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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n012.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 18:41:23 EDT 2022

% Result   : Theorem 1.82s 0.62s
% Output   : Refutation 1.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   64 (  12 unt;   3 typ;   0 def)
%            Number of atoms       :  380 (  99 equ)
%            Maximal formula atoms :   34 (   6 avg)
%            Number of connectives :  474 ( 155   ~; 146   |; 144   &)
%                                         (   2 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  134 (  83   !;  51   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_27,type,
    sQ59_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_28,type,
    sQ60_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_29,type,
    sQ61_eqProxy: ( $real * $real ) > $o ).

fof(f1311,plain,
    $false,
    inference(subsumption_resolution,[],[f1310,f672]) ).

fof(f672,plain,
    ssList(sK20),
    inference(literal_reordering,[],[f415]) ).

fof(f415,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f266]) ).

fof(f266,plain,
    ( ssList(sK18)
    & ssList(sK20)
    & ssList(sK21)
    & sK18 = sK20
    & sK21 = sK19
    & ! [X4] :
        ( ( ( ( ssList(sK22(X4))
              & segmentP(sK21,app(app(cons(X4,nil),sK22(X4)),cons(X4,nil))) )
            | ~ memberP(sK21,X4)
            | memberP(sK20,X4) )
          & ( ( memberP(sK21,X4)
              & ! [X6] :
                  ( ~ ssList(X6)
                  | ~ segmentP(sK21,app(app(cons(X4,nil),X6),cons(X4,nil))) ) )
            | ~ memberP(sK20,X4) ) )
        | ~ ssItem(X4) )
    & nil != sK18
    & nil = sK19
    & ssList(sK19) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f109,f265,f264,f263,f262,f261]) ).

fof(f261,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ssList(X3)
                    & X0 = X2
                    & X1 = X3
                    & ! [X4] :
                        ( ( ( ? [X5] :
                                ( ssList(X5)
                                & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                            | ~ memberP(X3,X4)
                            | 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 != X0
                    & nil = X1 ) )
            & ssList(X1) ) )
   => ( ssList(sK18)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & sK18 = X2
                  & X1 = X3
                  & ! [X4] :
                      ( ( ( ? [X5] :
                              ( ssList(X5)
                              & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                          | ~ memberP(X3,X4)
                          | 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 != sK18
                  & nil = X1 ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f262,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssList(X3)
                & sK18 = X2
                & X1 = X3
                & ! [X4] :
                    ( ( ( ? [X5] :
                            ( ssList(X5)
                            & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                        | ~ memberP(X3,X4)
                        | 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 != sK18
                & nil = X1 ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & sK18 = X2
              & sK19 = X3
              & ! [X4] :
                  ( ( ( ? [X5] :
                          ( ssList(X5)
                          & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                      | ~ memberP(X3,X4)
                      | 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 != sK18
              & nil = sK19 ) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f263,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ssList(X3)
            & sK18 = X2
            & sK19 = X3
            & ! [X4] :
                ( ( ( ? [X5] :
                        ( ssList(X5)
                        & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                    | ~ memberP(X3,X4)
                    | 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 != sK18
            & nil = sK19 ) )
   => ( ssList(sK20)
      & ? [X3] :
          ( ssList(X3)
          & sK18 = sK20
          & sK19 = X3
          & ! [X4] :
              ( ( ( ? [X5] :
                      ( ssList(X5)
                      & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                  | ~ memberP(X3,X4)
                  | memberP(sK20,X4) )
                & ( ( memberP(X3,X4)
                    & ! [X6] :
                        ( ~ ssList(X6)
                        | ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) )
                  | ~ memberP(sK20,X4) ) )
              | ~ ssItem(X4) )
          & nil != sK18
          & nil = sK19 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f264,plain,
    ( ? [X3] :
        ( ssList(X3)
        & sK18 = sK20
        & sK19 = X3
        & ! [X4] :
            ( ( ( ? [X5] :
                    ( ssList(X5)
                    & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                | ~ memberP(X3,X4)
                | memberP(sK20,X4) )
              & ( ( memberP(X3,X4)
                  & ! [X6] :
                      ( ~ ssList(X6)
                      | ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) ) )
                | ~ memberP(sK20,X4) ) )
            | ~ ssItem(X4) )
        & nil != sK18
        & nil = sK19 )
   => ( ssList(sK21)
      & sK18 = sK20
      & sK21 = sK19
      & ! [X4] :
          ( ( ( ? [X5] :
                  ( ssList(X5)
                  & segmentP(sK21,app(app(cons(X4,nil),X5),cons(X4,nil))) )
              | ~ memberP(sK21,X4)
              | memberP(sK20,X4) )
            & ( ( memberP(sK21,X4)
                & ! [X6] :
                    ( ~ ssList(X6)
                    | ~ segmentP(sK21,app(app(cons(X4,nil),X6),cons(X4,nil))) ) )
              | ~ memberP(sK20,X4) ) )
          | ~ ssItem(X4) )
      & nil != sK18
      & nil = sK19 ) ),
    introduced(choice_axiom,[]) ).

fof(f265,plain,
    ! [X4] :
      ( ? [X5] :
          ( ssList(X5)
          & segmentP(sK21,app(app(cons(X4,nil),X5),cons(X4,nil))) )
     => ( ssList(sK22(X4))
        & segmentP(sK21,app(app(cons(X4,nil),sK22(X4)),cons(X4,nil))) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & X0 = X2
                  & X1 = X3
                  & ! [X4] :
                      ( ( ( ? [X5] :
                              ( ssList(X5)
                              & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                          | ~ memberP(X3,X4)
                          | 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 != X0
                  & nil = X1 ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f108]) ).

fof(f108,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( nil != X0
                  & X0 = X2
                  & nil = X1
                  & ! [X4] :
                      ( ( ( ? [X5] :
                              ( ssList(X5)
                              & segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                          | ~ memberP(X3,X4)
                          | 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) )
                  & X1 = X3
                  & 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
                      | nil != X1
                      | ? [X4] :
                          ( ( ( memberP(X2,X4)
                              & ( ? [X6] :
                                    ( ssList(X6)
                                    & segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil))) )
                                | ~ memberP(X3,X4) ) )
                            | ( ! [X5] :
                                  ( ssList(X5)
                                 => ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) )
                              & ~ memberP(X2,X4)
                              & memberP(X3,X4) ) )
                          & ssItem(X4) )
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f1310,plain,
    ~ ssList(sK20),
    inference(subsumption_resolution,[],[f1309,f703]) ).

fof(f703,plain,
    sK20 != sK19,
    inference(literal_reordering,[],[f578]) ).

fof(f578,plain,
    sK20 != sK19,
    inference(definition_unfolding,[],[f407,f406,f413]) ).

fof(f413,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f266]) ).

fof(f406,plain,
    nil = sK19,
    inference(cnf_transformation,[],[f266]) ).

fof(f407,plain,
    nil != sK18,
    inference(cnf_transformation,[],[f266]) ).

fof(f1309,plain,
    ( sK20 = sK19
    | ~ ssList(sK20) ),
    inference(resolution,[],[f1308,f671]) ).

fof(f671,plain,
    ! [X0] :
      ( ssItem(sK24(X0))
      | sK19 = X0
      | ~ ssList(X0) ),
    inference(literal_reordering,[],[f580]) ).

fof(f580,plain,
    ! [X0] :
      ( sK19 = X0
      | ssItem(sK24(X0))
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f422,f406]) ).

fof(f422,plain,
    ! [X0] :
      ( nil = X0
      | ssItem(sK24(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f269,plain,
    ! [X0] :
      ( nil = X0
      | ( ssItem(sK24(X0))
        & cons(sK24(X0),sK23(X0)) = X0
        & ssList(sK23(X0)) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f184,f268,f267]) ).

fof(f267,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssItem(X2)
              & cons(X2,X1) = X0 )
          & ssList(X1) )
     => ( ? [X2] :
            ( ssItem(X2)
            & cons(X2,sK23(X0)) = X0 )
        & ssList(sK23(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f268,plain,
    ! [X0] :
      ( ? [X2] :
          ( ssItem(X2)
          & cons(X2,sK23(X0)) = X0 )
     => ( ssItem(sK24(X0))
        & cons(sK24(X0),sK23(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f184,plain,
    ! [X0] :
      ( nil = X0
      | ? [X1] :
          ( ? [X2] :
              ( ssItem(X2)
              & cons(X2,X1) = X0 )
          & ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f183]) ).

fof(f183,plain,
    ! [X0] :
      ( nil = X0
      | ? [X1] :
          ( ? [X2] :
              ( ssItem(X2)
              & cons(X2,X1) = X0 )
          & ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

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

fof(f1308,plain,
    ~ ssItem(sK24(sK20)),
    inference(subsumption_resolution,[],[f1307,f703]) ).

fof(f1307,plain,
    ( ~ ssItem(sK24(sK20))
    | sK20 = sK19 ),
    inference(subsumption_resolution,[],[f1306,f672]) ).

fof(f1306,plain,
    ( ~ ssList(sK20)
    | ~ ssItem(sK24(sK20))
    | sK20 = sK19 ),
    inference(resolution,[],[f1247,f717]) ).

fof(f717,plain,
    ! [X0] :
      ( ssList(sK23(X0))
      | sK19 = X0
      | ~ ssList(X0) ),
    inference(literal_reordering,[],[f582]) ).

fof(f582,plain,
    ! [X0] :
      ( sK19 = X0
      | ssList(sK23(X0))
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f420,f406]) ).

fof(f420,plain,
    ! [X0] :
      ( nil = X0
      | ssList(sK23(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f1247,plain,
    ( ~ ssList(sK23(sK20))
    | ~ ssItem(sK24(sK20)) ),
    inference(subsumption_resolution,[],[f1246,f1049]) ).

fof(f1049,plain,
    ! [X4] :
      ( ~ memberP(sK20,X4)
      | ~ ssItem(X4) ),
    inference(subsumption_resolution,[],[f673,f699]) ).

fof(f699,plain,
    ! [X0] :
      ( ~ memberP(sK19,X0)
      | ~ ssItem(X0) ),
    inference(literal_reordering,[],[f598]) ).

fof(f598,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(sK19,X0) ),
    inference(definition_unfolding,[],[f476,f406]) ).

fof(f476,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    inference(cnf_transformation,[],[f215]) ).

fof(f215,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f673,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | ~ memberP(sK20,X4)
      | memberP(sK19,X4) ),
    inference(literal_reordering,[],[f576]) ).

fof(f576,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | ~ memberP(sK20,X4)
      | memberP(sK19,X4) ),
    inference(definition_unfolding,[],[f409,f412]) ).

fof(f412,plain,
    sK21 = sK19,
    inference(cnf_transformation,[],[f266]) ).

fof(f409,plain,
    ! [X4] :
      ( memberP(sK21,X4)
      | ~ memberP(sK20,X4)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f266]) ).

fof(f1246,plain,
    ( ~ ssItem(sK24(sK20))
    | memberP(sK20,sK24(sK20))
    | ~ ssList(sK23(sK20)) ),
    inference(superposition,[],[f1036,f1132]) ).

fof(f1132,plain,
    sK20 = cons(sK24(sK20),sK23(sK20)),
    inference(subsumption_resolution,[],[f1129,f703]) ).

fof(f1129,plain,
    ( sK20 = cons(sK24(sK20),sK23(sK20))
    | sK20 = sK19 ),
    inference(resolution,[],[f665,f672]) ).

fof(f665,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | sK19 = X0
      | cons(sK24(X0),sK23(X0)) = X0 ),
    inference(literal_reordering,[],[f581]) ).

fof(f581,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | cons(sK24(X0),sK23(X0)) = X0
      | sK19 = X0 ),
    inference(definition_unfolding,[],[f421,f406]) ).

fof(f421,plain,
    ! [X0] :
      ( nil = X0
      | cons(sK24(X0),sK23(X0)) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f269]) ).

fof(f1036,plain,
    ! [X2,X1] :
      ( memberP(cons(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssItem(X1) ),
    inference(duplicate_literal_removal,[],[f724]) ).

fof(f724,plain,
    ! [X2,X1] :
      ( ~ ssList(X2)
      | memberP(cons(X1,X2),X1)
      | ~ ssItem(X1)
      | ~ ssItem(X1) ),
    inference(literal_reordering,[],[f641]) ).

fof(f641,plain,
    ! [X2,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1)
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f494]) ).

fof(f494,plain,
    ! [X2,X0,X1] :
      ( ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X0)
      | X0 != X1
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f307]) ).

fof(f307,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssItem(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ( ( memberP(cons(X1,X2),X0)
                  | ( X0 != X1
                    & ~ memberP(X2,X0) ) )
                & ( X0 = X1
                  | memberP(X2,X0)
                  | ~ memberP(cons(X1,X2),X0) ) ) ) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f306]) ).

fof(f306,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssItem(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ( ( memberP(cons(X1,X2),X0)
                  | ( X0 != X1
                    & ~ memberP(X2,X0) ) )
                & ( X0 = X1
                  | memberP(X2,X0)
                  | ~ memberP(cons(X1,X2),X0) ) ) ) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f131]) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC046+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n012.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 17:58:35 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.53  % (4975)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.54  % (4983)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.54  % (4979)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.54  % (4991)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.56  % (4971)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.56  TRYING [1]
% 0.19/0.56  % (4973)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.49/0.57  % (4978)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.49/0.57  TRYING [2]
% 1.49/0.58  % (4987)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.49/0.58  % (4980)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.49/0.58  % (4969)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.82/0.59  % (4974)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.82/0.59  % (4977)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.82/0.59  % (4992)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.82/0.60  % (4990)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.82/0.60  % (4977)Instruction limit reached!
% 1.82/0.60  % (4977)------------------------------
% 1.82/0.60  % (4977)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.82/0.60  % (4977)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.82/0.60  % (4977)Termination reason: Unknown
% 1.82/0.60  % (4977)Termination phase: Preprocessing 2
% 1.82/0.60  
% 1.82/0.60  % (4977)Memory used [KB]: 1023
% 1.82/0.60  % (4977)Time elapsed: 0.005 s
% 1.82/0.60  % (4977)Instructions burned: 2 (million)
% 1.82/0.60  % (4977)------------------------------
% 1.82/0.60  % (4977)------------------------------
% 1.82/0.60  % (4989)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.82/0.60  % (4984)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.82/0.60  % (4972)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.82/0.60  % (4983)First to succeed.
% 1.82/0.60  % (4975)Instruction limit reached!
% 1.82/0.60  % (4975)------------------------------
% 1.82/0.60  % (4975)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.82/0.61  % (4970)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.82/0.61  % (4975)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.82/0.61  % (4975)Termination reason: Unknown
% 1.82/0.61  % (4975)Termination phase: Finite model building SAT solving
% 1.82/0.61  
% 1.82/0.61  % (4975)Memory used [KB]: 7164
% 1.82/0.61  % (4975)Time elapsed: 0.168 s
% 1.82/0.61  % (4975)Instructions burned: 52 (million)
% 1.82/0.61  % (4975)------------------------------
% 1.82/0.61  % (4975)------------------------------
% 1.82/0.61  % (4998)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.82/0.61  % (4976)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.82/0.62  % (4983)Refutation found. Thanks to Tanya!
% 1.82/0.62  % SZS status Theorem for theBenchmark
% 1.82/0.62  % SZS output start Proof for theBenchmark
% See solution above
% 1.82/0.62  % (4983)------------------------------
% 1.82/0.62  % (4983)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.82/0.62  % (4983)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.82/0.62  % (4983)Termination reason: Refutation
% 1.82/0.62  
% 1.82/0.62  % (4983)Memory used [KB]: 6652
% 1.82/0.62  % (4983)Time elapsed: 0.030 s
% 1.82/0.62  % (4983)Instructions burned: 32 (million)
% 1.82/0.62  % (4983)------------------------------
% 1.82/0.62  % (4983)------------------------------
% 1.82/0.62  % (4968)Success in time 0.265 s
%------------------------------------------------------------------------------