TSTP Solution File: NUM629+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM629+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 : n022.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 : Fri Sep  1 20:21:39 EDT 2023

% Result   : Theorem 29.18s 4.59s
% Output   : Refutation 29.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   65 (  16 unt;   0 def)
%            Number of atoms       :  343 (  30 equ)
%            Maximal formula atoms :   22 (   5 avg)
%            Number of connectives :  386 ( 108   ~;  89   |; 155   &)
%                                         (  13 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  12 con; 0-2 aty)
%            Number of variables   :  105 (;  96   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f283872,plain,
    $false,
    inference(subsumption_resolution,[],[f283871,f49322]) ).

fof(f49322,plain,
    ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD),
    inference(unit_resulting_resolution,[],[f1343,f48780,f1164]) ).

fof(f1164,plain,
    ! [X0,X1] :
      ( ~ aSubsetOf0(X1,X0)
      | sP79(X0,X1)
      | ~ sP80(X0) ),
    inference(cnf_transformation,[],[f661]) ).

fof(f661,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ~ sP79(X0,X1) )
          & ( sP79(X0,X1)
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ sP80(X0) ),
    inference(nnf_transformation,[],[f377]) ).

fof(f377,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> sP79(X0,X1) )
      | ~ sP80(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP80])]) ).

fof(f48780,plain,
    ~ sP79(xD,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(unit_resulting_resolution,[],[f756,f29922,f1167]) ).

fof(f1167,plain,
    ! [X3,X0,X1] :
      ( ~ sP79(X0,X1)
      | ~ aElementOf0(X3,X1)
      | aElementOf0(X3,X0) ),
    inference(cnf_transformation,[],[f666]) ).

fof(f666,plain,
    ! [X0,X1] :
      ( ( sP79(X0,X1)
        | ( ~ aElementOf0(sK143(X0,X1),X0)
          & aElementOf0(sK143(X0,X1),X1) )
        | ~ aSet0(X1) )
      & ( ( ! [X3] :
              ( aElementOf0(X3,X0)
              | ~ aElementOf0(X3,X1) )
          & aSet0(X1) )
        | ~ sP79(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK143])],[f664,f665]) ).

fof(f665,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK143(X0,X1),X0)
        & aElementOf0(sK143(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f664,plain,
    ! [X0,X1] :
      ( ( sP79(X0,X1)
        | ? [X2] :
            ( ~ aElementOf0(X2,X0)
            & aElementOf0(X2,X1) )
        | ~ aSet0(X1) )
      & ( ( ! [X3] :
              ( aElementOf0(X3,X0)
              | ~ aElementOf0(X3,X1) )
          & aSet0(X1) )
        | ~ sP79(X0,X1) ) ),
    inference(rectify,[],[f663]) ).

fof(f663,plain,
    ! [X0,X1] :
      ( ( sP79(X0,X1)
        | ? [X2] :
            ( ~ aElementOf0(X2,X0)
            & aElementOf0(X2,X1) )
        | ~ aSet0(X1) )
      & ( ( ! [X2] :
              ( aElementOf0(X2,X0)
              | ~ aElementOf0(X2,X1) )
          & aSet0(X1) )
        | ~ sP79(X0,X1) ) ),
    inference(flattening,[],[f662]) ).

fof(f662,plain,
    ! [X0,X1] :
      ( ( sP79(X0,X1)
        | ? [X2] :
            ( ~ aElementOf0(X2,X0)
            & aElementOf0(X2,X1) )
        | ~ aSet0(X1) )
      & ( ( ! [X2] :
              ( aElementOf0(X2,X0)
              | ~ aElementOf0(X2,X1) )
          & aSet0(X1) )
        | ~ sP79(X0,X1) ) ),
    inference(nnf_transformation,[],[f376]) ).

fof(f376,plain,
    ! [X0,X1] :
      ( sP79(X0,X1)
    <=> ( ! [X2] :
            ( aElementOf0(X2,X0)
            | ~ aElementOf0(X2,X1) )
        & aSet0(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP79])]) ).

fof(f29922,plain,
    aElementOf0(sK108,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(unit_resulting_resolution,[],[f755,f925]) ).

fof(f925,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xP)
      | aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f157,plain,
    ( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    & ! [X0] :
        ( aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aElementOf0(X0,xP) ) ),
    inference(ennf_transformation,[],[f113]) ).

fof(f113,axiom,
    ( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    & ! [X0] :
        ( aElementOf0(X0,xP)
       => aElementOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    file('/export/starexec/sandbox/tmp/tmp.k9ppb9alA8/Vampire---4.8_4500',m__5334) ).

fof(f755,plain,
    aElementOf0(sK108,xP),
    inference(cnf_transformation,[],[f416]) ).

fof(f416,plain,
    ( ~ aElementOf0(xP,slbdtsldtrb0(xD,xk))
    & ~ aSubsetOf0(xP,xD)
    & ~ aElementOf0(sK108,xD)
    & aElementOf0(sK108,xP) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f140,f415]) ).

fof(f415,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,xD)
        & aElementOf0(X0,xP) )
   => ( ~ aElementOf0(sK108,xD)
      & aElementOf0(sK108,xP) ) ),
    introduced(choice_axiom,[]) ).

fof(f140,plain,
    ( ~ aElementOf0(xP,slbdtsldtrb0(xD,xk))
    & ~ aSubsetOf0(xP,xD)
    & ? [X0] :
        ( ~ aElementOf0(X0,xD)
        & aElementOf0(X0,xP) ) ),
    inference(ennf_transformation,[],[f116]) ).

fof(f116,negated_conjecture,
    ~ ( aElementOf0(xP,slbdtsldtrb0(xD,xk))
      | aSubsetOf0(xP,xD)
      | ! [X0] :
          ( aElementOf0(X0,xP)
         => aElementOf0(X0,xD) ) ),
    inference(negated_conjecture,[],[f115]) ).

fof(f115,conjecture,
    ( aElementOf0(xP,slbdtsldtrb0(xD,xk))
    | aSubsetOf0(xP,xD)
    | ! [X0] :
        ( aElementOf0(X0,xP)
       => aElementOf0(X0,xD) ) ),
    file('/export/starexec/sandbox/tmp/tmp.k9ppb9alA8/Vampire---4.8_4500',m__) ).

fof(f756,plain,
    ~ aElementOf0(sK108,xD),
    inference(cnf_transformation,[],[f416]) ).

fof(f1343,plain,
    sP80(xD),
    inference(unit_resulting_resolution,[],[f940,f1170]) ).

fof(f1170,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | sP80(X0) ),
    inference(cnf_transformation,[],[f378]) ).

fof(f378,plain,
    ! [X0] :
      ( sP80(X0)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f208,f377,f376]) ).

fof(f208,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
                | ~ aElementOf0(X2,X1) )
            & aSet0(X1) ) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,X0) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.k9ppb9alA8/Vampire---4.8_4500',mDefSub) ).

fof(f940,plain,
    aSet0(xD),
    inference(cnf_transformation,[],[f495]) ).

fof(f495,plain,
    ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
    & ! [X0] :
        ( ( aElementOf0(X0,xD)
          | szmzizndt0(sdtlpdtrp0(xN,xn)) = X0
          | ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
          | ~ aElement0(X0) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X0
            & aElementOf0(X0,sdtlpdtrp0(xN,xn))
            & aElement0(X0) )
          | ~ aElementOf0(X0,xD) ) )
    & aSet0(xD)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xn)) ) ),
    inference(flattening,[],[f494]) ).

fof(f494,plain,
    ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
    & ! [X0] :
        ( ( aElementOf0(X0,xD)
          | szmzizndt0(sdtlpdtrp0(xN,xn)) = X0
          | ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
          | ~ aElement0(X0) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X0
            & aElementOf0(X0,sdtlpdtrp0(xN,xn))
            & aElement0(X0) )
          | ~ aElementOf0(X0,xD) ) )
    & aSet0(xD)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xn)) ) ),
    inference(nnf_transformation,[],[f163]) ).

fof(f163,plain,
    ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
    & ! [X0] :
        ( aElementOf0(X0,xD)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xn))
          & aElement0(X0) ) )
    & aSet0(xD)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xn)) ) ),
    inference(ennf_transformation,[],[f125]) ).

fof(f125,plain,
    ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
    & ! [X0] :
        ( aElementOf0(X0,xD)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xn))
          & aElement0(X0) ) )
    & aSet0(xD)
    & ! [X1] :
        ( aElementOf0(X1,sdtlpdtrp0(xN,xn))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) ) ),
    inference(rectify,[],[f114]) ).

fof(f114,axiom,
    ( xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))
    & ! [X0] :
        ( aElementOf0(X0,xD)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xn)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xn))
          & aElement0(X0) ) )
    & aSet0(xD)
    & ! [X0] :
        ( aElementOf0(X0,sdtlpdtrp0(xN,xn))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.k9ppb9alA8/Vampire---4.8_4500',m__5585) ).

fof(f283871,plain,
    aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xD),
    inference(forward_demodulation,[],[f283819,f945]) ).

fof(f945,plain,
    xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
    inference(cnf_transformation,[],[f495]) ).

fof(f283819,plain,
    aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
    inference(unit_resulting_resolution,[],[f251656,f856]) ).

fof(f856,plain,
    ! [X0] :
      ( ~ sP23(X0)
      | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
    inference(cnf_transformation,[],[f470]) ).

fof(f470,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        & ! [X1] :
            ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
        & sP22(X0)
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        & ! [X2] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      | ~ sP23(X0) ),
    inference(rectify,[],[f469]) ).

fof(f469,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        & ! [X2] :
            ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
        & sP22(X0)
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        & ! [X4] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
            | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      | ~ sP23(X0) ),
    inference(nnf_transformation,[],[f307]) ).

fof(f307,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        & ! [X2] :
            ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
        & sP22(X0)
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        & ! [X4] :
            ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
            | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
      | ~ sP23(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).

fof(f251656,plain,
    sP23(xn),
    inference(unit_resulting_resolution,[],[f908,f1748,f2276,f870]) ).

fof(f870,plain,
    ! [X0] :
      ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,X0))
      | sP23(X0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f308,plain,
    ( ! [X0] :
        ( sP23(X0)
        | ~ isCountable0(sdtlpdtrp0(xN,X0))
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
          & sP20(X0) )
        | ~ aElementOf0(X0,szNzAzT0) )
    & xS = sdtlpdtrp0(xN,sz00)
    & szNzAzT0 = szDzozmdt0(xN)
    & aFunction0(xN) ),
    inference(definition_folding,[],[f149,f307,f306,f305,f304]) ).

fof(f304,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ aElementOf0(X1,szNzAzT0)
          & aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
      | ~ aSet0(sdtlpdtrp0(xN,X0))
      | ~ sP20(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).

fof(f305,plain,
    ! [X3,X0] :
      ( sP21(X3,X0)
    <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
        & aElementOf0(X3,sdtlpdtrp0(xN,X0))
        & aElement0(X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).

fof(f306,plain,
    ! [X0] :
      ( ! [X3] :
          ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        <=> sP21(X3,X0) )
      | ~ sP22(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).

fof(f149,plain,
    ( ! [X0] :
        ( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X2] :
              ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              | ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
          & ! [X3] :
              ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                & aElement0(X3) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X4] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
              | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
        | ~ isCountable0(sdtlpdtrp0(xN,X0))
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
          & ( ? [X1] :
                ( ~ aElementOf0(X1,szNzAzT0)
                & aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
            | ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
        | ~ aElementOf0(X0,szNzAzT0) )
    & xS = sdtlpdtrp0(xN,sz00)
    & szNzAzT0 = szDzozmdt0(xN)
    & aFunction0(xN) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ( ! [X0] :
        ( ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X2] :
              ( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              | ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
          & ! [X3] :
              ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                & aElement0(X3) ) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
          & ! [X4] :
              ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4)
              | ~ aElementOf0(X4,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) )
        | ~ isCountable0(sdtlpdtrp0(xN,X0))
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
          & ( ? [X1] :
                ( ~ aElementOf0(X1,szNzAzT0)
                & aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
            | ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
        | ~ aElementOf0(X0,szNzAzT0) )
    & xS = sdtlpdtrp0(xN,sz00)
    & szNzAzT0 = szDzozmdt0(xN)
    & aFunction0(xN) ),
    inference(ennf_transformation,[],[f119]) ).

fof(f119,plain,
    ( ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
       => ( ( isCountable0(sdtlpdtrp0(xN,X0))
            & ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
              | ( ! [X1] :
                    ( aElementOf0(X1,sdtlpdtrp0(xN,X0))
                   => aElementOf0(X1,szNzAzT0) )
                & aSet0(sdtlpdtrp0(xN,X0)) ) ) )
         => ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X2] :
                ( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
               => aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
            & ! [X3] :
                ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
                  & aElementOf0(X3,sdtlpdtrp0(xN,X0))
                  & aElement0(X3) ) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X4] :
                ( aElementOf0(X4,sdtlpdtrp0(xN,X0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X4) )
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
    & xS = sdtlpdtrp0(xN,sz00)
    & szNzAzT0 = szDzozmdt0(xN)
    & aFunction0(xN) ),
    inference(rectify,[],[f81]) ).

fof(f81,axiom,
    ( ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
       => ( ( isCountable0(sdtlpdtrp0(xN,X0))
            & ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
              | ( ! [X1] :
                    ( aElementOf0(X1,sdtlpdtrp0(xN,X0))
                   => aElementOf0(X1,szNzAzT0) )
                & aSet0(sdtlpdtrp0(xN,X0)) ) ) )
         => ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X1] :
                ( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
               => aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
            & ! [X1] :
                ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
              <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
                  & aElementOf0(X1,sdtlpdtrp0(xN,X0))
                  & aElement0(X1) ) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            & ! [X1] :
                ( aElementOf0(X1,sdtlpdtrp0(xN,X0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
    & xS = sdtlpdtrp0(xN,sz00)
    & szNzAzT0 = szDzozmdt0(xN)
    & aFunction0(xN) ),
    file('/export/starexec/sandbox/tmp/tmp.k9ppb9alA8/Vampire---4.8_4500',m__3623) ).

fof(f2276,plain,
    aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0),
    inference(unit_resulting_resolution,[],[f1393,f948]) ).

fof(f948,plain,
    ! [X0] :
      ( ~ sP24(X0)
      | aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
    inference(cnf_transformation,[],[f496]) ).

fof(f496,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,szNzAzT0)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aSet0(sdtlpdtrp0(xN,X0)) )
      | ~ sP24(X0) ),
    inference(nnf_transformation,[],[f309]) ).

fof(f309,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,szNzAzT0)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aSet0(sdtlpdtrp0(xN,X0)) )
      | ~ sP24(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).

fof(f1393,plain,
    sP24(xn),
    inference(unit_resulting_resolution,[],[f908,f950]) ).

fof(f950,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | sP24(X0) ),
    inference(cnf_transformation,[],[f310]) ).

fof(f310,plain,
    ! [X0] :
      ( sP24(X0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(definition_folding,[],[f164,f309]) ).

fof(f164,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,szNzAzT0)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aSet0(sdtlpdtrp0(xN,X0)) )
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f82,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,sdtlpdtrp0(xN,X0))
           => aElementOf0(X1,szNzAzT0) )
        & aSet0(sdtlpdtrp0(xN,X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.k9ppb9alA8/Vampire---4.8_4500',m__3671) ).

fof(f1748,plain,
    isCountable0(sdtlpdtrp0(xN,xn)),
    inference(unit_resulting_resolution,[],[f1393,f949]) ).

fof(f949,plain,
    ! [X0] :
      ( ~ sP24(X0)
      | isCountable0(sdtlpdtrp0(xN,X0)) ),
    inference(cnf_transformation,[],[f496]) ).

fof(f908,plain,
    aElementOf0(xn,szNzAzT0),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,axiom,
    ( xp = sdtlpdtrp0(xe,xn)
    & aElementOf0(xn,szNzAzT0)
    & aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & szDzizrdt0(xd) = sdtlpdtrp0(xd,xn)
    & aElementOf0(xn,szDzozmdt0(xd)) ),
    file('/export/starexec/sandbox/tmp/tmp.k9ppb9alA8/Vampire---4.8_4500',m__5309) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : NUM629+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37  % Computer : n022.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Wed Aug 30 14:59:23 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.23/0.42  % (4734)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43  % (4743)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.23/0.43  % (4737)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.23/0.43  % (4738)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.23/0.43  % (4740)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.43  % (4739)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.23/0.43  % (4741)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.23/0.43  % (4742)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.23/0.49  TRYING [1]
% 0.23/0.50  TRYING [2]
% 1.19/0.58  TRYING [3]
% 3.15/0.86  TRYING [4]
% 8.53/1.64  TRYING [5]
% 16.00/2.78  TRYING [1]
% 17.57/2.99  TRYING [1]
% 18.11/3.06  TRYING [2]
% 19.01/3.19  TRYING [2]
% 20.18/3.35  TRYING [6]
% 29.18/4.58  % (4743)First to succeed.
% 29.18/4.59  % (4743)Refutation found. Thanks to Tanya!
% 29.18/4.59  % SZS status Theorem for Vampire---4
% 29.18/4.59  % SZS output start Proof for Vampire---4
% See solution above
% 29.18/4.59  % (4743)------------------------------
% 29.18/4.59  % (4743)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 29.18/4.59  % (4743)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 29.18/4.59  % (4743)Termination reason: Refutation
% 29.18/4.59  
% 29.18/4.59  % (4743)Memory used [KB]: 156202
% 29.18/4.59  % (4743)Time elapsed: 4.152 s
% 29.18/4.59  % (4743)------------------------------
% 29.18/4.59  % (4743)------------------------------
% 29.18/4.59  % (4734)Success in time 4.214 s
% 29.18/4.59  % Vampire---4.8 exiting
%------------------------------------------------------------------------------