TSTP Solution File: NUM601+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM601+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 : n009.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 : Sun May  5 08:39:27 EDT 2024

% Result   : Theorem 34.19s 5.28s
% Output   : Refutation 34.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   75 (  19 unt;   0 def)
%            Number of atoms       :  350 (  47 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  381 ( 106   ~;  90   |; 149   &)
%                                         (  10 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   8 con; 0-2 aty)
%            Number of variables   :  122 ( 104   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f442655,plain,
    $false,
    inference(subsumption_resolution,[],[f442654,f41267]) ).

fof(f41267,plain,
    ~ aSubsetOf0(sdtlpdtrp0(xN,sK134(sK108)),xS),
    inference(unit_resulting_resolution,[],[f1284,f35360,f1071]) ).

fof(f1071,plain,
    ! [X0,X1] :
      ( ~ aSubsetOf0(X1,X0)
      | sP79(X0,X1)
      | ~ sP80(X0) ),
    inference(cnf_transformation,[],[f620]) ).

fof(f620,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ~ sP79(X0,X1) )
          & ( sP79(X0,X1)
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ sP80(X0) ),
    inference(nnf_transformation,[],[f344]) ).

fof(f344,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> sP79(X0,X1) )
      | ~ sP80(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP80])]) ).

fof(f35360,plain,
    ~ sP79(xS,sdtlpdtrp0(xN,sK134(sK108))),
    inference(unit_resulting_resolution,[],[f715,f29147,f1074]) ).

fof(f1074,plain,
    ! [X3,X0,X1] :
      ( ~ sP79(X0,X1)
      | ~ aElementOf0(X3,X1)
      | aElementOf0(X3,X0) ),
    inference(cnf_transformation,[],[f625]) ).

fof(f625,plain,
    ! [X0,X1] :
      ( ( sP79(X0,X1)
        | ( ~ aElementOf0(sK141(X0,X1),X0)
          & aElementOf0(sK141(X0,X1),X1) )
        | ~ aSet0(X1) )
      & ( ( ! [X3] :
              ( aElementOf0(X3,X0)
              | ~ aElementOf0(X3,X1) )
          & aSet0(X1) )
        | ~ sP79(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK141])],[f623,f624]) ).

fof(f624,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK141(X0,X1),X0)
        & aElementOf0(sK141(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f623,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,[],[f622]) ).

fof(f622,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,[],[f621]) ).

fof(f621,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,[],[f343]) ).

fof(f343,plain,
    ! [X0,X1] :
      ( sP79(X0,X1)
    <=> ( ! [X2] :
            ( aElementOf0(X2,X0)
            | ~ aElementOf0(X2,X1) )
        & aSet0(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP79])]) ).

fof(f29147,plain,
    aElementOf0(sK108,sdtlpdtrp0(xN,sK134(sK108))),
    inference(forward_demodulation,[],[f29122,f13257]) ).

fof(f13257,plain,
    sK108 = sdtlpdtrp0(xe,sK134(sK108)),
    inference(unit_resulting_resolution,[],[f1339,f1009]) ).

fof(f1009,plain,
    ! [X0] :
      ( ~ sP69(X0)
      | sdtlpdtrp0(xe,sK134(X0)) = X0 ),
    inference(cnf_transformation,[],[f587]) ).

fof(f587,plain,
    ! [X0] :
      ( ( sdtlpdtrp0(xe,sK134(X0)) = X0
        & aElementOf0(sK134(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
        & szDzizrdt0(xd) = sdtlpdtrp0(xd,sK134(X0))
        & aElementOf0(sK134(X0),szNzAzT0) )
      | ~ sP69(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f585,f586]) ).

fof(f586,plain,
    ! [X0] :
      ( ? [X1] :
          ( sdtlpdtrp0(xe,X1) = X0
          & aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
          & aElementOf0(X1,szNzAzT0) )
     => ( sdtlpdtrp0(xe,sK134(X0)) = X0
        & aElementOf0(sK134(X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
        & szDzizrdt0(xd) = sdtlpdtrp0(xd,sK134(X0))
        & aElementOf0(sK134(X0),szNzAzT0) ) ),
    introduced(choice_axiom,[]) ).

fof(f585,plain,
    ! [X0] :
      ( ? [X1] :
          ( sdtlpdtrp0(xe,X1) = X0
          & aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
          & aElementOf0(X1,szNzAzT0) )
      | ~ sP69(X0) ),
    inference(rectify,[],[f584]) ).

fof(f584,plain,
    ! [X0] :
      ( ? [X2] :
          ( sdtlpdtrp0(xe,X2) = X0
          & aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
          & aElementOf0(X2,szNzAzT0) )
      | ~ sP69(X0) ),
    inference(nnf_transformation,[],[f328]) ).

fof(f328,plain,
    ! [X0] :
      ( ? [X2] :
          ( sdtlpdtrp0(xe,X2) = X0
          & aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
          & aElementOf0(X2,szNzAzT0) )
      | ~ sP69(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP69])]) ).

fof(f1339,plain,
    sP69(sK108),
    inference(unit_resulting_resolution,[],[f714,f1011]) ).

fof(f1011,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xO)
      | sP69(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f329,plain,
    ! [X0] :
      ( sP69(X0)
      | ( ~ aElementOf0(X0,xO)
        & ! [X1] :
            ( sdtlpdtrp0(xe,X1) != X0
            | ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
    inference(definition_folding,[],[f143,f328]) ).

fof(f143,plain,
    ! [X0] :
      ( ? [X2] :
          ( sdtlpdtrp0(xe,X2) = X0
          & aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
          & aElementOf0(X2,szNzAzT0) )
      | ( ~ aElementOf0(X0,xO)
        & ! [X1] :
            ( sdtlpdtrp0(xe,X1) != X0
            | ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
    inference(ennf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ( aElementOf0(X0,xO)
        | ? [X1] :
            ( sdtlpdtrp0(xe,X1) = X0
            & aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
     => ? [X2] :
          ( sdtlpdtrp0(xe,X2) = X0
          & aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & szDzizrdt0(xd) = sdtlpdtrp0(xd,X2)
          & aElementOf0(X2,szNzAzT0) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,axiom,
    ! [X0] :
      ( ( aElementOf0(X0,xO)
        | ? [X1] :
            ( sdtlpdtrp0(xe,X1) = X0
            & aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
     => ? [X1] :
          ( sdtlpdtrp0(xe,X1) = X0
          & aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & sdtlpdtrp0(xd,X1) = szDzizrdt0(xd)
          & aElementOf0(X1,szNzAzT0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4982) ).

fof(f714,plain,
    aElementOf0(sK108,xO),
    inference(cnf_transformation,[],[f383]) ).

fof(f383,plain,
    ( ~ aSubsetOf0(xO,xS)
    & ~ aElementOf0(sK108,xS)
    & aElementOf0(sK108,xO) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f119,f382]) ).

fof(f382,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,xS)
        & aElementOf0(X0,xO) )
   => ( ~ aElementOf0(sK108,xS)
      & aElementOf0(sK108,xO) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ( ~ aSubsetOf0(xO,xS)
    & ? [X0] :
        ( ~ aElementOf0(X0,xS)
        & aElementOf0(X0,xO) ) ),
    inference(ennf_transformation,[],[f99]) ).

fof(f99,negated_conjecture,
    ~ ( aSubsetOf0(xO,xS)
      | ! [X0] :
          ( aElementOf0(X0,xO)
         => aElementOf0(X0,xS) ) ),
    inference(negated_conjecture,[],[f98]) ).

fof(f98,conjecture,
    ( aSubsetOf0(xO,xS)
    | ! [X0] :
        ( aElementOf0(X0,xO)
       => aElementOf0(X0,xS) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f29122,plain,
    aElementOf0(sdtlpdtrp0(xe,sK134(sK108)),sdtlpdtrp0(xN,sK134(sK108))),
    inference(unit_resulting_resolution,[],[f1479,f720]) ).

fof(f720,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ),
    inference(cnf_transformation,[],[f384]) ).

fof(f384,plain,
    ! [X0] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
        & ! [X1] :
            ( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f247]) ).

fof(f247,plain,
    ! [X0] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
        & ! [X1] :
            ( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f1479,plain,
    sP0(sK134(sK108)),
    inference(unit_resulting_resolution,[],[f1473,f725]) ).

fof(f725,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f248]) ).

fof(f248,plain,
    ( ! [X0] :
        ( sP0(X0)
        | ~ aElementOf0(X0,szNzAzT0) )
    & szNzAzT0 = szDzozmdt0(xe)
    & aFunction0(xe) ),
    inference(definition_folding,[],[f120,f247]) ).

fof(f120,plain,
    ( ! [X0] :
        ( ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
          & ! [X1] :
              ( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
              | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
          & aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) )
        | ~ aElementOf0(X0,szNzAzT0) )
    & szNzAzT0 = szDzozmdt0(xe)
    & aFunction0(xe) ),
    inference(ennf_transformation,[],[f91]) ).

fof(f91,axiom,
    ( ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
       => ( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
          & ! [X1] :
              ( aElementOf0(X1,sdtlpdtrp0(xN,X0))
             => sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
          & aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0)) ) )
    & szNzAzT0 = szDzozmdt0(xe)
    & aFunction0(xe) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).

fof(f1473,plain,
    aElementOf0(sK134(sK108),szNzAzT0),
    inference(unit_resulting_resolution,[],[f1339,f1006]) ).

fof(f1006,plain,
    ! [X0] :
      ( ~ sP69(X0)
      | aElementOf0(sK134(X0),szNzAzT0) ),
    inference(cnf_transformation,[],[f587]) ).

fof(f715,plain,
    ~ aElementOf0(sK108,xS),
    inference(cnf_transformation,[],[f383]) ).

fof(f1284,plain,
    sP80(xS),
    inference(unit_resulting_resolution,[],[f838,f1077]) ).

fof(f1077,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | sP80(X0) ),
    inference(cnf_transformation,[],[f345]) ).

fof(f345,plain,
    ! [X0] :
      ( sP80(X0)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f175,f344,f343]) ).

fof(f175,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/benchmark/theBenchmark.p',mDefSub) ).

fof(f838,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ( isCountable0(xS)
    & aSubsetOf0(xS,szNzAzT0)
    & ! [X0] :
        ( aElementOf0(X0,szNzAzT0)
        | ~ aElementOf0(X0,xS) )
    & aSet0(xS) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,axiom,
    ( isCountable0(xS)
    & aSubsetOf0(xS,szNzAzT0)
    & ! [X0] :
        ( aElementOf0(X0,xS)
       => aElementOf0(X0,szNzAzT0) )
    & aSet0(xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).

fof(f442654,plain,
    aSubsetOf0(sdtlpdtrp0(xN,sK134(sK108)),xS),
    inference(forward_demodulation,[],[f442402,f822]) ).

fof(f822,plain,
    xS = sdtlpdtrp0(xN,sz00),
    inference(cnf_transformation,[],[f275]) ).

fof(f275,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,[],[f128,f274,f273,f272,f271]) ).

fof(f271,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(f272,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(f273,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(f274,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(f128,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,[],[f127]) ).

fof(f127,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,[],[f102]) ).

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

fof(f442402,plain,
    aSubsetOf0(sdtlpdtrp0(xN,sK134(sK108)),sdtlpdtrp0(xN,sz00)),
    inference(unit_resulting_resolution,[],[f1473,f1534,f1022,f1020]) ).

fof(f1020,plain,
    ! [X0,X1] :
      ( ~ sdtlseqdt0(X1,X0)
      | aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
        & ! [X2] :
            ( aElementOf0(X2,sdtlpdtrp0(xN,X1))
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
      | ~ sdtlseqdt0(X1,X0)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f146]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
        & ! [X2] :
            ( aElementOf0(X2,sdtlpdtrp0(xN,X1))
            | ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
      | ~ sdtlseqdt0(X1,X0)
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X0,szNzAzT0) )
     => ( sdtlseqdt0(X1,X0)
       => ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
          & ! [X2] :
              ( aElementOf0(X2,sdtlpdtrp0(xN,X0))
             => aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).

fof(f1022,plain,
    aElementOf0(sz00,szNzAzT0),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    aElementOf0(sz00,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).

fof(f1534,plain,
    sdtlseqdt0(sz00,sK134(sK108)),
    inference(unit_resulting_resolution,[],[f1473,f1080]) ).

fof(f1080,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szNzAzT0)
      | sdtlseqdt0(sz00,X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,plain,
    ! [X0] :
      ( sdtlseqdt0(sz00,X0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => sdtlseqdt0(sz00,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : NUM601+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 13:46:38 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (13861)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (13864)WARNING: value z3 for option sas not known
% 0.15/0.38  % (13864)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)
% 0.15/0.39  % (13863)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (13865)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (13862)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (13866)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)
% 0.15/0.39  % (13868)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)
% 0.15/0.39  % (13867)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)
% 0.22/0.45  TRYING [1]
% 0.22/0.45  TRYING [2]
% 0.22/0.51  TRYING [3]
% 2.03/0.65  TRYING [4]
% 4.55/1.04  TRYING [5]
% 10.93/1.97  TRYING [6]
% 12.41/2.23  TRYING [1]
% 13.71/2.37  TRYING [2]
% 18.08/2.95  TRYING [1]
% 19.28/3.12  TRYING [2]
% 21.54/3.45  TRYING [3]
% 27.28/4.26  TRYING [3]
% 27.28/4.27  TRYING [7]
% 34.19/5.27  % (13868)First to succeed.
% 34.19/5.27  % (13868)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13861"
% 34.19/5.28  % (13868)Refutation found. Thanks to Tanya!
% 34.19/5.28  % SZS status Theorem for theBenchmark
% 34.19/5.28  % SZS output start Proof for theBenchmark
% See solution above
% 34.19/5.29  % (13868)------------------------------
% 34.19/5.29  % (13868)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 34.19/5.29  % (13868)Termination reason: Refutation
% 34.19/5.29  
% 34.19/5.29  % (13868)Memory used [KB]: 164693
% 34.19/5.29  % (13868)Time elapsed: 4.883 s
% 34.19/5.29  % (13868)Instructions burned: 15447 (million)
% 34.19/5.29  % (13861)Success in time 4.84 s
%------------------------------------------------------------------------------