TSTP Solution File: NUM573+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM573+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 : Tue Apr 30 14:34:07 EDT 2024

% Result   : Theorem 124.05s 18.11s
% Output   : Refutation 124.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   79 (  23 unt;   0 def)
%            Number of atoms       :  376 (  36 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  421 ( 124   ~; 111   |; 149   &)
%                                         (   6 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :  113 (  99   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f896540,plain,
    $false,
    inference(subsumption_resolution,[],[f889425,f481]) ).

fof(f481,plain,
    ~ aElementOf0(sK58,sdtlpdtrp0(xN,xj)),
    inference(cnf_transformation,[],[f287]) ).

fof(f287,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
    & ~ aElementOf0(sK58,sdtlpdtrp0(xN,xj))
    & aElementOf0(sK58,sdtlpdtrp0(xN,xi))
    & sdtlseqdt0(xj,xi)
    & xi = szszuzczcdt0(sK59)
    & aElementOf0(sK59,szNzAzT0)
    & sdtlseqdt0(xj,xi) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59])],[f284,f286,f285]) ).

fof(f285,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xj))
        & aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
   => ( ~ aElementOf0(sK58,sdtlpdtrp0(xN,xj))
      & aElementOf0(sK58,sdtlpdtrp0(xN,xi)) ) ),
    introduced(choice_axiom,[]) ).

fof(f286,plain,
    ( ? [X1] :
        ( szszuzczcdt0(X1) = xi
        & aElementOf0(X1,szNzAzT0) )
   => ( xi = szszuzczcdt0(sK59)
      & aElementOf0(sK59,szNzAzT0) ) ),
    introduced(choice_axiom,[]) ).

fof(f284,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,[],[f99]) ).

fof(f99,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,[],[f98]) ).

fof(f98,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,[],[f87]) ).

fof(f87,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,[],[f86]) ).

fof(f86,negated_conjecture,
    ~ ( ( ? [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)) ) ) ) ),
    inference(negated_conjecture,[],[f85]) ).

fof(f85,conjecture,
    ( ( ? [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/benchmark/theBenchmark.p',m__) ).

fof(f889425,plain,
    aElementOf0(sK58,sdtlpdtrp0(xN,xj)),
    inference(superposition,[],[f480,f889315]) ).

fof(f889315,plain,
    xj = xi,
    inference(unit_resulting_resolution,[],[f533,f532,f479,f889124,f757]) ).

fof(f757,plain,
    ! [X0,X1] :
      ( ~ sdtlseqdt0(X1,X0)
      | X0 = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f197]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X0,szNzAzT0) )
     => ( ( sdtlseqdt0(X1,X0)
          & sdtlseqdt0(X0,X1) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).

fof(f889124,plain,
    sdtlseqdt0(xi,xj),
    inference(forward_demodulation,[],[f889092,f478]) ).

fof(f478,plain,
    xi = szszuzczcdt0(sK59),
    inference(cnf_transformation,[],[f287]) ).

fof(f889092,plain,
    sdtlseqdt0(szszuzczcdt0(sK59),xj),
    inference(unit_resulting_resolution,[],[f532,f477,f888949,f755]) ).

fof(f755,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,szNzAzT0)
      | sdtlseqdt0(X0,X1)
      | sdtlseqdt0(szszuzczcdt0(X1),X0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(szszuzczcdt0(X1),X0)
      | sdtlseqdt0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f193]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(szszuzczcdt0(X1),X0)
      | sdtlseqdt0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X0,szNzAzT0) )
     => ( sdtlseqdt0(szszuzczcdt0(X1),X0)
        | sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).

fof(f888949,plain,
    ~ sdtlseqdt0(xj,sK59),
    inference(unit_resulting_resolution,[],[f477,f532,f1210,f481,f888939,f580]) ).

fof(f580,plain,
    ! [X2,X0,X1] :
      ( ~ iLess0(X0,xi)
      | ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
      | aElementOf0(X2,sdtlpdtrp0(xN,X1))
      | ~ sdtlseqdt0(X1,X0)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
        & ! [X2] :
            ( aElementOf0(X2,sdtlpdtrp0(xN,X1))
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
      | ~ iLess0(X0,xi)
      | ~ sdtlseqdt0(X1,X0)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
        & ! [X2] :
            ( aElementOf0(X2,sdtlpdtrp0(xN,X1))
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
      | ~ iLess0(X0,xi)
      | ~ sdtlseqdt0(X1,X0)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X0,szNzAzT0) )
     => ( sdtlseqdt0(X1,X0)
       => ( iLess0(X0,xi)
         => ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
            & ! [X2] :
                ( aElementOf0(X2,sdtlpdtrp0(xN,X0))
               => aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3754) ).

fof(f888939,plain,
    aElementOf0(sK58,sdtlpdtrp0(xN,sK59)),
    inference(unit_resulting_resolution,[],[f888826,f514]) ).

fof(f514,plain,
    ! [X0,X1] :
      ( ~ sP3(X0,X1)
      | aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
    inference(cnf_transformation,[],[f304]) ).

fof(f304,plain,
    ! [X0,X1] :
      ( ( sP3(X0,X1)
        | szmzizndt0(sdtlpdtrp0(xN,X1)) = X0
        | ~ aElementOf0(X0,sdtlpdtrp0(xN,X1))
        | ~ aElement0(X0) )
      & ( ( szmzizndt0(sdtlpdtrp0(xN,X1)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,X1))
          & aElement0(X0) )
        | ~ sP3(X0,X1) ) ),
    inference(rectify,[],[f303]) ).

fof(f303,plain,
    ! [X3,X0] :
      ( ( sP3(X3,X0)
        | szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
        | ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
        | ~ aElement0(X3) )
      & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
          & aElementOf0(X3,sdtlpdtrp0(xN,X0))
          & aElement0(X3) )
        | ~ sP3(X3,X0) ) ),
    inference(flattening,[],[f302]) ).

fof(f302,plain,
    ! [X3,X0] :
      ( ( sP3(X3,X0)
        | szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
        | ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
        | ~ aElement0(X3) )
      & ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
          & aElementOf0(X3,sdtlpdtrp0(xN,X0))
          & aElement0(X3) )
        | ~ sP3(X3,X0) ) ),
    inference(nnf_transformation,[],[f213]) ).

fof(f213,plain,
    ! [X3,X0] :
      ( sP3(X3,X0)
    <=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
        & aElementOf0(X3,sdtlpdtrp0(xN,X0))
        & aElement0(X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f888826,plain,
    sP3(sK58,sK59),
    inference(unit_resulting_resolution,[],[f149390,f348125,f511]) ).

fof(f511,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
      | sP3(X1,X0)
      | ~ sP4(X0) ),
    inference(cnf_transformation,[],[f301]) ).

fof(f301,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            | ~ sP3(X1,X0) )
          & ( sP3(X1,X0)
            | ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
      | ~ sP4(X0) ),
    inference(rectify,[],[f300]) ).

fof(f300,plain,
    ! [X0] :
      ( ! [X3] :
          ( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
            | ~ sP3(X3,X0) )
          & ( sP3(X3,X0)
            | ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
      | ~ sP4(X0) ),
    inference(nnf_transformation,[],[f214]) ).

fof(f214,plain,
    ! [X0] :
      ( ! [X3] :
          ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
        <=> sP3(X3,X0) )
      | ~ sP4(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f348125,plain,
    aElementOf0(sK58,sdtmndt0(sdtlpdtrp0(xN,sK59),szmzizndt0(sdtlpdtrp0(xN,sK59)))),
    inference(unit_resulting_resolution,[],[f480,f204755]) ).

fof(f204755,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
      | aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK59),szmzizndt0(sdtlpdtrp0(xN,sK59)))) ),
    inference(subsumption_resolution,[],[f204751,f149336]) ).

fof(f149336,plain,
    sP5(sK59),
    inference(unit_resulting_resolution,[],[f477,f920,f1115,f523]) ).

fof(f523,plain,
    ! [X0] :
      ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,X0))
      | sP5(X0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f216,plain,
    ( ! [X0] :
        ( sP5(X0)
        | ~ isCountable0(sdtlpdtrp0(xN,X0))
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
          & sP2(X0) )
        | ~ aElementOf0(X0,szNzAzT0) )
    & xS = sdtlpdtrp0(xN,sz00)
    & szNzAzT0 = szDzozmdt0(xN)
    & aFunction0(xN) ),
    inference(definition_folding,[],[f103,f215,f214,f213,f212]) ).

fof(f212,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ aElementOf0(X1,szNzAzT0)
          & aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
      | ~ aSet0(sdtlpdtrp0(xN,X0))
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f215,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)))
        & sP4(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)) )
      | ~ sP5(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

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(flattening,[],[f102]) ).

fof(f102,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/benchmark/theBenchmark.p',m__3623) ).

fof(f1115,plain,
    aSubsetOf0(sdtlpdtrp0(xN,sK59),szNzAzT0),
    inference(unit_resulting_resolution,[],[f816,f536]) ).

fof(f536,plain,
    ! [X0] :
      ( ~ sP6(X0)
      | aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f308,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,szNzAzT0)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aSet0(sdtlpdtrp0(xN,X0)) )
      | ~ sP6(X0) ),
    inference(nnf_transformation,[],[f217]) ).

fof(f217,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,szNzAzT0)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aSet0(sdtlpdtrp0(xN,X0)) )
      | ~ sP6(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f816,plain,
    sP6(sK59),
    inference(unit_resulting_resolution,[],[f477,f538]) ).

fof(f538,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | sP6(X0) ),
    inference(cnf_transformation,[],[f218]) ).

fof(f218,plain,
    ! [X0] :
      ( sP6(X0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(definition_folding,[],[f105,f217]) ).

fof(f105,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/sandbox2/benchmark/theBenchmark.p',m__3671) ).

fof(f920,plain,
    isCountable0(sdtlpdtrp0(xN,sK59)),
    inference(unit_resulting_resolution,[],[f816,f537]) ).

fof(f537,plain,
    ! [X0] :
      ( ~ sP6(X0)
      | isCountable0(sdtlpdtrp0(xN,X0)) ),
    inference(cnf_transformation,[],[f308]) ).

fof(f204751,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
      | aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK59),szmzizndt0(sdtlpdtrp0(xN,sK59))))
      | ~ sP5(sK59) ),
    inference(superposition,[],[f508,f478]) ).

fof(f508,plain,
    ! [X0,X1] :
      ( ~ aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
      | aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
      | ~ sP5(X0) ),
    inference(cnf_transformation,[],[f299]) ).

fof(f299,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)))
        & sP4(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)) )
      | ~ sP5(X0) ),
    inference(rectify,[],[f298]) ).

fof(f298,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)))
        & sP4(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)) )
      | ~ sP5(X0) ),
    inference(nnf_transformation,[],[f215]) ).

fof(f149390,plain,
    sP4(sK59),
    inference(unit_resulting_resolution,[],[f149336,f506]) ).

fof(f506,plain,
    ! [X0] :
      ( ~ sP5(X0)
      | sP4(X0) ),
    inference(cnf_transformation,[],[f299]) ).

fof(f1210,plain,
    iLess0(sK59,xi),
    inference(forward_demodulation,[],[f1203,f478]) ).

fof(f1203,plain,
    iLess0(sK59,szszuzczcdt0(sK59)),
    inference(unit_resulting_resolution,[],[f477,f644]) ).

fof(f644,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | iLess0(X0,szszuzczcdt0(X0)) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => iLess0(X0,szszuzczcdt0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).

fof(f477,plain,
    aElementOf0(sK59,szNzAzT0),
    inference(cnf_transformation,[],[f287]) ).

fof(f479,plain,
    sdtlseqdt0(xj,xi),
    inference(cnf_transformation,[],[f287]) ).

fof(f532,plain,
    aElementOf0(xj,szNzAzT0),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,axiom,
    ( aElementOf0(xi,szNzAzT0)
    & aElementOf0(xj,szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).

fof(f533,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnf_transformation,[],[f83]) ).

fof(f480,plain,
    aElementOf0(sK58,sdtlpdtrp0(xN,xi)),
    inference(cnf_transformation,[],[f287]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : NUM573+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36  % Computer : n017.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Mon Apr 29 23:11:18 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.13/0.36  % (1420)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38  % (1423)WARNING: value z3 for option sas not known
% 0.13/0.38  % (1424)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38  % (1426)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 theBenchmark for (522ds/0Mi)
% 0.13/0.38  % (1422)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38  % (1427)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 theBenchmark for (497ds/0Mi)
% 0.13/0.38  % (1421)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38  % (1423)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 theBenchmark for (569ds/0Mi)
% 0.13/0.39  % (1425)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 theBenchmark for (531ds/0Mi)
% 0.20/0.41  TRYING [1]
% 0.20/0.42  TRYING [2]
% 0.20/0.44  TRYING [3]
% 0.20/0.55  TRYING [4]
% 3.65/0.90  TRYING [5]
% 9.22/1.76  TRYING [6]
% 14.39/2.47  TRYING [1]
% 15.58/2.67  TRYING [2]
% 19.92/3.28  TRYING [1]
% 21.95/3.50  TRYING [2]
% 23.53/3.75  TRYING [7]
% 27.42/4.32  TRYING [3]
% 33.26/5.15  TRYING [3]
% 52.81/7.93  TRYING [8]
% 119.86/17.54  TRYING [4]
% 123.61/18.05  % (1427)First to succeed.
% 124.05/18.11  % (1427)Refutation found. Thanks to Tanya!
% 124.05/18.11  % SZS status Theorem for theBenchmark
% 124.05/18.11  % SZS output start Proof for theBenchmark
% See solution above
% 124.05/18.11  % (1427)------------------------------
% 124.05/18.11  % (1427)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 124.05/18.11  % (1427)Termination reason: Refutation
% 124.05/18.11  
% 124.05/18.11  % (1427)Memory used [KB]: 300330
% 124.05/18.11  % (1427)Time elapsed: 17.676 s
% 124.05/18.11  % (1427)Instructions burned: 33633 (million)
% 124.05/18.11  % (1427)------------------------------
% 124.05/18.11  % (1427)------------------------------
% 124.05/18.11  % (1420)Success in time 17.632 s
%------------------------------------------------------------------------------