TSTP Solution File: NUM574+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM574+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 : n003.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 12:12:13 EDT 2023

% Result   : Theorem 0.22s 0.44s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   65 (  22 unt;   0 def)
%            Number of atoms       :  281 (  58 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  317 ( 101   ~;  82   |; 104   &)
%                                         (   5 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   9 con; 0-2 aty)
%            Number of variables   :   69 (;  56   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f964,plain,
    $false,
    inference(subsumption_resolution,[],[f956,f938]) ).

fof(f938,plain,
    aElementOf0(sK22,xS),
    inference(backward_demodulation,[],[f656,f936]) ).

fof(f936,plain,
    xS = sF53,
    inference(forward_demodulation,[],[f932,f409]) ).

fof(f409,plain,
    xS = sdtlpdtrp0(xN,sz00),
    inference(cnf_transformation,[],[f256]) ).

fof(f256,plain,
    ( ! [X0] :
        ( sP1(X0)
        | ~ isCountable0(sdtlpdtrp0(xN,X0))
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
          & ( ( ~ aElementOf0(sK25(X0),szNzAzT0)
              & aElementOf0(sK25(X0),sdtlpdtrp0(xN,X0)) )
            | ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
        | ~ aElementOf0(X0,szNzAzT0) )
    & xS = sdtlpdtrp0(xN,sz00)
    & szNzAzT0 = szDzozmdt0(xN)
    & aFunction0(xN) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f214,f255]) ).

fof(f255,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ aElementOf0(X1,szNzAzT0)
          & aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
     => ( ~ aElementOf0(sK25(X0),szNzAzT0)
        & aElementOf0(sK25(X0),sdtlpdtrp0(xN,X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f214,plain,
    ( ! [X0] :
        ( sP1(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(definition_folding,[],[f104,f213,f212]) ).

fof(f212,plain,
    ! [X0] :
      ( ! [X3] :
          ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
            & aElementOf0(X3,sdtlpdtrp0(xN,X0))
            & aElement0(X3) ) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f213,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)))
        & sP0(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)) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f104,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,[],[f103]) ).

fof(f103,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,[],[f89]) ).

fof(f89,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/sandbox2/tmp/tmp.tMeyjiz0td/Vampire---4.8_557',m__3623) ).

fof(f932,plain,
    sdtlpdtrp0(xN,sz00) = sF53,
    inference(backward_demodulation,[],[f652,f927]) ).

fof(f927,plain,
    sz00 = xi,
    inference(subsumption_resolution,[],[f926,f422]) ).

fof(f422,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,axiom,
    ( aElementOf0(xi,szNzAzT0)
    & aElementOf0(xj,szNzAzT0) ),
    file('/export/starexec/sandbox2/tmp/tmp.tMeyjiz0td/Vampire---4.8_557',m__3786) ).

fof(f926,plain,
    ( sz00 = xi
    | ~ aElementOf0(xi,szNzAzT0) ),
    inference(equality_resolution,[],[f925]) ).

fof(f925,plain,
    ! [X10] :
      ( xi != X10
      | sz00 = X10
      | ~ aElementOf0(X10,szNzAzT0) ),
    inference(subsumption_resolution,[],[f919,f525]) ).

fof(f525,plain,
    ! [X0] :
      ( aElementOf0(sK41(X0),szNzAzT0)
      | sz00 = X0
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f315]) ).

fof(f315,plain,
    ! [X0] :
      ( ( szszuzczcdt0(sK41(X0)) = X0
        & aElementOf0(sK41(X0),szNzAzT0) )
      | sz00 = X0
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f151,f314]) ).

fof(f314,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aElementOf0(X1,szNzAzT0) )
     => ( szszuzczcdt0(sK41(X0)) = X0
        & aElementOf0(sK41(X0),szNzAzT0) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aElementOf0(X1,szNzAzT0) )
      | sz00 = X0
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ? [X1] :
          ( szszuzczcdt0(X1) = X0
          & aElementOf0(X1,szNzAzT0) )
      | sz00 = X0
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ( ? [X1] :
            ( szszuzczcdt0(X1) = X0
            & aElementOf0(X1,szNzAzT0) )
        | sz00 = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tMeyjiz0td/Vampire---4.8_557',mNatExtra) ).

fof(f919,plain,
    ! [X10] :
      ( xi != X10
      | ~ aElementOf0(sK41(X10),szNzAzT0)
      | sz00 = X10
      | ~ aElementOf0(X10,szNzAzT0) ),
    inference(superposition,[],[f663,f526]) ).

fof(f526,plain,
    ! [X0] :
      ( szszuzczcdt0(sK41(X0)) = X0
      | sz00 = X0
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f315]) ).

fof(f663,plain,
    ! [X1] :
      ( szszuzczcdt0(X1) != xi
      | ~ aElementOf0(X1,szNzAzT0) ),
    inference(subsumption_resolution,[],[f662,f654]) ).

fof(f654,plain,
    ~ aSubsetOf0(sF53,sF54),
    inference(definition_folding,[],[f376,f653,f652]) ).

fof(f653,plain,
    sdtlpdtrp0(xN,xj) = sF54,
    introduced(function_definition,[]) ).

fof(f376,plain,
    ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
    inference(cnf_transformation,[],[f244]) ).

fof(f244,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    & ~ aElementOf0(sK22,sdtlpdtrp0(xN,xj))
    & aElementOf0(sK22,sdtlpdtrp0(xN,xi))
    & sdtlseqdt0(xj,xi) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f100,f243]) ).

fof(f243,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xj))
        & aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
   => ( ~ aElementOf0(sK22,sdtlpdtrp0(xN,xj))
      & aElementOf0(sK22,sdtlpdtrp0(xN,xi)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    & ? [X0] :
        ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xj))
        & aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
    & sdtlseqdt0(xj,xi) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    & ? [X0] :
        ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xj))
        & aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
    & sdtlseqdt0(xj,xi) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f87,negated_conjecture,
    ~ ( sdtlseqdt0(xj,xi)
     => ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
        | ! [X0] :
            ( aElementOf0(X0,sdtlpdtrp0(xN,xi))
           => aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ),
    inference(negated_conjecture,[],[f86]) ).

fof(f86,conjecture,
    ( sdtlseqdt0(xj,xi)
   => ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      | ! [X0] :
          ( aElementOf0(X0,sdtlpdtrp0(xN,xi))
         => aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tMeyjiz0td/Vampire---4.8_557',m__) ).

fof(f662,plain,
    ! [X1] :
      ( aSubsetOf0(sF53,sF54)
      | szszuzczcdt0(X1) != xi
      | ~ aElementOf0(X1,szNzAzT0) ),
    inference(forward_demodulation,[],[f661,f652]) ).

fof(f661,plain,
    ! [X1] :
      ( aSubsetOf0(sdtlpdtrp0(xN,xi),sF54)
      | szszuzczcdt0(X1) != xi
      | ~ aElementOf0(X1,szNzAzT0) ),
    inference(forward_demodulation,[],[f660,f653]) ).

fof(f660,plain,
    ! [X1] :
      ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      | szszuzczcdt0(X1) != xi
      | ~ aElementOf0(X1,szNzAzT0) ),
    inference(subsumption_resolution,[],[f659,f373]) ).

fof(f373,plain,
    sdtlseqdt0(xj,xi),
    inference(cnf_transformation,[],[f244]) ).

fof(f659,plain,
    ! [X1] :
      ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      | ~ sdtlseqdt0(xj,xi)
      | szszuzczcdt0(X1) != xi
      | ~ aElementOf0(X1,szNzAzT0) ),
    inference(duplicate_literal_removal,[],[f424]) ).

fof(f424,plain,
    ! [X1] :
      ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      | ~ sdtlseqdt0(xj,xi)
      | szszuzczcdt0(X1) != xi
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ sdtlseqdt0(xj,xi) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f257,plain,
    ( ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      & ! [X0] :
          ( aElementOf0(X0,sdtlpdtrp0(xN,xj))
          | ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) )
    | ~ sdtlseqdt0(xj,xi)
    | ! [X1] :
        ( szszuzczcdt0(X1) != xi
        | ~ aElementOf0(X1,szNzAzT0) )
    | ~ sdtlseqdt0(xj,xi) ),
    inference(rectify,[],[f107]) ).

fof(f107,plain,
    ( ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      & ! [X1] :
          ( aElementOf0(X1,sdtlpdtrp0(xN,xj))
          | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ) )
    | ~ sdtlseqdt0(xj,xi)
    | ! [X0] :
        ( szszuzczcdt0(X0) != xi
        | ~ aElementOf0(X0,szNzAzT0) )
    | ~ sdtlseqdt0(xj,xi) ),
    inference(flattening,[],[f106]) ).

fof(f106,plain,
    ( ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
      & ! [X1] :
          ( aElementOf0(X1,sdtlpdtrp0(xN,xj))
          | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ) )
    | ~ sdtlseqdt0(xj,xi)
    | ! [X0] :
        ( szszuzczcdt0(X0) != xi
        | ~ aElementOf0(X0,szNzAzT0) )
    | ~ sdtlseqdt0(xj,xi) ),
    inference(ennf_transformation,[],[f90]) ).

fof(f90,plain,
    ( ( ? [X0] :
          ( szszuzczcdt0(X0) = xi
          & aElementOf0(X0,szNzAzT0) )
      & sdtlseqdt0(xj,xi) )
   => ( sdtlseqdt0(xj,xi)
     => ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
        & ! [X1] :
            ( aElementOf0(X1,sdtlpdtrp0(xN,xi))
           => aElementOf0(X1,sdtlpdtrp0(xN,xj)) ) ) ) ),
    inference(rectify,[],[f85]) ).

fof(f85,axiom,
    ( ( ? [X0] :
          ( szszuzczcdt0(X0) = xi
          & aElementOf0(X0,szNzAzT0) )
      & sdtlseqdt0(xj,xi) )
   => ( sdtlseqdt0(xj,xi)
     => ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
        & ! [X0] :
            ( aElementOf0(X0,sdtlpdtrp0(xN,xi))
           => aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.tMeyjiz0td/Vampire---4.8_557',m__3786_02) ).

fof(f652,plain,
    sdtlpdtrp0(xN,xi) = sF53,
    introduced(function_definition,[]) ).

fof(f656,plain,
    aElementOf0(sK22,sF53),
    inference(definition_folding,[],[f374,f652]) ).

fof(f374,plain,
    aElementOf0(sK22,sdtlpdtrp0(xN,xi)),
    inference(cnf_transformation,[],[f244]) ).

fof(f956,plain,
    ~ aElementOf0(sK22,xS),
    inference(backward_demodulation,[],[f655,f955]) ).

fof(f955,plain,
    xS = sF54,
    inference(forward_demodulation,[],[f954,f409]) ).

fof(f954,plain,
    sdtlpdtrp0(xN,sz00) = sF54,
    inference(backward_demodulation,[],[f653,f951]) ).

fof(f951,plain,
    sz00 = xj,
    inference(subsumption_resolution,[],[f948,f421]) ).

fof(f421,plain,
    aElementOf0(xj,szNzAzT0),
    inference(cnf_transformation,[],[f83]) ).

fof(f948,plain,
    ( sz00 = xj
    | ~ aElementOf0(xj,szNzAzT0) ),
    inference(resolution,[],[f921,f928]) ).

fof(f928,plain,
    sdtlseqdt0(xj,sz00),
    inference(backward_demodulation,[],[f373,f927]) ).

fof(f921,plain,
    ! [X1] :
      ( ~ sdtlseqdt0(X1,sz00)
      | sz00 = X1
      | ~ aElementOf0(X1,szNzAzT0) ),
    inference(subsumption_resolution,[],[f912,f525]) ).

fof(f912,plain,
    ! [X1] :
      ( ~ sdtlseqdt0(X1,sz00)
      | ~ aElementOf0(sK41(X1),szNzAzT0)
      | sz00 = X1
      | ~ aElementOf0(X1,szNzAzT0) ),
    inference(superposition,[],[f519,f526]) ).

fof(f519,plain,
    ! [X0] :
      ( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ! [X0] :
      ( ~ sdtlseqdt0(szszuzczcdt0(X0),sz00)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ~ sdtlseqdt0(szszuzczcdt0(X0),sz00) ),
    file('/export/starexec/sandbox2/tmp/tmp.tMeyjiz0td/Vampire---4.8_557',mNoScLessZr) ).

fof(f655,plain,
    ~ aElementOf0(sK22,sF54),
    inference(definition_folding,[],[f375,f653]) ).

fof(f375,plain,
    ~ aElementOf0(sK22,sdtlpdtrp0(xN,xj)),
    inference(cnf_transformation,[],[f244]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM574+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n003.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   : Fri Aug 25 11:46:38 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.tMeyjiz0td/Vampire---4.8_557
% 0.14/0.36  % (683)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (685)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.42  % (687)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.42  % (686)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)
% 0.22/0.42  % (688)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)
% 0.22/0.42  % (684)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)
% 0.22/0.42  % (689)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)
% 0.22/0.44  % (687)First to succeed.
% 0.22/0.44  % (687)Refutation found. Thanks to Tanya!
% 0.22/0.44  % SZS status Theorem for Vampire---4
% 0.22/0.44  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45  % (687)------------------------------
% 0.22/0.45  % (687)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45  % (687)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45  % (687)Termination reason: Refutation
% 0.22/0.45  
% 0.22/0.45  % (687)Memory used [KB]: 6140
% 0.22/0.45  % (687)Time elapsed: 0.022 s
% 0.22/0.45  % (687)------------------------------
% 0.22/0.45  % (687)------------------------------
% 0.22/0.45  % (683)Success in time 0.084 s
% 0.22/0.45  % Vampire---4.8 exiting
%------------------------------------------------------------------------------