TSTP Solution File: NUM535+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUM535+2 : 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_sat --cores 0 -t %d %s

% Computer : n014.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 18:05:41 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  140 (   9 unt;   0 def)
%            Number of atoms       :  608 (  68 equ)
%            Maximal formula atoms :   26 (   4 avg)
%            Number of connectives :  707 ( 239   ~; 247   |; 154   &)
%                                         (  45 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   32 (  30 usr;  27 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   81 (  70   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f656,plain,
    $false,
    inference(avatar_sat_refutation,[],[f215,f240,f251,f261,f262,f267,f271,f277,f291,f299,f311,f323,f328,f349,f352,f611,f624,f630,f636,f649,f654,f655]) ).

fof(f655,plain,
    ( spl17_26
    | ~ spl17_18 ),
    inference(avatar_split_clause,[],[f575,f275,f335]) ).

fof(f335,plain,
    ( spl17_26
  <=> ! [X0] :
        ( aElementOf0(X0,sF15)
        | xx = X0
        | ~ aElementOf0(X0,sF16) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).

fof(f275,plain,
    ( spl17_18
  <=> ! [X0] :
        ( xx = X0
        | aElementOf0(X0,sF15)
        | ~ aElementOf0(X0,sdtpldt0(sF15,xx)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).

fof(f575,plain,
    ( ! [X0] :
        ( ~ aElementOf0(X0,sF16)
        | aElementOf0(X0,sF15)
        | xx = X0 )
    | ~ spl17_18 ),
    inference(forward_demodulation,[],[f276,f181]) ).

fof(f181,plain,
    sdtpldt0(sF15,xx) = sF16,
    introduced(function_definition,[]) ).

fof(f276,plain,
    ( ! [X0] :
        ( xx = X0
        | ~ aElementOf0(X0,sdtpldt0(sF15,xx))
        | aElementOf0(X0,sF15) )
    | ~ spl17_18 ),
    inference(avatar_component_clause,[],[f275]) ).

fof(f654,plain,
    ( spl17_14
    | ~ spl17_19
    | ~ spl17_45 ),
    inference(avatar_contradiction_clause,[],[f653]) ).

fof(f653,plain,
    ( $false
    | spl17_14
    | ~ spl17_19
    | ~ spl17_45 ),
    inference(subsumption_resolution,[],[f650,f283]) ).

fof(f283,plain,
    ( aElementOf0(xx,sF16)
    | ~ spl17_19 ),
    inference(avatar_component_clause,[],[f281]) ).

fof(f281,plain,
    ( spl17_19
  <=> aElementOf0(xx,sF16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).

fof(f650,plain,
    ( ~ aElementOf0(xx,sF16)
    | spl17_14
    | ~ spl17_45 ),
    inference(superposition,[],[f612,f606]) ).

fof(f606,plain,
    ( xx = sK9
    | ~ spl17_45 ),
    inference(avatar_component_clause,[],[f604]) ).

fof(f604,plain,
    ( spl17_45
  <=> xx = sK9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).

fof(f612,plain,
    ( ~ aElementOf0(sK9,sF16)
    | spl17_14 ),
    inference(forward_demodulation,[],[f250,f181]) ).

fof(f250,plain,
    ( ~ aElementOf0(sK9,sdtpldt0(sF15,xx))
    | spl17_14 ),
    inference(avatar_component_clause,[],[f248]) ).

fof(f248,plain,
    ( spl17_14
  <=> aElementOf0(sK9,sdtpldt0(sF15,xx)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).

fof(f649,plain,
    ( ~ spl17_12
    | spl17_14
    | ~ spl17_16
    | ~ spl17_46 ),
    inference(avatar_contradiction_clause,[],[f648]) ).

fof(f648,plain,
    ( $false
    | ~ spl17_12
    | spl17_14
    | ~ spl17_16
    | ~ spl17_46 ),
    inference(subsumption_resolution,[],[f647,f612]) ).

fof(f647,plain,
    ( aElementOf0(sK9,sF16)
    | ~ spl17_12
    | ~ spl17_16
    | ~ spl17_46 ),
    inference(subsumption_resolution,[],[f643,f348]) ).

fof(f348,plain,
    ( aElement0(sK9)
    | ~ spl17_16 ),
    inference(subsumption_resolution,[],[f344,f151]) ).

fof(f151,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    aSet0(xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617) ).

fof(f344,plain,
    ( aElement0(sK9)
    | ~ aSet0(xS)
    | ~ spl17_16 ),
    inference(resolution,[],[f165,f260]) ).

fof(f260,plain,
    ( aElementOf0(sK9,xS)
    | ~ spl17_16 ),
    inference(avatar_component_clause,[],[f258]) ).

fof(f258,plain,
    ( spl17_16
  <=> aElementOf0(sK9,xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,X0)
      | aElement0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | ! [X1] :
          ( ~ aElementOf0(X1,X0)
          | aElement0(X1) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

fof(f643,plain,
    ( ~ aElement0(sK9)
    | aElementOf0(sK9,sF16)
    | ~ spl17_12
    | ~ spl17_46 ),
    inference(resolution,[],[f610,f338]) ).

fof(f338,plain,
    ( ! [X0] :
        ( ~ aElementOf0(X0,sF15)
        | aElementOf0(X0,sF16)
        | ~ aElement0(X0) )
    | ~ spl17_12 ),
    inference(forward_demodulation,[],[f239,f181]) ).

fof(f239,plain,
    ( ! [X0] :
        ( ~ aElement0(X0)
        | ~ aElementOf0(X0,sF15)
        | aElementOf0(X0,sdtpldt0(sF15,xx)) )
    | ~ spl17_12 ),
    inference(avatar_component_clause,[],[f238]) ).

fof(f238,plain,
    ( spl17_12
  <=> ! [X0] :
        ( ~ aElement0(X0)
        | aElementOf0(X0,sdtpldt0(sF15,xx))
        | ~ aElementOf0(X0,sF15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).

fof(f610,plain,
    ( aElementOf0(sK9,sF15)
    | ~ spl17_46 ),
    inference(avatar_component_clause,[],[f608]) ).

fof(f608,plain,
    ( spl17_46
  <=> aElementOf0(sK9,sF15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).

fof(f636,plain,
    ( spl17_25
    | ~ spl17_48 ),
    inference(avatar_contradiction_clause,[],[f635]) ).

fof(f635,plain,
    ( $false
    | spl17_25
    | ~ spl17_48 ),
    inference(subsumption_resolution,[],[f633,f102]) ).

fof(f102,plain,
    aElementOf0(xx,xS),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,axiom,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__617_02) ).

fof(f633,plain,
    ( ~ aElementOf0(xx,xS)
    | spl17_25
    | ~ spl17_48 ),
    inference(superposition,[],[f322,f623]) ).

fof(f623,plain,
    ( xx = sK10
    | ~ spl17_48 ),
    inference(avatar_component_clause,[],[f621]) ).

fof(f621,plain,
    ( spl17_48
  <=> xx = sK10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).

fof(f322,plain,
    ( ~ aElementOf0(sK10,xS)
    | spl17_25 ),
    inference(avatar_component_clause,[],[f320]) ).

fof(f320,plain,
    ( spl17_25
  <=> aElementOf0(sK10,xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).

fof(f630,plain,
    ( ~ spl17_17
    | spl17_25
    | ~ spl17_47 ),
    inference(avatar_contradiction_clause,[],[f629]) ).

fof(f629,plain,
    ( $false
    | ~ spl17_17
    | spl17_25
    | ~ spl17_47 ),
    inference(subsumption_resolution,[],[f626,f322]) ).

fof(f626,plain,
    ( aElementOf0(sK10,xS)
    | ~ spl17_17
    | ~ spl17_47 ),
    inference(resolution,[],[f619,f266]) ).

fof(f266,plain,
    ( ! [X0] :
        ( ~ aElementOf0(X0,sF15)
        | aElementOf0(X0,xS) )
    | ~ spl17_17 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f265,plain,
    ( spl17_17
  <=> ! [X0] :
        ( ~ aElementOf0(X0,sF15)
        | aElementOf0(X0,xS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).

fof(f619,plain,
    ( aElementOf0(sK10,sF15)
    | ~ spl17_47 ),
    inference(avatar_component_clause,[],[f617]) ).

fof(f617,plain,
    ( spl17_47
  <=> aElementOf0(sK10,sF15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).

fof(f624,plain,
    ( spl17_47
    | spl17_48
    | ~ spl17_23
    | ~ spl17_26 ),
    inference(avatar_split_clause,[],[f614,f335,f308,f621,f617]) ).

fof(f308,plain,
    ( spl17_23
  <=> aElementOf0(sK10,sF16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).

fof(f614,plain,
    ( xx = sK10
    | aElementOf0(sK10,sF15)
    | ~ spl17_23
    | ~ spl17_26 ),
    inference(resolution,[],[f336,f310]) ).

fof(f310,plain,
    ( aElementOf0(sK10,sF16)
    | ~ spl17_23 ),
    inference(avatar_component_clause,[],[f308]) ).

fof(f336,plain,
    ( ! [X0] :
        ( ~ aElementOf0(X0,sF16)
        | aElementOf0(X0,sF15)
        | xx = X0 )
    | ~ spl17_26 ),
    inference(avatar_component_clause,[],[f335]) ).

fof(f611,plain,
    ( spl17_45
    | spl17_46
    | ~ spl17_16
    | ~ spl17_20 ),
    inference(avatar_split_clause,[],[f544,f289,f258,f608,f604]) ).

fof(f289,plain,
    ( spl17_20
  <=> ! [X0] :
        ( aElementOf0(X0,sF15)
        | xx = X0
        | ~ aElementOf0(X0,xS)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).

fof(f544,plain,
    ( aElementOf0(sK9,sF15)
    | xx = sK9
    | ~ spl17_16
    | ~ spl17_20 ),
    inference(subsumption_resolution,[],[f526,f348]) ).

fof(f526,plain,
    ( ~ aElement0(sK9)
    | aElementOf0(sK9,sF15)
    | xx = sK9
    | ~ spl17_16
    | ~ spl17_20 ),
    inference(resolution,[],[f290,f260]) ).

fof(f290,plain,
    ( ! [X0] :
        ( ~ aElementOf0(X0,xS)
        | xx = X0
        | aElementOf0(X0,sF15)
        | ~ aElement0(X0) )
    | ~ spl17_20 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f352,plain,
    ( spl17_19
    | ~ spl17_5 ),
    inference(avatar_split_clause,[],[f351,f204,f281]) ).

fof(f204,plain,
    ( spl17_5
  <=> aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).

fof(f351,plain,
    ( aElementOf0(xx,sF16)
    | ~ spl17_5 ),
    inference(forward_demodulation,[],[f350,f181]) ).

fof(f350,plain,
    ( aElementOf0(xx,sdtpldt0(sF15,xx))
    | ~ spl17_5 ),
    inference(forward_demodulation,[],[f206,f180]) ).

fof(f180,plain,
    sdtmndt0(xS,xx) = sF15,
    introduced(function_definition,[]) ).

fof(f206,plain,
    ( aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ spl17_5 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f349,plain,
    spl17_6,
    inference(avatar_split_clause,[],[f345,f208]) ).

fof(f208,plain,
    ( spl17_6
  <=> aElement0(xx) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).

fof(f345,plain,
    aElement0(xx),
    inference(subsumption_resolution,[],[f343,f151]) ).

fof(f343,plain,
    ( ~ aSet0(xS)
    | aElement0(xx) ),
    inference(resolution,[],[f165,f102]) ).

fof(f328,plain,
    ( spl17_7
    | ~ spl17_9 ),
    inference(avatar_split_clause,[],[f103,f221,f212]) ).

fof(f212,plain,
    ( spl17_7
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).

fof(f221,plain,
    ( spl17_9
  <=> sP4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).

fof(f103,plain,
    ( ~ sP4
    | sP0 ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ( ( aSet0(sdtmndt0(xS,xx))
      & sP1
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ~ aElementOf0(sK9,sdtpldt0(sdtmndt0(xS,xx),xx))
      & aElementOf0(sK9,xS)
      & ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
      & sP0 )
    | ~ sP4 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f59,f60]) ).

fof(f60,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
        & aElementOf0(X0,xS) )
   => ( ~ aElementOf0(sK9,sdtpldt0(sdtmndt0(xS,xx),xx))
      & aElementOf0(sK9,xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ( ( aSet0(sdtmndt0(xS,xx))
      & sP1
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ? [X0] :
          ( ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
          & aElementOf0(X0,xS) )
      & ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
      & sP0 )
    | ~ sP4 ),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ( ( aSet0(sdtmndt0(xS,xx))
      & sP1
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ? [X2] :
          ( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
          & aElementOf0(X2,xS) )
      & ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
      & sP0 )
    | ~ sP4 ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ( ( aSet0(sdtmndt0(xS,xx))
      & sP1
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ? [X2] :
          ( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
          & aElementOf0(X2,xS) )
      & ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
      & sP0 )
    | ~ sP4 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f323,plain,
    ( ~ spl17_25
    | spl17_9 ),
    inference(avatar_split_clause,[],[f130,f221,f320]) ).

fof(f130,plain,
    ( sP4
    | ~ aElementOf0(sK10,xS) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( ( sP3
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ~ aElementOf0(sK10,xS)
      & aElementOf0(sK10,sdtpldt0(sdtmndt0(xS,xx),xx))
      & ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
      & aSet0(sdtmndt0(xS,xx))
      & sP2 )
    | sP4 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f73,f74]) ).

fof(f74,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,xS)
        & aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
   => ( ~ aElementOf0(sK10,xS)
      & aElementOf0(sK10,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ( ( sP3
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ? [X0] :
          ( ~ aElementOf0(X0,xS)
          & aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
      & ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
      & aSet0(sdtmndt0(xS,xx))
      & sP2 )
    | sP4 ),
    inference(rectify,[],[f51]) ).

fof(f51,plain,
    ( ( sP3
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ? [X5] :
          ( ~ aElementOf0(X5,xS)
          & aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
      & ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
      & aSet0(sdtmndt0(xS,xx))
      & sP2 )
    | sP4 ),
    inference(definition_folding,[],[f42,f50,f49,f48,f47,f46]) ).

fof(f46,plain,
    ( ! [X1] :
        ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
            | xx = X1 )
          & aElement0(X1) )
      <=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f47,plain,
    ( ! [X0] :
        ( ( xx != X0
          & aElement0(X0)
          & aElementOf0(X0,xS) )
      <=> aElementOf0(X0,sdtmndt0(xS,xx)) )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f48,plain,
    ( ! [X3] :
        ( ( aElement0(X3)
          & aElementOf0(X3,xS)
          & xx != X3 )
      <=> aElementOf0(X3,sdtmndt0(xS,xx)) )
    | ~ sP2 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f49,plain,
    ( ! [X4] :
        ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
      <=> ( aElement0(X4)
          & ( aElementOf0(X4,sdtmndt0(xS,xx))
            | xx = X4 ) ) )
    | ~ sP3 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f42,plain,
    ( ( ! [X4] :
          ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
        <=> ( aElement0(X4)
            & ( aElementOf0(X4,sdtmndt0(xS,xx))
              | xx = X4 ) ) )
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ? [X5] :
          ( ~ aElementOf0(X5,xS)
          & aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
      & ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
      & aSet0(sdtmndt0(xS,xx))
      & ! [X3] :
          ( ( aElement0(X3)
            & aElementOf0(X3,xS)
            & xx != X3 )
        <=> aElementOf0(X3,sdtmndt0(xS,xx)) ) )
    | ( aSet0(sdtmndt0(xS,xx))
      & ! [X0] :
          ( ( xx != X0
            & aElement0(X0)
            & aElementOf0(X0,xS) )
        <=> aElementOf0(X0,sdtmndt0(xS,xx)) )
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ? [X2] :
          ( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
          & aElementOf0(X2,xS) )
      & ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
      & ! [X1] :
          ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
              | xx = X1 )
            & aElement0(X1) )
        <=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ( ( ? [X5] :
          ( ~ aElementOf0(X5,xS)
          & aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx)) )
      & ~ aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS)
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & ! [X4] :
          ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
        <=> ( aElement0(X4)
            & ( aElementOf0(X4,sdtmndt0(xS,xx))
              | xx = X4 ) ) )
      & aSet0(sdtmndt0(xS,xx))
      & ! [X3] :
          ( ( aElement0(X3)
            & aElementOf0(X3,xS)
            & xx != X3 )
        <=> aElementOf0(X3,sdtmndt0(xS,xx)) ) )
    | ( ? [X2] :
          ( ~ aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx))
          & aElementOf0(X2,xS) )
      & ~ aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx))
      & ! [X1] :
          ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
              | xx = X1 )
            & aElement0(X1) )
        <=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
      & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
      & aSet0(sdtmndt0(xS,xx))
      & ! [X0] :
          ( ( xx != X0
            & aElement0(X0)
            & aElementOf0(X0,xS) )
        <=> aElementOf0(X0,sdtmndt0(xS,xx)) ) ) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,plain,
    ~ ( ( ( aSet0(sdtmndt0(xS,xx))
          & ! [X3] :
              ( ( aElement0(X3)
                & aElementOf0(X3,xS)
                & xx != X3 )
            <=> aElementOf0(X3,sdtmndt0(xS,xx)) ) )
       => ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
            & ! [X4] :
                ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
              <=> ( aElement0(X4)
                  & ( aElementOf0(X4,sdtmndt0(xS,xx))
                    | xx = X4 ) ) ) )
         => ( ! [X5] :
                ( aElementOf0(X5,sdtpldt0(sdtmndt0(xS,xx),xx))
               => aElementOf0(X5,xS) )
            | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) )
      & ( ( aSet0(sdtmndt0(xS,xx))
          & ! [X0] :
              ( ( xx != X0
                & aElement0(X0)
                & aElementOf0(X0,xS) )
            <=> aElementOf0(X0,sdtmndt0(xS,xx)) ) )
       => ( ( ! [X1] :
                ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
                    | xx = X1 )
                  & aElement0(X1) )
              <=> aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
            & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
         => ( ! [X2] :
                ( aElementOf0(X2,xS)
               => aElementOf0(X2,sdtpldt0(sdtmndt0(xS,xx),xx)) )
            | aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ( ( ( aSet0(sdtmndt0(xS,xx))
          & ! [X0] :
              ( ( xx != X0
                & aElement0(X0)
                & aElementOf0(X0,xS) )
            <=> aElementOf0(X0,sdtmndt0(xS,xx)) ) )
       => ( ( ! [X0] :
                ( ( ( aElementOf0(X0,sdtmndt0(xS,xx))
                    | xx = X0 )
                  & aElement0(X0) )
              <=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
            & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
         => ( ! [X0] :
                ( aElementOf0(X0,xS)
               => aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
            | aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
      & ( ( ! [X0] :
              ( aElementOf0(X0,sdtmndt0(xS,xx))
            <=> ( xx != X0
                & aElement0(X0)
                & aElementOf0(X0,xS) ) )
          & aSet0(sdtmndt0(xS,xx)) )
       => ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
            & ! [X0] :
                ( ( aElement0(X0)
                  & ( xx = X0
                    | aElementOf0(X0,sdtmndt0(xS,xx)) ) )
              <=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
         => ( ! [X0] :
                ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
               => aElementOf0(X0,xS) )
            | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ( ( ( aSet0(sdtmndt0(xS,xx))
        & ! [X0] :
            ( ( xx != X0
              & aElement0(X0)
              & aElementOf0(X0,xS) )
          <=> aElementOf0(X0,sdtmndt0(xS,xx)) ) )
     => ( ( ! [X0] :
              ( ( ( aElementOf0(X0,sdtmndt0(xS,xx))
                  | xx = X0 )
                & aElement0(X0) )
            <=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
          & aSet0(sdtpldt0(sdtmndt0(xS,xx),xx)) )
       => ( ! [X0] :
              ( aElementOf0(X0,xS)
             => aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
          | aSubsetOf0(xS,sdtpldt0(sdtmndt0(xS,xx),xx)) ) ) )
    & ( ( ! [X0] :
            ( aElementOf0(X0,sdtmndt0(xS,xx))
          <=> ( xx != X0
              & aElement0(X0)
              & aElementOf0(X0,xS) ) )
        & aSet0(sdtmndt0(xS,xx)) )
     => ( ( aSet0(sdtpldt0(sdtmndt0(xS,xx),xx))
          & ! [X0] :
              ( ( aElement0(X0)
                & ( xx = X0
                  | aElementOf0(X0,sdtmndt0(xS,xx)) ) )
            <=> aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
       => ( ! [X0] :
              ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
             => aElementOf0(X0,xS) )
          | aSubsetOf0(sdtpldt0(sdtmndt0(xS,xx),xx),xS) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f311,plain,
    ( spl17_23
    | spl17_9 ),
    inference(avatar_split_clause,[],[f183,f221,f308]) ).

fof(f183,plain,
    ( sP4
    | aElementOf0(sK10,sF16) ),
    inference(definition_folding,[],[f129,f181,f180]) ).

fof(f129,plain,
    ( aElementOf0(sK10,sdtpldt0(sdtmndt0(xS,xx),xx))
    | sP4 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f299,plain,
    ( spl17_9
    | spl17_1 ),
    inference(avatar_split_clause,[],[f132,f187,f221]) ).

fof(f187,plain,
    ( spl17_1
  <=> sP3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).

fof(f132,plain,
    ( sP3
    | sP4 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f291,plain,
    ( ~ spl17_10
    | spl17_20 ),
    inference(avatar_split_clause,[],[f287,f289,f227]) ).

fof(f227,plain,
    ( spl17_10
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).

fof(f287,plain,
    ! [X0] :
      ( aElementOf0(X0,sF15)
      | ~ sP1
      | ~ aElement0(X0)
      | ~ aElementOf0(X0,xS)
      | xx = X0 ),
    inference(forward_demodulation,[],[f118,f180]) ).

fof(f118,plain,
    ! [X0] :
      ( ~ sP1
      | ~ aElement0(X0)
      | xx = X0
      | ~ aElementOf0(X0,xS)
      | aElementOf0(X0,sdtmndt0(xS,xx)) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ( ! [X0] :
        ( ( ( xx != X0
            & aElement0(X0)
            & aElementOf0(X0,xS) )
          | ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
        & ( aElementOf0(X0,sdtmndt0(xS,xx))
          | xx = X0
          | ~ aElement0(X0)
          | ~ aElementOf0(X0,xS) ) )
    | ~ sP1 ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ( ! [X0] :
        ( ( ( xx != X0
            & aElement0(X0)
            & aElementOf0(X0,xS) )
          | ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
        & ( aElementOf0(X0,sdtmndt0(xS,xx))
          | xx = X0
          | ~ aElement0(X0)
          | ~ aElementOf0(X0,xS) ) )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f47]) ).

fof(f277,plain,
    ( ~ spl17_1
    | spl17_18 ),
    inference(avatar_split_clause,[],[f273,f275,f187]) ).

fof(f273,plain,
    ! [X0] :
      ( xx = X0
      | ~ aElementOf0(X0,sdtpldt0(sF15,xx))
      | ~ sP3
      | aElementOf0(X0,sF15) ),
    inference(forward_demodulation,[],[f272,f180]) ).

fof(f272,plain,
    ! [X0] :
      ( aElementOf0(X0,sF15)
      | ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ sP3
      | xx = X0 ),
    inference(forward_demodulation,[],[f110,f180]) ).

fof(f110,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtmndt0(xS,xx))
      | ~ sP3
      | ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
      | xx = X0 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ( ! [X0] :
        ( ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
          | ~ aElement0(X0)
          | ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
            & xx != X0 ) )
        & ( ( aElement0(X0)
            & ( aElementOf0(X0,sdtmndt0(xS,xx))
              | xx = X0 ) )
          | ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
    | ~ sP3 ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ( ! [X4] :
        ( ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
          | ~ aElement0(X4)
          | ( ~ aElementOf0(X4,sdtmndt0(xS,xx))
            & xx != X4 ) )
        & ( ( aElement0(X4)
            & ( aElementOf0(X4,sdtmndt0(xS,xx))
              | xx = X4 ) )
          | ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
    | ~ sP3 ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ( ! [X4] :
        ( ( aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx))
          | ~ aElement0(X4)
          | ( ~ aElementOf0(X4,sdtmndt0(xS,xx))
            & xx != X4 ) )
        & ( ( aElement0(X4)
            & ( aElementOf0(X4,sdtmndt0(xS,xx))
              | xx = X4 ) )
          | ~ aElementOf0(X4,sdtpldt0(sdtmndt0(xS,xx),xx)) ) )
    | ~ sP3 ),
    inference(nnf_transformation,[],[f49]) ).

fof(f271,plain,
    ( spl17_10
    | ~ spl17_9 ),
    inference(avatar_split_clause,[],[f108,f221,f227]) ).

fof(f108,plain,
    ( ~ sP4
    | sP1 ),
    inference(cnf_transformation,[],[f61]) ).

fof(f267,plain,
    ( spl17_17
    | ~ spl17_4 ),
    inference(avatar_split_clause,[],[f263,f199,f265]) ).

fof(f199,plain,
    ( spl17_4
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).

fof(f263,plain,
    ! [X0] :
      ( ~ sP2
      | ~ aElementOf0(X0,sF15)
      | aElementOf0(X0,xS) ),
    inference(forward_demodulation,[],[f116,f180]) ).

fof(f116,plain,
    ! [X0] :
      ( aElementOf0(X0,xS)
      | ~ sP2
      | ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ( ! [X0] :
        ( ( ( aElement0(X0)
            & aElementOf0(X0,xS)
            & xx != X0 )
          | ~ aElementOf0(X0,sdtmndt0(xS,xx)) )
        & ( aElementOf0(X0,sdtmndt0(xS,xx))
          | ~ aElement0(X0)
          | ~ aElementOf0(X0,xS)
          | xx = X0 ) )
    | ~ sP2 ),
    inference(rectify,[],[f66]) ).

fof(f66,plain,
    ( ! [X3] :
        ( ( ( aElement0(X3)
            & aElementOf0(X3,xS)
            & xx != X3 )
          | ~ aElementOf0(X3,sdtmndt0(xS,xx)) )
        & ( aElementOf0(X3,sdtmndt0(xS,xx))
          | ~ aElement0(X3)
          | ~ aElementOf0(X3,xS)
          | xx = X3 ) )
    | ~ sP2 ),
    inference(flattening,[],[f65]) ).

fof(f65,plain,
    ( ! [X3] :
        ( ( ( aElement0(X3)
            & aElementOf0(X3,xS)
            & xx != X3 )
          | ~ aElementOf0(X3,sdtmndt0(xS,xx)) )
        & ( aElementOf0(X3,sdtmndt0(xS,xx))
          | ~ aElement0(X3)
          | ~ aElementOf0(X3,xS)
          | xx = X3 ) )
    | ~ sP2 ),
    inference(nnf_transformation,[],[f48]) ).

fof(f262,plain,
    ( spl17_4
    | spl17_9 ),
    inference(avatar_split_clause,[],[f126,f221,f199]) ).

fof(f126,plain,
    ( sP4
    | sP2 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f261,plain,
    ( ~ spl17_9
    | spl17_16 ),
    inference(avatar_split_clause,[],[f105,f258,f221]) ).

fof(f105,plain,
    ( aElementOf0(sK9,xS)
    | ~ sP4 ),
    inference(cnf_transformation,[],[f61]) ).

fof(f251,plain,
    ( ~ spl17_9
    | ~ spl17_14 ),
    inference(avatar_split_clause,[],[f246,f248,f221]) ).

fof(f246,plain,
    ( ~ aElementOf0(sK9,sdtpldt0(sF15,xx))
    | ~ sP4 ),
    inference(forward_demodulation,[],[f106,f180]) ).

fof(f106,plain,
    ( ~ aElementOf0(sK9,sdtpldt0(sdtmndt0(xS,xx),xx))
    | ~ sP4 ),
    inference(cnf_transformation,[],[f61]) ).

fof(f240,plain,
    ( ~ spl17_7
    | spl17_12 ),
    inference(avatar_split_clause,[],[f236,f238,f212]) ).

fof(f236,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ~ aElementOf0(X0,sF15)
      | ~ sP0
      | aElementOf0(X0,sdtpldt0(sF15,xx)) ),
    inference(forward_demodulation,[],[f235,f180]) ).

fof(f235,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtpldt0(sF15,xx))
      | ~ aElementOf0(X0,sdtmndt0(xS,xx))
      | ~ sP0
      | ~ aElement0(X0) ),
    inference(forward_demodulation,[],[f123,f180]) ).

fof(f123,plain,
    ! [X0] :
      ( ~ sP0
      | ~ aElement0(X0)
      | aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
      | ~ aElementOf0(X0,sdtmndt0(xS,xx)) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( ! [X0] :
        ( ( ( ( aElementOf0(X0,sdtmndt0(xS,xx))
              | xx = X0 )
            & aElement0(X0) )
          | ~ aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx)) )
        & ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
          | ( ~ aElementOf0(X0,sdtmndt0(xS,xx))
            & xx != X0 )
          | ~ aElement0(X0) ) )
    | ~ sP0 ),
    inference(rectify,[],[f71]) ).

fof(f71,plain,
    ( ! [X1] :
        ( ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
              | xx = X1 )
            & aElement0(X1) )
          | ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
        & ( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
          | ( ~ aElementOf0(X1,sdtmndt0(xS,xx))
            & xx != X1 )
          | ~ aElement0(X1) ) )
    | ~ sP0 ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ( ! [X1] :
        ( ( ( ( aElementOf0(X1,sdtmndt0(xS,xx))
              | xx = X1 )
            & aElement0(X1) )
          | ~ aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx)) )
        & ( aElementOf0(X1,sdtpldt0(sdtmndt0(xS,xx),xx))
          | ( ~ aElementOf0(X1,sdtmndt0(xS,xx))
            & xx != X1 )
          | ~ aElement0(X1) ) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f46]) ).

fof(f215,plain,
    ( spl17_5
    | ~ spl17_6
    | ~ spl17_7 ),
    inference(avatar_split_clause,[],[f173,f212,f208,f204]) ).

fof(f173,plain,
    ( ~ sP0
    | ~ aElement0(xx)
    | aElementOf0(xx,sdtpldt0(sdtmndt0(xS,xx),xx)) ),
    inference(equality_resolution,[],[f122]) ).

fof(f122,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtpldt0(sdtmndt0(xS,xx),xx))
      | xx != X0
      | ~ aElement0(X0)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f72]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 07:09:48 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  % (12847)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48  % (12838)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)
% 0.20/0.49  % (12834)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)
% 0.20/0.49  % (12834)Refutation not found, incomplete strategy% (12834)------------------------------
% 0.20/0.49  % (12834)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (12855)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.51  % (12834)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (12834)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51  
% 0.20/0.51  % (12834)Memory used [KB]: 5628
% 0.20/0.51  % (12834)Time elapsed: 0.103 s
% 0.20/0.51  % (12834)Instructions burned: 6 (million)
% 0.20/0.51  % (12834)------------------------------
% 0.20/0.51  % (12834)------------------------------
% 0.20/0.51  % (12847)First to succeed.
% 0.20/0.51  % (12847)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (12847)------------------------------
% 0.20/0.51  % (12847)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (12847)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (12847)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (12847)Memory used [KB]: 5756
% 0.20/0.51  % (12847)Time elapsed: 0.099 s
% 0.20/0.51  % (12847)Instructions burned: 12 (million)
% 0.20/0.51  % (12847)------------------------------
% 0.20/0.51  % (12847)------------------------------
% 0.20/0.51  % (12830)Success in time 0.152 s
%------------------------------------------------------------------------------