TSTP Solution File: NUM537+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM537+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_uns --cores 0 -t %d %s

% Computer : n011.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 18:00:26 EDT 2022

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   81 (   7 unt;   0 def)
%            Number of atoms       :  500 (  69 equ)
%            Maximal formula atoms :   42 (   6 avg)
%            Number of connectives :  617 ( 198   ~; 193   |; 170   &)
%                                         (  34 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   20 (  18 usr;  15 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   79 (  67   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f663,plain,
    $false,
    inference(avatar_sat_refutation,[],[f444,f482,f488,f495,f497,f513,f542,f543,f556,f602,f616,f629,f643,f651,f653,f661]) ).

fof(f661,plain,
    ( ~ spl6_8
    | ~ spl6_18 ),
    inference(avatar_contradiction_clause,[],[f659]) ).

fof(f659,plain,
    ( $false
    | ~ spl6_8
    | ~ spl6_18 ),
    inference(resolution,[],[f654,f269]) ).

fof(f269,plain,
    ~ aElementOf0(xx,xS),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ~ aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679_02) ).

fof(f654,plain,
    ( aElementOf0(xx,xS)
    | ~ spl6_8
    | ~ spl6_18 ),
    inference(backward_demodulation,[],[f381,f593]) ).

fof(f593,plain,
    ( xx = sK1
    | ~ spl6_18 ),
    inference(avatar_component_clause,[],[f591]) ).

fof(f591,plain,
    ( spl6_18
  <=> xx = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).

fof(f381,plain,
    ( aElementOf0(sK1,xS)
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f379]) ).

fof(f379,plain,
    ( spl6_8
  <=> aElementOf0(sK1,xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

fof(f653,plain,
    ( ~ spl6_21
    | spl6_19
    | ~ spl6_8 ),
    inference(avatar_split_clause,[],[f652,f379,f595,f609]) ).

fof(f609,plain,
    ( spl6_21
  <=> aSet0(xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).

fof(f595,plain,
    ( spl6_19
  <=> aElement0(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).

fof(f652,plain,
    ( aElement0(sK1)
    | ~ aSet0(xS)
    | ~ spl6_8 ),
    inference(resolution,[],[f381,f273]) ).

fof(f273,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,X0)
      | ~ aSet0(X0)
      | aElement0(X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,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(f651,plain,
    ( spl6_15
    | ~ spl6_14
    | ~ spl6_23 ),
    inference(avatar_split_clause,[],[f647,f640,f409,f415]) ).

fof(f415,plain,
    ( spl6_15
  <=> aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).

fof(f409,plain,
    ( spl6_14
  <=> aElementOf0(sK0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).

fof(f640,plain,
    ( spl6_23
  <=> xx = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).

fof(f647,plain,
    ( aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ spl6_14
    | ~ spl6_23 ),
    inference(backward_demodulation,[],[f411,f642]) ).

fof(f642,plain,
    ( xx = sK0
    | ~ spl6_23 ),
    inference(avatar_component_clause,[],[f640]) ).

fof(f411,plain,
    ( aElementOf0(sK0,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ spl6_14 ),
    inference(avatar_component_clause,[],[f409]) ).

fof(f643,plain,
    ( spl6_5
    | spl6_23
    | ~ spl6_1
    | ~ spl6_13
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f635,f409,f404,f350,f640,f365]) ).

fof(f365,plain,
    ( spl6_5
  <=> aElementOf0(sK0,xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

fof(f350,plain,
    ( spl6_1
  <=> ! [X4] :
        ( ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
        | aElementOf0(X4,sdtpldt0(xS,xx)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f404,plain,
    ( spl6_13
  <=> ! [X3] :
        ( ~ aElementOf0(X3,sdtpldt0(xS,xx))
        | xx = X3
        | aElementOf0(X3,xS) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).

fof(f635,plain,
    ( xx = sK0
    | aElementOf0(sK0,xS)
    | ~ spl6_1
    | ~ spl6_13
    | ~ spl6_14 ),
    inference(resolution,[],[f630,f405]) ).

fof(f405,plain,
    ( ! [X3] :
        ( ~ aElementOf0(X3,sdtpldt0(xS,xx))
        | xx = X3
        | aElementOf0(X3,xS) )
    | ~ spl6_13 ),
    inference(avatar_component_clause,[],[f404]) ).

fof(f630,plain,
    ( aElementOf0(sK0,sdtpldt0(xS,xx))
    | ~ spl6_1
    | ~ spl6_14 ),
    inference(resolution,[],[f411,f351]) ).

fof(f351,plain,
    ( ! [X4] :
        ( ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
        | aElementOf0(X4,sdtpldt0(xS,xx)) )
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f350]) ).

fof(f629,plain,
    ( ~ spl6_8
    | ~ spl6_19
    | ~ spl6_2
    | spl6_20 ),
    inference(avatar_split_clause,[],[f628,f599,f353,f595,f379]) ).

fof(f353,plain,
    ( spl6_2
  <=> ! [X0] :
        ( ~ aElementOf0(X0,xS)
        | ~ aElement0(X0)
        | aElementOf0(X0,sdtpldt0(xS,xx)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f599,plain,
    ( spl6_20
  <=> aElementOf0(sK1,sdtpldt0(xS,xx)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).

fof(f628,plain,
    ( ~ aElement0(sK1)
    | ~ aElementOf0(sK1,xS)
    | ~ spl6_2
    | spl6_20 ),
    inference(resolution,[],[f601,f354]) ).

fof(f354,plain,
    ( ! [X0] :
        ( aElementOf0(X0,sdtpldt0(xS,xx))
        | ~ aElementOf0(X0,xS)
        | ~ aElement0(X0) )
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f353]) ).

fof(f601,plain,
    ( ~ aElementOf0(sK1,sdtpldt0(xS,xx))
    | spl6_20 ),
    inference(avatar_component_clause,[],[f599]) ).

fof(f616,plain,
    spl6_21,
    inference(avatar_contradiction_clause,[],[f615]) ).

fof(f615,plain,
    ( $false
    | spl6_21 ),
    inference(resolution,[],[f611,f76]) ).

fof(f76,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,axiom,
    ( aElement0(xx)
    & aSet0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__679) ).

fof(f611,plain,
    ( ~ aSet0(xS)
    | spl6_21 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f602,plain,
    ( spl6_18
    | ~ spl6_19
    | ~ spl6_20
    | ~ spl6_3
    | spl6_6 ),
    inference(avatar_split_clause,[],[f589,f370,f357,f599,f595,f591]) ).

fof(f357,plain,
    ( spl6_3
  <=> ! [X4] :
        ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
        | xx = X4
        | ~ aElement0(X4)
        | ~ aElementOf0(X4,sdtpldt0(xS,xx)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

fof(f370,plain,
    ( spl6_6
  <=> aElementOf0(sK1,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

fof(f589,plain,
    ( ~ aElementOf0(sK1,sdtpldt0(xS,xx))
    | ~ aElement0(sK1)
    | xx = sK1
    | ~ spl6_3
    | spl6_6 ),
    inference(resolution,[],[f358,f372]) ).

fof(f372,plain,
    ( ~ aElementOf0(sK1,sdtmndt0(sdtpldt0(xS,xx),xx))
    | spl6_6 ),
    inference(avatar_component_clause,[],[f370]) ).

fof(f358,plain,
    ( ! [X4] :
        ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
        | ~ aElementOf0(X4,sdtpldt0(xS,xx))
        | ~ aElement0(X4)
        | xx = X4 )
    | ~ spl6_3 ),
    inference(avatar_component_clause,[],[f357]) ).

fof(f556,plain,
    ( spl6_2
    | spl6_2 ),
    inference(avatar_split_clause,[],[f223,f353,f353]) ).

fof(f223,plain,
    ! [X3,X0] :
      ( aElementOf0(X3,sdtpldt0(xS,xx))
      | aElementOf0(X0,sdtpldt0(xS,xx))
      | ~ aElement0(X0)
      | ~ aElementOf0(X3,xS)
      | ~ aElement0(X3)
      | ~ aElementOf0(X0,xS) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ( ( ! [X0] :
          ( ( ( aElement0(X0)
              & ( aElementOf0(X0,xS)
                | xx = X0 ) )
            | ~ aElementOf0(X0,sdtpldt0(xS,xx)) )
          & ( aElementOf0(X0,sdtpldt0(xS,xx))
            | ~ aElement0(X0)
            | ( ~ aElementOf0(X0,xS)
              & xx != X0 ) ) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & aElementOf0(sK0,sdtmndt0(sdtpldt0(xS,xx),xx))
      & ~ aElementOf0(sK0,xS)
      & ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
      & ! [X2] :
          ( ( ( aElementOf0(X2,sdtpldt0(xS,xx))
              & xx != X2
              & aElement0(X2) )
            | ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) )
          & ( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X2,sdtpldt0(xS,xx))
            | xx = X2
            | ~ aElement0(X2) ) )
      & aSet0(sdtpldt0(xS,xx)) )
    | ( ! [X3] :
          ( ( aElementOf0(X3,sdtpldt0(xS,xx))
            | ( ~ aElementOf0(X3,xS)
              & xx != X3 )
            | ~ aElement0(X3) )
          & ( ( ( aElementOf0(X3,xS)
                | xx = X3 )
              & aElement0(X3) )
            | ~ aElementOf0(X3,sdtpldt0(xS,xx)) ) )
      & ! [X4] :
          ( ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X4,sdtpldt0(xS,xx))
            | xx = X4
            | ~ aElement0(X4) )
          & ( ( aElementOf0(X4,sdtpldt0(xS,xx))
              & xx != X4
              & aElement0(X4) )
            | ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
      & ~ aElementOf0(sK1,sdtmndt0(sdtpldt0(xS,xx),xx))
      & aElementOf0(sK1,xS)
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & aSet0(sdtpldt0(xS,xx))
      & ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f50,f52,f51]) ).

fof(f51,plain,
    ( ? [X1] :
        ( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
        & ~ aElementOf0(X1,xS) )
   => ( aElementOf0(sK0,sdtmndt0(sdtpldt0(xS,xx),xx))
      & ~ aElementOf0(sK0,xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ( ? [X5] :
        ( ~ aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
        & aElementOf0(X5,xS) )
   => ( ~ aElementOf0(sK1,sdtmndt0(sdtpldt0(xS,xx),xx))
      & aElementOf0(sK1,xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ( ( ! [X0] :
          ( ( ( aElement0(X0)
              & ( aElementOf0(X0,xS)
                | xx = X0 ) )
            | ~ aElementOf0(X0,sdtpldt0(xS,xx)) )
          & ( aElementOf0(X0,sdtpldt0(xS,xx))
            | ~ aElement0(X0)
            | ( ~ aElementOf0(X0,xS)
              & xx != X0 ) ) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & ? [X1] :
          ( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
          & ~ aElementOf0(X1,xS) )
      & ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
      & ! [X2] :
          ( ( ( aElementOf0(X2,sdtpldt0(xS,xx))
              & xx != X2
              & aElement0(X2) )
            | ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx)) )
          & ( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X2,sdtpldt0(xS,xx))
            | xx = X2
            | ~ aElement0(X2) ) )
      & aSet0(sdtpldt0(xS,xx)) )
    | ( ! [X3] :
          ( ( aElementOf0(X3,sdtpldt0(xS,xx))
            | ( ~ aElementOf0(X3,xS)
              & xx != X3 )
            | ~ aElement0(X3) )
          & ( ( ( aElementOf0(X3,xS)
                | xx = X3 )
              & aElement0(X3) )
            | ~ aElementOf0(X3,sdtpldt0(xS,xx)) ) )
      & ! [X4] :
          ( ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X4,sdtpldt0(xS,xx))
            | xx = X4
            | ~ aElement0(X4) )
          & ( ( aElementOf0(X4,sdtpldt0(xS,xx))
              & xx != X4
              & aElement0(X4) )
            | ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
      & ? [X5] :
          ( ~ aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
          & aElementOf0(X5,xS) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & aSet0(sdtpldt0(xS,xx))
      & ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
    inference(rectify,[],[f49]) ).

fof(f49,plain,
    ( ( ! [X0] :
          ( ( ( aElement0(X0)
              & ( aElementOf0(X0,xS)
                | xx = X0 ) )
            | ~ aElementOf0(X0,sdtpldt0(xS,xx)) )
          & ( aElementOf0(X0,sdtpldt0(xS,xx))
            | ~ aElement0(X0)
            | ( ~ aElementOf0(X0,xS)
              & xx != X0 ) ) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & ? [X2] :
          ( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
          & ~ aElementOf0(X2,xS) )
      & ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
      & ! [X1] :
          ( ( ( aElementOf0(X1,sdtpldt0(xS,xx))
              & xx != X1
              & aElement0(X1) )
            | ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) )
          & ( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X1,sdtpldt0(xS,xx))
            | xx = X1
            | ~ aElement0(X1) ) )
      & aSet0(sdtpldt0(xS,xx)) )
    | ( ! [X3] :
          ( ( aElementOf0(X3,sdtpldt0(xS,xx))
            | ( ~ aElementOf0(X3,xS)
              & xx != X3 )
            | ~ aElement0(X3) )
          & ( ( ( aElementOf0(X3,xS)
                | xx = X3 )
              & aElement0(X3) )
            | ~ aElementOf0(X3,sdtpldt0(xS,xx)) ) )
      & ! [X4] :
          ( ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X4,sdtpldt0(xS,xx))
            | xx = X4
            | ~ aElement0(X4) )
          & ( ( aElementOf0(X4,sdtpldt0(xS,xx))
              & xx != X4
              & aElement0(X4) )
            | ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
      & ? [X5] :
          ( ~ aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
          & aElementOf0(X5,xS) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & aSet0(sdtpldt0(xS,xx))
      & ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
    inference(flattening,[],[f48]) ).

fof(f48,plain,
    ( ( ! [X0] :
          ( ( ( aElement0(X0)
              & ( aElementOf0(X0,xS)
                | xx = X0 ) )
            | ~ aElementOf0(X0,sdtpldt0(xS,xx)) )
          & ( aElementOf0(X0,sdtpldt0(xS,xx))
            | ~ aElement0(X0)
            | ( ~ aElementOf0(X0,xS)
              & xx != X0 ) ) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & ? [X2] :
          ( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
          & ~ aElementOf0(X2,xS) )
      & ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
      & ! [X1] :
          ( ( ( aElementOf0(X1,sdtpldt0(xS,xx))
              & xx != X1
              & aElement0(X1) )
            | ~ aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) )
          & ( aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X1,sdtpldt0(xS,xx))
            | xx = X1
            | ~ aElement0(X1) ) )
      & aSet0(sdtpldt0(xS,xx)) )
    | ( ! [X3] :
          ( ( aElementOf0(X3,sdtpldt0(xS,xx))
            | ( ~ aElementOf0(X3,xS)
              & xx != X3 )
            | ~ aElement0(X3) )
          & ( ( ( aElementOf0(X3,xS)
                | xx = X3 )
              & aElement0(X3) )
            | ~ aElementOf0(X3,sdtpldt0(xS,xx)) ) )
      & ! [X4] :
          ( ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ~ aElementOf0(X4,sdtpldt0(xS,xx))
            | xx = X4
            | ~ aElement0(X4) )
          & ( ( aElementOf0(X4,sdtpldt0(xS,xx))
              & xx != X4
              & aElement0(X4) )
            | ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
      & ? [X5] :
          ( ~ aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
          & aElementOf0(X5,xS) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & aSet0(sdtpldt0(xS,xx))
      & ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f37,plain,
    ( ( ! [X0] :
          ( ( aElement0(X0)
            & ( aElementOf0(X0,xS)
              | xx = X0 ) )
        <=> aElementOf0(X0,sdtpldt0(xS,xx)) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & ? [X2] :
          ( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
          & ~ aElementOf0(X2,xS) )
      & ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
      & ! [X1] :
          ( ( aElementOf0(X1,sdtpldt0(xS,xx))
            & xx != X1
            & aElement0(X1) )
        <=> aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) )
      & aSet0(sdtpldt0(xS,xx)) )
    | ( ! [X3] :
          ( aElementOf0(X3,sdtpldt0(xS,xx))
        <=> ( ( aElementOf0(X3,xS)
              | xx = X3 )
            & aElement0(X3) ) )
      & ! [X4] :
          ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
        <=> ( aElementOf0(X4,sdtpldt0(xS,xx))
            & xx != X4
            & aElement0(X4) ) )
      & ? [X5] :
          ( ~ aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
          & aElementOf0(X5,xS) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & aSet0(sdtpldt0(xS,xx))
      & ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ( ( ? [X2] :
          ( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
          & ~ aElementOf0(X2,xS) )
      & ~ aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS)
      & ! [X1] :
          ( ( aElementOf0(X1,sdtpldt0(xS,xx))
            & xx != X1
            & aElement0(X1) )
        <=> aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) )
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & aSet0(sdtpldt0(xS,xx))
      & ! [X0] :
          ( ( aElement0(X0)
            & ( aElementOf0(X0,xS)
              | xx = X0 ) )
        <=> aElementOf0(X0,sdtpldt0(xS,xx)) ) )
    | ( ? [X5] :
          ( ~ aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx))
          & aElementOf0(X5,xS) )
      & ~ aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
      & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
      & ! [X4] :
          ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
        <=> ( aElementOf0(X4,sdtpldt0(xS,xx))
            & xx != X4
            & aElement0(X4) ) )
      & aSet0(sdtpldt0(xS,xx))
      & ! [X3] :
          ( aElementOf0(X3,sdtpldt0(xS,xx))
        <=> ( ( aElementOf0(X3,xS)
              | xx = X3 )
            & aElement0(X3) ) ) ) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ( ( ( aSet0(sdtpldt0(xS,xx))
          & ! [X0] :
              ( ( aElement0(X0)
                & ( aElementOf0(X0,xS)
                  | xx = X0 ) )
            <=> aElementOf0(X0,sdtpldt0(xS,xx)) ) )
       => ( ( ! [X1] :
                ( ( aElementOf0(X1,sdtpldt0(xS,xx))
                  & xx != X1
                  & aElement0(X1) )
              <=> aElementOf0(X1,sdtmndt0(sdtpldt0(xS,xx),xx)) )
            & aSet0(sdtmndt0(sdtpldt0(xS,xx),xx)) )
         => ( ! [X2] :
                ( aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
               => aElementOf0(X2,xS) )
            | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) )
      & ( ( aSet0(sdtpldt0(xS,xx))
          & ! [X3] :
              ( aElementOf0(X3,sdtpldt0(xS,xx))
            <=> ( ( aElementOf0(X3,xS)
                  | xx = X3 )
                & aElement0(X3) ) ) )
       => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
            & ! [X4] :
                ( aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
              <=> ( aElementOf0(X4,sdtpldt0(xS,xx))
                  & xx != X4
                  & aElement0(X4) ) ) )
         => ( ! [X5] :
                ( aElementOf0(X5,xS)
               => aElementOf0(X5,sdtmndt0(sdtpldt0(xS,xx),xx)) )
            | aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ( ( ( aSet0(sdtpldt0(xS,xx))
          & ! [X0] :
              ( ( aElement0(X0)
                & ( aElementOf0(X0,xS)
                  | xx = X0 ) )
            <=> aElementOf0(X0,sdtpldt0(xS,xx)) ) )
       => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
            & ! [X0] :
                ( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
              <=> ( aElement0(X0)
                  & aElementOf0(X0,sdtpldt0(xS,xx))
                  & xx != X0 ) ) )
         => ( ! [X0] :
                ( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
               => aElementOf0(X0,xS) )
            | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) )
      & ( ( ! [X0] :
              ( aElementOf0(X0,sdtpldt0(xS,xx))
            <=> ( aElement0(X0)
                & ( aElementOf0(X0,xS)
                  | xx = X0 ) ) )
          & aSet0(sdtpldt0(xS,xx)) )
       => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
            & ! [X0] :
                ( ( aElement0(X0)
                  & xx != X0
                  & aElementOf0(X0,sdtpldt0(xS,xx)) )
              <=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
         => ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
            | ! [X0] :
                ( aElementOf0(X0,xS)
               => aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ( ( ( aSet0(sdtpldt0(xS,xx))
        & ! [X0] :
            ( ( aElement0(X0)
              & ( aElementOf0(X0,xS)
                | xx = X0 ) )
          <=> aElementOf0(X0,sdtpldt0(xS,xx)) ) )
     => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
          & ! [X0] :
              ( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
            <=> ( aElement0(X0)
                & aElementOf0(X0,sdtpldt0(xS,xx))
                & xx != X0 ) ) )
       => ( ! [X0] :
              ( aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx))
             => aElementOf0(X0,xS) )
          | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) )
    & ( ( ! [X0] :
            ( aElementOf0(X0,sdtpldt0(xS,xx))
          <=> ( aElement0(X0)
              & ( aElementOf0(X0,xS)
                | xx = X0 ) ) )
        & aSet0(sdtpldt0(xS,xx)) )
     => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
          & ! [X0] :
              ( ( aElement0(X0)
                & xx != X0
                & aElementOf0(X0,sdtpldt0(xS,xx)) )
            <=> aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) )
       => ( aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx))
          | ! [X0] :
              ( aElementOf0(X0,xS)
             => aElementOf0(X0,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f543,plain,
    ( ~ spl6_6
    | spl6_14 ),
    inference(avatar_split_clause,[],[f176,f409,f370]) ).

fof(f176,plain,
    ( aElementOf0(sK0,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aElementOf0(sK1,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f542,plain,
    ( spl6_3
    | spl6_3 ),
    inference(avatar_split_clause,[],[f102,f357,f357]) ).

fof(f102,plain,
    ! [X2,X4] :
      ( ~ aElement0(X2)
      | aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
      | ~ aElementOf0(X4,sdtpldt0(xS,xx))
      | ~ aElement0(X4)
      | xx = X2
      | ~ aElementOf0(X2,sdtpldt0(xS,xx))
      | aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
      | xx = X4 ),
    inference(cnf_transformation,[],[f53]) ).

fof(f513,plain,
    ( spl6_8
    | ~ spl6_5 ),
    inference(avatar_split_clause,[],[f162,f365,f379]) ).

fof(f162,plain,
    ( ~ aElementOf0(sK0,xS)
    | aElementOf0(sK1,xS) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f497,plain,
    ( spl6_13
    | spl6_13 ),
    inference(avatar_split_clause,[],[f234,f404,f404]) ).

fof(f234,plain,
    ! [X3,X0] :
      ( xx = X3
      | aElementOf0(X0,xS)
      | ~ aElementOf0(X3,sdtpldt0(xS,xx))
      | aElementOf0(X3,xS)
      | ~ aElementOf0(X0,sdtpldt0(xS,xx))
      | xx = X0 ),
    inference(cnf_transformation,[],[f53]) ).

fof(f495,plain,
    ( spl6_14
    | spl6_8 ),
    inference(avatar_split_clause,[],[f175,f379,f409]) ).

fof(f175,plain,
    ( aElementOf0(sK1,xS)
    | aElementOf0(sK0,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f488,plain,
    ~ spl6_15,
    inference(avatar_split_clause,[],[f345,f415]) ).

fof(f345,plain,
    ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)),
    inference(duplicate_literal_removal,[],[f317]) ).

fof(f317,plain,
    ( ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
    | ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(equality_resolution,[],[f316]) ).

fof(f316,plain,
    ! [X4] :
      ( ~ aElementOf0(xx,sdtmndt0(sdtpldt0(xS,xx),xx))
      | xx != X4
      | ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(equality_resolution,[],[f126]) ).

fof(f126,plain,
    ! [X2,X4] :
      ( xx != X2
      | ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
      | xx != X4
      | ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f482,plain,
    ( spl6_1
    | spl6_1 ),
    inference(avatar_split_clause,[],[f140,f350,f350]) ).

fof(f140,plain,
    ! [X2,X4] :
      ( ~ aElementOf0(X4,sdtmndt0(sdtpldt0(xS,xx),xx))
      | ~ aElementOf0(X2,sdtmndt0(sdtpldt0(xS,xx),xx))
      | aElementOf0(X2,sdtpldt0(xS,xx))
      | aElementOf0(X4,sdtpldt0(xS,xx)) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f444,plain,
    ( ~ spl6_6
    | ~ spl6_5 ),
    inference(avatar_split_clause,[],[f163,f365,f370]) ).

fof(f163,plain,
    ( ~ aElementOf0(sK0,xS)
    | ~ aElementOf0(sK1,sdtmndt0(sdtpldt0(xS,xx),xx)) ),
    inference(cnf_transformation,[],[f53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : NUM537+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 06:51:25 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.19/0.43  % (15282)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.44  % (15282)Instruction limit reached!
% 0.19/0.44  % (15282)------------------------------
% 0.19/0.44  % (15282)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.44  % (15273)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.44  % (15282)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.44  % (15282)Termination reason: Unknown
% 0.19/0.44  % (15282)Termination phase: Property scanning
% 0.19/0.44  
% 0.19/0.44  % (15282)Memory used [KB]: 1535
% 0.19/0.44  % (15282)Time elapsed: 0.003 s
% 0.19/0.44  % (15282)Instructions burned: 3 (million)
% 0.19/0.44  % (15282)------------------------------
% 0.19/0.44  % (15282)------------------------------
% 0.19/0.44  % (15276)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)
% 0.19/0.45  % (15291)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.45  % (15280)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.45  % (15278)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.45  % (15277)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.45  % (15283)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.45  % (15290)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.45  % (15273)Refutation not found, incomplete strategy% (15273)------------------------------
% 0.19/0.45  % (15273)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.45  % (15273)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.45  % (15273)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.45  
% 0.19/0.45  % (15273)Memory used [KB]: 1663
% 0.19/0.45  % (15273)Time elapsed: 0.065 s
% 0.19/0.45  % (15273)Instructions burned: 14 (million)
% 0.19/0.45  % (15273)------------------------------
% 0.19/0.45  % (15273)------------------------------
% 0.19/0.46  % (15270)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.46  % (15270)Instruction limit reached!
% 0.19/0.46  % (15270)------------------------------
% 0.19/0.46  % (15270)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.46  % (15270)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.46  % (15270)Termination reason: Unknown
% 0.19/0.46  % (15270)Termination phase: Saturation
% 0.19/0.46  
% 0.19/0.46  % (15270)Memory used [KB]: 6012
% 0.19/0.46  % (15270)Time elapsed: 0.003 s
% 0.19/0.46  % (15270)Instructions burned: 4 (million)
% 0.19/0.46  % (15270)------------------------------
% 0.19/0.46  % (15270)------------------------------
% 0.19/0.46  % (15278)Instruction limit reached!
% 0.19/0.46  % (15278)------------------------------
% 0.19/0.46  % (15278)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.46  % (15278)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.46  % (15278)Termination reason: Unknown
% 0.19/0.46  % (15278)Termination phase: Saturation
% 0.19/0.46  
% 0.19/0.46  % (15278)Memory used [KB]: 6268
% 0.19/0.46  % (15278)Time elapsed: 0.080 s
% 0.19/0.46  % (15278)Instructions burned: 14 (million)
% 0.19/0.46  % (15278)------------------------------
% 0.19/0.46  % (15278)------------------------------
% 0.19/0.47  % (15280)Refutation not found, incomplete strategy% (15280)------------------------------
% 0.19/0.47  % (15280)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (15280)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (15280)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47  
% 0.19/0.47  % (15280)Memory used [KB]: 1663
% 0.19/0.47  % (15280)Time elapsed: 0.078 s
% 0.19/0.47  % (15280)Instructions burned: 5 (million)
% 0.19/0.47  % (15280)------------------------------
% 0.19/0.47  % (15280)------------------------------
% 0.19/0.47  % (15268)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.47  % (15269)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.47  % (15284)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  % (15290)First to succeed.
% 0.19/0.47  % (15287)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.47  % (15290)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (15290)------------------------------
% 0.19/0.47  % (15290)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (15290)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (15290)Termination reason: Refutation
% 0.19/0.47  
% 0.19/0.47  % (15290)Memory used [KB]: 6396
% 0.19/0.47  % (15290)Time elapsed: 0.078 s
% 0.19/0.47  % (15290)Instructions burned: 13 (million)
% 0.19/0.47  % (15290)------------------------------
% 0.19/0.47  % (15290)------------------------------
% 0.19/0.47  % (15267)Success in time 0.118 s
%------------------------------------------------------------------------------