(f205,plain,
    sK8 = sK10,
    inference(cnf_transformation,[],[f161]) ).

fof(f213,plain,
    nil != sK8,
    inference(cnf_transformation,[],[f161]) ).

fof(f353,plain,
    ( sK9 = sK10
    | spl13_2 ),
    inference(subsumption_resolution,[],[f352,f204]) ).

fof(f204,plain,
    ssList(sK10),
    inference(cnf_transformation,[],[f161]) ).

fof(f352,plain,
    ( ~ ssList(sK10)
    | sK9 = sK10
    | spl13_2 ),
    inference(resolution,[],[f333,f223]) ).

fof(f223,plain,
    ! [X0] :
      ( ssList(sK2(X0))
      | sK9 = X0
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f176,f207]) ).

fof(f176,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | ssList(sK2(X0)) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | ( ssList(sK2(X0))
        & cons(sK3(X0),sK2(X0)) = X0
        & ssItem(sK3(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f101,f143,f142]) ).

fof(f142,plain,
    ! [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
     => ( ssList(sK2(X0))
        & ? [X2] :
            ( cons(X2,sK2(X0)) = X0
            & ssItem(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK2(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK3(X0),sK2(X0)) = X0
        & ssItem(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) ) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( nil = X0
      | ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil = X0
        | ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( cons(X2,X1) = X0
                & ssItem(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

fof(f333,plain,
    ( ~ ssList(sK2(sK10))
    | spl13_2 ),
    inference(avatar_component_clause,[],[f331]) ).

fof(f331,plain,
    ( spl13_2
  <=> ssList(sK2(sK10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f342,plain,
    spl13_1,
    inference(avatar_contradiction_clause,[],[f341]) ).

fof(f341,plain,
    ( $false
    | spl13_1 ),
    inference(subsumption_resolution,[],[f340,f204]) ).

fof(f340,plain,
    ( ~ ssList(sK10)
    | spl13_1 ),
    inference(subsumption_resolution,[],[f339,f234]) ).

fof(f339,plain,
    ( sK9 = sK10
    | ~ ssList(sK10)
    | spl13_1 ),
    inference(resolution,[],[f329,f225]) ).

fof(f225,plain,
    ! [X0] :
      ( ssItem(sK3(X0))
      | ~ ssList(X0)
      | sK9 = X0 ),
    inference(definition_unfolding,[],[f174,f207]) ).

fof(f174,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | ssItem(sK3(X0)) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f329,plain,
    ( ~ ssItem(sK3(sK10))
    | spl13_1 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f338,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | spl13_3 ),
    inference(avatar_split_clause,[],[f322,f335,f331,f327]) ).

fof(f322,plain,
    ( memberP(sK10,sK3(sK10))
    | ~ ssList(sK2(sK10))
    | ~ ssItem(sK3(sK10)) ),
    inference(superposition,[],[f247,f294]) ).

fof(f294,plain,
    cons(sK3(sK10),sK2(sK10)) = sK10,
    inference(subsumption_resolution,[],[f292,f234]) ).

fof(f292,plain,
    ( sK9 = sK10
    | cons(sK3(sK10),sK2(sK10)) = sK10 ),
    inference(resolution,[],[f224,f204]) ).

fof(f224,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | sK9 = X0
      | cons(sK3(X0),sK2(X0)) = X0 ),
    inference(definition_unfolding,[],[f175,f207]) ).

fof(f175,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(X0)
      | cons(sK3(X0),sK2(X0)) = X0 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f247,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f241]) ).

fof(f241,plain,
    ! [X2,X1] :
      ( ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X1)
      | memberP(cons(X1,X2),X1) ),
    inference(equality_resolution,[],[f164]) ).

fof(f164,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X0)
      | memberP(cons(X1,X2),X0)
      | X0 != X1
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ( ( X0 = X1
                  | memberP(X2,X0)
                  | ~ memberP(cons(X1,X2),X0) )
                & ( memberP(cons(X1,X2),X0)
                  | ( X0 != X1
                    & ~ memberP(X2,X0) ) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) ) ),
    inference(flattening,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ( ( X0 = X1
                  | memberP(X2,X0)
                  | ~ memberP(cons(X1,X2),X0) )
                & ( memberP(cons(X1,X2),X0)
                  | ( X0 != X1
                    & ~ memberP(X2,X0) ) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) ) ),
    inference(nnf_transformation,[],[f131]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ( ( X0 = X1
                  | memberP(X2,X0) )
              <=> memberP(cons(X1,X2),X0) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( X0 = X1
                  | memberP(X2,X0) )
              <=> memberP(cons(X1,X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC046+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n018.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    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 18:03:25 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (29287)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)
% 0.20/0.51  % (29303)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)
% 0.20/0.51  % (29295)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)
% 0.20/0.51  % (29303)First to succeed.
% 1.28/0.52  % (29278)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)
% 1.28/0.52  % (29281)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)
% 1.28/0.53  % (29274)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.41/0.53  % (29301)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)
% 1.41/0.54  % (29303)Refutation found. Thanks to Tanya!
% 1.41/0.54  % SZS status Theorem for theBenchmark
% 1.41/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.54  % (29303)------------------------------
% 1.41/0.54  % (29303)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.41/0.54  % (29303)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.41/0.54  % (29303)Termination reason: Refutation
% 1.41/0.54  
% 1.41/0.54  % (29303)Memory used [KB]: 6268
% 1.41/0.54  % (29303)Time elapsed: 0.111 s
% 1.41/0.54  % (29303)Instructions burned: 11 (million)
% 1.41/0.54  % (29303)------------------------------
% 1.41/0.54  % (29303)------------------------------
% 1.41/0.54  % (29273)Success in time 0.183 s
%------------------------------------------------------------------------------