TSTP Solution File: NUM558+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n015.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 : Thu Aug 31 12:11:23 EDT 2023

% Result   : Theorem 0.23s 0.46s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   47 (  12 unt;   0 def)
%            Number of atoms       :  399 (  62 equ)
%            Maximal formula atoms :   43 (   8 avg)
%            Number of connectives :  488 ( 136   ~; 111   |; 200   &)
%                                         (   6 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;  10 con; 0-2 aty)
%            Number of variables   :   92 (;  74   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f816,plain,
    $false,
    inference(avatar_sat_refutation,[],[f447,f479,f813]) ).

fof(f813,plain,
    ~ spl21_2,
    inference(avatar_contradiction_clause,[],[f812]) ).

fof(f812,plain,
    ( $false
    | ~ spl21_2 ),
    inference(subsumption_resolution,[],[f809,f446]) ).

fof(f446,plain,
    ( aElementOf0(xx,xP)
    | ~ spl21_2 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f444,plain,
    ( spl21_2
  <=> aElementOf0(xx,xP) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).

fof(f809,plain,
    ~ aElementOf0(xx,xP),
    inference(resolution,[],[f804,f304]) ).

fof(f304,plain,
    aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
    & xk = sbrdtbr0(xP)
    & aSubsetOf0(xP,xS)
    & ! [X0] :
        ( aElementOf0(X0,xS)
        | ~ aElementOf0(X0,xP) ) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,axiom,
    ( aElementOf0(xP,slbdtsldtrb0(xS,xk))
    & xk = sbrdtbr0(xP)
    & aSubsetOf0(xP,xS)
    & ! [X0] :
        ( aElementOf0(X0,xP)
       => aElementOf0(X0,xS) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701',m__2378) ).

fof(f804,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
      | ~ aElementOf0(xx,X0) ),
    inference(resolution,[],[f803,f290]) ).

fof(f290,plain,
    ! [X4] :
      ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
      | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) ),
    inference(cnf_transformation,[],[f186]) ).

fof(f186,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & aElementOf0(sK6,slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X1) != xk
          | ( ~ aSubsetOf0(X1,xS)
            & ( ( ~ aElementOf0(sK7(X1),xS)
                & aElementOf0(sK7(X1),X1) )
              | ~ aSet0(X1) ) ) )
        & ( ( sbrdtbr0(X1) = xk
            & aSubsetOf0(X1,xS)
            & ! [X3] :
                ( aElementOf0(X3,xS)
                | ~ aElementOf0(X3,X1) )
            & aSet0(X1) )
          | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ( ~ aElementOf0(sK8(X5),xT)
                & aElementOf0(sK8(X5),X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ( ~ aElementOf0(sK9(X8),xS)
                & aElementOf0(sK9(X8),X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f181,f185,f184,f183,f182]) ).

fof(f182,plain,
    ( ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
   => aElementOf0(sK6,slbdtsldtrb0(xS,xk)) ),
    introduced(choice_axiom,[]) ).

fof(f183,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,xS)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK7(X1),xS)
        & aElementOf0(sK7(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f184,plain,
    ! [X5] :
      ( ? [X6] :
          ( ~ aElementOf0(X6,xT)
          & aElementOf0(X6,X5) )
     => ( ~ aElementOf0(sK8(X5),xT)
        & aElementOf0(sK8(X5),X5) ) ),
    introduced(choice_axiom,[]) ).

fof(f185,plain,
    ! [X8] :
      ( ? [X9] :
          ( ~ aElementOf0(X9,xS)
          & aElementOf0(X9,X8) )
     => ( ~ aElementOf0(sK9(X8),xS)
        & aElementOf0(sK9(X8),X8) ) ),
    introduced(choice_axiom,[]) ).

fof(f181,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X1) != xk
          | ( ~ aSubsetOf0(X1,xS)
            & ( ? [X2] :
                  ( ~ aElementOf0(X2,xS)
                  & aElementOf0(X2,X1) )
              | ~ aSet0(X1) ) ) )
        & ( ( sbrdtbr0(X1) = xk
            & aSubsetOf0(X1,xS)
            & ! [X3] :
                ( aElementOf0(X3,xS)
                | ~ aElementOf0(X3,X1) )
            & aSet0(X1) )
          | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(rectify,[],[f86]) ).

fof(f86,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
    & ! [X0] :
        ( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X0) != xk
          | ( ~ aSubsetOf0(X0,xS)
            & ( ? [X1] :
                  ( ~ aElementOf0(X1,xS)
                  & aElementOf0(X1,X0) )
              | ~ aSet0(X0) ) ) )
        & ( ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X2] :
                ( aElementOf0(X2,xS)
                | ~ aElementOf0(X2,X0) )
            & aSet0(X0) )
          | ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
    & ! [X0] :
        ( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X0) != xk
          | ( ~ aSubsetOf0(X0,xS)
            & ( ? [X1] :
                  ( ~ aElementOf0(X1,xS)
                  & aElementOf0(X1,X0) )
              | ~ aSet0(X0) ) ) )
        & ( ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X2] :
                ( aElementOf0(X2,xS)
                | ~ aElementOf0(X2,X0) )
            & aSet0(X0) )
          | ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f76,plain,
    ( ~ ( ! [X0] :
            ( ( ( sbrdtbr0(X0) = xk
                & ( aSubsetOf0(X0,xS)
                  | ( ! [X1] :
                        ( aElementOf0(X1,X0)
                       => aElementOf0(X1,xS) )
                    & aSet0(X0) ) ) )
             => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
            & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
             => ( sbrdtbr0(X0) = xk
                & aSubsetOf0(X0,xS)
                & ! [X2] :
                    ( aElementOf0(X2,X0)
                   => aElementOf0(X2,xS) )
                & aSet0(X0) ) ) )
       => ( slcrc0 = slbdtsldtrb0(xS,xk)
          | ~ ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xS,xk))
       => aElementOf0(X4,slbdtsldtrb0(xT,xk)) )
    & ! [X5] :
        ( ( ( xk = sbrdtbr0(X5)
            & ( aSubsetOf0(X5,xT)
              | ( ! [X6] :
                    ( aElementOf0(X6,X5)
                   => aElementOf0(X6,xT) )
                & aSet0(X5) ) ) )
         => aElementOf0(X5,slbdtsldtrb0(xT,xk)) )
        & ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
         => ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,X5)
               => aElementOf0(X7,xT) )
            & aSet0(X5) ) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( ( xk = sbrdtbr0(X8)
            & ( aSubsetOf0(X8,xS)
              | ( ! [X9] :
                    ( aElementOf0(X9,X8)
                   => aElementOf0(X9,xS) )
                & aSet0(X8) ) ) )
         => aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
        & ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
         => ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,X8)
               => aElementOf0(X10,xS) )
            & aSet0(X8) ) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(rectify,[],[f63]) ).

fof(f63,axiom,
    ( ~ ( ! [X0] :
            ( ( ( sbrdtbr0(X0) = xk
                & ( aSubsetOf0(X0,xS)
                  | ( ! [X1] :
                        ( aElementOf0(X1,X0)
                       => aElementOf0(X1,xS) )
                    & aSet0(X0) ) ) )
             => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
            & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
             => ( sbrdtbr0(X0) = xk
                & aSubsetOf0(X0,xS)
                & ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xS) )
                & aSet0(X0) ) ) )
       => ( slcrc0 = slbdtsldtrb0(xS,xk)
          | ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X0] :
        ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
       => aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
    & ! [X0] :
        ( ( ( sbrdtbr0(X0) = xk
            & ( aSubsetOf0(X0,xT)
              | ( ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xT) )
                & aSet0(X0) ) ) )
         => aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
        & ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
         => ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xT)
            & ! [X1] :
                ( aElementOf0(X1,X0)
               => aElementOf0(X1,xT) )
            & aSet0(X0) ) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X0] :
        ( ( ( sbrdtbr0(X0) = xk
            & ( aSubsetOf0(X0,xS)
              | ( ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xS) )
                & aSet0(X0) ) ) )
         => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
        & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
         => ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X1] :
                ( aElementOf0(X1,X0)
               => aElementOf0(X1,xS) )
            & aSet0(X0) ) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701',m__2227) ).

fof(f803,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,slbdtsldtrb0(xT,xk))
      | ~ aElementOf0(xx,X0) ),
    inference(resolution,[],[f284,f245]) ).

fof(f245,plain,
    ~ aElementOf0(xx,xT),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ~ aElementOf0(xx,xT),
    inference(flattening,[],[f73]) ).

fof(f73,negated_conjecture,
    ~ aElementOf0(xx,xT),
    inference(negated_conjecture,[],[f72]) ).

fof(f72,conjecture,
    aElementOf0(xx,xT),
    file('/export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701',m__) ).

fof(f284,plain,
    ! [X7,X5] :
      ( aElementOf0(X7,xT)
      | ~ aElementOf0(X7,X5)
      | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ),
    inference(cnf_transformation,[],[f186]) ).

fof(f479,plain,
    spl21_1,
    inference(avatar_contradiction_clause,[],[f478]) ).

fof(f478,plain,
    ( $false
    | spl21_1 ),
    inference(subsumption_resolution,[],[f475,f260]) ).

fof(f260,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    ( sz00 != xk
    & aSet0(xT)
    & aSet0(xS) ),
    file('/export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701',m__2202_02) ).

fof(f475,plain,
    ( ~ aSet0(xS)
    | spl21_1 ),
    inference(resolution,[],[f474,f248]) ).

fof(f248,plain,
    aElementOf0(xx,xS),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701',m__2256) ).

fof(f474,plain,
    ( ! [X0] :
        ( ~ aElementOf0(xx,X0)
        | ~ aSet0(X0) )
    | spl21_1 ),
    inference(resolution,[],[f320,f442]) ).

fof(f442,plain,
    ( ~ aElement0(xx)
    | spl21_1 ),
    inference(avatar_component_clause,[],[f440]) ).

fof(f440,plain,
    ( spl21_1
  <=> aElement0(xx) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).

fof(f320,plain,
    ! [X0,X1] :
      ( aElement0(X1)
      | ~ aElementOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( aElement0(X1)
          | ~ aElementOf0(X1,X0) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701',mEOfElem) ).

fof(f447,plain,
    ( ~ spl21_1
    | spl21_2 ),
    inference(avatar_split_clause,[],[f418,f444,f440]) ).

fof(f418,plain,
    ( aElementOf0(xx,xP)
    | ~ aElement0(xx) ),
    inference(equality_resolution,[],[f272]) ).

fof(f272,plain,
    ! [X0] :
      ( aElementOf0(X0,xP)
      | xx != X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( ( aElementOf0(X0,xP)
          | ( xx != X0
            & ~ aElementOf0(X0,sdtmndt0(xQ,xy)) )
          | ~ aElement0(X0) )
        & ( ( ( xx = X0
              | aElementOf0(X0,sdtmndt0(xQ,xy)) )
            & aElement0(X0) )
          | ~ aElementOf0(X0,xP) ) )
    & aSet0(xP)
    & ! [X1] :
        ( ( aElementOf0(X1,sdtmndt0(xQ,xy))
          | xy = X1
          | ~ aElementOf0(X1,xQ)
          | ~ aElement0(X1) )
        & ( ( xy != X1
            & aElementOf0(X1,xQ)
            & aElement0(X1) )
          | ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    inference(flattening,[],[f179]) ).

fof(f179,plain,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( ( aElementOf0(X0,xP)
          | ( xx != X0
            & ~ aElementOf0(X0,sdtmndt0(xQ,xy)) )
          | ~ aElement0(X0) )
        & ( ( ( xx = X0
              | aElementOf0(X0,sdtmndt0(xQ,xy)) )
            & aElement0(X0) )
          | ~ aElementOf0(X0,xP) ) )
    & aSet0(xP)
    & ! [X1] :
        ( ( aElementOf0(X1,sdtmndt0(xQ,xy))
          | xy = X1
          | ~ aElementOf0(X1,xQ)
          | ~ aElement0(X1) )
        & ( ( xy != X1
            & aElementOf0(X1,xQ)
            & aElement0(X1) )
          | ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( aElementOf0(X0,xP)
      <=> ( ( xx = X0
            | aElementOf0(X0,sdtmndt0(xQ,xy)) )
          & aElement0(X0) ) )
    & aSet0(xP)
    & ! [X1] :
        ( aElementOf0(X1,sdtmndt0(xQ,xy))
      <=> ( xy != X1
          & aElementOf0(X1,xQ)
          & aElement0(X1) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    inference(rectify,[],[f70]) ).

fof(f70,axiom,
    ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx)
    & ! [X0] :
        ( aElementOf0(X0,xP)
      <=> ( ( xx = X0
            | aElementOf0(X0,sdtmndt0(xQ,xy)) )
          & aElement0(X0) ) )
    & aSet0(xP)
    & ! [X0] :
        ( aElementOf0(X0,sdtmndt0(xQ,xy))
      <=> ( xy != X0
          & aElementOf0(X0,xQ)
          & aElement0(X0) ) )
    & aSet0(sdtmndt0(xQ,xy)) ),
    file('/export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701',m__2357) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37  % Computer : n015.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Fri Aug 25 18:10:22 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.7A47Sm4qJ9/Vampire---4.8_32701
% 0.15/0.37  % (346)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (348)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.23/0.44  % (351)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.23/0.44  % (347)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.23/0.44  % (350)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.23/0.44  % (352)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.23/0.44  % (353)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.23/0.44  % (349)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.23/0.45  % (350)First to succeed.
% 0.23/0.46  % (350)Refutation found. Thanks to Tanya!
% 0.23/0.46  % SZS status Theorem for Vampire---4
% 0.23/0.46  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.46  % (350)------------------------------
% 0.23/0.46  % (350)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.46  % (350)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.46  % (350)Termination reason: Refutation
% 0.23/0.46  
% 0.23/0.46  % (350)Memory used [KB]: 5884
% 0.23/0.46  % (350)Time elapsed: 0.020 s
% 0.23/0.46  % (350)------------------------------
% 0.23/0.46  % (350)------------------------------
% 0.23/0.46  % (346)Success in time 0.08 s
% 0.23/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------