TSTP Solution File: RNG106+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : RNG106+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : n019.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 18:15:01 EDT 2022

% Result   : Theorem 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   98 (   7 unt;   0 def)
%            Number of atoms       :  527 (  75 equ)
%            Maximal formula atoms :   17 (   5 avg)
%            Number of connectives :  674 ( 245   ~; 245   |; 150   &)
%                                         (  15 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   9 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   1 con; 0-3 aty)
%            Number of variables   :  161 ( 115   !;  46   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f505,plain,
    $false,
    inference(avatar_sat_refutation,[],[f337,f344,f346,f353,f365,f435,f440,f445,f473,f504]) ).

fof(f504,plain,
    ( ~ spl25_1
    | ~ spl25_4
    | ~ spl25_5
    | ~ spl25_7
    | ~ spl25_10
    | ~ spl25_11 ),
    inference(avatar_contradiction_clause,[],[f503]) ).

fof(f503,plain,
    ( $false
    | ~ spl25_1
    | ~ spl25_4
    | ~ spl25_5
    | ~ spl25_7
    | ~ spl25_10
    | ~ spl25_11 ),
    inference(subsumption_resolution,[],[f502,f433]) ).

fof(f433,plain,
    ( aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_11 ),
    inference(avatar_component_clause,[],[f432]) ).

fof(f432,plain,
    ( spl25_11
  <=> aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_11])]) ).

fof(f502,plain,
    ( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_1
    | ~ spl25_4
    | ~ spl25_5
    | ~ spl25_7
    | ~ spl25_10
    | ~ spl25_11 ),
    inference(subsumption_resolution,[],[f500,f429]) ).

fof(f429,plain,
    ( aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_10 ),
    inference(avatar_component_clause,[],[f428]) ).

fof(f428,plain,
    ( spl25_10
  <=> aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_10])]) ).

fof(f500,plain,
    ( ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_1
    | ~ spl25_4
    | ~ spl25_5
    | ~ spl25_7
    | ~ spl25_11 ),
    inference(resolution,[],[f499,f343]) ).

fof(f343,plain,
    ( ! [X0,X1] :
        ( aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
        | ~ aElementOf0(X1,slsdtgt0(xc))
        | ~ aElementOf0(X0,slsdtgt0(xc)) )
    | ~ spl25_4 ),
    inference(avatar_component_clause,[],[f342]) ).

fof(f342,plain,
    ( spl25_4
  <=> ! [X0,X1] :
        ( aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
        | ~ aElementOf0(X0,slsdtgt0(xc))
        | ~ aElementOf0(X1,slsdtgt0(xc)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_4])]) ).

fof(f499,plain,
    ( ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
    | ~ spl25_1
    | ~ spl25_5
    | ~ spl25_7
    | ~ spl25_11 ),
    inference(subsumption_resolution,[],[f498,f433]) ).

fof(f498,plain,
    ( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
    | ~ spl25_1
    | ~ spl25_5
    | ~ spl25_7 ),
    inference(subsumption_resolution,[],[f497,f207]) ).

fof(f207,plain,
    ~ aIdeal0(slsdtgt0(xc)),
    inference(cnf_transformation,[],[f131]) ).

fof(f131,plain,
    ( ! [X0,X1,X2] :
        ( ~ aElement0(X2)
        | ~ aElementOf0(X1,slsdtgt0(xc))
        | ~ aElementOf0(X0,slsdtgt0(xc))
        | ( sdtasdt0(xc,sK5(X0,X1,X2)) = X1
          & aElement0(sK5(X0,X1,X2))
          & aElement0(sK6(X0,X1,X2))
          & sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)))
          & sdtasdt0(xc,sK6(X0,X1,X2)) = X0
          & aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
          & aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
          & sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) ) )
    & ~ aIdeal0(slsdtgt0(xc)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f128,f130,f129]) ).

fof(f129,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( sdtasdt0(xc,X3) = X1
          & aElement0(X3)
          & ? [X4] :
              ( aElement0(X4)
              & sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(X3,X4))
              & sdtasdt0(xc,X4) = X0
              & aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
              & aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
              & sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) )
     => ( sdtasdt0(xc,sK5(X0,X1,X2)) = X1
        & aElement0(sK5(X0,X1,X2))
        & ? [X4] :
            ( aElement0(X4)
            & sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),X4))
            & sdtasdt0(xc,X4) = X0
            & aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
            & aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
            & sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( aElement0(X4)
          & sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),X4))
          & sdtasdt0(xc,X4) = X0
          & aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
          & aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
          & sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) )
     => ( aElement0(sK6(X0,X1,X2))
        & sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)))
        & sdtasdt0(xc,sK6(X0,X1,X2)) = X0
        & aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
        & aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
        & sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(sK5(X0,X1,X2),X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ( ! [X0,X1,X2] :
        ( ~ aElement0(X2)
        | ~ aElementOf0(X1,slsdtgt0(xc))
        | ~ aElementOf0(X0,slsdtgt0(xc))
        | ? [X3] :
            ( sdtasdt0(xc,X3) = X1
            & aElement0(X3)
            & ? [X4] :
                ( aElement0(X4)
                & sdtpldt0(X1,X0) = sdtasdt0(xc,sdtpldt0(X3,X4))
                & sdtasdt0(xc,X4) = X0
                & aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
                & aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
                & sdtasdt0(X2,X1) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
    & ~ aIdeal0(slsdtgt0(xc)) ),
    inference(rectify,[],[f93]) ).

fof(f93,plain,
    ( ! [X1,X0,X2] :
        ( ~ aElement0(X2)
        | ~ aElementOf0(X0,slsdtgt0(xc))
        | ~ aElementOf0(X1,slsdtgt0(xc))
        | ? [X3] :
            ( sdtasdt0(xc,X3) = X0
            & aElement0(X3)
            & ? [X4] :
                ( aElement0(X4)
                & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
                & sdtasdt0(xc,X4) = X1
                & aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
    & ~ aIdeal0(slsdtgt0(xc)) ),
    inference(flattening,[],[f92]) ).

fof(f92,plain,
    ( ~ aIdeal0(slsdtgt0(xc))
    & ! [X1,X0,X2] :
        ( ? [X3] :
            ( sdtasdt0(xc,X3) = X0
            & aElement0(X3)
            & ? [X4] :
                ( aElement0(X4)
                & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
                & sdtasdt0(xc,X4) = X1
                & aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) )
        | ~ aElementOf0(X0,slsdtgt0(xc))
        | ~ aElementOf0(X1,slsdtgt0(xc))
        | ~ aElement0(X2) ) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,negated_conjecture,
    ~ ( ! [X1,X0,X2] :
          ( ( aElementOf0(X0,slsdtgt0(xc))
            & aElementOf0(X1,slsdtgt0(xc))
            & aElement0(X2) )
         => ? [X3] :
              ( sdtasdt0(xc,X3) = X0
              & aElement0(X3)
              & ? [X4] :
                  ( aElement0(X4)
                  & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
                  & sdtasdt0(xc,X4) = X1
                  & aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                  & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                  & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
     => aIdeal0(slsdtgt0(xc)) ),
    inference(negated_conjecture,[],[f39]) ).

fof(f39,conjecture,
    ( ! [X1,X0,X2] :
        ( ( aElementOf0(X0,slsdtgt0(xc))
          & aElementOf0(X1,slsdtgt0(xc))
          & aElement0(X2) )
       => ? [X3] :
            ( sdtasdt0(xc,X3) = X0
            & aElement0(X3)
            & ? [X4] :
                ( aElement0(X4)
                & sdtpldt0(X0,X1) = sdtasdt0(xc,sdtpldt0(X3,X4))
                & sdtasdt0(xc,X4) = X1
                & aElementOf0(sdtasdt0(X2,X0),slsdtgt0(xc))
                & aElementOf0(sdtpldt0(X0,X1),slsdtgt0(xc))
                & sdtasdt0(X2,X0) = sdtasdt0(xc,sdtasdt0(X3,X2)) ) ) )
   => aIdeal0(slsdtgt0(xc)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f497,plain,
    ( ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
    | aIdeal0(slsdtgt0(xc))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_1
    | ~ spl25_5
    | ~ spl25_7 ),
    inference(subsumption_resolution,[],[f496,f401]) ).

fof(f401,plain,
    ( aElement0(sK13(slsdtgt0(xc)))
    | ~ spl25_7 ),
    inference(avatar_component_clause,[],[f399]) ).

fof(f399,plain,
    ( spl25_7
  <=> aElement0(sK13(slsdtgt0(xc))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_7])]) ).

fof(f496,plain,
    ( ~ aElement0(sK13(slsdtgt0(xc)))
    | ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | aIdeal0(slsdtgt0(xc))
    | ~ spl25_1
    | ~ spl25_5 ),
    inference(subsumption_resolution,[],[f494,f357]) ).

fof(f357,plain,
    ( aSet0(slsdtgt0(xc))
    | ~ spl25_5 ),
    inference(avatar_component_clause,[],[f356]) ).

fof(f356,plain,
    ( spl25_5
  <=> aSet0(slsdtgt0(xc)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_5])]) ).

fof(f494,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | aIdeal0(slsdtgt0(xc))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ aElementOf0(sdtpldt0(sK11(slsdtgt0(xc)),sK12(slsdtgt0(xc))),slsdtgt0(xc))
    | ~ aElement0(sK13(slsdtgt0(xc)))
    | ~ spl25_1 ),
    inference(resolution,[],[f239,f333]) ).

fof(f333,plain,
    ( ! [X2,X1] :
        ( aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
        | ~ aElementOf0(X1,slsdtgt0(xc))
        | ~ aElement0(X2) )
    | ~ spl25_1 ),
    inference(avatar_component_clause,[],[f332]) ).

fof(f332,plain,
    ( spl25_1
  <=> ! [X2,X1] :
        ( aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
        | ~ aElementOf0(X1,slsdtgt0(xc))
        | ~ aElement0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_1])]) ).

fof(f239,plain,
    ! [X0] :
      ( ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0)
      | ~ aSet0(X0)
      | aIdeal0(X0)
      | ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ( ( ( ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0)
              & aElementOf0(sK12(X0),X0) )
            | ( aElement0(sK13(X0))
              & ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0) ) )
          & aElementOf0(sK11(X0),X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtpldt0(X4,X5),X0)
                    | ~ aElementOf0(X5,X0) )
                & ! [X6] :
                    ( ~ aElement0(X6)
                    | aElementOf0(sdtasdt0(X6,X4),X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f149,f152,f151,f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( ? [X2] :
                ( ~ aElementOf0(sdtpldt0(X1,X2),X0)
                & aElementOf0(X2,X0) )
            | ? [X3] :
                ( aElement0(X3)
                & ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
          & aElementOf0(X1,X0) )
     => ( ( ? [X2] :
              ( ~ aElementOf0(sdtpldt0(sK11(X0),X2),X0)
              & aElementOf0(X2,X0) )
          | ? [X3] :
              ( aElement0(X3)
              & ~ aElementOf0(sdtasdt0(X3,sK11(X0)),X0) ) )
        & aElementOf0(sK11(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ aElementOf0(sdtpldt0(sK11(X0),X2),X0)
          & aElementOf0(X2,X0) )
     => ( ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0)
        & aElementOf0(sK12(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f152,plain,
    ! [X0] :
      ( ? [X3] :
          ( aElement0(X3)
          & ~ aElementOf0(sdtasdt0(X3,sK11(X0)),X0) )
     => ( aElement0(sK13(X0))
        & ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f149,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtpldt0(X1,X2),X0)
                  & aElementOf0(X2,X0) )
              | ? [X3] :
                  ( aElement0(X3)
                  & ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtpldt0(X4,X5),X0)
                    | ~ aElementOf0(X5,X0) )
                & ! [X6] :
                    ( ~ aElement0(X6)
                    | aElementOf0(sdtasdt0(X6,X4),X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(rectify,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtpldt0(X1,X2),X0)
                  & aElementOf0(X2,X0) )
              | ? [X3] :
                  ( aElement0(X3)
                  & ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtpldt0(X1,X2),X0)
                    | ~ aElementOf0(X2,X0) )
                & ! [X3] :
                    ( ~ aElement0(X3)
                    | aElementOf0(sdtasdt0(X3,X1),X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(flattening,[],[f147]) ).

fof(f147,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtpldt0(X1,X2),X0)
                  & aElementOf0(X2,X0) )
              | ? [X3] :
                  ( aElement0(X3)
                  & ~ aElementOf0(sdtasdt0(X3,X1),X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtpldt0(X1,X2),X0)
                    | ~ aElementOf0(X2,X0) )
                & ! [X3] :
                    ( ~ aElement0(X3)
                    | aElementOf0(sdtasdt0(X3,X1),X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( ( ! [X2] :
                  ( aElementOf0(sdtpldt0(X1,X2),X0)
                  | ~ aElementOf0(X2,X0) )
              & ! [X3] :
                  ( ~ aElement0(X3)
                  | aElementOf0(sdtasdt0(X3,X1),X0) ) )
            | ~ aElementOf0(X1,X0) )
        & aSet0(X0) ) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ( aSet0(X0)
        & ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElementOf0(X2,X0)
                 => aElementOf0(sdtpldt0(X1,X2),X0) )
              & ! [X3] :
                  ( aElement0(X3)
                 => aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) )
    <=> aIdeal0(X0) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElementOf0(X2,X0)
                 => aElementOf0(sdtpldt0(X1,X2),X0) )
              & ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) ) ) )
        & aSet0(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).

fof(f473,plain,
    ( ~ spl25_5
    | spl25_11 ),
    inference(avatar_contradiction_clause,[],[f472]) ).

fof(f472,plain,
    ( $false
    | ~ spl25_5
    | spl25_11 ),
    inference(subsumption_resolution,[],[f471,f357]) ).

fof(f471,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | spl25_11 ),
    inference(subsumption_resolution,[],[f470,f207]) ).

fof(f470,plain,
    ( aIdeal0(slsdtgt0(xc))
    | ~ aSet0(slsdtgt0(xc))
    | spl25_11 ),
    inference(resolution,[],[f434,f236]) ).

fof(f236,plain,
    ! [X0] :
      ( aElementOf0(sK11(X0),X0)
      | ~ aSet0(X0)
      | aIdeal0(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f434,plain,
    ( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | spl25_11 ),
    inference(avatar_component_clause,[],[f432]) ).

fof(f445,plain,
    ( ~ spl25_5
    | spl25_7
    | spl25_10 ),
    inference(avatar_contradiction_clause,[],[f444]) ).

fof(f444,plain,
    ( $false
    | ~ spl25_5
    | spl25_7
    | spl25_10 ),
    inference(subsumption_resolution,[],[f443,f400]) ).

fof(f400,plain,
    ( ~ aElement0(sK13(slsdtgt0(xc)))
    | spl25_7 ),
    inference(avatar_component_clause,[],[f399]) ).

fof(f443,plain,
    ( aElement0(sK13(slsdtgt0(xc)))
    | ~ spl25_5
    | spl25_10 ),
    inference(subsumption_resolution,[],[f442,f207]) ).

fof(f442,plain,
    ( aIdeal0(slsdtgt0(xc))
    | aElement0(sK13(slsdtgt0(xc)))
    | ~ spl25_5
    | spl25_10 ),
    inference(subsumption_resolution,[],[f441,f357]) ).

fof(f441,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | aElement0(sK13(slsdtgt0(xc)))
    | aIdeal0(slsdtgt0(xc))
    | spl25_10 ),
    inference(resolution,[],[f430,f238]) ).

fof(f238,plain,
    ! [X0] :
      ( aElementOf0(sK12(X0),X0)
      | aElement0(sK13(X0))
      | ~ aSet0(X0)
      | aIdeal0(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f430,plain,
    ( ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | spl25_10 ),
    inference(avatar_component_clause,[],[f428]) ).

fof(f440,plain,
    ( ~ spl25_11
    | ~ spl25_7
    | spl25_10
    | ~ spl25_1
    | ~ spl25_5 ),
    inference(avatar_split_clause,[],[f439,f356,f332,f428,f399,f432]) ).

fof(f439,plain,
    ( aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ aElement0(sK13(slsdtgt0(xc)))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_1
    | ~ spl25_5 ),
    inference(subsumption_resolution,[],[f438,f207]) ).

fof(f438,plain,
    ( aIdeal0(slsdtgt0(xc))
    | aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ aElement0(sK13(slsdtgt0(xc)))
    | ~ spl25_1
    | ~ spl25_5 ),
    inference(subsumption_resolution,[],[f436,f357]) ).

fof(f436,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | aIdeal0(slsdtgt0(xc))
    | ~ aElement0(sK13(slsdtgt0(xc)))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_1 ),
    inference(resolution,[],[f237,f333]) ).

fof(f237,plain,
    ! [X0] :
      ( ~ aElementOf0(sdtasdt0(sK13(X0),sK11(X0)),X0)
      | ~ aSet0(X0)
      | aElementOf0(sK12(X0),X0)
      | aIdeal0(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f435,plain,
    ( ~ spl25_10
    | spl25_7
    | ~ spl25_11
    | ~ spl25_4
    | ~ spl25_5 ),
    inference(avatar_split_clause,[],[f426,f356,f342,f432,f399,f428]) ).

fof(f426,plain,
    ( ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | aElement0(sK13(slsdtgt0(xc)))
    | ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_4
    | ~ spl25_5 ),
    inference(subsumption_resolution,[],[f425,f357]) ).

fof(f425,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | aElement0(sK13(slsdtgt0(xc)))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ spl25_4 ),
    inference(subsumption_resolution,[],[f423,f207]) ).

fof(f423,plain,
    ( aElement0(sK13(slsdtgt0(xc)))
    | ~ aElementOf0(sK12(slsdtgt0(xc)),slsdtgt0(xc))
    | aIdeal0(slsdtgt0(xc))
    | ~ aElementOf0(sK11(slsdtgt0(xc)),slsdtgt0(xc))
    | ~ aSet0(slsdtgt0(xc))
    | ~ spl25_4 ),
    inference(resolution,[],[f240,f343]) ).

fof(f240,plain,
    ! [X0] :
      ( ~ aElementOf0(sdtpldt0(sK11(X0),sK12(X0)),X0)
      | aElement0(sK13(X0))
      | ~ aSet0(X0)
      | aIdeal0(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f365,plain,
    spl25_5,
    inference(avatar_contradiction_clause,[],[f364]) ).

fof(f364,plain,
    ( $false
    | spl25_5 ),
    inference(subsumption_resolution,[],[f363,f206]) ).

fof(f206,plain,
    aElement0(xc),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    aElement0(xc),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).

fof(f363,plain,
    ( ~ aElement0(xc)
    | spl25_5 ),
    inference(resolution,[],[f358,f279]) ).

fof(f279,plain,
    ! [X0] :
      ( aSet0(slsdtgt0(X0))
      | ~ aElement0(X0) ),
    inference(equality_resolution,[],[f199]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | aSet0(X1)
      | slsdtgt0(X0) != X1 ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ( ( ! [X3] :
                    ( sdtasdt0(X0,X3) != sK2(X0,X1)
                    | ~ aElement0(X3) )
                | ~ aElementOf0(sK2(X0,X1),X1) )
              & ( ( sdtasdt0(X0,sK3(X0,X1)) = sK2(X0,X1)
                  & aElement0(sK3(X0,X1)) )
                | aElementOf0(sK2(X0,X1),X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X5] :
                  ( ( aElementOf0(X5,X1)
                    | ! [X6] :
                        ( sdtasdt0(X0,X6) != X5
                        | ~ aElement0(X6) ) )
                  & ( ( sdtasdt0(X0,sK4(X0,X5)) = X5
                      & aElement0(sK4(X0,X5)) )
                    | ~ aElementOf0(X5,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f123,f126,f125,f124]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( sdtasdt0(X0,X3) != X2
                | ~ aElement0(X3) )
            | ~ aElementOf0(X2,X1) )
          & ( ? [X4] :
                ( sdtasdt0(X0,X4) = X2
                & aElement0(X4) )
            | aElementOf0(X2,X1) ) )
     => ( ( ! [X3] :
              ( sdtasdt0(X0,X3) != sK2(X0,X1)
              | ~ aElement0(X3) )
          | ~ aElementOf0(sK2(X0,X1),X1) )
        & ( ? [X4] :
              ( sK2(X0,X1) = sdtasdt0(X0,X4)
              & aElement0(X4) )
          | aElementOf0(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( sK2(X0,X1) = sdtasdt0(X0,X4)
          & aElement0(X4) )
     => ( sdtasdt0(X0,sK3(X0,X1)) = sK2(X0,X1)
        & aElement0(sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( sdtasdt0(X0,X7) = X5
          & aElement0(X7) )
     => ( sdtasdt0(X0,sK4(X0,X5)) = X5
        & aElement0(sK4(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( sdtasdt0(X0,X3) != X2
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X4] :
                      ( sdtasdt0(X0,X4) = X2
                      & aElement0(X4) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X5] :
                  ( ( aElementOf0(X5,X1)
                    | ! [X6] :
                        ( sdtasdt0(X0,X6) != X5
                        | ~ aElement0(X6) ) )
                  & ( ? [X7] :
                        ( sdtasdt0(X0,X7) = X5
                        & aElement0(X7) )
                    | ~ aElementOf0(X5,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) ) ),
    inference(rectify,[],[f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( sdtasdt0(X0,X3) != X2
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X3] :
                      ( sdtasdt0(X0,X3) = X2
                      & aElement0(X3) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( ( aElementOf0(X2,X1)
                    | ! [X3] :
                        ( sdtasdt0(X0,X3) != X2
                        | ~ aElement0(X3) ) )
                  & ( ? [X3] :
                        ( sdtasdt0(X0,X3) = X2
                        & aElement0(X3) )
                    | ~ aElementOf0(X2,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) ) ),
    inference(flattening,[],[f121]) ).

fof(f121,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ! [X1] :
          ( ( slsdtgt0(X0) = X1
            | ? [X2] :
                ( ( ! [X3] :
                      ( sdtasdt0(X0,X3) != X2
                      | ~ aElement0(X3) )
                  | ~ aElementOf0(X2,X1) )
                & ( ? [X3] :
                      ( sdtasdt0(X0,X3) = X2
                      & aElement0(X3) )
                  | aElementOf0(X2,X1) ) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( ( aElementOf0(X2,X1)
                    | ! [X3] :
                        ( sdtasdt0(X0,X3) != X2
                        | ~ aElement0(X3) ) )
                  & ( ? [X3] :
                        ( sdtasdt0(X0,X3) = X2
                        & aElement0(X3) )
                    | ~ aElementOf0(X2,X1) ) )
              & aSet0(X1) )
            | slsdtgt0(X0) != X1 ) ) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ! [X1] :
          ( slsdtgt0(X0) = X1
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
              <=> ? [X3] :
                    ( sdtasdt0(X0,X3) = X2
                    & aElement0(X3) ) )
            & aSet0(X1) ) ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ! [X1] :
          ( slsdtgt0(X0) = X1
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
              <=> ? [X3] :
                    ( sdtasdt0(X0,X3) = X2
                    & aElement0(X3) ) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).

fof(f358,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | spl25_5 ),
    inference(avatar_component_clause,[],[f356]) ).

fof(f353,plain,
    ~ spl25_2,
    inference(avatar_contradiction_clause,[],[f352]) ).

fof(f352,plain,
    ( $false
    | ~ spl25_2 ),
    inference(subsumption_resolution,[],[f351,f206]) ).

fof(f351,plain,
    ( ~ aElement0(xc)
    | ~ spl25_2 ),
    inference(resolution,[],[f350,f279]) ).

fof(f350,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | ~ spl25_2 ),
    inference(subsumption_resolution,[],[f347,f207]) ).

fof(f347,plain,
    ( ~ aSet0(slsdtgt0(xc))
    | aIdeal0(slsdtgt0(xc))
    | ~ spl25_2 ),
    inference(resolution,[],[f236,f336]) ).

fof(f336,plain,
    ( ! [X0] : ~ aElementOf0(X0,slsdtgt0(xc))
    | ~ spl25_2 ),
    inference(avatar_component_clause,[],[f335]) ).

fof(f335,plain,
    ( spl25_2
  <=> ! [X0] : ~ aElementOf0(X0,slsdtgt0(xc)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_2])]) ).

fof(f346,plain,
    ~ spl25_3,
    inference(avatar_contradiction_clause,[],[f345]) ).

fof(f345,plain,
    ( $false
    | ~ spl25_3 ),
    inference(subsumption_resolution,[],[f206,f340]) ).

fof(f340,plain,
    ( ! [X2] : ~ aElement0(X2)
    | ~ spl25_3 ),
    inference(avatar_component_clause,[],[f339]) ).

fof(f339,plain,
    ( spl25_3
  <=> ! [X2] : ~ aElement0(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).

fof(f344,plain,
    ( spl25_3
    | spl25_4 ),
    inference(avatar_split_clause,[],[f209,f342,f339]) ).

fof(f209,plain,
    ! [X2,X0,X1] :
      ( aElementOf0(sdtpldt0(X1,X0),slsdtgt0(xc))
      | ~ aElementOf0(X1,slsdtgt0(xc))
      | ~ aElementOf0(X0,slsdtgt0(xc))
      | ~ aElement0(X2) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f337,plain,
    ( spl25_1
    | spl25_2 ),
    inference(avatar_split_clause,[],[f210,f335,f332]) ).

fof(f210,plain,
    ! [X2,X0,X1] :
      ( ~ aElementOf0(X0,slsdtgt0(xc))
      | aElementOf0(sdtasdt0(X2,X1),slsdtgt0(xc))
      | ~ aElement0(X2)
      | ~ aElementOf0(X1,slsdtgt0(xc)) ),
    inference(cnf_transformation,[],[f131]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : RNG106+1 : TPTP v8.1.0. Released v4.0.0.
% 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
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 12:12:20 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.43  % (23285)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.44  % (23301)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)
% 0.19/0.44  % (23293)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)
% 0.19/0.47  % (23301)First to succeed.
% 0.19/0.48  % (23301)Refutation found. Thanks to Tanya!
% 0.19/0.48  % SZS status Theorem for theBenchmark
% 0.19/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48  % (23301)------------------------------
% 0.19/0.48  % (23301)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (23301)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (23301)Termination reason: Refutation
% 0.19/0.48  
% 0.19/0.48  % (23301)Memory used [KB]: 6268
% 0.19/0.48  % (23301)Time elapsed: 0.088 s
% 0.19/0.48  % (23301)Instructions burned: 11 (million)
% 0.19/0.48  % (23301)------------------------------
% 0.19/0.48  % (23301)------------------------------
% 0.19/0.48  % (23276)Success in time 0.132 s
%------------------------------------------------------------------------------